research papers
Optimal estimated standard uncertainties of reflection intensities for kinematical
from 3D electron diffraction data^{a}Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic, and ^{b}University of Bremen, Bremen, Germany
^{*}Correspondence email: palat@fzu.cz
Estimating the error in the merged reflection intensities requires a full understanding of all the possible sources of error arising from the measurements. Most diffractionspot integration methods focus mainly on errors arising from counting statistics for the estimation of uncertainties associated with the reflection intensities. This treatment may be incomplete and partly inadequate. In an attempt to fully understand and identify all the contributions to these errors, three methods are examined for the correction of estimated errors of reflection intensities in electron diffraction data. For a direct comparison, the three methods are applied to a set of organic and inorganic test cases. It is demonstrated that applying the corrections of a specific model that include terms dependent on the original uncertainty and the largest intensity of the symmetryrelated reflections improves the overall structure quality of the given data set and improves the final R_{all} factor. This error model is implemented in the data reduction software PETS2.
Keywords: error modelling; error analysis; data reduction; electron diffraction.
1. Introduction
The use of electron diffraction (ED) for et al., 2007), rotation electron diffraction (RED) (Zhang et al., 2010) and precession electron diffraction tomography (PEDT) (Mugnaioli et al., 2009). Since the rise of sensitive detectors with negligible readout time, continuousrotation 3D ED has become the most popular protocol for data acquisition (Nederlof et al., 2013; Nannenga et al., 2014; Wang et al., 2017). Several software suites are available nowadays for 3D ED data reduction, thus allowing a 3D visualization of the data set, the determination of cell parameters, reconstruction of the 3D and extraction of reflection intensities with their estimated standard uncertainties (e.s.u.'s). Determining the e.s.u.'s of the reflection intensities is challenging. Error estimates of reflection intensities from electroncounting statistics alone may underestimate the real uncertainty associated with the measurements. The accurate estimation of e.s.u.'s is important throughout the process of crystallographic structure analysis. The result of structure and the accuracy of the refined parameters depend on the correct estimation of the e.s.u.'s.
determination has grown rapidly over the past decade, particularly thanks to the introduction of 3D methods for the systematic acquisition and analysis of diffracted intensities. 3D ED techniques have been shown to be powerful for of crystals that are too small for singlecrystal Xray These techniques benefit from the strong Coulomb interaction between electrons and matter. This allows 3D singlecrystal ED to be obtained from nanocrystals that are about eight orders of magnitude smaller in volume than those needed for singlecrystal Xray diffraction. Several 3D ED techniques, which share the common concept of tilting a crystal around the goniometer axis and acquiring a series of ED patterns, have been presented and developed over the years. These include automated diffraction tomography (ADT) (KolbThe determination of reflection e.s.u.'s is an important part of the data reduction process. It has turned out that pure countingstatisticsbased estimates are not optimal, and other effects must be included in the determination of e.s.u.'s. The model describing the adjustment of e.s.u.'s is called the error model. The practice of refining the error model and correcting for various effects has a long history (Diamond, 1969; Abrahams & Keve, 1971; Rossmann et al., 1979; Schwarzenbach et al., 1989; Howell & Smith, 1992; Leslie, 1999; Evans, 2006, 2011).
This paper aims to analyse methods of treating the error estimates of the integrated intensities from 3D ED data for the purpose of kinematical PETS2 (Palatinus et al., 2019) and refined using JANA2020 (Petříček et al., 2023), but the general ideas also apply to other implementations of 3D ED data reduction software.
and indicate the best error model. All the structures studied in this paper are processed using2. Experimental, data processing and setup
Throughout the text we use three data sets to assess and validate the presented methods. The materials are the natural zeolite natrolite, (S)(+)ibuprofen and the amino acid Lalanine.
2.1. Natrolite
Continuousrotation 3D ED experiments were performed at different spots of the selected crystal which showed signs of mosaicity of about 0.15°. The crystal diffracted up to a resolution d* of about 1.6 Å^{−1} at a temperature of 293 K (see Tables 1 and 2).


A centre of symmetry was added in the averaging process in JANA2020. The default weighting scheme with weights was and an extinction correction was applied in the The model was refined against F^{2} and against all reflections. The geometry of the water molecule was restrained to distances of 0.9584 Å between H atoms and their relative O atom and to an angle of 104.45°. All nonH atoms were refined with anisotropic displacement parameters (ADPs). A riding model was used for the ADPs of H atoms, with an extension factor of 1.2. Reference lengths of nonH atoms for the calculation of the rootmeansquare deviation (RMSD) were taken from a singlecrystal Xray diffraction (XRD) study on natrolite (Capitelli & Derebe, 2007).
2.2. (S)(+)ibuprofen
Continuousrotation 3D ED experiments were performed at different spots of two selected crystals which showed signs of mosaicity of 0.135°. Two data sets were collected and then merged. The crystals diffracted up to a resolution of about 1 Å^{−1} at a temperature of T = 95.15 K (see Tables 3 and 4).


A centre of symmetry was added in the averaging process in JANA2020. The default weighting scheme with weights was and an extinction correction was applied in the The model was refined against F^{2} and against all reflections. H atoms bonded to carbon were placed in idealized positions. H atoms bonded to oxygen were restrained at distances of 0.98 Å away from their relative O atom and the COH angle of molecule A was restrained to be equal to its corresponding analogue in molecule B.
XRDbased reference atomic distances for the calculation of RMSD were taken from King et al. (2011).
2.3. Lalanine
Continuousrotation 3D ED experiments were performed at different spots of a selected crystal which showed signs of mosaicity of 0.3°. One data set was collected and used. The crystal diffracted up to a resolution of about 2.0 Å^{−1} at a temperature of T = 100 K (see Tables 5 and 6).


A centre of symmetry was added in JANA2020 in the averaging process. The default weighting scheme with weights was and an extinction correction was applied in the The model was refined against F^{2} and against all reflections. All nonH atoms were refined with ADPs. A riding model was used for the ADPs of H atoms, with an extension factor of 1.2.
XRDbased reference atomic distances for the calculation of RMSDs were taken from Parsons et al. (2013).
3. Methods of adjustment of error estimates
In this section, we examine three approaches for the correction of error estimates. In PETS2, the integral intensity of a reflection on a single diffraction pattern is calculated as
where p_{i} is the detector count in pixel i in the S and b_{i} is the estimated background value for the same pixels. The summation runs over a region S. The background values are estimated from the detector count in the rim around the peak region S: , where n_{rim} is the number of pixels in the rim. The total estimated background in the region S is given by and the backgroundcorrected integrated intensity can then be expressed as
PETS2 employs the following formula to calculate the e.s.u. of each pixel (Waterman & Evans, 2010):
where G, γ and are the noise parameters characterizing each detector. γ is a `cascade factor', accounting for the intensitydependent increase of variance above the Poissonstatistics value, and is a `pixel factor' which corresponds to the variance of pixel values of a dark image. G is the gain factor of the detector used that converts the number of incident electrons to the number of counts in the digitized diffraction image (detectorreadout values).
Then, using the propagationoferrors method, the variance of the integrated intensity can be expressed as
This represents the variance in the integrated intensity, taking into account the Poisson noise and detectorrelated increase of the variance. It is crucial to have reasonable values of G, γ and to obtain accurate error estimates (Waterman & Evans, 2010).
However, these Poissonbased standard deviations underestimate the true e.s.u.'s, and additional adjustment needs to be made to these e.s.u.'s to address any additional uncertainty introduced by other sources of errors than the Poisson noise and detector, such as instrumental instability. One way to deal with these errors is to inflate the error estimates by adding extra terms that account for the additional uncertainty.
3.1. Methodology
The starting idea is based on the analysis of intensity distribution of multiply measured and symmetryequivalent reflections. In an ideal data set, these reflections should have identical intensities. In practice, this is not the case due to, for example, statistical noise and nonkinematical scattering. The e.s.u.'s of individual reflections should thus properly characterize any deviation from the expected equality of multiply measured reflections. Based on this concept, various methods can be devised that produce better de facto standard in modern dataprocessing software. However, to our knowledge, its validity for 3D ED data has not yet been investigated. There are at least two reasons why it cannot be automatically assumed that the method developed for Xray diffraction data is also valid for 3D ED data. First, the nature of errors in the 3D ED data is different. The most significant deviations from the ideal kinematical intensities do not arise from random errors and instrumental effects, but from the effects. These effects are unavoidable in 3D ED data. Strictly speaking, these effects are not sources of errors in the data, and they should be modelled as part of the calculation of calculated intensities in the process (Palatinus, Petříček & Corrêa, 2015; Palatinus, Correa et al., 2015). However, when kinematical approximation is used in the these effects effectively turn into errors in reflection intensities which, although not random, may be reflected in the values of e.s.u.'s. The second reason for special consideration is that, compared with Xray diffraction data, the spread of the equivalent intensities around the mean value is typically much larger than in Xray data. This is again caused mainly by the but also often by radiation damage of the crystal, and it is reflected in increased values of R_{int}, which frequently reach 20% or more (Bruhn et al., 2021). This large spread may lead to larger corrections to e.s.u.'s and may induce effects that are not significant in Xray diffraction data. The analysis in this paper shows this is indeed the case.
estimates. Using such a method has become aIn the following, we analyse and compare three models for adjusting the e.s.u.'s of three different 3D ED experimental data sets. The efficiency of each method is assessed in a number of ways. We first evaluate the quality of each error model by checking the normality of the obtained distribution of residuals. A kinematical
is then performed and the figures of merit are compared. The assessment is also based on comparing the RMSD of refined lengths and the RMSD of atomic shifts for all nonH atoms with reference structures.3.2. Model 0: no adjustment
For comparison purposes, the model with no adjustment to e.s.u.'s is also included in the analysis and it is denoted model 0. In this model, the e.s.u.'s are calculated using equation (4) without further modifications.
3.3. Model 1: using equivalent errors
In the first adjustment model, the reflection e.s.u.'s are calculated from the variation of symmetryrelated intensities around their mean. The e.s.u. is calculated as a sample standard deviation from the n measurements of the symmetryequivalent reflections. Given a reflection index h with n measurements of the intensity of h or its symmetry equivalent, we define the lth measurement of h as . All are associated with a common e.s.u. defined as
The division by instead of n is known as Bessel's correction, and it corrects for the bias in the estimation of the population standard deviation from only the sample of the population. The mean of all the symmetryrelated measurements is used to estimate the reflection intensity :
This model does not use the original Poisson counting error estimates and assumes that a large enough sample of equivalent reflections is available to reliably estimate the uncertainty. This assumption is often not well fulfilled because 3D ED data sets from lowsymmetry crystals, in particular, exhibit a limited completeness and redundancy. In extreme cases, a number of reflections may be measured only once (n = 1), and their e.s.u.'s cannot be calculated using the above relation. To include these reflections in the structure we construct a lookup table which allows estimation of the e.s.u.'s of those reflections from the e.s.u.'s of other reflections with similar resolution and intensity. Firstly, we sort the reflections in order of increasing intensity and then we divide them into ten intensity bins with N / 10 reflections in each bin (N is the total number of reflections). The second binning divides the reflections into resolution bins with a bin width of 0.2 Å^{−1}. Then the average of e.s.u.'s of all reflections in the same bin is calculated and assigned as the e.s.u. of all individually measured reflections in the same bin. The residuals in the original data (model 0) clearly deviate from a normal distribution as shown in Fig. 1(a) for natrolite, Fig. 2(a) for (S)(+)ibuprofen and Fig. 3(a) for Lalanine. Figs. 1(b), 2(b), 3(b) show the analogous figures corresponding to the adjusted data according to model 1. The straight horizontal segments (constant steps) in the normal probability plot of this model at the sample quantile of −0.707 and 0.707, and the peaks in the histograms of normalized deviations at ±0.707 are due to reflections measured twice (n = 2), as follows from equations (5), (6) and (8) for the special case of n = 2. This feature and the general mismatch between the distribution of the residuals and the expected normal distribution show that model 1 is not optimal for lowmultiplicity data sets. The analysis of the structure refinements shows (Section 4.1) that this model leads to a worse (ibuprofen and Lalanine) or only marginally better (natrolite) structure model than model 0.
3.4. Model 2: threeparameter model using average intensities of symmetryrelated reflections
This model was first introduced by Evans (2006). It uses the normal probability plot (Abrahams & Keve, 1971) to adjust the error estimates of the integrated intensities. The model introduces a small number (two or three) of correction parameters that are used to modify the e.s.u.'s. The correction factors are optimized to make the normal probability plot as linear as possible. In this paper, we follow the notations of the three correction parameters from Brewster et al. (2019). The corrected error estimates are given by
with , s_{B} and being the correction parameters. Two of the three parameters have a physical interpretation. According to Evans (2011), is understood as a correction factor for unknown errors independent of the intensity value including uncertainty in the detector gain used to estimate Poissonian errors. It acts like a scaling factor. is a parameter that accounts for any errors that are proportional to the intensity such as instrument instabilities. s_{B} has no direct physical meaning and it is excluded in some programs [such as XDS (Kabsch, 2010)], but it is an obvious addition to the parameter set, and in this work we include it to provide maximum flexibility of the fitting.
3.4.1. Normalized deviation
Estimates of error such as represent the statistically expected deviation of the measurement's intensity from the unknown population mean value. Assuming a Gaussian distribution of the intensity errors, the normalized deviations of the measurements from the mean value of the symmetryrelated reflections are expected to be distributed according to a standard normal distribution. The normalized deviations for are given by
According to Evans (2006), is the mean of the measurements of h excluding the lth reflection . In this work, we consider as the average intensity over all observations of reflection h including the lth reflection:
This means that for reflections measured only once, where , the corresponding normalized deviation will be 0. This choice affects mainly the ), excluding a strong reflection from the calculation of , the resulting average intensity is reduced. The normalized deviation will consequently get larger, leading to larger error estimates, higher and consequently fewer observed reflections (see Section 5.1 for discussion of the meaning of observed reflections in 3D ED data). When all reflections are included in the calculation of the average, the parameter is reduced, leading to a larger number of observed reflections. In the work of Evans (2006), the average intensity is also a weighted average, where the weights are given by inverse variance estimates of the individual observations. This approach biases the average intensity towards the weaker reflections, which have, in general, lower e.s.u.'s and hence higher weights, leading to the same effects as excluding strong reflections from the average, discussed above. We also tested this approach and concluded that the nonweighted average gives better results.
of the parameter. In the approach used by Evans (2006The aim of the method is adjustment of the parameters , and s_{B} to make the distribution of the normalized deviations as close as possible to the standard normal distribution, i.e. a Gaussian distribution centred on zero with a standard deviation of 1.
3.4.2. Normal probability plot technique
The values of the correction parameters , s_{B} and can be conveniently determined by optimizing the normal probability plot (Abrahams & Keve, 1971). The normal probability plot is a plot of the sorted normalized deviations versus the perfectly distributed quantiles x_{i} expected for a normal distribution. The values of x_{i} are known as the theoretical quantiles and they correspond to a normal distribution of zero mean and standard deviation of 1. A normal probability plot of a variable with perfect standard normal distribution is a line with intercept 0 and slope 1. To find the matching normal distribution quantiles, we first calculate the cumulative distribution function (CDF) of the standard normal distribution. It is usually denoted by and has the general form
The ith element of a sorted sample with standard normal distribution represents the value with . Conversely, the inverse of the CDF gives the expected value of the ith element of a sorted sample, i.e. the socalled theoretical quantile of the standard normal distribution.
The normal probability plot thus contains N points with coordinates , where is the ith normalized deviation in the list sorted from the smallest to the largest normalized deviation. The individual reflections having are not included in the list. Figs. 1, 2 and 3 show normal probability plots for different error models for all three experimental data sets. The values of , s_{B} and can be adjusted to make the normal probability plot as close to the ideal straight line with slope 1 as possible.
3.4.3. Initial parameters
Evans (2006) proposed obtaining the initial value of by fitting the slope of the central part of the normal probability plot in the theoretical quantiles range between −0.5 and 0.5. However, we observed that the leastsquares fitting procedure is so robust that good convergence is obtained even if the fit starts from the default values , s_{B} = 0 and .
3.4.4. Corrected error estimates
Using equation (7) for , we calculate the adjusted error estimates using the current set of correction parameters. Then, the new normalized deviations are computed using
These normalized deviations are then sorted, and a new normal plot is calculated. To obtain optimal values of the correction parameters, we minimize the quantity , which designates the sum of the squared difference between the adjusted normalized deviations and the theoretical quantiles. Note that, after one minimization, the normalized deviations must be resorted, as their order may change.
After sorting, a new minimization must be performed, and the supercycle repeated until convergence. As the number of data points is large and the number of fitted parameters is small, the convergence is usually rapid and robust. Figs. 1(a), 2(a) and 3(a) show the original and Figs. 1(c), 2(c) and 3(c) the optimized normal probability plots and the histograms of the adjusted normalized deviations and their comparison with the standard normal distribution of natrolite, (S)(+)ibuprofen and Lalanine, respectively.
3.5. Model 3: threeparameter model using the largest intensities of symmetryrelated reflections
Model 2 provides a clear improvement in comparison with model 1 or with unmodified e.s.u.'s. However, upon closer inspection, this model suffers from certain inadequacies. As shown in Figs. 1(c), 2(c) and 3(c), the normal probability plots representing the adjusted normalized deviations versus the theoretical quantiles in the case of model 2 do not match the line of slope 1, especially at the tails. By investigating the individual cases, we realized that model 2 provides poor results, especially for reflections that exhibit a considerable variation among the intensities of the symmetryrelated reflections, i.e. if the variation is large compared with the intensity value itself. Upon optimization of the three errormodel parameters, this model tries to compensate for this variation by assigning very large error estimates to very strong reflections. This leads to, among other effects, a notable reduction in the number of observed reflections. This problem is not very severe for typical Xray diffraction data, where the symmetryrelated reflections tend to have very similar intensities, but it is significant in 3D ED data, where the intensity variation can be very large. To correct this problem, we propose a new model (model 3), which is very similar to model 2 except that in this correction method we use the largest intensity of the symmetryrelated reflections for the calculations of the corrected error estimates rather than the average intensity . The corrected error estimates are thus given by
Here is the largest intensity of all the symmetryrelated reflections of reflection h. The procedure for the optimization of the model parameters is the same as in model 2. The effect of this change is the decrease of the fitted values s_{fac}, s_{B} and s_{add}. For reflection groups with little variation around this means a smaller , because the errormodel parameters are smaller and . However, for reflection groups with large variation, the smaller values of the errormodel parameters are compensated by replacing the (smaller) by the larger . The net result is then a relative increase of the of reflection groups with a large variation compared with the reflection groups with a small variation.
Figs. 1(d), 2(d) and 3(d) show the final normal probability plots for this model. These can be compared with the other models. There is a pronounced improvement in the fitting of the normalized deviations of the error estimates. The improvement is also visible in the distribution of the normalized deviations of this model which shows that the adjusted normalized deviations are more accurately normally distributed in model 3 than in any other model including model 2.
3.5.1. Outlier rejection
There is usually a group of errors that do not match the statistical distribution. They are most frequently caused by unpredictable experimental effects that cannot be corrected for. Measurements affected by such errors are known as outliers (Blessing, 1997). It is advantageous to exclude such outliers from the final data set, as they most likely indicate an erroneous measurement that cannot be properly fitted by the structure model.
We tested a number of outlier rejection algorithms, including the algorithm used in SCALA (or AIMLESS) (Evans, 2006). Finally, we converged to the use of Tukey's simple but very robust rule of thumb that is based on the quartiles of the given data set (Tukey, 1977): firstly, calculate the first quartile Q_{1} of (25% of the normalized residuals are less than or equal to this value) and the third quartile Q_{3} (25% of the values are greater than or equal to this value). Outliers are then defined as all values that fall outside the range
Tukey proposed using k = 1.5 to identify outliers.
As the exclusion of outliers has an impact on the normal probability plot and hence on the refined error model, an iterative procedure needs to be adopted. Firstly, consider the original data set before applying any corrections to the e.s.u.'s and apply Tukey's outlier rejection procedure as described above. In the case of only two equivalent reflections, if one is marked as an outlier, the other is marked too. Then, apply the errormodel s_{fac}, s_{B} and s_{add}, excluding the outliers from the calculation. Use the obtained values to correct the e.s.u.'s of all the reflections including the outliers. Apply Tukey's outlier rejection again to the new data set with adjusted e.s.u.'s. Iterate the errormodel and outlier rejection until the values of the correction parameters s_{fac}, s_{B} and s_{add} converge and the number of identified outliers does not change. In the tests presented in this paper, the value of k = 1.5 proved to be an appropriate value. However, in specific cases, this parameter may be adjusted to increase or reduce the number of outliers, if needed.
to calculate the values of the correction parametersKinematical Lalanine, respectively, representing 0.65%, 1.7% and 2.69% of all measured reflections. The kinematical results after applying the above outlier rejection algorithm are shown in Table 10.
was carried out on each of the three data sets with outliers rejected to demonstrate the potential impact of the abovedescribed outlier rejection approach, using model 3. The algorithm rejected 35, 66 and 93 outliers in the data of natrolite, ibuprofen and4. Results
To assess the efficiency of each of the models presented above, we apply the above error correction models to data from three materials, as described in Section 2. Each data set was processed using the software PETS2. All structures could be solved from the data by the chargeflipping algorithm as implemented in Superflip (Palatinus & Chapuis, 2007) and refinements within the kinematical approximation were performed in JANA2020. Input data from models 0, 1, 2 and 3 were subject to using the same data processing procedure, the same starting structure model, the same parameters etc. The only difference was in the e.s.u.'s assigned to the intensities based on individual error models. The residual factors , and were calculated by JANA2020 based on the common definitions:
where u is the instability factor and the sum runs over all reflections in the case of and , and only over observed reflections with for the calculation of . is the number of reflections with , is the total number of reflections used in the is the conventional R factor (R1) based on observed reflections, is the weighted R factor based on all reflections.
The application of the above weighting scheme is equivalent to changing the value of the coefficient to . With the default value of u used in JANA2020 (u = 0.01, see Section 2) the change is negligible. We therefore decided to keep the default settings used in JANA2020.
The accuracy of the refined model is characterized by the RMSD of the
lengths for all nonH atoms from the respective reference values. Another assessment metric is based on the RMSD of atomic shifts of all nonH atoms from atom positions in the reference structures.4.1. results
The kinematical for natrolite, Table 8 for (S)(+)ibuprofen and Table 9 for Lalanine. These tables also contain the RMSD values of the refined lengths for each model and of the distances of all nonH atoms from the positions in the reference structure. An important remark here is that the conventional is not a particularly good measure of the quality, as different error models result in a different number of observed reflections (see Section 5 for more discussion on observed reflections). tends to increase with increasing . A more robust way of assessing the different models and the quality of data in 3D ED is to compare the factors instead, which are directly comparable, as the complete set of intensities is the same for all models. Tables 7, 8 and 9 show that model 3 is the best error correction model for all tested data sets and across all comparison metrics, with a single exception of the RMSD of bond lengths for Lalanine, which is better for model 2 than model 3, but the difference is marginal.
results are shown in Table 7



4.1.1. Natrolite
In the case of natrolite, model 1 using the standard deviation method for the error estimates introduces an evident improvement in the R factors and the goodnessoffit parameter compared with the original model (Table 7). It further gives the best factor among all other models. However, as stated earlier, a good measure of comparison for the different techniques is rather than . The RMSDs of bond lengths and of the atomic shifts are better than those of the original model. Fig. 1(b) shows the relative improvement in the normal probability plot as well as the distribution of the adjusted normalized deviations compared with the model 0 [Fig. 1(a)].
As for model 2, in the case of natrolite, the values of the three correction parameters are: , s_{B} = 0.14643 and . From Table 7, it is obvious that there is a drop in and a dramatic increase in . This is the main drawback of this model. The refined structure model of natrolite is considerably improved upon applying the corrected errors of model 2 as can be seen from the RMSD values.
The values of the three correction parameters in the case of natrolite, model 3, are: , s_{B} = 0.0464 and . Model 3 introduces an overall improvement of all the parameters. Firstly, the number of observed reflections is the highest of all models. As compared with model 2, this illustrates the benefit of using the largest intensity of the symmetryrelated reflections for adjusting the error estimates, rather than the average intensity. This is also clear from the normal plots of natrolite (Fig. 1) where the normal plot of model 3 [Fig. 1(d)] is the most favourable. The distribution of the normalized deviations of natrolite in Fig. 1(d) also provides the best fit to a standard normal distribution. The data in this case have more positive deviations than negative deviations and this explains the slight shift of the histogram to the left [Fig. 1(d)]. The value is the best as well and it is 1.11 percentage points less than that of the original model. More importantly, the refined structure of natrolite corresponding to this model is the most accurate when compared with the reference model (Capitelli & Derebe, 2007), showing the best RMSD values of the bond lengths and the atomic positions of all nonH atoms. The kinematical of model 3 of natrolite after the outlier rejection introduces a slight improvement in the factor. The RMSD values for atomic shifts and bond lengths as shown in Table 10 are almost the same.

4.1.2. Ibuprofen
In the case of (S)(+)ibuprofen, the situation is different regarding model 1. The latter does not present any improvement from the original model. On the contrary, the structure is slightly deformed. The of the H atoms of hydroxyl groups was not stable. The aromatic carbon ring is also significantly distorted, leading to worse RMSD values as compared with the reference (King et al., 2011). This is obvious from the distribution of data [Fig. 2(b)]. The two peaks at −0.707 and 0.707 indicate a high number of symmetryrelated reflections (19%) that are measured only twice (n = 2).
Regarding the results of model 2 in the case of (S)(+)ibuprofen, the three correction parameters are: = 0.712995, s_{B} = 0.15164 and . is reasonable for this data set and it is not reduced as compared with model 0. The normal plot in Fig. 2(c) shows a noticeable improvement from the original normal plot [Fig. 2(a)], but it is still not a perfectly fitting line. A positive and a negative tail are present, in addition to some other slight deviations from the theoretical line of slope 1. and the goodnessoffit factors are enhanced, while still records the highest value in this model. The structure model is better than the original one based on the RMSD values.
Finally, for model 3 in the case of (S)(+)ibuprofen, the three correction parameters are: , s_{B} = 0.0051 and . Again, this model has the largest number of observed reflections. The factor is reduced by 0.73 from that of the original model. The normal plot of the normalized deviations based on this model as shown in Fig. 2(d) is the nearest to normally distributed data. Fig. 2(d) also reveals the significance of this model in adjusting the sample data to better fit a standard Gaussian distribution. Additionally, the refined structure from model 3 is the most accurate among the others as indicated by the RMSD (Table 8). The kinematical of model 3 after the outlier rejection in this case improves slightly the R factors (Table 10). The RMSDs for lengths and atomic positions from the respective reference values improve as well after discarding the outliers.
4.1.3. Lalanine
In the case of Lalanine, model 1 does not introduce any improvement of model 0. On the contrary, the value of the factor is increased, and the refined structure is deformed rather than enhanced by comparing the RMSD of bond lengths and atomic shifts of nonH atoms (Table 9).
As for model 2 in the case of Lalanine, the three correction parameters are: , s_{B} = 0.0668 and . The structure of this model has indeed the best value of RMSD of the bond lengths and the goodnessoffit factor is enhanced, but the number of observed reflections is the lowest among the other models and the factor is also larger than that of model 0. This case again confirms the main drawbacks of this model. The normal plot in Fig. 3(c) shows a noticeable improvement from the original normal plot [Fig. 3(a)], but it is still not a perfectly fitting line. A recognizable positive tail is present in addition to some other slight deviations from the theoretical line of slope 1.
For model 3, this last data set again confirms that this is the best error correction model among the others. The factor and the number of observed reflections are the best and, above all, the structure has the lowest RMSD of atomic shifts as compared with the reference (Parsons et al., 2013). Fig. 3(d) shows a noticeable improvement in the normal probability plot and the distribution of the adjusted normalized deviations. The three correction parameters are now: , s_{B} = 0.0042 and . The kinematical results in the absence of outliers have indeed been improved as shown in Table 10. The factor decreases from 14.73 to 14.16. The RMSDs for bond lengths and atomic shifts have been improved slightly after rejecting the 93 outliers.
5. Discussion
5.1. Observed reflections
It is customary to present R value R1, calculated only on sufficiently strong reflections. A typical criterion is I > 3σ(I). The rationale behind this tradition is that weak reflections contain essentially only noise, and they do not provide useful information on the quality of the fit. The term used for reflections stronger than the selected criterion is `observed reflections'. The term `observed' refers to the experiment, and to the fact that a reflection with I > 3σ(I) is usually visible in the diffraction pattern as a distinct intensity maximum, i.e. can be observed in the pattern. This is, however, meaningful only if σ(I) is calculated from counting statistics only. As soon as σ(I) is modified to account for other errors, the term `observed' loses its original meaning. Specifically, when σ(I) is significantly increased due to the errormodel correction, a reflection, which is clearly visible in the diffraction pattern, becomes formally `unobserved', i.e. has I < 3σ(I). This is not a very big problem for typical Xray diffraction data, where the corrections to the counting statistic σ(I) are generally small and affect mostly the strong reflections. However, it becomes a problem for data with dominant systematic errors, like those caused by the dynamical effects in 3D ED data. As an example, Fig. 4 shows an image of a reflection, which, after the errormodel correction, has I = 1.85σ(I). Although the reflection is nominally unobserved, it is actually quite strong and clearly visible in the experimental data. The problem becomes even more serious when the `obs' values are used for comparison between refinements. Different error models lead to different corrections to σ(I), hence to a different number of reflections with I > 3σ(I) and, as a consequence, to incomparable values of R(obs) and other obsrelated statistics. As an example, error correction according to model 1 for natrolite yields 876 observed reflections with I > 3σ(I) and R1(obs) of 13.37%, while model 3 gives 1007 observed reflections (out of 1279) and R1(obs) of 14.67%. Thus, superficially, model 1 may appear to give a significantly better result, but it is just an artefact of the number of observed reflections. R1(all) as well as other statistics clearly show that the result from model 3 is superior.
characteristics, typically the unweightedOne could thus conclude that the use of the term `observed reflection' and related quantities is not meaningful for 3D ED data and should be discontinued. Other methods of estimating the amount of information present, e.g. the correlationbased techniques commonly used in macromolecular crystallography, may be more suitable. Until then, the scientists working with these data should be aware of the caveat just described, and use the term `observed reflections' with caution and with awareness of its limitations.
5.2. Features of the error correction models
A thorough comparison of the refinements reveals that in all cases the set of adjustments propagated in error model 3 gives significantly improved results.
Model 1 did not present any improvement in the cases of (S)(+)ibuprofen and Lalanine. In the case of natrolite, the structure is slightly enhanced. Model 1 is expected to be more successful with data with a high multiplicity of symmetryrelated reflections since the only information it is based on is the observed variation among these reflections. Stated differently, estimates of the individual errors of this model, derived only from the standard error of the mean of the reflections, become less adequate in the case of data with a low redundancy of symmetryrelated reflections. This in turn may result in serious inaccuracy of the refined structure model. (S)(+)ibuprofen for instance has a monoclinic and thus many reflections have a low redundancy of 2. This explains the significant improvement in the case of natrolite, which has an orthorhombic of higher redundancy. In the case of Lalanine, although it has an orthorhombic many reflections of this data set (25%) have a multiplicity of n = 2 due to the low completeness of the data set. This explains the inefficiency of model 1 in this case.
Model 2 clearly provides an improvement, but it still has some deficiencies that need to be worked through. In some cases (natrolite and Lalanine) an obvious drop in was evident. By looking at the correction parameters, we notice that in both cases one of these parameters is larger than 1 ( for natrolite and for Lalanine). This signifies a substantial inflation of error estimates. This inflation makes the model less reliable in many situations. In the case of ibuprofen, all the correction parameters are less than 1 and the inflation of the e.s.u.'s is not so dramatic. This is due to the fact that ibuprofen is monoclinic. The variations among the intensities of the symmetryrelated reflections are less prominent. This means the values of the correction parameters are not so large and thus remains reasonable for this data set and does not need to be reduced.
In fact, the correction parameters and of a well processed data set should have their values close to 1 and 0, respectively. s_{B} is usually negligible with a value close to 0. The exact values will certainly depend on the of the corresponding data set, the redundancy of the symmetryrelated reflections and the variations among their intensities. It is worth noting that the three refined parameters of model 3 in general have lower values than their analogues of model 2 for all three samples. In model 3, less compensation is needed to correct for the gain detector uncertainty and other types of errors, owing to the use of the largest intensity of symmetryrelated observations instead. Model 3 adjusts the error estimates of the strongest reflections without unnecessary exaggeration of the e.s.u.'s. It provides a good compromise between adjusting the error estimates and maintaining a decent number of observed reflections.
6. Conclusion
Various models for adjustment of estimated standard uncertainties of reflection intensities in 3D ED data were investigated with the aim of verifying if the models commonly used for singlecrystal Xray diffraction data are also suitable for 3D ED data. The tests on three experimental data sets showed that the best model is model 3, which differs from the commonly used approach by employing the maximum of the symmetryequivalent intensities in the calculation of normalized residuals rather than the average value.
It is not surprising that accurate estimates of the e.s.u.'s are useful, but it is notable how much improvement model 3 brings to the kinematical R factors. The benefits of model 3 are expected to be most pronounced in data with low redundancy and large variation in the intensities of symmetryrelated reflections. It may be expected that with data obtained by averaging a large number of individual data sets, an approach becoming more and more popular in contemporary 3D ED studies, the differences between the models would become smaller.
compared with the case with no errormodel adjustment, but also with the other tested models. The benefits of using the model include an overall enhanced accuracy of atomic positions, lengths and improvedThe procedure according to model 3 is implemented in the software package PETS2 (Palatinus et al., 2019), available at https://pets.fzu.cz/.
Supporting information
https://doi.org/10.1107/S2053273323005053/pl5027sup1.cif
contains datablocks global, ibuprofen_model0, ibuprofen_model1, ibuprofen_model2, ibuprofen_model3, ibuprofen_model3_outliers, Lalanine_model0, Lalanine_model1, Lalanine_model2, Lalanine_model3, Lalanine_model3_outliers, natrolite_model0, natrolite_model1, natrolite_model2, natrolite_model3, natrolite_model3_outliers. DOI:Structure factors: contains datablock ibuprofen_model0. DOI: https://doi.org/10.1107/S2053273323005053/pl5027ibuprofen_model0sup2.hkl
Structure factors: contains datablock ibuprofen_model1. DOI: https://doi.org/10.1107/S2053273323005053/pl5027ibuprofen_model1sup3.hkl
Structure factors: contains datablock ibuprofen_model2. DOI: https://doi.org/10.1107/S2053273323005053/pl5027ibuprofen_model2sup4.hkl
Structure factors: contains datablock ibuprofen_model3. DOI: https://doi.org/10.1107/S2053273323005053/pl5027ibuprofen_model3sup5.hkl
Structure factors: contains datablock Lalanine_model0. DOI: https://doi.org/10.1107/S2053273323005053/pl5027Lalanine_model0sup6.hkl
Structure factors: contains datablock Lalanine_model1. DOI: https://doi.org/10.1107/S2053273323005053/pl5027Lalanine_model1sup7.hkl
Structure factors: contains datablock Lalanine_model2. DOI: https://doi.org/10.1107/S2053273323005053/pl5027Lalanine_model2sup8.hkl
Structure factors: contains datablock Lalanine_model3. DOI: https://doi.org/10.1107/S2053273323005053/pl5027Lalanine_model3sup9.hkl
Structure factors: contains datablock natrolite_model0. DOI: https://doi.org/10.1107/S2053273323005053/pl5027natrolite_model0sup10.hkl
Structure factors: contains datablock natrolite_model1. DOI: https://doi.org/10.1107/S2053273323005053/pl5027natrolite_model1sup11.hkl
Structure factors: contains datablock natrolite_model2. DOI: https://doi.org/10.1107/S2053273323005053/pl5027natrolite_model2sup12.hkl
Structure factors: contains datablock natrolite_model3. DOI: https://doi.org/10.1107/S2053273323005053/pl5027natrolite_model3sup13.hkl
Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2053273323005053/pl5027ibuprofen_model3_outlierssup14.hkl
Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2053273323005053/pl5027Lalanine_model3_outlierssup15.hkl
Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2053273323005053/pl5027natrolite_model3_outlierssup16.hkl
For all structures, data collection: selfwritten scripts, OLYMPUS iTEM. Cell
PETS2(ver 2.2.20220612.1425) for ibuprofen_model0, ibuprofen_model1, ibuprofen_model2, ibuprofen_model3, ibuprofen_model3_outliers; PETS2 for Lalanine_model0, Lalanine_model1, Lalanine_model2, Lalanine_model3, Lalanine_model3_outliers, natrolite_model0, natrolite_model1, natrolite_model2, natrolite_model3, natrolite_model3_outliers. Data reduction: PETS2(ver 2.2.20220612.1425) for ibuprofen_model0, ibuprofen_model1, ibuprofen_model2, ibuprofen_model3, ibuprofen_model3_outliers; PETS2 for Lalanine_model0, Lalanine_model1, Lalanine_model2, Lalanine_model3, Lalanine_model3_outliers, natrolite_model0, natrolite_model1, natrolite_model2, natrolite_model3, natrolite_model3_outliers. Program(s) used to solve structure: superflip for ibuprofen_model0, ibuprofen_model1, ibuprofen_model2, ibuprofen_model3, ibuprofen_model3_outliers, Lalanine_model0, Lalanine_model1, Lalanine_model2, Lalanine_model3, Lalanine_model3_outliers. Program(s) used to refine structure: JANA2020 for ibuprofen_model0, ibuprofen_model1, ibuprofen_model2, ibuprofen_model3, ibuprofen_model3_outliers; Jana2020 for Lalanine_model0, Lalanine_model1, Lalanine_model2, Lalanine_model3, Lalanine_model3_outliers, natrolite_model0, natrolite_model1, natrolite_model2, natrolite_model3, natrolite_model3_outliers. For all structures, molecular graphics: VESTA 3.C_{13}H_{18}O_{2}  Z = 4 
M_{r} = 206.3  F(000) = 184.42 
Monoclinic, P2_{1}  D_{x} = 1.102 Mg m^{−}^{3} 
Hall symbol: P 2yb  Electrons 200 KeV radiation, λ = 0.0251 Å 
a = 12.368 (4) Å  Cell parameters from 3884 reflections 
b = 8.021 (3) Å  θ = 0.1–0.7° 
c = 13.536 (5) Å  T = 95 K 
β = 112.24 (3)°  Block 
V = 1242.9 (8) Å^{3} 
TEM FEI Tecnai G2 20 diffractometer  R_{int} = 0.166 
Radiation source: Lab6 cathode  θ_{max} = 0.7°, θ_{min} = 0.1° 
continuous–rotation 3D ED scans  h = −12→12 
3884 measured reflections  k = −8→8 
1212 independent reflections  l = −13→13 
825 reflections with I > 3σ(I) 
Refinement on F^{2}  H atoms treated by a mixture of independent and constrained refinement 
R[F > 3σ(F)] = 0.179  Weighting scheme based on measured s.u.'s w = 1/(σ^{2}(I) + 0.0004I^{2}) 
wR(F) = 0.319  (Δ/σ)_{max} = 0.047 
S = 4.41  Δρ_{max} = 0.25 e Å^{−}^{3} 
1212 reflections  Δρ_{min} = −0.24 e Å^{−}^{3} 
127 parameters  Extinction correction: SHELXL2017/1 (Sheldrick, 2015), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
3 restraints  Extinction coefficient: 2.4 (3) 
139 constraints 
x  y  z  U_{iso}*/U_{eq}  
O1a  0.344 (3)  0.514 (4)  1.164 (2)  0.059 (8)*  
O2a  0.240 (3)  0.677 (3)  1.048 (2)  0.060 (8)*  
H1a  0.317 (6)  0.730 (15)  1.080 (11)  0.12*  
C1a  0.247 (3)  0.531 (4)  1.091 (3)  0.051 (8)*  
C2a  0.149 (2)  0.397 (3)  1.066 (2)  0.040 (7)*  
H2a  0.150229  0.30286  1.121346  0.0793*  
C3a  0.164 (2)  0.325 (3)  0.9677 (19)  0.027 (6)*  
C4a  0.239 (2)  0.171 (3)  0.987 (2)  0.037 (7)*  
H4a  0.284447  0.121734  1.064232  0.0745*  
C5a  0.245 (3)  0.095 (4)  0.891 (2)  0.043 (7)*  
H5a  0.311599  0.005793  0.899672  0.0864*  
C6a  0.169 (2)  0.1332  0.7920 (17)  0.010 (5)*  
C7a  0.106 (3)  0.271 (3)  0.780 (2)  0.045 (8)*  
H7a  0.070872  0.319979  0.701662  0.0902*  
C8a  0.079 (3)  0.360 (4)  0.8546 (19)  0.030 (6)*  
H8a  0.007645  0.443457  0.835449  0.0602*  
C9a  0.167 (2)  0.034 (3)  0.6914 (16)  0.021 (6)*  
H9a1  0.165206  0.118365  0.630676  0.0416*  
H9a2  0.2464  −0.033998  0.710937  0.0416*  
C10a  0.063 (2)  −0.087 (3)  0.6476 (18)  0.038 (7)*  
H10a  −0.015368  −0.022613  0.637023  0.0757*  
C11a  0.071 (3)  −0.156 (4)  0.547 (2)  0.061 (8)*  
H11a  0.113587  −0.068615  0.515919  0.1216*  
H11b  0.119272  −0.26894  0.565218  0.1216*  
H11c  −0.014171  −0.179554  0.490623  0.1216*  
C12a  0.067 (3)  −0.234 (3)  0.722 (2)  0.042 (7)*  
H12a  0.005104  −0.325295  0.679731  0.0837*  
H12b  0.152067  −0.287625  0.750667  0.0837*  
H12c  0.048121  −0.190607  0.787662  0.0837*  
C13a  0.038 (3)  0.489 (4)  1.052 (3)  0.078 (10)*  
H13a  −0.032147  0.403167  1.029827  0.1556*  
H13b  0.046829  0.547217  1.124998  0.1556*  
H13c  0.022156  0.580348  0.991843  0.1556*  
O2b  0.534 (3)  −0.294 (3)  0.224 (2)  0.040 (6)*  
O1b  0.412 (2)  −0.133 (3)  0.100 (2)  0.041 (6)*  
H1b  0.462 (5)  −0.359 (12)  0.206 (10)  0.0806*  
C1b  0.508 (3)  −0.158 (4)  0.173 (3)  0.051 (8)*  
C2b  0.605 (3)  −0.036 (4)  0.190 (2)  0.071 (10)*  
H2b  0.677977  −0.110467  0.195386  0.1417*  
C3b  0.609 (3)  0.072 (4)  0.294 (2)  0.045 (8)*  
C4b  0.686 (3)  −0.001 (4)  0.397 (2)  0.042 (7)*  
H4b  0.735548  −0.111027  0.401697  0.0833*  
C5b  0.689 (2)  0.082 (3)  0.4872 (19)  0.025 (6)*  
H5b  0.748524  0.041844  0.562622  0.0506*  
C6b  0.612 (3)  0.225 (3)  0.483 (2)  0.048 (8)*  
C7b  0.552 (3)  0.301 (4)  0.388 (2)  0.041 (7)*  
H7b  0.513453  0.420727  0.379418  0.0827*  
C8b  0.548 (3)  0.190 (3)  0.294 (2)  0.038 (7)*  
H8b  0.482951  0.220726  0.218468  0.0767*  
C9b  0.638 (2)  0.311 (3)  0.5903 (16)  0.026 (6)*  
H9b1  0.652055  0.220411  0.650716  0.0511*  
H9b2  0.562099  0.371268  0.59037  0.0511*  
C10b  0.741 (3)  0.436 (3)  0.6260 (19)  0.042 (8)*  
H10b  0.815415  0.366829  0.629367  0.0835*  
C11b  0.752 (3)  0.518 (4)  0.740 (2)  0.066 (9)*  
H11d  0.728972  0.427322  0.785553  0.1311*  
H11e  0.695289  0.621451  0.725844  0.1311*  
H11f  0.839378  0.55695  0.782082  0.1311*  
C12b  0.726 (3)  0.579 (4)  0.5518 (19)  0.049 (7)*  
H12d  0.796882  0.662814  0.584632  0.0972*  
H12e  0.723823  0.534224  0.477342  0.0972*  
H12f  0.646719  0.641323  0.540533  0.0972*  
C13b  0.603 (2)  0.081 (3)  0.1053 (19)  0.034 (6)*  
H13d  0.517116  0.126244  0.064935  0.0672*  
H13e  0.659822  0.182806  0.140009  0.0672*  
H13f  0.631702  0.019313  0.050272  0.0672* 
O1a—C1a  1.24 (4)  O2b—H1b  0.98 (8) 
O2a—H1a  0.98 (9)  O2b—C1b  1.27 (4) 
O2a—C1a  1.30 (4)  O1b—C1b  1.24 (4) 
C1a—C2a  1.56 (4)  C1b—C2b  1.50 (5) 
C2a—H2a  1.06  C2b—H2b  1.06 
C2a—C3a  1.53 (4)  C2b—C3b  1.64 (5) 
C2a—C13a  1.50 (5)  C2b—C13b  1.47 (4) 
C3a—C4a  1.51 (4)  C3b—C4b  1.49 (4) 
C3a—C8a  1.52 (3)  C3b—C8b  1.21 (4) 
C4a—H4a  1.06  C4b—H4b  1.06 
C4a—C5a  1.46 (4)  C4b—C5b  1.38 (4) 
C5a—H5a  1.06  C5b—H5b  1.06 
C5a—C6a  1.35 (3)  C5b—C6b  1.48 (4) 
C6a—C7a  1.33 (3)  C6b—C7b  1.37 (4) 
C6a—C9a  1.57 (3)  C6b—C9b  1.53 (4) 
C7a—H7a  1.06  C7b—H7b  1.06 
C7a—C8a  1.37 (4)  C7b—C8b  1.54 (4) 
C8a—H8a  1.06  C8b—H8b  1.06 
C9a—H9a1  1.06  C9b—H9b1  1.06 
C9a—H9a2  1.06  C9b—H9b2  1.06 
C9a—C10a  1.54 (4)  C9b—C10b  1.54 (4) 
C10a—H10a  1.06  C10b—H10b  1.06 
C10a—C11a  1.50 (5)  C10b—C11b  1.63 (4) 
C10a—C12a  1.54 (4)  C10b—C12b  1.49 (4) 
C11a—H11a  1.06  C11b—H11d  1.06 
C11a—H11b  1.06  C11b—H11e  1.06 
C11a—H11c  1.06  C11b—H11f  1.06 
C12a—H12a  1.06  C12b—H12d  1.06 
C12a—H12b  1.06  C12b—H12e  1.06 
C12a—H12c  1.06  C12b—H12f  1.06 
C13a—H13a  1.06  C13b—H13d  1.06 
C13a—H13b  1.06  C13b—H13e  1.06 
C13a—H13c  1.06  C13b—H13f  1.06 
H1a—O2a—C1a  108 (7)  H1b—O2b—C1b  108 (6) 
O1a—C1a—O2a  110 (3)  O2b—C1b—O1b  123 (3) 
O1a—C1a—C2a  122 (3)  O2b—C1b—C2b  117 (3) 
O2a—C1a—C2a  127 (3)  O1b—C1b—C2b  119 (3) 
C1a—C2a—H2a  122.57  C1b—C2b—H2b  104.91 
C1a—C2a—C3a  96 (3)  C1b—C2b—C3b  104 (3) 
C1a—C2a—C13a  107 (2)  C1b—C2b—C13b  122 (2) 
H2a—C2a—C3a  111.55  H2b—C2b—C3b  119.03 
H2a—C2a—C13a  101.9  H2b—C2b—C13b  100.27 
C3a—C2a—C13a  119 (2)  C3b—C2b—C13b  108 (2) 
C2a—C3a—C4a  116 (2)  C2b—C3b—C4b  114 (3) 
C2a—C3a—C8a  123 (2)  C2b—C3b—C8b  127 (3) 
C4a—C3a—C8a  118 (2)  C4b—C3b—C8b  119 (3) 
C3a—C4a—H4a  122.41  C3b—C4b—H4b  122.13 
C3a—C4a—C5a  115 (2)  C3b—C4b—C5b  116 (3) 
H4a—C4a—C5a  122.41  H4b—C4b—C5b  122.13 
C4a—C5a—H5a  118.78  C4b—C5b—H5b  118.51 
C4a—C5a—C6a  122 (3)  C4b—C5b—C6b  123 (2) 
H5a—C5a—C6a  118.78  H5b—C5b—C6b  118.51 
C5a—C6a—C7a  118 (2)  C5b—C6b—C7b  119 (3) 
C5a—C6a—C9a  121 (2)  C5b—C6b—C9b  114 (2) 
C7a—C6a—C9a  120 (2)  C7b—C6b—C9b  123 (2) 
C6a—C7a—H7a  115.13  C6b—C7b—H7b  124.43 
C6a—C7a—C8a  130 (3)  C6b—C7b—C8b  111 (3) 
H7a—C7a—C8a  115.13  H7b—C7b—C8b  124.43 
C3a—C8a—C7a  112 (2)  C3b—C8b—C7b  129 (2) 
C3a—C8a—H8a  123.97  C3b—C8b—H8b  115.58 
C7a—C8a—H8a  123.97  C7b—C8b—H8b  115.58 
C6a—C9a—H9a1  109.47  C6b—C9b—H9b1  109.47 
C6a—C9a—H9a2  109.47  C6b—C9b—H9b2  109.47 
C6a—C9a—C10a  113 (2)  C6b—C9b—C10b  117 (3) 
H9a1—C9a—H9a2  105.73  H9b1—C9b—H9b2  101.14 
H9a1—C9a—C10a  109.47  H9b1—C9b—C10b  109.47 
H9a2—C9a—C10a  109.47  H9b2—C9b—C10b  109.47 
C9a—C10a—H10a  109.43  C9b—C10b—H10b  105.71 
C9a—C10a—C11a  104 (2)  C9b—C10b—C11b  109 (3) 
C9a—C10a—C12a  114.3 (18)  C9b—C10b—C12b  114 (2) 
H10a—C10a—C11a  115.33  H10b—C10b—C11b  114.07 
H10a—C10a—C12a  105.52  H10b—C10b—C12b  108.51 
C11a—C10a—C12a  108 (2)  C11b—C10b—C12b  106 (2) 
C10a—C11a—H11a  109.47  C10b—C11b—H11d  109.47 
C10a—C11a—H11b  109.47  C10b—C11b—H11e  109.47 
C10a—C11a—H11c  109.47  C10b—C11b—H11f  109.47 
H11a—C11a—H11b  109.47  H11d—C11b—H11e  109.47 
H11a—C11a—H11c  109.47  H11d—C11b—H11f  109.47 
H11b—C11a—H11c  109.47  H11e—C11b—H11f  109.47 
C10a—C12a—H12a  109.47  C10b—C12b—H12d  109.47 
C10a—C12a—H12b  109.47  C10b—C12b—H12e  109.47 
C10a—C12a—H12c  109.47  C10b—C12b—H12f  109.47 
H12a—C12a—H12b  109.47  H12d—C12b—H12e  109.47 
H12a—C12a—H12c  109.47  H12d—C12b—H12f  109.47 
H12b—C12a—H12c  109.47  H12e—C12b—H12f  109.47 
C2a—C13a—H13a  109.47  C2b—C13b—H13d  109.47 
C2a—C13a—H13b  109.47  C2b—C13b—H13e  109.47 
C2a—C13a—H13c  109.47  C2b—C13b—H13f  109.47 
H13a—C13a—H13b  109.47  H13d—C13b—H13e  109.47 
H13a—C13a—H13c  109.47  H13d—C13b—H13f  109.47 
H13b—C13a—H13c  109.47  H13e—C13b—H13f  109.47 
D—H···A  D—H  H···A  D···A  D—H···A 
O2a—H1a···O1b^{i}  0.98 (9)  1.56 (11)  2.49 (4)  158 (11) 
O2a—H1a···C1b^{i}  0.98 (9)  2.39 (9)  3.37 (4)  174 (12) 
O2b—H1b···O1a^{ii}  0.98 (8)  1.69 (8)  2.67 (4)  173 (12) 
Symmetry codes: (i) x, y+1, z+1; (ii) x, y−1, z−1. 
C_{13}H_{18}O_{2}  Z = 4 
M_{r} = 206.3  F(000) = 184.42 
Monoclinic, P2_{1}  D_{x} = 1.102 Mg m^{−}^{3} 
Hall symbol: P 2yb  Electrons 200 KeV radiation, λ = 0.0251 Å 
a = 12.368 (4) Å  Cell parameters from 3884 reflections 
b = 8.021 (3) Å  θ = 0.1–0.7° 
c = 13.536 (5) Å  T = 95 K 
β = 112.24 (3)°  Block 
V = 1242.9 (8) Å^{3} 
TEM FEI Tecnai G2 20 diffractometer  R_{int} = 0.166 
Radiation source: Lab6 cathode  θ_{max} = 0.7°, θ_{min} = 0.1° 
continuous–rotation 3D ED scans  h = −12→12 
3884 measured reflections  k = −8→8 
1212 independent reflections  l = −13→13 
856 reflections with I > 3σ(I) 
Refinement on F^{2}  H atoms treated by a mixture of independent and constrained refinement 
R[F > 3σ(F)] = 0.191  Weighting scheme based on measured s.u.'s w = 1/(σ^{2}(I) + 0.0004I^{2}) 
wR(F) = 0.407  (Δ/σ)_{max} = 1.619 
S = 5.46  Δρ_{max} = 0.23 e Å^{−}^{3} 
1212 reflections  Δρ_{min} = −0.27 e Å^{−}^{3} 
127 parameters  Extinction correction: SHELXL2017/1 (Sheldrick, 2015), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
3 restraints  Extinction coefficient: 2.0 (4) 
139 constraints 
x  y  z  U_{iso}*/U_{eq}  
O1a  0.354 (2)  0.509 (5)  1.170 (2)  0.065 (7)*  
O2a  0.221 (3)  0.684 (5)  1.040 (2)  0.072 (8)*  
H1a  0.304 (6)  0.72 (2)  1.067 (17)  0.1444*  
C1a  0.248 (2)  0.538 (5)  1.093 (2)  0.063 (9)*  
C2a  0.155 (3)  0.407 (5)  1.063 (2)  0.058 (8)*  
H2a  0.156828  0.309315  1.115988  0.1168*  
C3a  0.1707 (17)  0.324 (4)  0.9688 (17)  0.026 (6)*  
C4a  0.2283 (19)  0.175 (4)  0.9856 (19)  0.033 (6)*  
H4a  0.260951  0.11825  1.061946  0.0661*  
C5a  0.244 (2)  0.094 (4)  0.8891 (18)  0.038 (7)*  
H5a  0.311882  0.0068  0.900557  0.0759*  
C6a  0.170 (2)  0.1332  0.7895 (17)  0.030 (7)*  
C7a  0.098 (2)  0.272 (4)  0.779 (2)  0.027 (6)*  
H7a  0.045285  0.313079  0.701064  0.0534*  
C8a  0.0932 (19)  0.352 (4)  0.8602 (16)  0.022 (5)*  
H8a  0.027634  0.444316  0.845671  0.0446*  
C9a  0.1823 (17)  0.032 (4)  0.6965 (16)  0.028 (5)*  
H9a1  0.188093  0.114757  0.637819  0.0563*  
H9a2  0.256648  −0.046642  0.72702  0.0563*  
C10a  0.060 (2)  −0.088 (4)  0.6425 (19)  0.050 (8)*  
H10a  −0.021005  −0.027668  0.628838  0.1006*  
C11a  0.057 (2)  −0.146 (4)  0.5391 (18)  0.042 (6)*  
H11a  0.130565  −0.223385  0.551067  0.0848*  
H11b  −0.020527  −0.215562  0.50007  0.0848*  
H11c  0.059106  −0.042561  0.491425  0.0848*  
C12a  0.080 (4)  −0.228 (6)  0.723 (3)  0.091 (12)*  
H12a  0.059194  −0.343704  0.682488  0.1812*  
H12b  0.168675  −0.228227  0.775992  0.1812*  
H12c  0.025846  −0.209569  0.767083  0.1812*  
C13a  0.037 (3)  0.494 (5)  1.054 (3)  0.077 (10)*  
H13a  −0.032258  0.405684  1.028417  0.1542*  
H13b  0.045257  0.540972  1.130241  0.1542*  
H13c  0.01746  0.593616  0.998867  0.1542*  
O2b  0.541 (3)  −0.302 (5)  0.226 (2)  0.067 (8)*  
O1b  0.409 (3)  −0.137 (5)  0.103 (2)  0.069 (8)*  
H1b  0.469 (9)  −0.35 (2)  0.174 (11)  0.1341*  
C1b  0.519 (2)  −0.154 (5)  0.173 (2)  0.059 (8)*  
C2b  0.617 (2)  −0.025 (4)  0.1949 (17)  0.039 (7)*  
H2b  0.699346  −0.080259  0.207597  0.0783*  
C3b  0.6056 (19)  0.069 (4)  0.2888 (18)  0.027 (6)*  
C4b  0.687 (2)  0.009 (5)  0.3948 (18)  0.056 (8)*  
H4b  0.746353  −0.088303  0.397637  0.112*  
C5b  0.690 (2)  0.079 (5)  0.495 (2)  0.047 (7)*  
H5b  0.736405  0.022522  0.569586  0.0936*  
C6b  0.624 (2)  0.229 (4)  0.4854 (19)  0.038 (7)*  
C7b  0.555 (3)  0.297 (6)  0.381 (2)  0.069 (9)*  
H7b  0.509753  0.412387  0.369388  0.1384*  
C8b  0.554 (2)  0.192 (4)  0.2965 (19)  0.030 (6)*  
H8b  0.491584  0.231141  0.221735  0.0606*  
C9b  0.653 (3)  0.315 (5)  0.589 (2)  0.061 (8)*  
H9b1  0.666291  0.225759  0.649833  0.1213*  
H9b2  0.574246  0.346463  0.599035  0.1213*  
C10b  0.734 (2)  0.446 (4)  0.6275 (16)  0.038 (7)*  
H10b  0.806282  0.376586  0.626647  0.0754*  
C11b  0.770 (3)  0.499 (5)  0.744 (2)  0.059 (8)*  
H11d  0.695148  0.531621  0.759656  0.1173*  
H11e  0.826823  0.603924  0.759193  0.1173*  
H11f  0.814478  0.399515  0.794602  0.1173*  
C12b  0.7240 (18)  0.591 (4)  0.5555 (18)  0.033 (6)*  
H12d  0.807942  0.642956  0.572354  0.0653*  
H12e  0.68843  0.550636  0.474968  0.0653*  
H12f  0.668594  0.682622  0.567885  0.0653*  
C13b  0.5950 (19)  0.096 (4)  0.1044 (17)  0.038 (6)*  
H13d  0.515208  0.15916  0.089567  0.0768*  
H13e  0.66423  0.183427  0.124938  0.0768*  
H13f  0.590027  0.030006  0.034862  0.0768* 
O1a—C1a  1.35 (3)  O2b—C1b  1.36 (5) 
O2a—H1a  0.99 (9)  O1b—C1b  1.34 (4) 
O2a—C1a  1.35 (5)  C1b—C2b  1.53 (5) 
C1a—C2a  1.50 (5)  C2b—H2b  1.06 
C2a—H2a  1.06  C2b—C3b  1.53 (4) 
C2a—C3a  1.51 (4)  C2b—C13b  1.50 (4) 
C2a—C13a  1.58 (5)  C3b—C4b  1.49 (3) 
C3a—C4a  1.37 (4)  C3b—C8b  1.20 (4) 
C3a—C8a  1.44 (3)  C4b—H4b  1.06 
C4a—H4a  1.06  C4b—C5b  1.46 (4) 
C4a—C5a  1.54 (4)  C5b—H5b  1.06 
C5a—H5a  1.06  C5b—C6b  1.43 (5) 
C5a—C6a  1.35 (3)  C6b—C7b  1.45 (4) 
C6a—C7a  1.39 (3)  C6b—C9b  1.48 (4) 
C6a—C9a  1.56 (3)  C7b—H7b  1.06 
C7a—H7a  1.06  C7b—C8b  1.42 (5) 
C7a—C8a  1.30 (4)  C8b—H8b  1.06 
C8a—H8a  1.06  C9b—H9b1  1.06 
C9a—H9a1  1.06  C9b—H9b2  1.06 
C9a—H9a2  1.06  C9b—C10b  1.41 (4) 
C10a—H10a  1.06  C10b—H10b  1.06 
C10a—C11a  1.46 (4)  C10b—C11b  1.53 (4) 
C10a—C12a  1.52 (5)  C10b—C12b  1.49 (4) 
C11a—H11a  1.06  C11b—H11d  1.06 
C11a—H11b  1.06  C11b—H11e  1.06 
C11a—H11c  1.06  C11b—H11f  1.06 
C12a—H12a  1.06  C12b—H12d  1.06 
C12a—H12b  1.06  C12b—H12e  1.06 
C12a—H12c  1.06  C12b—H12f  1.06 
C13a—H13a  1.06  C13b—H13d  1.06 
C13a—H13b  1.06  C13b—H13e  1.06 
C13a—H13c  1.06  C13b—H13f  1.06 
O2b—H1b  0.99 (12)  
H1a—O2a—C1a  93 (12)  O1b—C1b—C2b  126 (3) 
O1a—C1a—O2a  122 (3)  C1b—C2b—H2b  112.73 
O1a—C1a—C2a  121 (3)  C1b—C2b—C3b  100 (2) 
O2a—C1a—C2a  117 (2)  C1b—C2b—C13b  112.9 (19) 
C1a—C2a—H2a  121.17  H2b—C2b—C3b  117.15 
C1a—C2a—C3a  102 (3)  H2b—C2b—C13b  105.66 
C1a—C2a—C13a  108 (3)  C3b—C2b—C13b  108 (3) 
H2a—C2a—C3a  105.45  C2b—C3b—C4b  113 (2) 
H2a—C2a—C13a  99.16  C2b—C3b—C8b  134 (2) 
C3a—C2a—C13a  123 (2)  C4b—C3b—C8b  112 (3) 
C2a—C3a—C4a  118 (2)  C3b—C4b—H4b  118.76 
C2a—C3a—C8a  123 (2)  C3b—C4b—C5b  122 (3) 
C4a—C3a—C8a  114 (2)  H4b—C4b—C5b  118.76 
C3a—C4a—H4a  121.47  C4b—C5b—H5b  122.22 
C3a—C4a—C5a  117 (2)  C4b—C5b—C6b  116 (2) 
H4a—C4a—C5a  121.47  H5b—C5b—C6b  122.22 
C4a—C5a—H5a  120.19  C5b—C6b—C7b  121 (3) 
C4a—C5a—C6a  120 (3)  C5b—C6b—C9b  113 (2) 
H5a—C5a—C6a  120.19  C7b—C6b—C9b  126 (3) 
C5a—C6a—C7a  117 (2)  C6b—C7b—H7b  123.69 
C5a—C6a—C9a  117 (2)  C6b—C7b—C8b  113 (3) 
C7a—C6a—C9a  126.0 (19)  H7b—C7b—C8b  123.69 
C6a—C7a—H7a  118.68  C3b—C8b—C7b  136 (2) 
C6a—C7a—C8a  123 (2)  C3b—C8b—H8b  112.18 
H7a—C7a—C8a  118.68  C7b—C8b—H8b  112.18 
C3a—C8a—C7a  124 (3)  C6b—C9b—H9b1  109.47 
C3a—C8a—H8a  117.81  C6b—C9b—H9b2  109.47 
C7a—C8a—H8a  117.81  C6b—C9b—C10b  125 (3) 
C6a—C9a—H9a1  109.47  H9b1—C9b—H9b2  86.59 
C6a—C9a—H9a2  109.47  H9b1—C9b—C10b  109.47 
H9a1—C9a—H9a2  111.69  H9b2—C9b—C10b  109.47 
H10a—C10a—C11a  107.46  C9b—C10b—H10b  95.07 
H10a—C10a—C12a  110.49  C9b—C10b—C11b  119 (3) 
C11a—C10a—C12a  113 (3)  C9b—C10b—C12b  117.8 (19) 
C10a—C11a—H11a  109.47  H10b—C10b—C11b  103.74 
C10a—C11a—H11b  109.47  H10b—C10b—C12b  105.34 
C10a—C11a—H11c  109.47  C11b—C10b—C12b  112 (3) 
H11a—C11a—H11b  109.47  C10b—C11b—H11d  109.47 
H11a—C11a—H11c  109.47  C10b—C11b—H11e  109.47 
H11b—C11a—H11c  109.47  C10b—C11b—H11f  109.47 
C10a—C12a—H12a  109.47  H11d—C11b—H11e  109.47 
C10a—C12a—H12b  109.47  H11d—C11b—H11f  109.47 
C10a—C12a—H12c  109.47  H11e—C11b—H11f  109.47 
H12a—C12a—H12b  109.47  C10b—C12b—H12d  109.47 
H12a—C12a—H12c  109.47  C10b—C12b—H12e  109.47 
H12b—C12a—H12c  109.47  C10b—C12b—H12f  109.47 
C2a—C13a—H13a  109.47  H12d—C12b—H12e  109.47 
C2a—C13a—H13b  109.47  H12d—C12b—H12f  109.47 
C2a—C13a—H13c  109.47  H12e—C12b—H12f  109.47 
H13a—C13a—H13b  109.47  C2b—C13b—H13d  109.47 
H13a—C13a—H13c  109.47  C2b—C13b—H13e  109.47 
H13b—C13a—H13c  109.47  C2b—C13b—H13f  109.47 
H1b—O2b—C1b  93 (10)  H13d—C13b—H13e  109.47 
O2b—C1b—O1b  114 (3)  H13d—C13b—H13f  109.47 
O2b—C1b—C2b  120 (2)  H13e—C13b—H13f  109.47 
D—H···A  D—H  H···A  D···A  D—H···A 
O2a—H1a···O1b^{i}  0.99 (9)  1.67 (15)  2.58 (5)  153 (16) 
O2b—H1b···O1a^{ii}  0.99 (12)  1.79 (15)  2.63 (5)  141 (14) 
Symmetry codes: (i) x, y+1, z+1; (ii) x, y−1, z−1. 
C_{13}H_{18}O_{2}  Z = 4 
M_{r} = 206.3  F(000) = 184.42 
Monoclinic, P2_{1}  D_{x} = 1.102 Mg m^{−}^{3} 
Hall symbol: P 2yb  Electrons 200 KeV radiation, λ = 0.0251 Å 
a = 12.368 (4) Å  Cell parameters from 3884 reflections 
b = 8.021 (3) Å  θ = 0.1–0.7° 
c = 13.536 (5) Å  T = 95 K 
β = 112.24 (3)°  Block 
V = 1242.9 (8) Å^{3} 
TEM FEI Tecnai G2 20 diffractometer  R_{int} = 0.166 
Radiation source: Lab6 cathode  θ_{max} = 0.7°, θ_{min} = 0.1° 
continuous–rotation 3D ED scans  h = −12→12 
3884 measured reflections  k = −8→8 
1212 independent reflections  l = −13→13 
883 reflections with I > 3σ(I) 
Refinement on F^{2}  H atoms treated by a mixture of independent and constrained refinement 
R[F > 3σ(F)] = 0.188  Weighting scheme based on measured s.u.'s w = 1/(σ^{2}(I) + 0.0004I^{2}) 
wR(F) = 0.426  (Δ/σ)_{max} = 0.046 
S = 2.03  Δρ_{max} = 0.27 e Å^{−}^{3} 
1212 reflections  Δρ_{min} = −0.26 e Å^{−}^{3} 
127 parameters  Extinction correction: SHELXL2017/1 (Sheldrick, 2015), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
3 restraints  Extinction coefficient: 3.7 (9) 
139 constraints 
x  y  z  U_{iso}*/U_{eq}  
O1a  0.3483 (19)  0.520 (3)  1.1738 (15)  0.047 (5)*  
O2a  0.230 (2)  0.681 (3)  1.0468 (16)  0.049 (5)*  
H1a  0.291 (9)  0.763 (13)  1.080 (9)  0.0977*  
C1a  0.254 (2)  0.544 (3)  1.1011 (17)  0.037 (5)*  
C2a  0.155 (2)  0.408 (3)  1.0677 (17)  0.043 (6)*  
H2a  0.161004  0.313979  1.124761  0.0866*  
C3a  0.1671 (16)  0.331 (2)  0.9703 (13)  0.020 (4)*  
C4a  0.2346 (19)  0.185 (3)  0.9830 (16)  0.035 (5)*  
H4a  0.279552  0.136015  1.060603  0.0709*  
C5a  0.2434 (16)  0.101 (2)  0.8919 (12)  0.022 (4)*  
H5a  0.309796  0.010112  0.904912  0.0435*  
C6a  0.1708 (15)  0.1332  0.7919 (12)  0.009 (4)*  
C7a  0.0949 (19)  0.276 (3)  0.7758 (17)  0.032 (5)*  
H7a  0.044494  0.314088  0.696613  0.0631*  
C8a  0.0853 (18)  0.365 (3)  0.8575 (13)  0.031 (5)*  
H8a  0.020032  0.457851  0.841836  0.0622*  
C9a  0.1710 (16)  0.036 (2)  0.6962 (12)  0.020 (4)*  
H9a1  0.172883  0.120675  0.636497  0.0407*  
H9a2  0.247725  −0.037318  0.718552  0.0407*  
C10a  0.0560 (17)  −0.084 (3)  0.6472 (13)  0.029 (5)*  
H10a  −0.024033  −0.02508  0.637934  0.0576*  
C11a  0.062 (2)  −0.139 (3)  0.5431 (16)  0.042 (5)*  
H11a  0.082053  −0.035243  0.504681  0.0844*  
H11b  0.127539  −0.231109  0.557875  0.0844*  
H11c  −0.019944  −0.189306  0.493457  0.0844*  
C12a  0.067 (2)  −0.229 (3)  0.7203 (17)  0.042 (5)*  
H12a  0.003048  −0.319715  0.680316  0.0846*  
H12b  0.151229  −0.281542  0.74315  0.0846*  
H12c  0.053418  −0.187212  0.789239  0.0846*  
C13a  0.037 (3)  0.487 (4)  1.053 (2)  0.067 (7)*  
H13a  −0.02582  0.391412  1.041545  0.1349*  
H13b  0.045482  0.557643  1.121102  0.1349*  
H13c  0.010264  0.565243  0.984649  0.1349*  
O2b  0.541 (2)  −0.289 (3)  0.2291 (17)  0.055 (5)*  
O1b  0.413 (2)  −0.124 (3)  0.1015 (16)  0.051 (5)*  
H1b  0.475 (8)  −0.366 (14)  0.205 (10)  0.111*  
C1b  0.512 (2)  −0.146 (3)  0.1738 (16)  0.035 (5)*  
C2b  0.611 (2)  −0.023 (3)  0.1959 (16)  0.046 (6)*  
H2b  0.691943  −0.083435  0.211316  0.0914*  
C3b  0.611 (2)  0.073 (3)  0.2907 (16)  0.039 (5)*  
C4b  0.6879 (18)  0.008 (3)  0.3981 (14)  0.036 (5)*  
H4b  0.744922  −0.094793  0.406557  0.0713*  
C5b  0.6804 (19)  0.088 (3)  0.4849 (17)  0.039 (5)*  
H5b  0.726041  0.031082  0.559793  0.0784*  
C6b  0.6217 (19)  0.233 (3)  0.4882 (15)  0.030 (5)*  
C7b  0.550 (2)  0.298 (3)  0.3855 (16)  0.045 (6)*  
H7b  0.500624  0.409417  0.377044  0.0904*  
C8b  0.5479 (18)  0.202 (2)  0.2937 (15)  0.027 (5)*  
H8b  0.486875  0.242141  0.218764  0.0543*  
C9b  0.6377 (19)  0.321 (3)  0.5875 (15)  0.043 (5)*  
H9b1  0.646674  0.232646  0.648523  0.0864*  
H9b2  0.5577  0.376672  0.581319  0.0864*  
C10b  0.731 (2)  0.443 (3)  0.6263 (15)  0.043 (6)*  
H10b  0.801633  0.365674  0.628986  0.0867*  
C11b  0.756 (2)  0.519 (3)  0.7400 (18)  0.057 (6)*  
H11d  0.813729  0.439941  0.799233  0.1131*  
H11e  0.676206  0.529633  0.752029  0.1131*  
H11f  0.794042  0.638607  0.745324  0.1131*  
C12b  0.7173 (19)  0.601 (3)  0.5498 (14)  0.039 (5)*  
H12d  0.79347  0.675931  0.580418  0.0777*  
H12e  0.705614  0.559546  0.472097  0.0777*  
H12f  0.643753  0.672268  0.546386  0.0777*  
C13b  0.598 (2)  0.086 (3)  0.1012 (15)  0.041 (5)*  
H13d  0.50821  0.110426  0.057355  0.0812*  
H13e  0.642607  0.200281  0.128271  0.0812*  
H13f  0.634012  0.024541  0.05143  0.0812* 
O1a—C1a  1.22 (3)  O2b—H1b  0.98 (10) 
O2a—H1a  0.98 (10)  O2b—C1b  1.34 (3) 
O2a—C1a  1.29 (3)  O1b—C1b  1.26 (3) 
C1a—C2a  1.58 (3)  C1b—C2b  1.51 (3) 
C2a—H2a  1.06  C2b—H2b  1.06 
C2a—C3a  1.52 (3)  C2b—C3b  1.50 (3) 
C2a—C13a  1.53 (4)  C2b—C13b  1.51 (3) 
C3a—C4a  1.41 (3)  C3b—C4b  1.50 (3) 
C3a—C8a  1.50 (2)  C3b—C8b  1.30 (3) 
C4a—H4a  1.06  C4b—H4b  1.06 
C4a—C5a  1.45 (3)  C4b—C5b  1.37 (3) 
C5a—H5a  1.06  C5b—H5b  1.06 
C5a—C6a  1.34 (2)  C5b—C6b  1.38 (3) 
C6a—C7a  1.45 (2)  C6b—C7b  1.44 (3) 
C6a—C9a  1.51 (2)  C6b—C9b  1.46 (3) 
C7a—H7a  1.06  C7b—H7b  1.06 
C7a—C8a  1.36 (3)  C7b—C8b  1.46 (3) 
C8a—H8a  1.06  C8b—H8b  1.06 
C9a—H9a1  1.06  C9b—H9b1  1.06 
C9a—H9a2  1.06  C9b—H9b2  1.06 
C9a—C10a  1.64 (3)  C9b—C10b  1.45 (3) 
C10a—H10a  1.06  C10b—H10b  1.06 
C10a—C11a  1.50 (3)  C10b—C11b  1.57 (3) 
C10a—C12a  1.50 (3)  C10b—C12b  1.61 (3) 
C11a—H11a  1.06  C11b—H11d  1.06 
C11a—H11b  1.06  C11b—H11e  1.06 
C11a—H11c  1.06  C11b—H11f  1.06 
C12a—H12a  1.06  C12b—H12d  1.06 
C12a—H12b  1.06  C12b—H12e  1.06 
C12a—H12c  1.06  C12b—H12f  1.06 
C13a—H13a  1.06  C13b—H13d  1.06 
C13a—H13b  1.06  C13b—H13e  1.06 
C13a—H13c  1.06  C13b—H13f  1.06 
H1a—O2a—C1a  110 (6)  H1b—O2b—C1b  110 (6) 
O1a—C1a—O2a  123 (2)  O2b—C1b—O1b  122 (2) 
O1a—C1a—C2a  121 (2)  O2b—C1b—C2b  115.0 (19) 
O2a—C1a—C2a  115.9 (18)  O1b—C1b—C2b  123 (2) 
C1a—C2a—H2a  116.64  C1b—C2b—H2b  111.99 
C1a—C2a—C3a  102 (2)  C1b—C2b—C3b  104 (2) 
C1a—C2a—C13a  111 (2)  C1b—C2b—C13b  113.2 (16) 
H2a—C2a—C3a  109.9  H2b—C2b—C3b  112 
H2a—C2a—C13a  101.28  H2b—C2b—C13b  102.72 
C3a—C2a—C13a  117.2 (17)  C3b—C2b—C13b  113.2 (19) 
C2a—C3a—C4a  118.8 (16)  C2b—C3b—C4b  116.2 (19) 
C2a—C3a—C8a  124.0 (18)  C2b—C3b—C8b  129.0 (18) 
C4a—C3a—C8a  114.5 (17)  C4b—C3b—C8b  115 (2) 
C3a—C4a—H4a  119.48  C3b—C4b—H4b  122 
C3a—C4a—C5a  121.0 (17)  C3b—C4b—C5b  116 (2) 
H4a—C4a—C5a  119.48  H4b—C4b—C5b  122 
C4a—C5a—H5a  118.84  C4b—C5b—H5b  115.45 
C4a—C5a—C6a  122.3 (18)  C4b—C5b—C6b  129.1 (19) 
H5a—C5a—C6a  118.84  H5b—C5b—C6b  115.45 
C5a—C6a—C7a  117.1 (16)  C5b—C6b—C7b  115 (2) 
C5a—C6a—C9a  123.4 (14)  C5b—C6b—C9b  123.0 (17) 
C7a—C6a—C9a  119.4 (14)  C7b—C6b—C9b  122 (2) 
C6a—C7a—H7a  118.49  C6b—C7b—H7b  122.07 
C6a—C7a—C8a  123.0 (17)  C6b—C7b—C8b  116 (2) 
H7a—C7a—C8a  118.49  H7b—C7b—C8b  122.07 
C3a—C8a—C7a  120.0 (19)  C3b—C8b—C7b  129.1 (18) 
C3a—C8a—H8a  119.99  C3b—C8b—H8b  115.45 
C7a—C8a—H8a  119.99  C7b—C8b—H8b  115.45 
C6a—C9a—H9a1  109.47  C6b—C9b—H9b1  109.47 
C6a—C9a—H9a2  109.47  C6b—C9b—H9b2  109.47 
C6a—C9a—C10a  111.5 (16)  C6b—C9b—C10b  118 (2) 
H9a1—C9a—H9a2  107.37  H9b1—C9b—H9b2  99.43 
H9a1—C9a—C10a  109.47  H9b1—C9b—C10b  109.47 
H9a2—C9a—C10a  109.47  H9b2—C9b—C10b  109.47 
C9a—C10a—H10a  114.54  C9b—C10b—H10b  98.56 
C9a—C10a—C11a  102.1 (17)  C9b—C10b—C11b  117 (2) 
C9a—C10a—C12a  110.1 (13)  C9b—C10b—C12b  115.1 (15) 
H10a—C10a—C11a  113.14  H10b—C10b—C11b  109.93 
H10a—C10a—C12a  105.58  H10b—C10b—C12b  111.66 
C11a—C10a—C12a  111.6 (18)  C11b—C10b—C12b  105.0 (17) 
C10a—C11a—H11a  109.47  C10b—C11b—H11d  109.47 
C10a—C11a—H11b  109.47  C10b—C11b—H11e  109.47 
C10a—C11a—H11c  109.47  C10b—C11b—H11f  109.47 
H11a—C11a—H11b  109.47  H11d—C11b—H11e  109.47 
H11a—C11a—H11c  109.47  H11d—C11b—H11f  109.47 
H11b—C11a—H11c  109.47  H11e—C11b—H11f  109.47 
C10a—C12a—H12a  109.47  C10b—C12b—H12d  109.47 
C10a—C12a—H12b  109.47  C10b—C12b—H12e  109.47 
C10a—C12a—H12c  109.47  C10b—C12b—H12f  109.47 
H12a—C12a—H12b  109.47  H12d—C12b—H12e  109.47 
H12a—C12a—H12c  109.47  H12d—C12b—H12f  109.47 
H12b—C12a—H12c  109.47  H12e—C12b—H12f  109.47 
C2a—C13a—H13a  109.47  C2b—C13b—H13d  109.47 
C2a—C13a—H13b  109.47  C2b—C13b—H13e  109.47 
C2a—C13a—H13c  109.47  C2b—C13b—H13f  109.47 
H13a—C13a—H13b  109.47  H13d—C13b—H13e  109.47 
H13a—C13a—H13c  109.47  H13d—C13b—H13f  109.47 
H13b—C13a—H13c  109.47  H13e—C13b—H13f  109.47 
D—H···A  D—H  H···A  D···A  D—H···A 
O2a—H1a···O1b^{i}  0.98 (10)  1.68 (11)  2.62 (3)  158 (12) 
O2b—H1b···O1a^{ii}  0.98 (10)  1.72 (10)  2.69 (3)  170 (12) 
Symmetry codes: (i) x, y+1, z+1; (ii) x, y−1, z−1. 
C_{13}H_{18}O_{2}  Z = 4 
M_{r} = 206.3  F(000) = 184.42 
Monoclinic, P2_{1}  D_{x} = 1.102 Mg m^{−}^{3} 
Hall symbol: P 2yb  Electrons 200 KeV radiation, λ = 0.0251 Å 
a = 12.368 (4) Å  Cell parameters from 3884 reflections 
b = 8.021 (3) Å  θ = 0.1–0.7° 
c = 13.536 (5) Å  T = 95 K 
β = 112.24 (3)°  Block 
V = 1242.9 (8) Å^{3} 
TEM FEI Tecnai G2 20 diffractometer  R_{int} = 0.166 
Radiation source: Lab6 cathode  θ_{max} = 0.7°, θ_{min} = 0.1° 
continuous–rotation 3D ED scans  h = −12→12 
3884 measured reflections  k = −8→8 
1212 independent reflections  l = −13→13 
957 reflections with I > 3σ(I) 
Refinement on F^{2}  H atoms treated by a mixture of independent and constrained refinement 
R[F > 3σ(F)] = 0.190  Weighting scheme based on measured s.u.'s w = 1/(σ^{2}(I) + 0.0004I^{2}) 
wR(F) = 0.410  (Δ/σ)_{max} = 0.031 
S = 2.36  Δρ_{max} = 0.26 e Å^{−}^{3} 
1212 reflections  Δρ_{min} = −0.27 e Å^{−}^{3} 
127 parameters  Extinction correction: SHELXL2017/1 (Sheldrick, 2015), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
3 restraints  Extinction coefficient: 3.3 (7) 
139 constraints 
x  y  z  U_{iso}*/U_{eq}  
O1a  0.3481 (17)  0.518 (3)  1.1740 (14)  0.044 (5)*  
O2a  0.227 (2)  0.678 (3)  1.0457 (16)  0.050 (5)*  
H1a  0.294 (8)  0.754 (13)  1.077 (9)  0.1007*  
C1a  0.2554 (19)  0.543 (3)  1.1008 (16)  0.037 (5)*  
C2a  0.154 (2)  0.410 (3)  1.0672 (17)  0.045 (6)*  
H2a  0.158665  0.316531  1.124207  0.0901*  
C3a  0.1665 (15)  0.331 (2)  0.9692 (13)  0.020 (4)*  
C4a  0.2362 (19)  0.186 (3)  0.9848 (16)  0.037 (5)*  
H4a  0.282338  0.139272  1.06284  0.0748*  
C5a  0.2439 (16)  0.100 (3)  0.8917 (12)  0.025 (4)*  
H5a  0.309796  0.008596  0.903857  0.0494*  
C6a  0.1697 (15)  0.1332  0.7914 (12)  0.013 (4)*  
C7a  0.0948 (18)  0.275 (3)  0.7764 (16)  0.032 (5)*  
H7a  0.043562  0.312385  0.697338  0.0647*  
C8a  0.0859 (17)  0.366 (3)  0.8590 (13)  0.030 (5)*  
H8a  0.021344  0.459591  0.843702  0.0598*  
C9a  0.1714 (15)  0.039 (2)  0.6967 (12)  0.022 (4)*  
H9a1  0.173159  0.123895  0.637419  0.043*  
H9a2  0.247897  −0.035565  0.719715  0.043*  
C10a  0.0550 (17)  −0.082 (3)  0.6470 (13)  0.035 (5)*  
H10a  −0.025434  −0.0236  0.63671  0.0693*  
C11a  0.062 (2)  −0.140 (3)  0.5425 (16)  0.044 (5)*  
H11a  0.083217  −0.037445  0.503793  0.087*  
H11b  0.127389  −0.232889  0.558385  0.087*  
H11c  −0.019738  −0.190086  0.492498  0.087*  
C12a  0.070 (2)  −0.228 (3)  0.7222 (18)  0.048 (6)*  
H12a  0.00552  −0.31964  0.684604  0.0967*  
H12b  0.154178  −0.281271  0.741319  0.0967*  
H12c  0.061129  −0.186837  0.792984  0.0967*  
C13a  0.038 (2)  0.487 (3)  1.054 (2)  0.065 (7)*  
H13a  −0.02511  0.391528  1.041055  0.1291*  
H13b  0.046876  0.553957  1.124109  0.1291*  
H13c  0.011494  0.569012  0.987871  0.1291*  
O2b  0.540 (2)  −0.290 (3)  0.2286 (16)  0.055 (5)*  
O1b  0.414 (2)  −0.124 (3)  0.1026 (16)  0.054 (5)*  
H1b  0.471 (7)  −0.361 (14)  0.198 (9)  0.1096*  
C1b  0.513 (2)  −0.147 (3)  0.1736 (16)  0.039 (5)*  
C2b  0.610 (2)  −0.024 (3)  0.1965 (16)  0.048 (6)*  
H2b  0.689643  −0.08761  0.211948  0.0964*  
C3b  0.6114 (18)  0.074 (3)  0.2909 (15)  0.034 (5)*  
C4b  0.6883 (19)  0.007 (3)  0.3980 (15)  0.044 (5)*  
H4b  0.745023  −0.095095  0.405713  0.0871*  
C5b  0.6814 (17)  0.087 (3)  0.4866 (16)  0.037 (5)*  
H5b  0.726183  0.029854  0.561585  0.0745*  
C6b  0.6228 (18)  0.232 (3)  0.4872 (15)  0.030 (5)*  
C7b  0.550 (2)  0.298 (3)  0.3841 (16)  0.046 (6)*  
H7b  0.500169  0.408902  0.375764  0.0926*  
C8b  0.5492 (18)  0.205 (3)  0.2945 (14)  0.026 (5)*  
H8b  0.489581  0.246785  0.219415  0.0527*  
C9b  0.6386 (19)  0.323 (3)  0.5889 (15)  0.045 (5)*  
H9b1  0.649244  0.23528  0.650526  0.0902*  
H9b2  0.558154  0.37732  0.582554  0.0902*  
C10b  0.7300 (18)  0.446 (3)  0.6259 (14)  0.039 (5)*  
H10b  0.800282  0.37035  0.626245  0.0781*  
C11b  0.759 (2)  0.516 (3)  0.7412 (16)  0.054 (6)*  
H11d  0.68542  0.581528  0.743684  0.1082*  
H11e  0.831143  0.598531  0.761488  0.1082*  
H11f  0.779622  0.41617  0.796386  0.1082*  
C12b  0.7180 (18)  0.598 (3)  0.5514 (14)  0.039 (5)*  
H12d  0.795402  0.6702  0.580974  0.0777*  
H12e  0.70461  0.554867  0.473517  0.0777*  
H12f  0.645939  0.671744  0.548596  0.0777*  
C13b  0.599 (2)  0.090 (3)  0.1021 (15)  0.044 (5)*  
H13d  0.509821  0.123587  0.06172  0.0889*  
H13e  0.649616  0.198266  0.13044  0.0889*  
H13f  0.628367  0.025194  0.048842  0.0889* 
O1a—C1a  1.22 (2)  O2b—H1b  0.98 (10) 
O2a—H1a  0.98 (9)  O2b—C1b  1.34 (3) 
O2a—C1a  1.29 (3)  O1b—C1b  1.26 (3) 
C1a—C2a  1.58 (3)  C1b—C2b  1.49 (3) 
C2a—H2a  1.06  C2b—H2b  1.06 
C2a—C3a  1.53 (3)  C2b—C3b  1.49 (3) 
C2a—C13a  1.51 (4)  C2b—C13b  1.53 (3) 
C3a—C4a  1.42 (3)  C3b—C4b  1.50 (3) 
C3a—C8a  1.47 (2)  C3b—C8b  1.31 (3) 
C4a—H4a  1.06  C4b—H4b  1.06 
C4a—C5a  1.47 (3)  C4b—C5b  1.39 (3) 
C5a—H5a  1.06  C5b—H5b  1.06 
C5a—C6a  1.35 (2)  C5b—C6b  1.37 (3) 
C6a—C7a  1.43 (2)  C6b—C7b  1.45 (3) 
C6a—C9a  1.50 (2)  C6b—C9b  1.50 (3) 
C7a—H7a  1.06  C7b—H7b  1.06 
C7a—C8a  1.37 (3)  C7b—C8b  1.42 (3) 
C8a—H8a  1.06  C8b—H8b  1.06 
C9a—H9a1  1.06  C9b—H9b1  1.06 
C9a—H9a2  1.06  C9b—H9b2  1.06 
C9a—C10a  1.65 (3)  C9b—C10b  1.44 (3) 
C10a—H10a  1.06  C10b—H10b  1.06 
C10a—C11a  1.52 (3)  C10b—C11b  1.57 (3) 
C10a—C12a  1.52 (3)  C10b—C12b  1.55 (3) 
C11a—H11a  1.06  C11b—H11d  1.06 
C11a—H11b  1.06  C11b—H11e  1.06 
C11a—H11c  1.06  C11b—H11f  1.06 
C12a—H12a  1.06  C12b—H12d  1.06 
C12a—H12b  1.06  C12b—H12e  1.06 
C12a—H12c  1.06  C12b—H12f  1.06 
C13a—H13a  1.06  C13b—H13d  1.06 
C13a—H13b  1.06  C13b—H13e  1.06 
C13a—H13c  1.06  C13b—H13f  1.06 
H1a—O2a—C1a  106 (6)  H1b—O2b—C1b  106 (6) 
O1a—C1a—O2a  125 (2)  O2b—C1b—O1b  121 (2) 
O1a—C1a—C2a  122 (2)  O2b—C1b—C2b  116.2 (18) 
O2a—C1a—C2a  113.2 (17)  O1b—C1b—C2b  123 (2) 
C1a—C2a—H2a  116.63  C1b—C2b—H2b  109.61 
C1a—C2a—C3a  101 (2)  C1b—C2b—C3b  106 (2) 
C1a—C2a—C13a  112 (2)  C1b—C2b—C13b  114.0 (16) 
H2a—C2a—C3a  110.17  H2b—C2b—C3b  111.99 
H2a—C2a—C13a  99.4  H2b—C2b—C13b  103.62 
C3a—C2a—C13a  118.1 (17)  C3b—C2b—C13b  111.7 (19) 
C2a—C3a—C4a  117.8 (16)  C2b—C3b—C4b  116.1 (19) 
C2a—C3a—C8a  123.3 (18)  C2b—C3b—C8b  129.2 (17) 
C4a—C3a—C8a  116.5 (17)  C4b—C3b—C8b  114.5 (19) 
C3a—C4a—H4a  120.3  C3b—C4b—H4b  121.73 
C3a—C4a—C5a  119.4 (16)  C3b—C4b—C5b  117 (2) 
H4a—C4a—C5a  120.3  H4b—C4b—C5b  121.72 
C4a—C5a—H5a  119.01  C4b—C5b—H5b  116.55 
C4a—C5a—C6a  122.0 (17)  C4b—C5b—C6b  126.9 (19) 
H5a—C5a—C6a  119.01  H5b—C5b—C6b  116.55 
C5a—C6a—C7a  117.3 (16)  C5b—C6b—C7b  116 (2) 
C5a—C6a—C9a  122.5 (14)  C5b—C6b—C9b  122.1 (17) 
C7a—C6a—C9a  120.0 (14)  C7b—C6b—C9b  121.4 (19) 
C6a—C7a—H7a  118.25  C6b—C7b—H7b  122.36 
C6a—C7a—C8a  123.5 (17)  C6b—C7b—C8b  115 (2) 
H7a—C7a—C8a  118.25  H7b—C7b—C8b  122.36 
C3a—C8a—C7a  119.6 (19)  C3b—C8b—C7b  129.7 (17) 
C3a—C8a—H8a  120.21  C3b—C8b—H8b  115.15 
C7a—C8a—H8a  120.21  C7b—C8b—H8b  115.15 
C6a—C9a—H9a1  109.47  C6b—C9b—H9b1  109.47 
C6a—C9a—H9a2  109.47  C6b—C9b—H9b2  109.47 
C6a—C9a—C10a  110.6 (16)  C6b—C9b—C10b  118 (2) 
H9a1—C9a—H9a2  108.27  H9b1—C9b—H9b2  99.79 
H9a1—C9a—C10a  109.47  H9b1—C9b—C10b  109.47 
H9a2—C9a—C10a  109.47  H9b2—C9b—C10b  109.47 
C9a—C10a—H10a  115.17  C9b—C10b—H10b  98.11 
C9a—C10a—C11a  102.1 (17)  C9b—C10b—C11b  116 (2) 
C9a—C10a—C12a  108.3 (14)  C9b—C10b—C12b  116.3 (15) 
H10a—C10a—C11a  113.15  H10b—C10b—C11b  108.92 
H10a—C10a—C12a  107.51  H10b—C10b—C12b  109.18 
C11a—C10a—C12a  110.5 (19)  C11b—C10b—C12b  107.3 (18) 
C10a—C11a—H11a  109.47  C10b—C11b—H11d  109.47 
C10a—C11a—H11b  109.47  C10b—C11b—H11e  109.47 
C10a—C11a—H11c  109.47  C10b—C11b—H11f  109.47 
H11a—C11a—H11b  109.47  H11d—C11b—H11e  109.47 
H11a—C11a—H11c  109.47  H11d—C11b—H11f  109.47 
H11b—C11a—H11c  109.47  H11e—C11b—H11f  109.47 
C10a—C12a—H12a  109.47  C10b—C12b—H12d  109.47 
C10a—C12a—H12b  109.47  C10b—C12b—H12e  109.47 
C10a—C12a—H12c  109.47  C10b—C12b—H12f  109.47 
H12a—C12a—H12b  109.47  H12d—C12b—H12e  109.47 
H12a—C12a—H12c  109.47  H12d—C12b—H12f  109.47 
H12b—C12a—H12c  109.47  H12e—C12b—H12f  109.47 
C2a—C13a—H13a  109.47  C2b—C13b—H13d  109.47 
C2a—C13a—H13b  109.47  C2b—C13b—H13e  109.47 
C2a—C13a—H13c  109.47  C2b—C13b—H13f  109.47 
H13a—C13a—H13b  109.47  H13d—C13b—H13e  109.47 
H13a—C13a—H13c  109.47  H13d—C13b—H13f  109.47 
H13b—C13a—H13c  109.47  H13e—C13b—H13f  109.47 
D—H···A  D—H  H···A  D···A  D—H···A 
O2a—H1a···O1b^{i}  0.98 (9)  1.70 (10)  2.66 (3)  165 (12) 
O2b—H1b···O1a^{ii}  0.98 (10)  1.73 (10)  2.69 (3)  167 (12) 
Symmetry codes: (i) x, y+1, z+1; (ii) x, y−1, z−1. 
C_{13}H_{18}O_{2}  Z = 4 
M_{r} = 206.3  F(000) = 184.42 
Monoclinic, P2_{1}  D_{x} = 1.102 Mg m^{−}^{3} 
Hall symbol: P 2yb  Electrons 200 KeV radiation, λ = 0.0251 Å 
a = 12.368 (4) Å  Cell parameters from 3818 reflections 
b = 8.021 (3) Å  θ = 0.1–0.7° 
c = 13.536 (5) Å  T = 95 K 
β = 112.24 (3)°  Block 
V = 1242.9 (8) Å^{3} 
TEM FEI Tecnai G2 20 diffractometer  R_{int} = 0.158 
Radiation source: Lab6 cathode  θ_{max} = 0.7°, θ_{min} = 0.1° 
continuous–rotation 3D ED scans  h = −12→12 
3818 measured reflections  k = −8→8 
1209 independent reflections  l = −13→13 
972 reflections with I > 3σ(I) 
Refinement on F^{2}  H atoms treated by a mixture of independent and constrained refinement 
R[F > 3σ(F)] = 0.190  Weighting scheme based on measured s.u.'s w = 1/[σ^{2}(F_{o}^{2}) + (0.02P)^{2}] where P = (F_{o}^{2} + 2F_{c}^{2})/3 
wR(F) = 0.414  (Δ/σ)_{max} = 0.047 
S = 2.35  Δρ_{max} = 0.26 e Å^{−}^{3} 
1209 reflections  Δρ_{min} = −0.27 e Å^{−}^{3} 
127 parameters  Extinction correction: SHELXL2017/1 (Sheldrick, 2015), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
3 restraints  Extinction coefficient: 3.4 (7) 
139 constraints 
x  y  z  U_{iso}*/U_{eq}  
O1a  0.3488 (17)  0.518 (3)  1.1743 (14)  0.043 (4)*  
O2a  0.227 (2)  0.677 (3)  1.0449 (16)  0.050 (5)*  
H1a  0.292 (8)  0.754 (13)  1.077 (9)  0.1*  
C1a  0.2559 (18)  0.542 (3)  1.1008 (16)  0.036 (5)*  
C2a  0.155 (2)  0.411 (3)  1.0677 (16)  0.044 (6)*  
H2a  0.160723  0.319241  1.125872  0.0883*  
C3a  0.1663 (15)  0.331 (2)  0.9689 (13)  0.020 (4)*  
C4a  0.2369 (19)  0.186 (3)  0.9851 (16)  0.037 (5)*  
H4a  0.283943  0.14016  1.063165  0.0742*  
C5a  0.2434 (16)  0.100 (3)  0.8912 (12)  0.025 (4)*  
H5a  0.309033  0.008741  0.903009  0.0508*  
C6a  0.1692 (15)  0.1332  0.7912 (12)  0.014 (4)*  
C7a  0.0940 (18)  0.275 (3)  0.7759 (16)  0.032 (5)*  
H7a  0.042016  0.311025  0.696825  0.0633*  
C8a  0.0859 (17)  0.366 (3)  0.8596 (12)  0.029 (5)*  
H8a  0.021781  0.460545  0.84455  0.0576*  
C9a  0.1720 (15)  0.039 (2)  0.6970 (12)  0.022 (4)*  
H9a1  0.174095  0.124362  0.637894  0.0442*  
H9a2  0.247946  −0.036348  0.720715  0.0442*  
C10a  0.0544 (18)  −0.081 (3)  0.6469 (14)  0.036 (5)*  
H10a  −0.025973  −0.021774  0.636337  0.0719*  
C11a  0.061 (2)  −0.140 (3)  0.5414 (16)  0.044 (5)*  
H11a  0.080687  −0.037489  0.501712  0.0876*  
H11b  0.12719  −0.23164  0.557436  0.0876*  
H11c  −0.020494  −0.191954  0.492283  0.0876*  
C12a  0.071 (2)  −0.227 (3)  0.7229 (18)  0.049 (6)*  
H12a  0.006633  −0.319163  0.685963  0.0975*  
H12b  0.155168  −0.279441  0.741458  0.0975*  
H12c  0.062609  −0.18564  0.793927  0.0975*  
C13a  0.038 (2)  0.487 (3)  1.054 (2)  0.065 (7)*  
H13a  −0.025309  0.390626  1.040159  0.1297*  
H13b  0.045419  0.552031  1.124846  0.1297*  
H13c  0.010954  0.570358  0.988895  0.1297*  
O2b  0.539 (2)  −0.291 (3)  0.2281 (16)  0.056 (5)*  
O1b  0.414 (2)  −0.124 (3)  0.1029 (16)  0.055 (5)*  
H1b  0.471 (8)  −0.363 (14)  0.196 (9)  0.1114*  
C1b  0.5141 (19)  −0.147 (3)  0.1733 (15)  0.037 (5)*  
C2b  0.611 (2)  −0.024 (3)  0.1974 (16)  0.048 (6)*  
H2b  0.690731  −0.087699  0.214152  0.0951*  
C3b  0.6114 (18)  0.074 (3)  0.2908 (14)  0.031 (5)*  
C4b  0.6876 (19)  0.007 (3)  0.3974 (15)  0.046 (5)*  
H4b  0.743501  −0.096507  0.404539  0.0917*  
C5b  0.6820 (17)  0.086 (3)  0.4875 (16)  0.036 (5)*  
H5b  0.7273  0.029411  0.562563  0.0726*  
C6b  0.6233 (18)  0.231 (3)  0.4872 (15)  0.029 (5)*  
C7b  0.549 (2)  0.299 (3)  0.3833 (16)  0.047 (6)*  
H7b  0.498861  0.408531  0.375024  0.0934*  
C8b  0.5499 (17)  0.206 (3)  0.2947 (14)  0.025 (4)*  
H8b  0.491693  0.249657  0.219454  0.0494*  
C9b  0.6383 (18)  0.323 (3)  0.5890 (15)  0.044 (5)*  
H9b1  0.649084  0.23635  0.650935  0.0884*  
H9b2  0.557602  0.377566  0.582105  0.0884*  
C10b  0.7293 (17)  0.448 (3)  0.6258 (14)  0.036 (5)*  
H10b  0.798804  0.371298  0.624541  0.0727*  
C11b  0.760 (2)  0.515 (3)  0.7419 (16)  0.053 (6)*  
H11d  0.68935  0.585373  0.745158  0.1063*  
H11e  0.835563  0.591862  0.763369  0.1063*  
H11f  0.777478  0.413302  0.795682  0.1063*  
C12b  0.7187 (18)  0.599 (3)  0.5521 (14)  0.038 (5)*  
H12d  0.796782  0.669915  0.581852  0.0759*  
H12e  0.704626  0.556633  0.474015  0.0759*  
H12f  0.64741  0.674397  0.549845  0.0759*  
C13b  0.598 (2)  0.090 (3)  0.1023 (15)  0.046 (5)*  
H13d  0.510227  0.128717  0.064474  0.091*  
H13e  0.652406  0.196731  0.130031  0.091*  
H13f  0.624257  0.024596  0.04693  0.091* 
O1a—C1a  1.22 (2)  O2b—H1b  0.98 (10) 
O2a—H1a  0.98 (10)  O2b—C1b  1.34 (3) 
O2a—C1a  1.29 (3)  O1b—C1b  1.26 (3) 
C1a—C2a  1.56 (3)  C1b—C2b  1.49 (3) 
C2a—H2a  1.06  C2b—H2b  1.06 
C2a—C3a  1.54 (3)  C2b—C3b  1.49 (3) 
C2a—C13a  1.52 (4)  C2b—C13b  1.54 (3) 
C3a—C4a  1.42 (3)  C3b—C4b  1.49 (3) 
C3a—C8a  1.46 (2)  C3b—C8b  1.32 (3) 
C4a—H4a  1.06  C4b—H4b  1.06 
C4a—C5a  1.47 (3)  C4b—C5b  1.40 (3) 
C5a—H5a  1.06  C5b—H5b  1.06 
C5a—C6a  1.34 (2)  C5b—C6b  1.37 (3) 
C6a—C7a  1.43 (2)  C6b—C7b  1.46 (3) 
C6a—C9a  1.49 (2)  C6b—C9b  1.51 (3) 
C7a—H7a  1.06  C7b—H7b  1.06 
C7a—C8a  1.38 (3)  C7b—C8b  1.41 (3) 
C8a—H8a  1.06  C8b—H8b  1.06 
C9a—H9a1  1.06  C9b—H9b1  1.06 
C9a—H9a2  1.06  C9b—H9b2  1.06 
C9a—C10a  1.66 (3)  C9b—C10b  1.44 (3) 
C10a—H10a  1.06  C10b—H10b  1.06 
C10a—C11a  1.54 (3)  C10b—C11b  1.57 (3) 
C10a—C12a  1.53 (3)  C10b—C12b  1.55 (3) 
C11a—H11a  1.06  C11b—H11d  1.06 
C11a—H11b  1.06  C11b—H11e  1.06 
C11a—H11c  1.06  C11b—H11f  1.06 
C12a—H12a  1.06  C12b—H12d  1.06 
C12a—H12b  1.06  C12b—H12e  1.06 
C12a—H12c  1.06  C12b—H12f  1.06 
C13a—H13a  1.06  C13b—H13d  1.06 
C13a—H13b  1.06  C13b—H13e  1.06 
C13a—H13c  1.06  C13b—H13f  1.06 
H1a—O2a—C1a  106 (6)  H1b—O2b—C1b  106 (6) 
O1a—C1a—O2a  126 (2)  O2b—C1b—O1b  120 (2) 
O1a—C1a—C2a  122 (2)  O2b—C1b—C2b  116.7 (18) 
O2a—C1a—C2a  112.3 (17)  O1b—C1b—C2b  123 (2) 
C1a—C2a—H2a  115.58  C1b—C2b—H2b  109.55 
C1a—C2a—C3a  102 (2)  C1b—C2b—C3b  107 (2) 
C1a—C2a—C13a  113 (2)  C1b—C2b—C13b  113.3 (16) 
H2a—C2a—C3a  110.79  H2b—C2b—C3b  111.67 
H2a—C2a—C13a  99.16  H2b—C2b—C13b  104.68 
C3a—C2a—C13a  117.5 (17)  C3b—C2b—C13b  111.2 (19) 
C2a—C3a—C4a  117.3 (16)  C2b—C3b—C4b  115.4 (19) 
C2a—C3a—C8a  123.4 (17)  C2b—C3b—C8b  130.0 (17) 
C4a—C3a—C8a  117.0 (17)  C4b—C3b—C8b  114.5 (19) 
C3a—C4a—H4a  120.68  C3b—C4b—H4b  121.44 
C3a—C4a—C5a  118.6 (16)  C3b—C4b—C5b  117 (2) 
H4a—C4a—C5a  120.68  H4b—C4b—C5b  121.44 
C4a—C5a—H5a  118.74  C4b—C5b—H5b  117.13 
C4a—C5a—C6a  122.5 (17)  C4b—C5b—C6b  125.7 (19) 
H5a—C5a—C6a  118.74  H5b—C5b—C6b  117.13 
C5a—C6a—C7a  117.5 (16)  C5b—C6b—C7b  117.2 (19) 
C5a—C6a—C9a  122.2 (14)  C5b—C6b—C9b  122.0 (16) 
C7a—C6a—C9a  120.0 (14)  C7b—C6b—C9b  120.7 (19) 
C6a—C7a—H7a  118.48  C6b—C7b—H7b  122.65 
C6a—C7a—C8a  123.0 (16)  C6b—C7b—C8b  115 (2) 
H7a—C7a—C8a  118.48  H7b—C7b—C8b  122.65 
C3a—C8a—C7a  119.7 (19)  C3b—C8b—C7b  130.3 (17) 
C3a—C8a—H8a  120.17  C3b—C8b—H8b  114.86 
C7a—C8a—H8a  120.17  C7b—C8b—H8b  114.86 
C6a—C9a—H9a1  109.47  C6b—C9b—H9b1  109.47 
C6a—C9a—H9a2  109.47  C6b—C9b—H9b2  109.47 
C6a—C9a—C10a  110.0 (16)  C6b—C9b—C10b  118 (2) 
H9a1—C9a—H9a2  108.97  H9b1—C9b—H9b2  99.89 
H9a1—C9a—C10a  109.47  H9b1—C9b—C10b  109.47 
H9a2—C9a—C10a  109.47  H9b2—C9b—C10b  109.47 
C9a—C10a—H10a  115.52  C9b—C10b—H10b  97.31 
C9a—C10a—C11a  102.3 (17)  C9b—C10b—C11b  117 (2) 
C9a—C10a—C12a  107.4 (14)  C9b—C10b—C12b  117.0 (14) 
H10a—C10a—C11a  112.9  H10b—C10b—C11b  108.83 
H10a—C10a—C12a  108.3  H10b—C10b—C12b  108.33 
C11a—C10a—C12a  110.2 (19)  C11b—C10b—C12b  107.8 (18) 
C10a—C11a—H11a  109.47  C10b—C11b—H11d  109.47 
C10a—C11a—H11b  109.47  C10b—C11b—H11e  109.47 
C10a—C11a—H11c  109.47  C10b—C11b—H11f  109.47 
H11a—C11a—H11b  109.47  H11d—C11b—H11e  109.47 
H11a—C11a—H11c  109.47  H11d—C11b—H11f  109.47 
H11b—C11a—H11c  109.47  H11e—C11b—H11f  109.47 
C10a—C12a—H12a  109.47  C10b—C12b—H12d  109.47 
C10a—C12a—H12b  109.47  C10b—C12b—H12e  109.47 
C10a—C12a—H12c  109.47  C10b—C12b—H12f  109.47 
H12a—C12a—H12b  109.47  H12d—C12b—H12e  109.47 
H12a—C12a—H12c  109.47  H12d—C12b—H12f  109.47 
H12b—C12a—H12c  109.47  H12e—C12b—H12f  109.47 
C2a—C13a—H13a  109.47  C2b—C13b—H13d  109.47 
C2a—C13a—H13b  109.47  C2b—C13b—H13e  109.47 
C2a—C13a—H13c  109.47  C2b—C13b—H13f  109.47 
H13a—C13a—H13b  109.47  H13d—C13b—H13e  109.47 
H13a—C13a—H13c  109.47  H13d—C13b—H13f  109.47 
H13b—C13a—H13c  109.47  H13e—C13b—H13f  109.47 
D—H···A  D—H  H···A  D···A  D—H···A 
O2a—H1a···O1b^{i}  0.98 (10)  1.72 (10)  2.68 (3)  164 (12) 
O2b—H1b···O1a^{ii}  0.98 (10)  1.72 (10)  2.67 (3)  163 (12) 
Symmetry codes: (i) x, y+1, z+1; (ii) x, y−1, z−1. 
C_{3}H_{7}NO_{2}  Z = 4 
M_{r} = 89.1  F(000) = 69.628 
Orthorhombic, P2_{1}2_{1}2_{1}  D_{x} = 1.406 Mg m^{−}^{3} 
Hall symbol: P 2xab;2ybc;2zac  Electrons 200 KeV radiation, λ = 0.0251 Å 
a = 5.7733 (11) Å  Cell parameters from 3422 reflections 
b = 5.9524 (12) Å  θ = 0.1–1.4° 
c = 12.2465 (2) Å  T = 100 K 
V = 420.85 (14) Å^{3}  Irregular shape 
TEM FEI Tecnai G2 20 diffractometer  R_{int} = 0.111 
Radiation source: Lab6 cathode  θ_{max} = 1.4°, θ_{min} = 0.1° 
continuous–rotation 3D ED scans  h = −11→11 
3422 measured reflections  k = −9→9 
1127 independent reflections  l = −24→22 
1036 reflections with I > 3σ(I) 
Refinement on F^{2}  Hatom parameters constrained 
R[F^{2} > 2σ(F^{2})] = 0.143  Weighting scheme based on measured s.u.'s w = 1/[σ^{2}(F_{o}^{2}) + (0.02P)^{2}] where P = (F_{o}^{2} + 2F_{c}^{2})/3 
wR(F^{2}) = 0.348  (Δ/σ)_{max} = 0.004 
S = 8.76  Δρ_{max} = 0.15 e Å^{−}^{3} 
1127 reflections  Δρ_{min} = −0.17 e Å^{−}^{3} 
56 parameters  Extinction correction: SHELXL2017/1 (Sheldrick, 2015), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
0 restraints  Extinction coefficient: 32 (5) 
63 constraints 
x  y  z  U_{iso}*/U_{eq}  
O1  −0.1255 (7)  0.7271 (11)  0.4154 (4)  0.0194 (16)  
O2  −0.2617 (6)  0.4455 (10)  0.3150 (3)  0.0152 (13)  
C1  −0.1013 (7)  0.5560 (13)  0.3592 (4)  0.0135 (16)  
C2  0.1919 (8)  0.2676 (13)  0.4089 (4)  0.0198 (18)  
N1  0.3149 (7)  0.6537 (10)  0.3625 (4)  0.0160 (15)  
C3  0.1452 (7)  0.4687 (12)  0.3388 (4)  0.0147 (16)  
H1c3  0.163048  0.41892  0.256099  0.0176  
H1c2  0.364038  0.211791  0.395918  0.0237  
H2c2  0.074678  0.137288  0.38825  0.0237  
H3c2  0.169956  0.311443  0.492151  0.0237  
H1n1  0.287175  0.782907  0.310606  0.0192  
H2n1  0.293629  0.707121  0.440112  0.0192  
H3n1  0.477885  0.595588  0.352624  0.0192 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
O1  0.0124 (14)  0.024 (4)  0.022 (2)  0.000 (2)  0.0009 (15)  −0.0048 (19) 
O2  0.0063 (11)  0.015 (3)  0.025 (2)  −0.0004 (17)  0.0005 (13)  −0.0057 (17) 
C1  0.0075 (16)  0.018 (4)  0.016 (2)  −0.002 (2)  −0.0013 (17)  0.001 (2) 
C2  0.0148 (18)  0.023 (5)  0.022 (2)  0.000 (2)  −0.0012 (19)  −0.006 (2) 
N1  0.0110 (14)  0.016 (4)  0.021 (2)  −0.0004 (18)  0.0007 (17)  0.0042 (17) 
C3  0.0081 (15)  0.021 (4)  0.015 (2)  0.002 (2)  −0.0008 (16)  −0.005 (2) 
H1c3  0.009755  0.025538  0.017559  0.002616  −0.000991  −0.006428 
H1c2  0.017793  0.027562  0.025892  −0.000333  −0.001488  −0.007715 
H2c2  0.017793  0.027562  0.025892  −0.000333  −0.001488  −0.007715 
H3c2  0.017793  0.027562  0.025892  −0.000333  −0.001488  −0.007715 
H1n1  0.013253  0.018834  0.02561  −0.000436  0.000876  0.005039 
H2n1  0.013253  0.018834  0.02561  −0.000436  0.000876  0.005039 
H3n1  0.013253  0.018834  0.02561  −0.000436  0.000876  0.005039 
O1—C1  1.237 (9)  C2—H3c2  1.06 
O2—C1  1.258 (7)  N1—C3  1.502 (8) 
C1—C3  1.535 (6)  N1—H1n1  1.01 
C2—C3  1.498 (9)  N1—H2n1  1.01 
C2—H1c2  1.06  N1—H3n1  1.01 
C2—H2c2  1.06  C3—H1c3  1.06 
O1—C1—O2  125.9 (5)  C3—N1—H3n1  109.47 
O1—C1—C3  118.3 (5)  H1n1—N1—H2n1  109.47 
O2—C1—C3  115.8 (6)  H1n1—N1—H3n1  109.47 
C3—C2—H1c2  109.47  H2n1—N1—H3n1  109.47 
C3—C2—H2c2  109.47  C1—C3—C2  110.1 (4) 
C3—C2—H3c2  109.47  C1—C3—N1  108.9 (5) 
H1c2—C2—H2c2  109.47  C1—C3—H1c3  109.92 
H1c2—C2—H3c2  109.47  C2—C3—N1  111.0 (4) 
H2c2—C2—H3c2  109.47  C2—C3—H1c3  107.85 
C3—N1—H1n1  109.47  N1—C3—H1c3  109.04 
C3—N1—H2n1  109.47 
D—H···A  D—H  H···A  D···A  D—H···A 
C3—H1c3···O1^{i}  1.06  2.40  3.431 (7)  163.75 
N1—H1n1···O2^{ii}  1.01  1.82  2.799 (7)  161.34 
N1—H2n1···O1^{iii}  1.01  1.87  2.832 (6)  157.77 
N1—H3n1···O2^{iv}  1.01  1.81  2.802 (6)  167.00 
N1—H3n1···C1^{iv}  1.01  2.44  3.421 (6)  162.95 
Symmetry codes: (i) −x, y−1/2, −z+1/2; (ii) −x, y+1/2, −z+1/2; (iii) x+1/2, −y+3/2, −z+1; (iv) x+1, y, z. 
C_{3}H_{7}NO_{2}  Z = 4 
M_{r} = 89.1  F(000) = 69.628 
Orthorhombic, P2_{1}2_{1}2_{1}  D_{x} = 1.406 Mg m^{−}^{3} 
Hall symbol: P 2xab;2ybc;2zac  Electrons 200 KeV radiation, λ = 0.0251 Å 
a = 5.7733 (11) Å  Cell parameters from 3422 reflections 
b = 5.9524 (12) Å  θ = 0.1–1.4° 
c = 12.2465 (2) Å  T = 100 K 
V = 420.85 (14) Å^{3}  Irregular shape 
TEM FEI Tecnai G2 20 diffractometer  R_{int} = 0.111 
Radiation source: Lab6 cathode  θ_{max} = 1.4°, θ_{min} = 0.1° 
continuous–rotation 3D ED scans  h = −11→11 
3422 measured reflections  k = −9→9 
1127 independent reflections  l = −24→22 
922 reflections with I > 3σ(I) 
Refinement on F^{2}  Hatom parameters constrained 
R[F^{2} > 2σ(F^{2})] = 0.139  Weighting scheme based on measured s.u.'s w = 1/[σ^{2}(F_{o}^{2}) + (0.02P)^{2}] where P = (F_{o}^{2} + 2F_{c}^{2})/3 
wR(F^{2}) = 0.338  (Δ/σ)_{max} = 0.031 
S = 5.35  Δρ_{max} = 0.17 e Å^{−}^{3} 
1127 reflections  Δρ_{min} = −0.21 e Å^{−}^{3} 
56 parameters  Extinction correction: SHELXL2017/1 (Sheldrick, 2015), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
0 restraints  Extinction coefficient: 15 (2) 
63 constraints 
x  y  z  U_{iso}*/U_{eq}  
O1  −0.1255 (7)  0.7261 (9)  0.4150 (3)  0.0162 (10)  
O2  −0.2631 (6)  0.4407 (9)  0.3153 (3)  0.0157 (9)  
C1  −0.1014 (8)  0.5568 (10)  0.3600 (3)  0.0108 (10)  
C2  0.1960 (9)  0.2671 (12)  0.4091 (4)  0.0186 (15)  
N1  0.3148 (7)  0.6573 (8)  0.3611 (3)  0.0136 (12)  
C3  0.1445 (8)  0.4699 (11)  0.3390 (3)  0.0156 (13)  
H1c3  0.159651  0.418564  0.256373  0.0187  
H1c2  0.366103  0.209284  0.39265  0.0223  
H2c2  0.075479  0.137857  0.391252  0.0223  
H3c2  0.182477  0.311882  0.492639  0.0223  
H1n1  0.299026  0.708295  0.439396  0.0163  
H2n1  0.28167  0.78754  0.310604  0.0163  
H3n1  0.477652  0.601256  0.348072  0.0163 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
O1  0.0103 (13)  0.022 (2)  0.0167 (11)  −0.0059 (16)  0.0005 (14)  −0.0059 (12) 
O2  0.0047 (11)  0.025 (2)  0.0170 (11)  0.0024 (15)  0.0027 (10)  −0.0097 (11) 
C1  0.0067 (15)  0.015 (2)  0.0104 (11)  0.006 (2)  0.0009 (14)  −0.0019 (13) 
C2  0.016 (2)  0.017 (3)  0.0227 (18)  0.003 (2)  −0.0078 (19)  −0.0084 (15) 
N1  0.0105 (15)  0.013 (3)  0.0177 (13)  0.0074 (17)  −0.0001 (13)  −0.0055 (11) 
C3  0.0069 (15)  0.027 (3)  0.0124 (12)  0.0013 (18)  −0.0017 (14)  −0.0013 (15) 
H1c3  0.008277  0.032903  0.01487  0.001522  −0.00202  −0.001569 
H1c2  0.019111  0.020468  0.027206  0.004181  −0.009388  −0.010068 
H2c2  0.019111  0.020468  0.027206  0.004181  −0.009388  −0.010068 
H3c2  0.019111  0.020468  0.027206  0.004181  −0.009388  −0.010068 
H1n1  0.012596  0.015156  0.021192  0.008933  −0.00006  −0.006614 
H2n1  0.012596  0.015156  0.021192  0.008933  −0.00006  −0.006614 
H3n1  0.012596  0.015156  0.021192  0.008933  −0.00006  −0.006614 
O1—C1  1.221 (7)  C2—H3c2  1.06 
O2—C1  1.284 (6)  N1—C3  1.512 (7) 
C1—C3  1.533 (7)  N1—H1n1  1.01 
C2—C3  1.511 (9)  N1—H2n1  1.01 
C2—H1c2  1.06  N1—H3n1  1.01 
C2—H2c2  1.06  C3—H1c3  1.06 
O1—C1—O2  126.6 (5)  C3—N1—H3n1  109.47 
O1—C1—C3  118.5 (4)  H1n1—N1—H2n1  109.47 
O2—C1—C3  114.9 (5)  H1n1—N1—H3n1  109.47 
C3—C2—H1c2  109.47  H2n1—N1—H3n1  109.47 
C3—C2—H2c2  109.47  C1—C3—C2  110.9 (4) 
C3—C2—H3c2  109.47  C1—C3—N1  108.9 (5) 
H1c2—C2—H2c2  109.47  C1—C3—H1c3  109.51 
H1c2—C2—H3c2  109.47  C2—C3—N1  111.1 (4) 
H2c2—C2—H3c2  109.47  C2—C3—H1c3  107.23 
C3—N1—H1n1  109.47  N1—C3—H1c3  109.28 
C3—N1—H2n1  109.47 
D—H···A  D—H  H···A  D···A  D—H···A 
C3—H1c3···O1^{i}  1.06  2.40  3.434 (6)  164.89 
N1—H1n1···O1^{ii}  1.01  1.88  2.849 (5)  160.68 
N1—H2n1···O2^{iii}  1.01  1.79  2.757 (6)  158.01 
N1—H3n1···O2^{iv}  1.01  1.82  2.813 (6)  166.71 
N1—H3n1···C1^{iv}  1.01  2.45  3.423 (6)  161.77 
Symmetry codes: (i) −x, y−1/2, −z+1/2; (ii) x+1/2, −y+3/2, −z+1; (iii) −x, y+1/2, −z+1/2; (iv) x+1, y, z. 
C_{3}H_{7}NO_{2}  Z = 4 
M_{r} = 89.1  F(000) = 69.628 
Orthorhombic, P2_{1}2_{1}2_{1}  D_{x} = 1.406 Mg m^{−}^{3} 
Hall symbol: P 2xab;2ybc;2zac  Electrons 200 KeV radiation, λ = 0.0251 Å 
a = 5.7733 (11) Å  Cell parameters from 3422 reflections 
b = 5.9524 (12) Å  θ = 0.1–1.4° 
c = 12.2465 (2) Å  T = 100 K 
V = 420.85 (14) Å^{3}  Irregular shape 
TEM FEI Tecnai G2 20 diffractometer  R_{int} = 0.111 
Radiation source: Lab6 cathode  θ_{max} = 1.4°, θ_{min} = 0.1° 
continuous–rotation 3D ED scans  h = −11→11 
3422 measured reflections  k = −9→9 
1127 independent reflections  l = −24→22 
845 reflections with I > 3σ(I) 
Refinement on F^{2}  Hatom parameters constrained 
R[F^{2} > 2σ(F^{2})] = 0.140  Weighting scheme based on measured s.u.'s w = 1/[σ^{2}(F_{o}^{2}) + (0.02P)^{2}] where P = (F_{o}^{2} + 2F_{c}^{2})/3 
wR(F^{2}) = 0.345  (Δ/σ)_{max} = 0.029 
S = 2.03  Δρ_{max} = 0.29 e Å^{−}^{3} 
1127 reflections  Δρ_{min} = −0.17 e Å^{−}^{3} 
56 parameters  Extinction correction: SHELXL2017/1 (Sheldrick, 2015), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
0 restraints  Extinction coefficient: 51 (9) 
63 constraints 
x  y  z  U_{iso}*/U_{eq}  
O1  −0.1250 (5)  0.7273 (10)  0.4159 (3)  0.0189 (12)  
O2  −0.2612 (5)  0.4452 (8)  0.3155 (3)  0.0149 (10)  
C1  −0.1014 (6)  0.5553 (10)  0.3595 (3)  0.0115 (11)  
C2  0.1928 (7)  0.2661 (12)  0.4095 (4)  0.0202 (14)  
N1  0.3142 (5)  0.6531 (8)  0.3624 (3)  0.0143 (10)  
C3  0.1454 (5)  0.4701 (10)  0.3391 (3)  0.0132 (12)  
H1c3  0.163455  0.422061  0.25614  0.0158  
H1c2  0.365811  0.212  0.39729  0.0242  
H2c2  0.077385  0.135045  0.387752  0.0242  
H3c2  0.168404  0.308475  0.492782  0.0242  
H1n1  0.287995  0.781509  0.309918  0.0172  
H2n1  0.291942  0.707962  0.43975  0.0172  
H3n1  0.477069  0.594049  0.353404  0.0172 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
O1  0.0126 (10)  0.024 (3)  0.0203 (15)  0.0004 (14)  0.0005 (11)  −0.0059 (14) 
O2  0.0062 (8)  0.016 (2)  0.0228 (15)  −0.0003 (12)  0.0001 (10)  −0.0058 (12) 
C1  0.0075 (11)  0.012 (3)  0.0150 (16)  −0.0012 (15)  −0.0023 (12)  −0.0003 (14) 
C2  0.0159 (14)  0.022 (4)  0.0223 (18)  0.000 (2)  −0.0030 (14)  −0.0054 (17) 
N1  0.0085 (10)  0.015 (3)  0.0197 (15)  −0.0017 (13)  0.0011 (12)  0.0040 (12) 
C3  0.0075 (11)  0.018 (3)  0.0138 (15)  0.0025 (15)  −0.0011 (12)  −0.0020 (14) 
H1c3  0.009026  0.021987  0.016535  0.003056  −0.001353  −0.002415 
H1c2  0.019108  0.026869  0.026742  −0.000334  −0.003591  −0.006475 
H2c2  0.019108  0.026869  0.026742  −0.000334  −0.003591  −0.006475 
H3c2  0.019108  0.026869  0.026742  −0.000334  −0.003591  −0.006475 
H1n1  0.010244  0.017696  0.023592  −0.002059  0.001328  0.004762 
H2n1  0.010244  0.017696  0.023592  −0.002059  0.001328  0.004762 
H3n1  0.010244  0.017696  0.023592  −0.002059  0.001328  0.004762 
O1—C1  1.243 (8)  C2—H3c2  1.06 
O2—C1  1.254 (6)  N1—C3  1.489 (6) 
C1—C3  1.533 (5)  N1—H1n1  1.01 
C2—C3  1.514 (8)  N1—H2n1  1.01 
C2—H1c2  1.06  N1—H3n1  1.01 
C2—H2c2  1.06  C3—H1c3  1.06 
O1—C1—O2  126.1 (4)  C3—N1—H3n1  109.47 
O1—C1—C3  117.7 (4)  H1n1—N1—H2n1  109.47 
O2—C1—C3  116.2 (5)  H1n1—N1—H3n1  109.47 
C3—C2—H1c2  109.47  H2n1—N1—H3n1  109.47 
C3—C2—H2c2  109.47  C1—C3—C2  109.9 (3) 
C3—C2—H3c2  109.47  C1—C3—N1  109.6 (4) 
H1c2—C2—H2c2  109.47  C1—C3—H1c3  109.69 
H1c2—C2—H3c2  109.47  C2—C3—N1  111.0 (3) 
H2c2—C2—H3c2  109.47  C2—C3—H1c3  108.17 
C3—N1—H1n1  109.47  N1—C3—H1c3  108.49 
C3—N1—H2n1  109.47 
D—H···A  D—H  H···A  D···A  D—H···A 
C3—H1c3···O1^{i}  1.06  2.42  3.443 (6)  162.97 
N1—H1n1···O2^{ii}  1.01  1.83  2.804 (6)  162.19 
N1—H2n1···O1^{iii}  1.01  1.87  2.828 (5)  156.87 
N1—H3n1···O2^{iv}  1.01  1.81  2.805 (5)  167.05 
N1—H3n1···C1^{iv}  1.01  2.45  3.424 (4)  162.94 
Symmetry codes: (i) −x, y−1/2, −z+1/2; (ii) −x, y+1/2, −z+1/2; (iii) x+1/2, −y+3/2, −z+1; (iv) x+1, y, z. 
C_{3}H_{7}NO_{2}  Z = 4 
M_{r} = 89.1  F(000) = 69.628 
Orthorhombic, P2_{1}2_{1}2_{1}  D_{x} = 1.406 Mg m^{−}^{3} 
Hall symbol: P 2xab;2ybc;2zac  Electrons 200 KeV radiation, λ = 0.0251 Å 
a = 5.7733 (11) Å  Cell parameters from 3422 reflections 
b = 5.9524 (12) Å  θ = 0.1–1.4° 
c = 12.2465 (2) Å  T = 100 K 
V = 420.85 (14) Å^{3}  Irregular shape 
TEM FEI Tecnai G2 20 diffractometer  R_{int} = 0.111 
Radiation source: Lab6 cathode  θ_{max} = 1.4°, θ_{min} = 0.1° 
continuous–rotation 3D ED scans  h = −11→11 
3422 measured reflections  k = −9→9 
1127 independent reflections  l = −24→22 
1072 reflections with I > 3σ(I) 
Refinement on F^{2}  Hatom parameters constrained 
R[F^{2} > 2σ(F^{2})] = 0.144  Weighting scheme based on measured s.u.'s w = 1/[σ^{2}(F_{o}^{2}) + (0.02P)^{2}] where P = (F_{o}^{2} + 2F_{c}^{2})/3 
wR(F^{2}) = 0.355  (Δ/σ)_{max} = 0.017 
S = 2.57  Δρ_{max} = 0.23 e Å^{−}^{3} 
1127 reflections  Δρ_{min} = −0.18 e Å^{−}^{3} 
56 parameters  Extinction correction: SHELXL2017/1 (Sheldrick, 2015), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
0 restraints  Extinction coefficient: 30 (6) 
63 constraints 
x  y  z  U_{iso}*/U_{eq}  
O1  −0.1250 (5)  0.7269 (9)  0.4160 (3)  0.0175 (10)  
O2  −0.2613 (5)  0.4444 (8)  0.3156 (2)  0.0148 (8)  
C1  −0.1023 (5)  0.5551 (9)  0.3594 (3)  0.0099 (9)  
C2  0.1936 (7)  0.2658 (11)  0.4095 (3)  0.0180 (12)  
N1  0.3146 (5)  0.6533 (8)  0.3623 (3)  0.0132 (9)  
C3  0.1455 (5)  0.4702 (9)  0.3389 (3)  0.0114 (10)  
H1c3  0.162985  0.422487  0.255901  0.0137  
H1c2  0.366536  0.21167  0.396917  0.0216  
H2c2  0.078036  0.134659  0.388004  0.0216  
H3c2  0.170013  0.308233  0.492792  0.0216  
H1n1  0.288804  0.781524  0.309708  0.0159  
H2n1  0.292059  0.708341  0.439593  0.0159  
H3n1  0.477399  0.593918  0.353508  0.0159 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
O1  0.0119 (10)  0.023 (2)  0.0174 (12)  −0.0003 (13)  0.0011 (10)  −0.0065 (12) 
O2  0.0057 (8)  0.018 (2)  0.0203 (11)  −0.0016 (11)  0.0007 (9)  −0.0076 (11) 
C1  0.0063 (10)  0.009 (2)  0.0141 (13)  −0.0001 (14)  −0.0017 (11)  −0.0010 (11) 
C2  0.0136 (13)  0.019 (3)  0.0211 (15)  −0.0004 (18)  −0.0046 (13)  −0.0049 (14) 
N1  0.0084 (9)  0.013 (2)  0.0178 (13)  −0.0018 (12)  0.0019 (11)  0.0040 (11) 
C3  0.0061 (10)  0.016 (2)  0.0123 (12)  0.0029 (13)  −0.0011 (11)  −0.0003 (12) 
H1c3  0.007367  0.018937  0.014709  0.00346  −0.001367  −0.000356 
H1c2  0.016332  0.023241  0.025288  −0.000504  −0.005517  −0.005924 
H2c2  0.016332  0.023241  0.025288  −0.000504  −0.005517  −0.005924 
H3c2  0.016332  0.023241  0.025288  −0.000504  −0.005517  −0.005924 
H1n1  0.010054  0.016175  0.021337  −0.002188  0.002271  0.00478 
H2n1  0.010054  0.016175  0.021337  −0.002188  0.002271  0.00478 
H3n1  0.010054  0.016175  0.021337  −0.002188  0.002271  0.00478 
O1—C1  1.242 (7)  C2—H3c2  1.06 
O2—C1  1.251 (5)  N1—C3  1.491 (6) 
C1—C3  1.538 (5)  N1—H1n1  1.01 
C2—C3  1.518 (7)  N1—H2n1  1.01 
C2—H1c2  1.06  N1—H3n1  1.01 
C2—H2c2  1.06  C3—H1c3  1.06 
O1—C1—O2  126.6 (4)  C3—N1—H3n1  109.47 
O1—C1—C3  117.4 (3)  H1n1—N1—H2n1  109.47 
O2—C1—C3  116.1 (4)  H1n1—N1—H3n1  109.47 
C3—C2—H1c2  109.47  H2n1—N1—H3n1  109.47 
C3—C2—H2c2  109.47  C1—C3—C2  109.9 (3) 
C3—C2—H3c2  109.47  C1—C3—N1  109.7 (4) 
H1c2—C2—H2c2  109.47  C1—C3—H1c3  109.47 
H1c2—C2—H3c2  109.47  C2—C3—N1  110.9 (3) 
H2c2—C2—H3c2  109.47  C2—C3—H1c3  108.29 
C3—N1—H1n1  109.47  N1—C3—H1c3  108.52 
C3—N1—H2n1  109.47 
D—H···A  D—H  H···A  D···A  D—H···A 
C3—H1c3···O1^{i}  1.06  2.42  3.443 (5)  162.92 
N1—H1n1···O2^{ii}  1.01  1.82  2.801 (5)  162.24 
N1—H2n1···O1^{iii}  1.01  1.87  2.829 (5)  156.78 
N1—H3n1···O2^{iv}  1.01  1.81  2.805 (5)  166.90 
N1—H3n1···C1^{iv}  1.01  2.44  3.417 (4)  162.97 
Symmetry codes: (i) −x, y−1/2, −z+1/2; (ii) −x, y+1/2, −z+1/2; (iii) x+1/2, −y+3/2, −z+1; (iv) x+1, y, z. 
C_{3}H_{7}NO_{2}  Z = 4 
M_{r} = 89.1  F(000) = 69.628 
Orthorhombic, P2_{1}2_{1}2_{1}  D_{x} = 1.406 Mg m^{−}^{3} 
Hall symbol: P 2xab;2ybc;2zac  Electrons 200 KeV radiation, λ = 0.0251 Å 
a = 5.7733 (11) Å  Cell parameters from 3329 reflections 
b = 5.9524 (12) Å  θ = 0.1–1.4° 
c = 12.2465 (2) Å  T = 100 K 
V = 420.85 (14) Å^{3}  Irregular shape 
TEM FEI Tecnai G2 20 diffractometer  R_{int} = 0.099 
Radiation source: Lab6 cathode  θ_{max} = 1.4°, θ_{min} = 0.1° 
continuous–rotation 3D ED scans  h = −11→11 
3329 measured reflections  k = −9→9 
1123 independent reflections  l = −24→22 
927 reflections with I > 3σ(I) 
Refinement on F^{2}  Hatom parameters constrained 
R[F^{2} > 2σ(F^{2})] = 0.131  Weighting scheme based on measured s.u.'s w = 1/[σ^{2}(F_{o}^{2}) + (0.02P)^{2}] where P = (F_{o}^{2} + 2F_{c}^{2})/3 
wR(F^{2}) = 0.305  (Δ/σ)_{max} = 0.038 
S = 2.36  Δρ_{max} = 0.20 e Å^{−}^{3} 
1123 reflections  Δρ_{min} = −0.18 e Å^{−}^{3} 
56 parameters  Extinction correction: SHELXL2017/1 (Sheldrick, 2015), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
0 restraints  Extinction coefficient: 27 (4) 
63 constraints 
x  y  z  U_{iso}*/U_{eq}  
O1  −0.1249 (5)  0.7273 (9)  0.4160 (3)  0.0176 (10)  
O2  −0.2613 (4)  0.4449 (8)  0.3155 (2)  0.0149 (9)  
C1  −0.1018 (5)  0.5558 (9)  0.3600 (3)  0.0109 (10)  
C2  0.1935 (6)  0.2656 (11)  0.4097 (3)  0.0188 (13)  
N1  0.3149 (5)  0.6527 (8)  0.3623 (3)  0.0135 (9)  
C3  0.1454 (5)  0.4701 (9)  0.3390 (3)  0.0119 (10)  
H1c3  0.162343  0.422281  0.256023  0.0143  
H1c2  0.365583  0.210003  0.396279  0.0226  
H2c2  0.07621  0.135376  0.389019  0.0226  
H3c2  0.172249  0.308802  0.493053  0.0226  
H1n1  0.289925  0.780649  0.309432  0.0162  
H2n1  0.292019  0.708556  0.439467  0.0162  
H3n1  0.47758  0.592824  0.353903  0.0162 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
O1  0.0117 (9)  0.022 (3)  0.0187 (13)  0.0001 (13)  0.0011 (10)  −0.0055 (12) 
O2  0.0058 (8)  0.017 (2)  0.0214 (13)  −0.0008 (11)  0.0003 (9)  −0.0065 (12) 
C1  0.0065 (10)  0.012 (2)  0.0145 (14)  −0.0004 (15)  −0.0018 (11)  −0.0015 (13) 
C2  0.0136 (13)  0.022 (3)  0.0210 (16)  0.0016 (18)  −0.0035 (13)  −0.0040 (16) 
N1  0.0086 (9)  0.013 (2)  0.0186 (14)  −0.0008 (12)  0.0010 (11)  0.0041 (11) 
C3  0.0067 (10)  0.016 (3)  0.0127 (13)  0.0026 (14)  −0.0009 (11)  −0.0010 (13) 
H1c3  0.00802  0.019564  0.01525  0.003178  −0.001132  −0.001234 
H1c2  0.016282  0.0262  0.025254  0.001921  −0.004206  −0.004766 
H2c2  0.016282  0.0262  0.025254  0.001921  −0.004206  −0.004766 
H3c2  0.016282  0.0262  0.025254  0.001921  −0.004206  −0.004766 
H1n1  0.010286  0.016108  0.022305  −0.001  0.001198  0.004899 
H2n1  0.010286  0.016108  0.022305  −0.001  0.001198  0.004899 
H3n1  0.010286  0.016108  0.022305  −0.001  0.001198  0.004899 
O1—C1  1.237 (7)  C2—H3c2  1.06 
O2—C1  1.257 (5)  N1—C3  1.490 (6) 
C1—C3  1.537 (5)  N1—H1n1  1.01 
C2—C3  1.519 (7)  N1—H2n1  1.01 
C2—H1c2  1.06  N1—H3n1  1.01 
C2—H2c2  1.06  C3—H1c3  1.06 
O1—C1—O2  126.5 (4)  C3—N1—H3n1  109.47 
O1—C1—C3  117.8 (3)  H1n1—N1—H2n1  109.47 
O2—C1—C3  115.7 (4)  H1n1—N1—H3n1  109.47 
C3—C2—H1c2  109.47  H2n1—N1—H3n1  109.47 
C3—C2—H2c2  109.47  C1—C3—C2  109.9 (3) 
C3—C2—H3c2  109.47  C1—C3—N1  109.6 (4) 
H1c2—C2—H2c2  109.47  C1—C3—H1c3  109.55 
H1c2—C2—H3c2  109.47  C2—C3—N1  110.8 (3) 
H2c2—C2—H3c2  109.47  C2—C3—H1c3  108.32 
C3—N1—H1n1  109.47  N1—C3—H1c3  108.61 
C3—N1—H2n1  109.47 
D—H···A  D—H  H···A  D···A  D—H···A 
C3—H1c3···O1^{i}  1.06  2.41  3.443 (5)  163.19 
N1—H1n1···O2^{ii}  1.01  1.82  2.804 (5)  162.82 
N1—H2n1···O1^{iii}  1.01  1.87  2.829 (5)  156.55 
N1—H3n1···O2^{iv}  1.01  1.81  2.801 (4)  166.89 
N1—H3n1···C1^{iv}  1.01  2.44  3.417 (4)  162.66 
Symmetry codes: (i) −x, y−1/2, −z+1/2; (ii) −x, y+1/2, −z+1/2; (iii) x+1/2, −y+3/2, −z+1; (iv) x+1, y, z. 
Al_{2}H_{4}Na_{2}O_{12}Si_{3}  Z = 8 
M_{r} = 380.2  F(000) = 517.84 
Orthorhombic, Fdd2  D_{x} = 2.235 Mg m^{−}^{3} 
Hall symbol: F 2xuvw;2yuvw;2z  Electrons 200 KeV radiation, λ = 0.0251 Å 
a = 18.2872 (11) Å  Cell parameters from 5213 reflections 
b = 18.6660 (14) Å  θ = 0.1–1.2° 
c = 6.6222 (3) Å  T = 293 K 
V = 2260.5 (2) Å^{3}  Irregular shape 
TEM FEI Tecnai G2 20 diffractometer  R_{int} = 0.198 
Radiation source: Lab6 cathode  θ_{max} = 1.2°, θ_{min} = 0.1° 
continuous–rotation 3D ED scans  h = −29→29 
5213 measured reflections  k = −29→29 
1289 independent reflections  l = −10→10 
839 reflections with I > 3σ(I) 
Refinement on F^{2}  All Hatom parameters refined 
R[F^{2} > 2σ(F^{2})] = 0.146  Weighting scheme based on measured s.u.'s w = 1/(σ^{2}(I) + 0.0004I^{2}) 
wR(F^{2}) = 0.305  (Δ/σ)_{max} = 0.033 
S = 6.26  Δρ_{max} = 0.25 e Å^{−}^{3} 
1289 reflections  Δρ_{min} = −0.26 e Å^{−}^{3} 
93 parameters  Extinction correction: SHELXL2017/1 (Sheldrick, 2015), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
3 restraints  Extinction coefficient: 0.42 (5) 
13 constraints 
x  y  z  U_{iso}*/U_{eq}  
Si1  0  0  0  0.023 (2)  
Si2  0.0966 (2)  0.0386 (3)  −0.3722 (11)  0.0237 (17)  
Al1  −0.0371 (2)  0.0936 (4)  0.3836 (12)  0.0256 (19)  
Na1  −0.2186 (4)  0.0325 (5)  0.3831 (15)  0.043 (3)  
O1  0.0677 (4)  0.0215 (5)  −0.1404 (14)  0.034 (3)  
O2  −0.0224 (4)  0.0680 (6)  0.1347 (16)  0.040 (3)  
O3  −0.0690 (4)  0.1829 (5)  0.3914 (15)  0.029 (3)  
O4  −0.0987 (4)  0.0364 (6)  0.5043 (16)  0.039 (3)  
O5  0.0445 (3)  0.0962 (6)  0.5312 (14)  0.030 (3)  
O6  −0.3057 (6)  0.0588 (7)  0.6399 (19)  0.052 (4)  
H1  −0.3520 (16)  0.070 (3)  0.579 (7)  0.0621  
H2  −0.297 (3)  0.097 (2)  0.732 (8)  0.0621 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
Si1  0.012 (3)  0.049 (6)  0.008 (2)  0.001 (3)  0  0 
Si2  0.014 (2)  0.040 (4)  0.0172 (19)  −0.003 (2)  −0.005 (2)  0.001 (3) 
Al1  0.010 (2)  0.047 (5)  0.019 (2)  0.003 (2)  0.007 (2)  0.002 (3) 
Na1  0.029 (3)  0.062 (7)  0.039 (4)  −0.004 (3)  0.007 (4)  0.008 (5) 
O1  0.024 (3)  0.067 (7)  0.012 (3)  0.005 (4)  0.001 (3)  −0.009 (4) 
O2  0.021 (3)  0.075 (8)  0.026 (3)  −0.001 (4)  0.004 (4)  −0.020 (5) 
O3  0.018 (3)  0.050 (7)  0.020 (3)  −0.009 (3)  0.006 (3)  0.009 (5) 
O4  0.009 (3)  0.070 (8)  0.037 (4)  −0.003 (4)  −0.003 (3)  −0.002 (5) 
O5  0.003 (3)  0.057 (7)  0.029 (3)  0.002 (3)  −0.007 (3)  0.001 (4) 
O6  0.059 (6)  0.068 (9)  0.029 (4)  0.017 (5)  0.008 (5)  −0.013 (6) 
H1  0.070305  0.081352  0.034582  0.019866  0.009901  −0.015483 
H2  0.070305  0.081352  0.034582  0.019866  0.009901  −0.015483 
Si1—O1  1.599 (8)  Al1—O2  1.738 (13) 
Si1—O1^{i}  1.599 (8)  Al1—O3  1.766 (11) 
Si1—O2  1.604 (11)  Al1—O4  1.745 (11) 
Si1—O2^{i}  1.604 (11)  Al1—O5  1.786 (9) 
Si2—Al1^{ii}  3.107 (8)  Na1—Na1^{vii}  3.709 (14) 
Si2—Al1^{iii}  3.058 (8)  Na1—Na1^{viii}  3.709 (14) 
Si2—Na1^{iv}  3.060 (10)  Na1—O3^{ix}  2.521 (12) 
Si2—Na1^{iii}  3.545 (11)  Na1—O3^{x}  2.619 (13) 
Si2—O1  1.655 (11)  Na1—O4  2.336 (11) 
Si2—O3^{iii}  1.634 (8)  Na1—O5^{ix}  2.374 (14) 
Si2—O4^{iv}  1.622 (12)  Na1—O6  2.381 (15) 
Si2—O5^{ii}  1.573 (10)  Na1—O6^{vii}  2.387 (16) 
Al1—Na1  3.508 (9)  Na1—H2^{vii}  2.64 (4) 
Al1—Na1^{v}  3.106 (12)  O6—H1  0.96 (4) 
Al1—Na1^{vi}  3.899 (12)  O6—H2  0.96 (5) 
O1—Si1—O1^{i}  108.9 (4)  Si2^{xii}—Na1—O5^{ix}  20.8 (2) 
O1—Si1—O2  108.8 (5)  Si2^{xii}—Na1—O6  92.2 (4) 
O1—Si1—O2^{i}  108.9 (4)  Si2^{xii}—Na1—O6^{vii}  127.1 (4) 
O1^{i}—Si1—O2  108.9 (4)  Si2^{xii}—Na1—H2^{vii}  145.5 (11) 
O1^{i}—Si1—O2^{i}  108.8 (5)  Al1—Na1—Al1^{ix}  98.1 (3) 
O2—Si1—O2^{i}  112.4 (5)  Al1—Na1—Al1^{x}  105.6 (2) 
Al1^{ii}—Si2—Al1^{iii}  108.4 (2)  Al1—Na1—Na1^{vii}  113.6 (3) 
Al1^{ii}—Si2—Na1^{iv}  116.2 (3)  Al1—Na1—Na1^{viii}  113.5 (3) 
Al1^{ii}—Si2—Na1^{iii}  55.2 (2)  Al1—Na1—O3^{ix}  127.3 (4) 
Al1^{ii}—Si2—O1  107.1 (4)  Al1—Na1—O3^{x}  89.0 (3) 
Al1^{ii}—Si2—O3^{iii}  131.6 (5)  Al1—Na1—O4  26.1 (3) 
Al1^{ii}—Si2—O4^{iv}  92.3 (4)  Al1—Na1—O5^{ix}  66.1 (3) 
Al1^{ii}—Si2—O5^{ii}  23.9 (4)  Al1—Na1—O6  124.4 (5) 
Al1^{iii}—Si2—Na1^{iv}  79.2 (2)  Al1—Na1—O6^{vii}  93.3 (4) 
Al1^{iii}—Si2—Na1^{iii}  63.68 (19)  Al1—Na1—H2^{vii}  101.2 (11) 
Al1^{iii}—Si2—O1  110.5 (4)  Al1^{ix}—Na1—Al1^{x}  155.6 (3) 
Al1^{iii}—Si2—O3^{iii}  27.0 (4)  Al1^{ix}—Na1—Na1^{vii}  69.1 (3) 
Al1^{iii}—Si2—O4^{iv}  127.7 (4)  Al1^{ix}—Na1—Na1^{viii}  126.4 (3) 
Al1^{iii}—Si2—O5^{ii}  86.2 (4)  Al1^{ix}—Na1—O3^{ix}  34.6 (3) 
Na1^{iv}—Si2—Na1^{iii}  131.2 (3)  Al1^{ix}—Na1—O3^{x}  169.1 (4) 
Na1^{iv}—Si2—O1  129.8 (5)  Al1^{ix}—Na1—O4  122.6 (4) 
Na1^{iv}—Si2—O3^{iii}  58.8 (4)  Al1^{ix}—Na1—O5^{ix}  34.9 (2) 
Na1^{iv}—Si2—O4^{iv}  48.8 (3)  Al1^{ix}—Na1—O6  87.5 (4) 
Na1^{iv}—Si2—O5^{ii}  121.5 (5)  Al1^{ix}—Na1—O6^{vii}  104.3 (5) 
Na1^{iii}—Si2—O1  93.7 (4)  Al1^{ix}—Na1—H2^{vii}  121.9 (11) 
Na1^{iii}—Si2—O3^{iii}  90.6 (4)  Al1^{x}—Na1—Na1^{vii}  95.3 (3) 
Na1^{iii}—Si2—O4^{iv}  145.7 (5)  Al1^{x}—Na1—Na1^{viii}  48.1 (2) 
Na1^{iii}—Si2—O5^{ii}  32.5 (4)  Al1^{x}—Na1—O3^{ix}  121.4 (4) 
O1—Si2—O3^{iii}  108.3 (6)  Al1^{x}—Na1—O3^{x}  22.0 (2) 
O1—Si2—O4^{iv}  108.0 (6)  Al1^{x}—Na1—O4  81.7 (4) 
O1—Si2—O5^{ii}  108.4 (5)  Al1^{x}—Na1—O5^{ix}  168.7 (4) 
O3^{iii}—Si2—O4^{iv}  106.7 (5)  Al1^{x}—Na1—O6  84.3 (4) 
O3^{iii}—Si2—O5^{ii}  111.8 (6)  Al1^{x}—Na1—O6^{vii}  68.7 (4) 
O4^{iv}—Si2—O5^{ii}  113.5 (6)  Al1^{x}—Na1—H2^{vii}  47.7 (11) 
Si2^{xi}—Al1—Si2^{xii}  142.3 (3)  Na1^{vii}—Na1—Na1^{viii}  126.4 (3) 
Si2^{xi}—Al1—Na1  129.6 (3)  Na1^{vii}—Na1—O3^{ix}  44.9 (3) 
Si2^{xi}—Al1—Na1^{v}  69.6 (2)  Na1^{vii}—Na1—O3^{x}  115.6 (4) 
Si2^{xi}—Al1—Na1^{vi}  119.9 (2)  Na1^{vii}—Na1—O4  127.4 (4) 
Si2^{xi}—Al1—O2  106.3 (4)  Na1^{vii}—Na1—O5^{ix}  95.1 (4) 
Si2^{xi}—Al1—O3  123.8 (4)  Na1^{vii}—Na1—O6  119.8 (4) 
Si2^{xi}—Al1—O4  93.9 (4)  Na1^{vii}—Na1—O6^{vii}  38.9 (3) 
Si2^{xi}—Al1—O5  20.9 (4)  Na1^{vii}—Na1—H2^{vii}  52.8 (11) 
Si2^{xii}—Al1—Na1  64.9 (2)  Na1^{viii}—Na1—O3^{ix}  115.1 (3) 
Si2^{xii}—Al1—Na1^{v}  75.6 (2)  Na1^{viii}—Na1—O3^{x}  42.8 (3) 
Si2^{xii}—Al1—Na1^{vi}  50.43 (18)  Na1^{viii}—Na1—O4  89.7 (4) 
Si2^{xii}—Al1—O2  107.1 (4)  Na1^{viii}—Na1—O5^{ix}  126.7 (4) 
Si2^{xii}—Al1—O3  24.9 (3)  Na1^{viii}—Na1—O6  39.0 (4) 
Si2^{xii}—Al1—O4  89.9 (4)  Na1^{viii}—Na1—O6^{vii}  115.2 (5) 
Si2^{xii}—Al1—O5  124.6 (5)  Na1^{viii}—Na1—H2^{vii}  94.1 (11) 
Na1—Al1—Na1^{v}  128.6 (3)  O3^{ix}—Na1—O3^{x}  142.0 (4) 
Na1—Al1—Na1^{vi}  108.6 (2)  O3^{ix}—Na1—O4  153.4 (5) 
Na1—Al1—O2  93.2 (4)  O3^{ix}—Na1—O5^{ix}  69.4 (4) 
Na1—Al1—O3  89.7 (3)  O3^{ix}—Na1—O6  85.0 (4) 
Na1—Al1—O4  36.1 (3)  O3^{ix}—Na1—O6^{vii}  83.7 (5) 
Na1—Al1—O5  143.2 (5)  O3^{ix}—Na1—H2^{vii}  94.4 (11) 
Na1^{v}—Al1—Na1^{vi}  62.7 (3)  O3^{x}—Na1—O4  63.3 (4) 
Na1^{v}—Al1—O2  130.3 (5)  O3^{x}—Na1—O5^{ix}  146.8 (5) 
Na1^{v}—Al1—O3  54.2 (4)  O3^{x}—Na1—O6  81.7 (5) 
Na1^{v}—Al1—O4  118.2 (5)  O3^{x}—Na1—O6^{vii}  83.4 (5) 
Na1^{v}—Al1—O5  49.5 (4)  O3^{x}—Na1—H2^{vii}  64.2 (11) 
Na1^{vi}—Al1—O2  80.9 (5)  O4—Na1—O5^{ix}  88.5 (4) 
Na1^{vi}—Al1—O3  33.7 (4)  O4—Na1—O6  112.1 (5) 
Na1^{vi}—Al1—O4  140.0 (4)  O4—Na1—O6^{vii}  94.6 (5) 
Na1^{vi}—Al1—O5  100.7 (4)  O4—Na1—H2^{vii}  93.1 (11) 
O2—Al1—O3  109.8 (6)  O5^{ix}—Na1—O6  94.3 (5) 
O2—Al1—O4  111.5 (6)  O5^{ix}—Na1—O6^{vii}  118.0 (6) 
O2—Al1—O5  113.4 (5)  O5^{ix}—Na1—H2^{vii}  139.2 (12) 
O3—Al1—O4  110.6 (5)  O6—Na1—O6^{vii}  138.9 (5) 
O3—Al1—O5  103.5 (5)  O6—Na1—H2^{vii}  122.2 (11) 
O4—Al1—O5  107.8 (6)  O6^{vii}—Na1—H2^{vii}  21.2 (11) 
Si2^{xiii}—Na1—Si2^{xii}  99.7 (3)  Si1—O1—Si2  146.7 (6) 
Si2^{xiii}—Na1—Al1  56.72 (19)  Si1—O2—Al1  141.7 (7) 
Si2^{xiii}—Na1—Al1^{ix}  154.0 (3)  Si2^{xii}—O3—Al1  128.1 (6) 
Si2^{xiii}—Na1—Al1^{x}  50.40 (19)  Si2^{xii}—O3—Na1^{v}  129.7 (6) 
Si2^{xiii}—Na1—Na1^{vii}  123.8 (3)  Si2^{xii}—O3—Na1^{vi}  88.9 (5) 
Si2^{xiii}—Na1—Na1^{viii}  67.1 (2)  Al1—O3—Na1^{v}  91.1 (4) 
Si2^{xiii}—Na1—O3^{ix}  168.1 (5)  Al1—O3—Na1^{vi}  124.4 (5) 
Si2^{xiii}—Na1—O3^{x}  32.3 (2)  Na1^{v}—O3—Na1^{vi}  92.4 (4) 
Si2^{xiii}—Na1—O4  31.5 (3)  Si2^{xiii}—O4—Al1  138.1 (5) 
Si2^{xiii}—Na1—O5^{ix}  119.4 (3)  Si2^{xiii}—O4—Na1  99.7 (5) 
Si2^{xiii}—Na1—O6  101.5 (5)  Al1—O4—Na1  117.8 (6) 
Si2^{xiii}—Na1—O6^{vii}  85.0 (4)  Si2^{xi}—O5—Al1  135.3 (7) 
Si2^{xiii}—Na1—H2^{vii}  73.8 (11)  Si2^{xi}—O5—Na1^{v}  126.7 (6) 
Si2^{xii}—Na1—Al1  51.39 (17)  Al1—O5—Na1^{v}  95.6 (5) 
Si2^{xii}—Na1—Al1^{ix}  55.2 (2)  Na1—O6—Na1^{viii}  102.2 (5) 
Si2^{xii}—Na1—Al1^{x}  147.9 (3)  Na1—O6—H1  110 (3) 
Si2^{xii}—Na1—Na1^{vii}  113.8 (3)  Na1—O6—H2  120 (3) 
Si2^{xii}—Na1—Na1^{viii}  114.9 (3)  Na1^{viii}—O6—H1  127 (3) 
Si2^{xii}—Na1—O3^{ix}  89.9 (3)  Na1^{viii}—O6—H2  94 (3) 
Si2^{xii}—Na1—O3^{x}  126.0 (4)  H1—O6—H2  104 (4) 
Si2^{xii}—Na1—O4  70.0 (3)  Na1^{viii}—H2—O6  64 (2) 
Symmetry codes: (i) −x, −y, z; (ii) x, y, z−1; (iii) x+1/4, −y+1/4, z−3/4; (iv) −x, −y, z−1; (v) x+1/4, −y+1/4, z+1/4; (vi) −x−1/4, y+1/4, z−1/4; (vii) −x−1/2, −y, z−1/2; (viii) −x−1/2, −y, z+1/2; (ix) x−1/4, −y+1/4, z−1/4; (x) −x−1/4, y−1/4, z+1/4; (xi) x, y, z+1; (xii) x−1/4, −y+1/4, z+3/4; (xiii) −x, −y, z+1. 
D—H···A  D—H  H···A  D···A  D—H···A 
O6—H1···O1^{xiv}  0.96 (4)  2.25 (4)  3.049 (14)  140 (4) 
O6—H2···O2^{xii}  0.96 (5)  1.93 (5)  2.879 (16)  171 (4) 
Symmetry codes: (xii) x−1/4, −y+1/4, z+3/4; (xiv) x−1/2, y, z+1/2. 
Al_{2}H_{4}Na_{2}O_{12}Si_{3}  Z = 8 
M_{r} = 380.2  F(000) = 517.84 
Orthorhombic, Fdd2  D_{x} = 2.235 Mg m^{−}^{3} 
Hall symbol: F 2xuvw;2yuvw;2z  Electrons 200 KeV radiation, λ = 0.0251 Å 
a = 18.2872 (11) Å  Cell parameters from 5213 reflections 
b = 18.6660 (14) Å  θ = 0.1–1.2° 
c = 6.6222 (3) Å  T = 293 K 
V = 2260.5 (2) Å^{3}  Irregular shape 
TEM FEI Tecnai G2 20 diffractometer  R_{int} = 0.198 
Radiation source: Lab6 cathode  θ_{max} = 1.2°, θ_{min} = 0.1° 
continuous–rotation 3D ED scans  h = −29→29 
5213 measured reflections  k = −29→29 
1289 independent reflections  l = −10→10 
876 reflections with I > 3σ(I) 
Refinement on F^{2}  All Hatom parameters refined 
R[F^{2} > 2σ(F^{2})] = 0.134  Weighting scheme based on measured s.u.'s w = 1/(σ^{2}(I) + 0.0004I^{2}) 
wR(F^{2}) = 0.264  (Δ/σ)_{max} = 2.981 
S = 2.93  Δρ_{max} = 0.29 e Å^{−}^{3} 
1289 reflections  Δρ_{min} = −0.29 e Å^{−}^{3} 
93 parameters  Extinction correction: SHELXL2017/1 (Sheldrick, 2015), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
3 restraints  Extinction coefficient: 0.099 (17) 
13 constraints 
x  y  z  U_{iso}*/U_{eq}  
Si1  0  0  0  0.0218 (13)  
Si2  0.09670 (16)  0.03891 (18)  −0.3721 (11)  0.0197 (8)  
Al1  −0.03799 (17)  0.09429 (19)  0.3857 (12)  0.0212 (10)  
Na1  −0.2205 (3)  0.0310 (3)  0.3799 (16)  0.0331 (15)  
O1  0.0683 (3)  0.0226 (3)  −0.1437 (14)  0.0262 (15)  
O2  −0.0222 (3)  0.0681 (3)  0.1344 (17)  0.0310 (17)  
O3  −0.0691 (3)  0.1817 (2)  0.3883 (15)  0.0214 (14)  
O4  −0.0993 (2)  0.0363 (3)  0.5011 (16)  0.0252 (15)  
O5  0.0450 (2)  0.0958 (3)  0.5257 (15)  0.0280 (16)  
O6  −0.3065 (4)  0.0589 (5)  0.636 (2)  0.045 (2)  
H1  −0.293 (2)  0.042 (3)  0.504 (4)  0.0544  
H2  −0.2680 (19)  0.091 (2)  0.673 (7)  0.0544 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
Si1  0.0088 (16)  0.046 (3)  0.011 (2)  −0.0005 (14)  0  0 
Si2  0.0108 (12)  0.0323 (16)  0.0161 (14)  −0.0026 (9)  −0.0005 (14)  0.0000 (16) 
Al1  0.0096 (11)  0.0316 (18)  0.022 (2)  0.0038 (10)  0.0042 (18)  0.0044 (18) 
Na1  0.0217 (18)  0.052 (3)  0.025 (3)  0.0005 (14)  −0.005 (3)  −0.001 (3) 
O1  0.022 (2)  0.045 (3)  0.012 (3)  −0.0035 (18)  0.006 (2)  0.002 (2) 
O2  0.022 (2)  0.053 (3)  0.018 (3)  −0.001 (2)  0.003 (3)  −0.007 (3) 
O3  0.0155 (19)  0.023 (2)  0.026 (3)  0.0022 (13)  −0.004 (3)  0.002 (2) 
O4  0.0046 (16)  0.043 (3)  0.028 (3)  −0.0021 (14)  −0.001 (2)  0.007 (3) 
O5  0.0087 (19)  0.057 (3)  0.018 (3)  0.0030 (19)  −0.002 (2)  0.002 (3) 
O6  0.033 (3)  0.077 (5)  0.026 (4)  0.008 (3)  0.001 (4)  0.002 (4) 
H1  0.03969  0.092366  0.031226  0.009857  0.001785  0.002332 
H2  0.03969  0.092366  0.031226  0.009857  0.001785  0.002332 
Si1—O1  1.626 (7)  Al1—O3  1.728 (6) 
Si1—O1^{i}  1.626 (7)  Al1—O4  1.736 (8) 
Si1—O2  1.604 (8)  Al1—O5  1.778 (8) 
Si1—O2^{i}  1.604 (8)  Na1—Na1^{vii}  3.670 (14) 
Si2—Al1^{ii}  3.116 (7)  Na1—Na1^{viii}  3.670 (14) 
Si2—Al1^{iii}  3.034 (5)  Na1—O3^{ix}  2.510 (11) 
Si2—Na1^{iv}  3.086 (9)  Na1—O3^{x}  2.624 (11) 
Si2—Na1^{iii}  3.580 (6)  Na1—O4  2.359 (8) 
Si2—O1  1.628 (11)  Na1—O5^{ix}  2.418 (9) 
Si2—O3^{iii}  1.636 (6)  Na1—O6  2.371 (14) 
Si2—O4^{iv}  1.637 (8)  Na1—O6^{vii}  2.381 (14) 
Si2—O5^{ii}  1.575 (8)  Na1—H1  1.58 (4) 
Al1—Na1  3.540 (6)  Na1—H2  2.41 (4) 
Al1—Na1^{v}  3.092 (9)  Na1—H2^{vii}  2.67 (4) 
Al1—Na1^{vi}  3.878 (8)  O6—H1  0.96 (3) 
Al1—O2  1.758 (13)  O6—H2  0.96 (4) 
O1—Si1—O1^{i}  108.4 (4)  Al1—Na1—O6  122.9 (4) 
O1—Si1—O2  108.3 (3)  Al1—Na1—O6^{vii}  92.7 (3) 
O1—Si1—O2^{i}  109.6 (3)  Al1—Na1—H1  138.1 (15) 
O1^{i}—Si1—O2  109.6 (3)  Al1—Na1—H2  100.1 (9) 
O1^{i}—Si1—O2^{i}  108.3 (3)  Al1—Na1—H2^{vii}  111.4 (8) 
O2—Si1—O2^{i}  112.6 (5)  Al1^{ix}—Na1—Al1^{x}  157.1 (2) 
Al1^{ii}—Si2—Al1^{iii}  108.65 (18)  Al1^{ix}—Na1—Na1^{vii}  69.4 (2) 
Al1^{ii}—Si2—Na1^{iv}  116.5 (3)  Al1^{ix}—Na1—Na1^{viii}  126.3 (2) 
Al1^{ii}—Si2—Na1^{iii}  54.48 (16)  Al1^{ix}—Na1—O3^{ix}  33.96 (16) 
Al1^{ii}—Si2—O1  106.8 (3)  Al1^{ix}—Na1—O3^{x}  169.4 (4) 
Al1^{ii}—Si2—O3^{iii}  130.9 (4)  Al1^{ix}—Na1—O4  121.4 (3) 
Al1^{ii}—Si2—O4^{iv}  92.5 (3)  Al1^{ix}—Na1—O5^{ix}  35.03 (19) 
Al1^{ii}—Si2—O5^{ii}  23.1 (2)  Al1^{ix}—Na1—O6  86.7 (3) 
Al1^{iii}—Si2—Na1^{iv}  78.64 (17)  Al1^{ix}—Na1—O6^{vii}  105.0 (5) 
Al1^{iii}—Si2—Na1^{iii}  64.11 (12)  Al1^{ix}—Na1—H1  80.5 (15) 
Al1^{iii}—Si2—O1  109.9 (4)  Al1^{ix}—Na1—H2  85.6 (10) 
Al1^{iii}—Si2—O3^{iii}  26.37 (19)  Al1^{ix}—Na1—H2^{vii}  110.1 (10) 
Al1^{iii}—Si2—O4^{iv}  127.2 (3)  Al1^{x}—Na1—Na1^{vii}  97.1 (2) 
Al1^{iii}—Si2—O5^{ii}  86.6 (3)  Al1^{x}—Na1—Na1^{viii}  48.27 (17) 
Na1^{iv}—Si2—Na1^{iii}  130.6 (2)  Al1^{x}—Na1—O3^{ix}  123.8 (2) 
Na1^{iv}—Si2—O1  130.5 (3)  Al1^{x}—Na1—O3^{x}  21.49 (17) 
Na1^{iv}—Si2—O3^{iii}  58.3 (3)  Al1^{x}—Na1—O4  81.5 (2) 
Na1^{iv}—Si2—O4^{iv}  48.9 (2)  Al1^{x}—Na1—O5^{ix}  167.1 (4) 
Na1^{iv}—Si2—O5^{ii}  119.8 (5)  Al1^{x}—Na1—O6  84.9 (3) 
Na1^{iii}—Si2—O1  93.6 (3)  Al1^{x}—Na1—O6^{vii}  69.8 (3) 
Na1^{iii}—Si2—O3^{iii}  90.4 (2)  Al1^{x}—Na1—H1  85.8 (17) 
Na1^{iii}—Si2—O4^{iv}  144.8 (4)  Al1^{x}—Na1—H2  94.8 (10) 
Na1^{iii}—Si2—O5^{ii}  33.1 (3)  Al1^{x}—Na1—H2^{vii}  57.3 (9) 
O1—Si2—O3^{iii}  108.9 (6)  Na1^{vii}—Na1—Na1^{viii}  128.9 (2) 
O1—Si2—O4^{iv}  109.0 (4)  Na1^{vii}—Na1—O3^{ix}  45.6 (2) 
O1—Si2—O5^{ii}  109.5 (4)  Na1^{vii}—Na1—O3^{x}  116.6 (3) 
O3^{iii}—Si2—O4^{iv}  106.4 (4)  Na1^{vii}—Na1—O4  126.7 (4) 
O3^{iii}—Si2—O5^{ii}  110.9 (4)  Na1^{vii}—Na1—O5^{ix}  94.4 (4) 
O4^{iv}—Si2—O5^{ii}  112.1 (6)  Na1^{vii}—Na1—O6  121.3 (3) 
Si2^{xi}—Al1—Si2^{xii}  142.8 (3)  Na1^{vii}—Na1—O6^{vii}  39.3 (3) 
Si2^{xi}—Al1—Na1  129.8 (2)  Na1^{vii}—Na1—H1  105.3 (12) 
Si2^{xi}—Al1—Na1^{v}  70.43 (18)  Na1^{vii}—Na1—H2  140.2 (9) 
Si2^{xi}—Al1—Na1^{vi}  119.44 (15)  Na1^{vii}—Na1—H2^{vii}  40.9 (9) 
Si2^{xi}—Al1—O2  105.4 (3)  Na1^{viii}—Na1—O3^{ix}  116.8 (3) 
Si2^{xi}—Al1—O3  124.6 (4)  Na1^{viii}—Na1—O3^{x}  43.1 (2) 
Si2^{xi}—Al1—O4  94.4 (3)  Na1^{viii}—Na1—O4  89.0 (4) 
Si2^{xi}—Al1—O5  20.4 (2)  Na1^{viii}—Na1—O5^{ix}  126.3 (4) 
Si2^{xii}—Al1—Na1  65.45 (12)  Na1^{viii}—Na1—O6  39.5 (3) 
Si2^{xii}—Al1—Na1^{v}  75.24 (17)  Na1^{viii}—Na1—O6^{vii}  116.8 (4) 
Si2^{xii}—Al1—Na1^{vi}  51.28 (14)  Na1^{viii}—Na1—H1  47.5 (13) 
Si2^{xii}—Al1—O2  107.3 (4)  Na1^{viii}—Na1—H2  46.7 (10) 
Si2^{xii}—Al1—O3  24.86 (19)  Na1^{viii}—Na1—H2^{vii}  99.9 (9) 
Si2^{xii}—Al1—O4  90.4 (2)  O3^{ix}—Na1—O3^{x}  144.1 (3) 
Si2^{xii}—Al1—O5  126.2 (3)  O3^{ix}—Na1—O4  151.7 (4) 
Na1—Al1—Na1^{v}  129.3 (2)  O3^{ix}—Na1—O5^{ix}  68.8 (3) 
Na1—Al1—Na1^{vi}  109.44 (17)  O3^{ix}—Na1—O6  85.3 (4) 
Na1—Al1—O2  92.9 (3)  O3^{ix}—Na1—O6^{vii}  84.9 (4) 
Na1—Al1—O3  90.3 (2)  O3^{ix}—Na1—H1  71.9 (12) 
Na1—Al1—O4  35.7 (3)  O3^{ix}—Na1—H2  97.1 (10) 
Na1—Al1—O5  144.6 (4)  O3^{ix}—Na1—H2^{vii}  81.6 (9) 
Na1^{v}—Al1—Na1^{vi}  62.3 (2)  O3^{x}—Na1—O4  63.2 (3) 
Na1^{v}—Al1—O2  129.7 (3)  O3^{x}—Na1—O5^{ix}  145.6 (4) 
Na1^{v}—Al1—O3  54.2 (3)  O3^{x}—Na1—O6  82.6 (4) 
Na1^{v}—Al1—O4  119.8 (5)  O3^{x}—Na1—O6^{vii}  83.6 (4) 
Na1^{v}—Al1—O5  51.3 (3)  O3^{x}—Na1—H1  89.3 (15) 
Na1^{vi}—Al1—O2  80.2 (3)  O3^{x}—Na1—H2  84.6 (10) 
Na1^{vi}—Al1—O3  33.8 (3)  O3^{x}—Na1—H2^{vii}  75.7 (9) 
Na1^{vi}—Al1—O4  141.1 (2)  O4—Na1—O5^{ix}  87.0 (3) 
Na1^{vi}—Al1—O5  100.3 (3)  O4—Na1—O6  111.7 (5) 
O2—Al1—O3  109.0 (5)  O4—Na1—O6^{vii}  93.8 (3) 
O2—Al1—O4  110.4 (4)  O4—Na1—H1  127.5 (13) 
O2—Al1—O5  111.0 (4)  O4—Na1—H2  92.6 (10) 
O3—Al1—O4  111.8 (4)  O4—Na1—H2^{vii}  106.6 (8) 
O3—Al1—O5  105.1 (4)  O5^{ix}—Na1—O6  94.1 (4) 
O4—Al1—O5  109.4 (5)  O5^{ix}—Na1—O6^{vii}  116.9 (5) 
Si2^{xiii}—Na1—Si2^{xii}  98.47 (19)  O5^{ix}—Na1—H1  96.9 (17) 
Si2^{xiii}—Na1—Al1  56.22 (15)  O5^{ix}—Na1—H2  80.0 (10) 
Si2^{xiii}—Na1—Al1^{ix}  152.8 (2)  O5^{ix}—Na1—H2^{vii}  132.5 (10) 
Si2^{xiii}—Na1—Al1^{x}  50.09 (13)  O6—Na1—O6^{vii}  141.0 (4) 
Si2^{xiii}—Na1—Na1^{vii}  124.3 (2)  O6—Na1—H1  16.0 (12) 
Si2^{xiii}—Na1—Na1^{viii}  66.6 (2)  O6—Na1—H2  23.2 (9) 
Si2^{xiii}—Na1—O3^{ix}  169.7 (4)  O6—Na1—H2^{vii}  120.2 (9) 
Si2^{xiii}—Na1—O3^{x}  32.02 (16)  O6^{vii}—Na1—H1  128.5 (16) 
Si2^{xiii}—Na1—O4  31.5 (2)  O6^{vii}—Na1—H2  162.2 (10) 
Si2^{xiii}—Na1—O5^{ix}  117.9 (3)  O6^{vii}—Na1—H2^{vii}  20.9 (9) 
Si2^{xiii}—Na1—O6  101.5 (4)  H1—Na1—H2  38.1 (16) 
Si2^{xiii}—Na1—O6^{vii}  84.9 (3)  H1—Na1—H2^{vii}  108.4 (18) 
Si2^{xiii}—Na1—H1  113.4 (13)  H2—Na1—H2^{vii}  141.8 (13) 
Si2^{xiii}—Na1—H2  92.0 (10)  Si1—O1—Si2  146.8 (5) 
Si2^{xiii}—Na1—H2^{vii}  88.3 (9)  Si1—O2—Al1  141.9 (5) 
Si2^{xii}—Na1—Al1  50.43 (10)  Si2^{xii}—O3—Al1  128.8 (3) 
Si2^{xii}—Na1—Al1^{ix}  55.10 (15)  Si2^{xii}—O3—Na1^{v}  127.6 (5) 
Si2^{xii}—Na1—Al1^{x}  146.3 (3)  Si2^{xii}—O3—Na1^{vi}  89.7 (4) 
Si2^{xii}—Na1—Na1^{vii}  113.2 (3)  Al1—O3—Na1^{v}  91.8 (4) 
Si2^{xii}—Na1—Na1^{viii}  113.6 (3)  Al1—O3—Na1^{vi}  124.7 (5) 
Si2^{xii}—Na1—O3^{ix}  89.1 (2)  Na1^{v}—O3—Na1^{vi}  91.2 (3) 
Si2^{xii}—Na1—O3^{x}  124.8 (3)  Si2^{xiii}—O4—Al1  137.9 (3) 
Si2^{xii}—Na1—O4  68.85 (19)  Si2^{xiii}—O4—Na1  99.5 (3) 
Si2^{xii}—Na1—O5^{ix}  20.8 (2)  Al1—O4—Na1  118.9 (5) 
Si2^{xii}—Na1—O6  91.3 (3)  Si2^{xi}—O5—Al1  136.5 (4) 
Si2^{xii}—Na1—O6^{vii}  126.1 (4)  Si2^{xi}—O5—Na1^{v}  126.1 (5) 
Si2^{xii}—Na1—H1  99.5 (17)  Al1—O5—Na1^{v}  93.7 (3) 
Si2^{xii}—Na1—H2  71.7 (10)  Na1—O6—Na1^{viii}  101.1 (4) 
Si2^{xii}—Na1—H2^{vii}  145.9 (10)  Na1—O6—H1  27 (2) 
Al1—Na1—Al1^{ix}  97.51 (19)  Na1—O6—H2  80 (3) 
Al1—Na1—Al1^{x}  104.93 (18)  Na1^{viii}—O6—H1  110 (3) 
Al1—Na1—Na1^{vii}  113.1 (3)  Na1^{viii}—O6—H2  97 (3) 
Al1—Na1—Na1^{viii}  111.9 (3)  H1—O6—H2  104 (4) 
Al1—Na1—O3^{ix}  126.3 (3)  Na1—H1—O6  137 (3) 
Al1—Na1—O3^{x}  88.2 (2)  Na1—H2—Na1^{viii}  92.4 (13) 
Al1—Na1—O4  25.4 (2)  Na1—H2—O6  76 (3) 
Al1—Na1—O5^{ix}  64.87 (17)  Na1^{viii}—H2—O6  62 (2) 
Symmetry codes: (i) −x, −y, z; (ii) x, y, z−1; (iii) x+1/4, −y+1/4, z−3/4; (iv) −x, −y, z−1; (v) x+1/4, −y+1/4, z+1/4; (vi) −x−1/4, y+1/4, z−1/4; (vii) −x−1/2, −y, z−1/2; (viii) −x−1/2, −y, z+1/2; (ix) x−1/4, −y+1/4, z−1/4; (x) −x−1/4, y−1/4, z+1/4; (xi) x, y, z+1; (xii) x−1/4, −y+1/4, z+3/4; (xiii) −x, −y, z+1. 
D—H···A  D—H  H···A  D···A  D—H···A 
O6—H1···Na1  0.96 (3)  1.58 (4)  2.371 (14)  137 (3) 
O6—H2···O2^{xii}  0.96 (4)  2.20 (4)  2.892 (13)  128 (3) 
Symmetry code: (xii) x−1/4, −y+1/4, z+3/4. 
Al_{2}H_{4}Na_{2}O_{12}Si_{3}  Z = 8 
M_{r} = 380.2  F(000) = 517.84 
Orthorhombic, Fdd2  D_{x} = 2.235 Mg m^{−}^{3} 
Hall symbol: F 2xuvw;2yuvw;2z  Electrons 200 KeV radiation, λ = 0.0251 Å 
a = 18.2872 (11) Å  Cell parameters from 5213 reflections 
b = 18.6660 (14) Å  θ = 0.1–1.2° 
c = 6.6222 (3) Å  T = 293 K 
V = 2260.5 (2) Å^{3}  Irregular shape 
TEM FEI Tecnai G2 20 diffractometer  R_{int} = 0.198 
Radiation source: Lab6 cathode  θ_{max} = 1.2°, θ_{min} = 0.1° 
continuous–rotation 3D ED scans  h = −29→29 
5213 measured reflections  k = −29→29 
1289 independent reflections  l = −10→10 
801 reflections with I > 3σ(I) 
Refinement on F^{2}  All Hatom parameters refined 
R[F^{2} > 2σ(F^{2})] = 0.149  Weighting scheme based on measured s.u.'s w = 1/(σ^{2}(I) + 0.0004I^{2}) 
wR(F^{2}) = 0.406  (Δ/σ)_{max} = 0.048 
S = 1.48  Δρ_{max} = 0.30 e Å^{−}^{3} 
1289 reflections  Δρ_{min} = −0.24 e Å^{−}^{3} 
93 parameters  Extinction correction: SHELXL2017/1 (Sheldrick, 2015), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
3 restraints  Extinction coefficient: 0.64 (16) 
13 constraints 
x  y  z  U_{iso}*/U_{eq}  
Si1  0  0  0  0.0243 (13)  
Si2  0.09715 (17)  0.0386 (2)  −0.3724 (8)  0.0240 (9)  
Al1  −0.03703 (19)  0.0944 (2)  0.3853 (9)  0.0248 (10)  
Na1  −0.2201 (3)  0.0310 (4)  0.3836 (11)  0.0367 (15)  
O1  0.0696 (3)  0.0216 (4)  −0.1412 (10)  0.0324 (17)  
O2  −0.0226 (3)  0.0675 (4)  0.1345 (13)  0.0321 (16)  
O3  −0.0700 (3)  0.1818 (3)  0.3919 (12)  0.0266 (14)  
O4  −0.0993 (4)  0.0358 (4)  0.5042 (14)  0.0350 (18)  
O5  0.0434 (3)  0.0968 (4)  0.5272 (11)  0.0316 (16)  
O6  −0.3070 (4)  0.0599 (6)  0.6385 (15)  0.045 (2)  
H1  −0.3566 (10)  0.057 (3)  0.592 (8)  0.0544  
H2  −0.307 (3)  0.099 (2)  0.734 (7)  0.0544 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
Si1  0.0168 (18)  0.040 (3)  0.0165 (15)  −0.0007 (16)  0  0 
Si2  0.0114 (13)  0.044 (2)  0.0169 (11)  −0.0017 (10)  −0.0015 (10)  −0.0037 (14) 
Al1  0.0127 (13)  0.040 (2)  0.0216 (14)  0.0012 (11)  0.0000 (12)  0.0009 (15) 
Na1  0.022 (2)  0.060 (4)  0.0282 (19)  0.0025 (17)  0.0018 (17)  −0.004 (2) 
O1  0.016 (2)  0.065 (4)  0.0156 (18)  0.003 (2)  0.0066 (17)  −0.001 (2) 
O2  0.024 (3)  0.048 (4)  0.024 (2)  0.002 (2)  0.001 (2)  −0.004 (3) 
O3  0.014 (2)  0.036 (3)  0.030 (2)  0.0003 (15)  −0.003 (2)  −0.001 (2) 
O4  0.017 (2)  0.049 (4)  0.039 (3)  −0.004 (2)  0.004 (2)  0.006 (3) 
O5  0.013 (2)  0.060 (4)  0.0213 (19)  0.003 (2)  −0.0060 (18)  0.000 (2) 
O6  0.029 (3)  0.074 (5)  0.033 (3)  0.001 (3)  −0.001 (3)  0.004 (3) 
H1  0.034346  0.089062  0.039731  0.000906  −0.001612  0.004477 
H2  0.034346  0.089062  0.039731  0.000906  −0.001612  0.004477 
Si1—O1  1.630 (6)  Al1—O2  1.755 (10) 
Si1—O1^{i}  1.630 (6)  Al1—O3  1.739 (8) 
Si1—O2  1.597 (8)  Al1—O4  1.765 (9) 
Si1—O2^{i}  1.597 (8)  Al1—O5  1.746 (7) 
Si2—Al1^{ii}  3.112 (6)  Na1—Na1^{vii}  3.674 (10) 
Si2—Al1^{iii}  3.043 (5)  Na1—Na1^{viii}  3.674 (10) 
Si2—Na1^{iv}  3.058 (8)  Na1—O3^{ix}  2.526 (9) 
Si2—Na1^{iii}  3.586 (8)  Na1—O3^{x}  2.624 (10) 
Si2—O1  1.643 (8)  Na1—O4  2.350 (9) 
Si2—O3^{iii}  1.616 (6)  Na1—O5^{ix}  2.401 (11) 
Si2—O4^{iv}  1.612 (9)  Na1—O6  2.381 (11) 
Si2—O5^{ii}  1.609 (8)  Na1—O6^{vii}  2.400 (13) 
Al1—Na1  3.551 (7)  Na1—H2^{vii}  2.66 (4) 
Al1—Na1^{v}  3.100 (9)  O6—H1  0.96 (3) 
Al1—Na1^{vi}  3.862 (9)  O6—H2  0.96 (5) 
O1—Si1—O1^{i}  110.0 (3)  Si2^{xii}—Na1—O5^{ix}  21.37 (19) 
O1—Si1—O2  109.0 (4)  Si2^{xii}—Na1—O6  91.4 (3) 
O1—Si1—O2^{i}  108.3 (4)  Si2^{xii}—Na1—O6^{vii}  125.8 (3) 
O1^{i}—Si1—O2  108.3 (4)  Si2^{xii}—Na1—H2^{vii}  141.7 (11) 
O1^{i}—Si1—O2^{i}  109.0 (4)  Al1—Na1—Al1^{ix}  97.1 (2) 
O2—Si1—O2^{i}  112.2 (4)  Al1—Na1—Al1^{x}  105.52 (18) 
Al1^{ii}—Si2—Al1^{iii}  108.49 (18)  Al1—Na1—Na1^{vii}  112.9 (2) 
Al1^{ii}—Si2—Na1^{iv}  116.7 (2)  Al1—Na1—Na1^{viii}  112.5 (2) 
Al1^{ii}—Si2—Na1^{iii}  54.59 (15)  Al1—Na1—O3^{ix}  126.3 (3) 
Al1^{ii}—Si2—O1  107.6 (3)  Al1—Na1—O3^{x}  88.3 (2) 
Al1^{ii}—Si2—O3^{iii}  130.9 (3)  Al1—Na1—O4  25.9 (2) 
Al1^{ii}—Si2—O4^{iv}  92.7 (3)  Al1—Na1—O5^{ix}  65.6 (2) 
Al1^{ii}—Si2—O5^{ii}  22.9 (3)  Al1—Na1—O6  123.5 (4) 
Al1^{iii}—Si2—Na1^{iv}  78.56 (17)  Al1—Na1—O6^{vii}  92.5 (3) 
Al1^{iii}—Si2—Na1^{iii}  64.18 (14)  Al1—Na1—H2^{vii}  97.3 (11) 
Al1^{iii}—Si2—O1  109.6 (3)  Al1^{ix}—Na1—Al1^{x}  156.7 (2) 
Al1^{iii}—Si2—O3^{iii}  25.9 (2)  Al1^{ix}—Na1—Na1^{vii}  68.9 (2) 
Al1^{iii}—Si2—O4^{iv}  127.6 (3)  Al1^{ix}—Na1—Na1^{viii}  126.6 (2) 
Al1^{iii}—Si2—O5^{ii}  87.0 (3)  Al1^{ix}—Na1—O3^{ix}  34.11 (18) 
Na1^{iv}—Si2—Na1^{iii}  131.1 (2)  Al1^{ix}—Na1—O3^{x}  170.1 (3) 
Na1^{iv}—Si2—O1  129.5 (3)  Al1^{ix}—Na1—O4  121.5 (3) 
Na1^{iv}—Si2—O3^{iii}  59.1 (3)  Al1^{ix}—Na1—O5^{ix}  34.09 (19) 
Na1^{iv}—Si2—O4^{iv}  49.3 (3)  Al1^{ix}—Na1—O6  86.7 (3) 
Na1^{iv}—Si2—O5^{ii}  121.2 (4)  Al1^{ix}—Na1—O6^{vii}  104.7 (4) 
Na1^{iii}—Si2—O1  93.7 (3)  Al1^{ix}—Na1—H2^{vii}  123.9 (11) 
Na1^{iii}—Si2—O3^{iii}  90.0 (3)  Al1^{x}—Na1—Na1^{vii}  96.6 (2) 
Na1^{iii}—Si2—O4^{iv}  145.4 (4)  Al1^{x}—Na1—Na1^{viii}  48.50 (16) 
Na1^{iii}—Si2—O5^{ii}  32.9 (3)  Al1^{x}—Na1—O3^{ix}  123.1 (3) 
O1—Si2—O3^{iii}  107.4 (5)  Al1^{x}—Na1—O3^{x}  22.11 (17) 
O1—Si2—O4^{iv}  108.3 (5)  Al1^{x}—Na1—O4  81.7 (3) 
O1—Si2—O5^{ii}  109.1 (4)  Al1^{x}—Na1—O5^{ix}  168.5 (3) 
O3^{iii}—Si2—O4^{iv}  107.5 (4)  Al1^{x}—Na1—O6  85.5 (3) 
O3^{iii}—Si2—O5^{ii}  111.5 (4)  Al1^{x}—Na1—O6^{vii}  69.4 (3) 
O4^{iv}—Si2—O5^{ii}  112.8 (5)  Al1^{x}—Na1—H2^{vii}  48.4 (10) 
Si2^{xi}—Al1—Si2^{xii}  143.0 (2)  Na1^{vii}—Na1—Na1^{viii}  128.7 (2) 
Si2^{xi}—Al1—Na1  129.3 (2)  Na1^{vii}—Na1—O3^{ix}  45.6 (2) 
Si2^{xi}—Al1—Na1^{v}  70.52 (18)  Na1^{vii}—Na1—O3^{x}  116.6 (3) 
Si2^{xi}—Al1—Na1^{vi}  119.86 (16)  Na1^{vii}—Na1—O4  126.7 (3) 
Si2^{xi}—Al1—O2  105.9 (3)  Na1^{vii}—Na1—O5^{ix}  93.7 (3) 
Si2^{xi}—Al1—O3  125.1 (3)  Na1^{vii}—Na1—O6  120.8 (3) 
Si2^{xi}—Al1—O4  94.1 (3)  Na1^{vii}—Na1—O6^{vii}  39.6 (3) 
Si2^{xi}—Al1—O5  21.0 (3)  Na1^{vii}—Na1—H2^{vii}  55.5 (11) 
Si2^{xii}—Al1—Na1  65.36 (15)  Na1^{viii}—Na1—O3^{ix}  116.3 (3) 
Si2^{xii}—Al1—Na1^{v}  75.25 (18)  Na1^{viii}—Na1—O3^{x}  43.4 (2) 
Si2^{xii}—Al1—Na1^{vi}  50.89 (14)  Na1^{viii}—Na1—O4  89.2 (3) 
Si2^{xii}—Al1—O2  107.1 (3)  Na1^{viii}—Na1—O5^{ix}  126.5 (3) 
Si2^{xii}—Al1—O3  24.0 (2)  Na1^{viii}—Na1—O6  40.0 (3) 
Si2^{xii}—Al1—O4  90.2 (3)  Na1^{viii}—Na1—O6^{vii}  116.7 (4) 
Si2^{xii}—Al1—O5  125.3 (4)  Na1^{viii}—Na1—H2^{vii}  96.1 (11) 
Na1—Al1—Na1^{v}  128.6 (2)  O3^{ix}—Na1—O3^{x}  144.0 (3) 
Na1—Al1—Na1^{vi}  109.34 (18)  O3^{ix}—Na1—O4  152.1 (4) 
Na1—Al1—O2  92.5 (3)  O3^{ix}—Na1—O5^{ix}  68.1 (3) 
Na1—Al1—O3  89.2 (2)  O3^{ix}—Na1—O6  84.5 (3) 
Na1—Al1—O4  35.5 (3)  O3^{ix}—Na1—O6^{vii}  85.1 (4) 
Na1—Al1—O5  143.5 (4)  O3^{ix}—Na1—H2^{vii}  98.6 (11) 
Na1^{v}—Al1—Na1^{vi}  62.57 (19)  O3^{x}—Na1—O4  62.8 (3) 
Na1^{v}—Al1—O2  131.1 (3)  O3^{x}—Na1—O5^{ix}  146.4 (4) 
Na1^{v}—Al1—O3  54.5 (3)  O3^{x}—Na1—O6  83.4 (4) 
Na1^{v}—Al1—O4  118.9 (4)  O3^{x}—Na1—O6^{vii}  83.4 (4) 
Na1^{v}—Al1—O5  50.4 (3)  O3^{x}—Na1—H2^{vii}  63.3 (11) 
Na1^{vi}—Al1—O2  81.1 (3)  O4—Na1—O5^{ix}  88.1 (3) 
Na1^{vi}—Al1—O3  34.6 (3)  O4—Na1—O6  112.2 (4) 
Na1^{vi}—Al1—O4  140.6 (3)  O4—Na1—O6^{vii}  93.6 (4) 
Na1^{vi}—Al1—O5  100.4 (3)  O4—Na1—H2^{vii}  89.2 (11) 
O2—Al1—O3  110.1 (5)  O5^{ix}—Na1—O6  93.5 (4) 
O2—Al1—O4  110.0 (4)  O5^{ix}—Na1—O6^{vii}  116.9 (4) 
O2—Al1—O5  112.9 (4)  O5^{ix}—Na1—H2^{vii}  137.3 (11) 
O3—Al1—O4  110.3 (4)  O6—Na1—O6^{vii}  141.1 (4) 
O3—Al1—O5  104.8 (4)  O6—Na1—H2^{vii}  126.6 (11) 
O4—Al1—O5  108.6 (5)  O6^{vii}—Na1—H2^{vii}  21.0 (11) 
Si2^{xiii}—Na1—Si2^{xii}  98.78 (19)  Si1—O1—Si2  145.3 (4) 
Si2^{xiii}—Na1—Al1  56.41 (15)  Si1—O2—Al1  142.4 (5) 
Si2^{xiii}—Na1—Al1^{ix}  152.7 (3)  Si2^{xii}—O3—Al1  130.1 (4) 
Si2^{xiii}—Na1—Al1^{x}  50.54 (14)  Si2^{xii}—O3—Na1^{v}  128.4 (4) 
Si2^{xiii}—Na1—Na1^{vii}  124.1 (2)  Si2^{xii}—O3—Na1^{vi}  89.0 (4) 
Si2^{xiii}—Na1—Na1^{viii}  66.99 (19)  Al1—O3—Na1^{v}  91.3 (3) 
Si2^{xiii}—Na1—O3^{ix}  169.5 (3)  Al1—O3—Na1^{vi}  123.3 (4) 
Si2^{xiii}—Na1—O3^{x}  31.91 (16)  Na1^{v}—O3—Na1^{vi}  91.0 (3) 
Si2^{xiii}—Na1—O4  31.3 (2)  Si2^{xiii}—O4—Al1  138.1 (5) 
Si2^{xiii}—Na1—O5^{ix}  118.9 (3)  Si2^{xiii}—O4—Na1  99.3 (4) 
Si2^{xiii}—Na1—O6  102.3 (4)  Al1—O4—Na1  118.6 (5) 
Si2^{xiii}—Na1—O6^{vii}  84.6 (3)  Si2^{xi}—O5—Al1  136.1 (5) 
Si2^{xiii}—Na1—H2^{vii}  70.9 (11)  Si2^{xi}—O5—Na1^{v}  125.7 (4) 
Si2^{xii}—Na1—Al1  50.47 (12)  Al1—O5—Na1^{v}  95.5 (4) 
Si2^{xii}—Na1—Al1^{ix}  54.89 (15)  Na1—O6—Na1^{viii}  100.4 (4) 
Si2^{xii}—Na1—Al1^{x}  147.1 (2)  Na1—O6—H1  113 (3) 
Si2^{xii}—Na1—Na1^{vii}  112.8 (2)  Na1—O6—H2  130 (3) 
Si2^{xii}—Na1—Na1^{viii}  114.1 (2)  Na1^{viii}—O6—H1  112 (3) 
Si2^{xii}—Na1—O3^{ix}  89.0 (2)  Na1^{viii}—O6—H2  95 (3) 
Si2^{xii}—Na1—O3^{x}  125.0 (3)  H1—O6—H2  104 (4) 
Si2^{xii}—Na1—O4  69.2 (3)  Na1^{viii}—H2—O6  64 (2) 
Symmetry codes: (i) −x, −y, z; (ii) x, y, z−1; (iii) x+1/4, −y+1/4, z−3/4; (iv) −x, −y, z−1; (v) x+1/4, −y+1/4, z+1/4; (vi) −x−1/4, y+1/4, z−1/4; (vii) −x−1/2, −y, z−1/2; (viii) −x−1/2, −y, z+1/2; (ix) x−1/4, −y+1/4, z−1/4; (x) −x−1/4, y−1/4, z+1/4; (xi) x, y, z+1; (xii) x−1/4, −y+1/4, z+3/4; (xiii) −x, −y, z+1. 
D—H···A  D—H  H···A  D···A  D—H···A 
O6—H1···O1^{xiv}  0.96 (3)  2.16 (4)  3.005 (11)  147 (4) 
O6—H2···O2^{xii}  0.96 (5)  1.96 (5)  2.878 (13)  159 (4) 
Symmetry codes: (xii) x−1/4, −y+1/4, z+3/4; (xiv) x−1/2, y, z+1/2. 
Al_{2}H_{4}Na_{2}O_{12}Si_{3}  Z = 8 
M_{r} = 380.2  F(000) = 517.84 
Orthorhombic, Fdd2  D_{x} = 2.235 Mg m^{−}^{3} 
Hall symbol: F 2xuvw;2yuvw;2z  Electrons 200 KeV radiation, λ = 0.0251 Å 
a = 18.2872 (11) Å  Cell parameters from 5213 reflections 
b = 18.6660 (14) Å  θ = 0.1–1.2° 
c = 6.6222 (3) Å  T = 293 K 
V = 2260.5 (2) Å^{3}  Irregular shape 
TEM FEI Tecnai G2 20 diffractometer  R_{int} = 0.198 
Radiation source: Lab6 cathode  θ_{max} = 1.2°, θ_{min} = 0.1° 
continuous–rotation 3D ED scans  h = −29→29 
5213 measured reflections  k = −29→29 
1289 independent reflections  l = −10→10 
1007 reflections with I > 3σ(I) 
Refinement on F^{2}  All Hatom parameters refined 
R[F^{2} > 2σ(F^{2})] = 0.147  Weighting scheme based on measured s.u.'s w = 1/(σ^{2}(I) + 0.0004I^{2}) 
wR(F^{2}) = 0.363  (Δ/σ)_{max} = 0.035 
S = 1.78  Δρ_{max} = 0.28 e Å^{−}^{3} 
1289 reflections  Δρ_{min} = −0.24 e Å^{−}^{3} 
93 parameters  Extinction correction: SHELXL2017/1 (Sheldrick, 2015), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
3 restraints  Extinction coefficient: 0.40 (9) 
13 constraints 
x  y  z  U_{iso}*/U_{eq}  
Si1  0  0  0  0.0233 (12)  
Si2  0.09699 (16)  0.03848 (19)  −0.3724 (9)  0.0228 (8)  
Al1  −0.03714 (18)  0.0943 (2)  0.3857 (10)  0.0235 (9)  
Na1  −0.2203 (3)  0.0309 (3)  0.3829 (12)  0.0356 (14)  
O1  0.0695 (3)  0.0216 (4)  −0.1412 (11)  0.0306 (15)  
O2  −0.0224 (3)  0.0676 (4)  0.1353 (13)  0.0306 (15)  
O3  −0.0697 (3)  0.1818 (3)  0.3919 (12)  0.0251 (13)  
O4  −0.0992 (3)  0.0358 (4)  0.5026 (14)  0.0327 (17)  
O5  0.0437 (3)  0.0969 (4)  0.5268 (12)  0.0303 (15)  
O6  −0.3065 (4)  0.0598 (5)  0.6375 (16)  0.044 (2)  
H1  −0.3560 (10)  0.059 (3)  0.590 (7)  0.0526  
H2  −0.305 (2)  0.099 (2)  0.730 (7)  0.0526 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
Si1  0.0148 (16)  0.039 (3)  0.0162 (17)  −0.0014 (14)  0  0 
Si2  0.0107 (12)  0.0411 (19)  0.0166 (12)  −0.0015 (9)  −0.0012 (10)  −0.0023 (14) 
Al1  0.0125 (12)  0.038 (2)  0.0203 (14)  0.0019 (10)  0.0006 (12)  0.0004 (14) 
Na1  0.0218 (19)  0.056 (3)  0.029 (2)  0.0017 (15)  −0.0014 (18)  −0.003 (2) 
O1  0.0156 (19)  0.060 (4)  0.016 (2)  0.0029 (18)  0.0049 (18)  −0.001 (2) 
O2  0.022 (2)  0.049 (3)  0.021 (2)  0.0015 (18)  0.001 (2)  −0.004 (2) 
O3  0.0137 (18)  0.035 (3)  0.026 (2)  0.0004 (14)  −0.0029 (19)  −0.001 (2) 
O4  0.013 (2)  0.048 (3)  0.037 (3)  −0.0039 (16)  0.001 (2)  0.008 (3) 
O5  0.0121 (19)  0.057 (4)  0.022 (2)  0.0028 (18)  −0.0060 (18)  0.001 (2) 
O6  0.029 (3)  0.071 (5)  0.031 (3)  0.001 (3)  −0.002 (3)  0.001 (3) 
H1  0.035279  0.084949  0.037716  0.000837  −0.002722  0.001305 
H2  0.035279  0.084949  0.037716  0.000837  −0.002722  0.001305 
Si1—O1  1.628 (6)  Al1—O2  1.752 (10) 
Si1—O1^{i}  1.628 (6)  Al1—O3  1.740 (7) 
Si1—O2  1.601 (7)  Al1—O4  1.755 (8) 
Si1—O2^{i}  1.601 (7)  Al1—O5  1.750 (7) 
Si2—Al1^{ii}  3.110 (6)  Na1—Na1^{vii}  3.671 (11) 
Si2—Al1^{iii}  3.046 (5)  Na1—Na1^{viii}  3.671 (11) 
Si2—Na1^{iv}  3.064 (8)  Na1—O3^{ix}  2.517 (9) 
Si2—Na1^{iii}  3.589 (7)  Na1—O3^{x}  2.627 (10) 
Si2—O1  1.642 (9)  Na1—O4  2.353 (8) 
Si2—O3^{iii}  1.623 (6)  Na1—O5^{ix}  2.401 (10) 
Si2—O4^{iv}  1.615 (9)  Na1—O6  2.370 (12) 
Si2—O5^{ii}  1.607 (8)  Na1—O6^{vii}  2.398 (12) 
Al1—Na1  3.552 (6)  Na1—H2^{vii}  2.67 (4) 
Al1—Na1^{v}  3.098 (8)  O6—H1  0.96 (2) 
Al1—Na1^{vi}  3.867 (8)  O6—H2  0.96 (4) 
O1—Si1—O1^{i}  109.9 (3)  Si2^{xii}—Na1—O5^{ix}  21.24 (19) 
O1—Si1—O2  109.0 (3)  Si2^{xii}—Na1—O6  91.2 (3) 
O1—Si1—O2^{i}  108.5 (3)  Si2^{xii}—Na1—O6^{vii}  125.9 (3) 
O1^{i}—Si1—O2  108.5 (3)  Si2^{xii}—Na1—H2^{vii}  142.3 (10) 
O1^{i}—Si1—O2^{i}  109.0 (3)  Al1—Na1—Al1^{ix}  97.15 (19) 
O2—Si1—O2^{i}  111.9 (4)  Al1—Na1—Al1^{x}  105.34 (17) 
Al1^{ii}—Si2—Al1^{iii}  108.48 (17)  Al1—Na1—Na1^{vii}  112.9 (2) 
Al1^{ii}—Si2—Na1^{iv}  116.7 (3)  Al1—Na1—Na1^{viii}  112.3 (2) 
Al1^{ii}—Si2—Na1^{iii}  54.54 (14)  Al1—Na1—O3^{ix}  126.3 (3) 
Al1^{ii}—Si2—O1  107.6 (3)  Al1—Na1—O3^{x}  88.2 (2) 
Al1^{ii}—Si2—O3^{iii}  131.0 (3)  Al1—Na1—O4  25.6 (2) 
Al1^{ii}—Si2—O4^{iv}  92.5 (3)  Al1—Na1—O5^{ix}  65.44 (18) 
Al1^{ii}—Si2—O5^{ii}  23.2 (3)  Al1—Na1—O6  123.2 (3) 
Al1^{iii}—Si2—Na1^{iv}  78.53 (16)  Al1—Na1—O6^{vii}  92.6 (3) 
Al1^{iii}—Si2—Na1^{iii}  64.13 (13)  Al1—Na1—H2^{vii}  98.2 (9) 
Al1^{iii}—Si2—O1  109.5 (3)  Al1^{ix}—Na1—Al1^{x}  156.9 (2) 
Al1^{iii}—Si2—O3^{iii}  26.0 (2)  Al1^{ix}—Na1—Na1^{vii}  69.1 (2) 
Al1^{iii}—Si2—O4^{iv}  127.4 (3)  Al1^{ix}—Na1—Na1^{viii}  126.6 (2) 
Al1^{iii}—Si2—O5^{ii}  86.7 (3)  Al1^{ix}—Na1—O3^{ix}  34.15 (17) 
Na1^{iv}—Si2—Na1^{iii}  130.9 (2)  Al1^{ix}—Na1—O3^{x}  169.9 (3) 
Na1^{iv}—Si2—O1  129.6 (3)  Al1^{ix}—Na1—O4  121.3 (3) 
Na1^{iv}—Si2—O3^{iii}  59.0 (3)  Al1^{ix}—Na1—O5^{ix}  34.23 (18) 
Na1^{iv}—Si2—O4^{iv}  49.3 (3)  Al1^{ix}—Na1—O6  86.7 (3) 
Na1^{iv}—Si2—O5^{ii}  120.9 (4)  Al1^{ix}—Na1—O6^{vii}  104.7 (4) 
Na1^{iii}—Si2—O1  93.8 (3)  Al1^{ix}—Na1—H2^{vii}  123.5 (10) 
Na1^{iii}—Si2—O3^{iii}  90.0 (3)  Al1^{x}—Na1—Na1^{vii}  96.7 (2) 
Na1^{iii}—Si2—O4^{iv}  145.1 (4)  Al1^{x}—Na1—Na1^{viii}  48.45 (16) 
Na1^{iii}—Si2—O5^{ii}  32.8 (3)  Al1^{x}—Na1—O3^{ix}  123.3 (2) 
O1—Si2—O3^{iii}  107.4 (5)  Al1^{x}—Na1—O3^{x}  22.06 (16) 
O1—Si2—O4^{iv}  108.8 (5)  Al1^{x}—Na1—O4  81.7 (3) 
O1—Si2—O5^{ii}  109.4 (4)  Al1^{x}—Na1—O5^{ix}  168.2 (3) 
O3^{iii}—Si2—O4^{iv}  107.4 (4)  Al1^{x}—Na1—O6  85.4 (3) 
O3^{iii}—Si2—O5^{ii}  111.2 (4)  Al1^{x}—Na1—O6^{vii}  69.5 (3) 
O4^{iv}—Si2—O5^{ii}  112.6 (5)  Al1^{x}—Na1—H2^{vii}  48.6 (10) 
Si2^{xi}—Al1—Si2^{xii}  143.0 (2)  Na1^{vii}—Na1—Na1^{viii}  128.8 (2) 
Si2^{xi}—Al1—Na1  129.4 (2)  Na1^{vii}—Na1—O3^{ix}  45.7 (2) 
Si2^{xi}—Al1—Na1^{v}  70.63 (17)  Na1^{vii}—Na1—O3^{x}  116.7 (3) 
Si2^{xi}—Al1—Na1^{vi}  119.81 (15)  Na1^{vii}—Na1—O4  126.5 (3) 
Si2^{xi}—Al1—O2  105.7 (3)  Na1^{vii}—Na1—O5^{ix}  93.8 (3) 
Si2^{xi}—Al1—O3  124.9 (3)  Na1^{vii}—Na1—O6  121.1 (3) 
Si2^{xi}—Al1—O4  94.3 (3)  Na1^{vii}—Na1—O6^{vii}  39.4 (3) 
Si2^{xi}—Al1—O5  21.2 (3)  Na1^{vii}—Na1—H2^{vii}  54.8 (10) 
Si2^{xii}—Al1—Na1  65.37 (13)  Na1^{viii}—Na1—O3^{ix}  116.4 (3) 
Si2^{xii}—Al1—Na1^{v}  75.15 (16)  Na1^{viii}—Na1—O3^{x}  43.3 (2) 
Si2^{xii}—Al1—Na1^{vi}  50.94 (13)  Na1^{viii}—Na1—O4  89.2 (3) 
Si2^{xii}—Al1—O2  107.1 (3)  Na1^{viii}—Na1—O5^{ix}  126.5 (3) 
Si2^{xii}—Al1—O3  24.16 (18)  Na1^{viii}—Na1—O6  39.9 (3) 
Si2^{xii}—Al1—O4  90.3 (3)  Na1^{viii}—Na1—O6^{vii}  116.7 (3) 
Si2^{xii}—Al1—O5  125.3 (3)  Na1^{viii}—Na1—H2^{vii}  96.1 (10) 
Na1—Al1—Na1^{v}  128.7 (2)  O3^{ix}—Na1—O3^{x}  144.1 (3) 
Na1—Al1—Na1^{vi}  109.32 (17)  O3^{ix}—Na1—O4  151.9 (4) 
Na1—Al1—O2  92.6 (3)  O3^{ix}—Na1—O5^{ix}  68.2 (3) 
Na1—Al1—O3  89.4 (2)  O3^{ix}—Na1—O6  84.7 (3) 
Na1—Al1—O4  35.4 (3)  O3^{ix}—Na1—O6^{vii}  85.0 (4) 
Na1—Al1—O5  144.0 (4)  O3^{ix}—Na1—H2^{vii}  97.8 (10) 
Na1^{v}—Al1—Na1^{vi}  62.46 (19)  O3^{x}—Na1—O4  62.9 (3) 
Na1^{v}—Al1—O2  130.8 (3)  O3^{x}—Na1—O5^{ix}  146.2 (4) 
Na1^{v}—Al1—O3  54.3 (3)  O3^{x}—Na1—O6  83.2 (4) 
Na1^{v}—Al1—O4  119.3 (4)  O3^{x}—Na1—O6^{vii}  83.6 (3) 
Na1^{v}—Al1—O5  50.5 (3)  O3^{x}—Na1—H2^{vii}  63.8 (10) 
Na1^{vi}—Al1—O2  80.9 (3)  O4—Na1—O5^{ix}  87.8 (3) 
Na1^{vi}—Al1—O3  34.5 (3)  O4—Na1—O6  112.2 (4) 
Na1^{vi}—Al1—O4  140.7 (3)  O4—Na1—O6^{vii}  93.6 (3) 
Na1^{vi}—Al1—O5  100.2 (3)  O4—Na1—H2^{vii}  90.1 (10) 
O2—Al1—O3  110.0 (5)  O5^{ix}—Na1—O6  93.6 (4) 
O2—Al1—O4  109.9 (4)  O5^{ix}—Na1—O6^{vii}  116.8 (4) 
O2—Al1—O5  112.5 (4)  O5^{ix}—Na1—H2^{vii}  137.3 (10) 
O3—Al1—O4  110.6 (4)  O6—Na1—O6^{vii}  141.1 (4) 
O3—Al1—O5  104.5 (4)  O6—Na1—H2^{vii}  126.2 (10) 
O4—Al1—O5  109.2 (5)  O6^{vii}—Na1—H2^{vii}  20.9 (10) 
Si2^{xiii}—Na1—Si2^{xii}  98.63 (18)  Si1—O1—Si2  145.3 (4) 
Si2^{xiii}—Na1—Al1  56.23 (14)  Si1—O2—Al1  142.5 (5) 
Si2^{xiii}—Na1—Al1^{ix}  152.6 (2)  Si2^{xii}—O3—Al1  129.8 (4) 
Si2^{xiii}—Na1—Al1^{x}  50.53 (13)  Si2^{xii}—O3—Na1^{v}  128.3 (4) 
Si2^{xiii}—Na1—Na1^{vii}  124.2 (2)  Si2^{xii}—O3—Na1^{vi}  89.0 (3) 
Si2^{xiii}—Na1—Na1^{viii}  66.91 (19)  Al1—O3—Na1^{v}  91.5 (3) 
Si2^{xiii}—Na1—O3^{ix}  169.6 (3)  Al1—O3—Na1^{vi}  123.4 (4) 
Si2^{xiii}—Na1—O3^{x}  31.99 (15)  Na1^{v}—O3—Na1^{vi}  91.0 (3) 
Si2^{xiii}—Na1—O4  31.3 (2)  Si2^{xiii}—O4—Al1  138.0 (4) 
Si2^{xiii}—Na1—O5^{ix}  118.5 (3)  Si2^{xiii}—O4—Na1  99.4 (3) 
Si2^{xiii}—Na1—O6  102.1 (4)  Al1—O4—Na1  119.0 (5) 
Si2^{xiii}—Na1—O6^{vii}  84.8 (3)  Si2^{xi}—O5—Al1  135.7 (5) 
Si2^{xiii}—Na1—H2^{vii}  71.9 (10)  Si2^{xi}—O5—Na1^{v}  126.0 (4) 
Si2^{xii}—Na1—Al1  50.50 (11)  Al1—O5—Na1^{v}  95.3 (3) 
Si2^{xii}—Na1—Al1^{ix}  54.83 (14)  Na1—O6—Na1^{viii}  100.7 (4) 
Si2^{xii}—Na1—Al1^{x}  147.0 (2)  Na1—O6—H1  113 (3) 
Si2^{xii}—Na1—Na1^{vii}  112.8 (2)  Na1—O6—H2  127 (3) 
Si2^{xii}—Na1—Na1^{viii}  113.9 (2)  Na1^{viii}—O6—H1  114 (3) 
Si2^{xii}—Na1—O3^{ix}  89.0 (2)  Na1^{viii}—O6—H2  96 (3) 
Si2^{xii}—Na1—O3^{x}  124.9 (3)  H1—O6—H2  104 (4) 
Si2^{xii}—Na1—O4  69.2 (2)  Na1^{viii}—H2—O6  63 (2) 
Symmetry codes: (i) −x, −y, z; (ii) x, y, z−1; (iii) x+1/4, −y+1/4, z−3/4; (iv) −x, −y, z−1; (v) x+1/4, −y+1/4, z+1/4; (vi) −x−1/4, y+1/4, z−1/4; (vii) −x−1/2, −y, z−1/2; (viii) −x−1/2, −y, z+1/2; (ix) x−1/4, −y+1/4, z−1/4; (x) −x−1/4, y−1/4, z+1/4; (xi) x, y, z+1; (xii) x−1/4, −y+1/4, z+3/4; (xiii) −x, −y, z+1. 
D—H···A  D—H  H···A  D···A  D—H···A 
O6—H1···O1^{xiv}  0.96 (2)  2.17 (4)  3.009 (11)  146 (4) 
O6—H2···O2^{xii}  0.96 (4)  1.95 (4)  2.884 (12)  163 (4) 
Symmetry codes: (xii) x−1/4, −y+1/4, z+3/4; (xiv) x−1/2, y, z+1/2. 
Al_{2}H_{4}Na_{2}O_{12}Si_{3}  Z = 8 
M_{r} = 380.2  F(000) = 517.84 
Orthorhombic, Fdd2  D_{x} = 2.235 Mg m^{−}^{3} 
Hall symbol: F 2xuvw;2yuvw;2z  Electrons 200 KeV radiation, λ = 0.0251 Å 
a = 18.2872 (11) Å  Cell parameters from 5179 reflections 
b = 18.6660 (14) Å  θ = 0.1–1.2° 
c = 6.6222 (3) Å  T = 293 K 
V = 2260.5 (2) Å^{3}  Irregular shape 
TEM FEI Tecnai G2 20 diffractometer  R_{int} = 0.195 
Radiation source: Lab6 cathode  θ_{max} = 1.2°, θ_{min} = 0.1° 
continuous–rotation 3D ED scans  h = −29→29 
5179 measured reflections  k = −29→29 
1289 independent reflections  l = −10→10 
1008 reflections with I > 3σ(I) 
Refinement on F^{2}  All Hatom parameters refined 
R[F^{2} > 2σ(F^{2})] = 0.147  Weighting scheme based on measured s.u.'s w = 1/(σ^{2}(I) + 0.0004I^{2}) 
wR(F^{2}) = 0.366  (Δ/σ)_{max} = 0.017 
S = 1.78  Δρ_{max} = 0.28 e Å^{−}^{3} 
1289 reflections  Δρ_{min} = −0.24 e Å^{−}^{3} 
93 parameters  Extinction correction: SHELXL2017/1 (Sheldrick, 2015), Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
3 restraints  Extinction coefficient: 0.40 (9) 
13 constraints 
x  y  z  U_{iso}*/U_{eq}  
Si1  0  0  0  0.0234 (12)  
Si2  0.09700 (16)  0.03849 (19)  −0.3720 (9)  0.0228 (8)  
Al1  −0.03715 (18)  0.0943 (2)  0.3857 (10)  0.0235 (9)  
Na1  −0.2203 (3)  0.0309 (3)  0.3831 (12)  0.0355 (14)  
O1  0.0695 (3)  0.0217 (4)  −0.1408 (11)  0.0306 (15)  
O2  −0.0224 (3)  0.0676 (4)  0.1355 (13)  0.0306 (15)  
O3  −0.0697 (3)  0.1818 (3)  0.3921 (12)  0.0253 (13)  
O4  −0.0993 (3)  0.0358 (4)  0.5029 (14)  0.0328 (17)  
O5  0.0437 (3)  0.0968 (4)  0.5270 (12)  0.0303 (15)  
O6  −0.3065 (4)  0.0599 (5)  0.6376 (16)  0.044 (2)  
H1  −0.3559 (10)  0.059 (3)  0.590 (7)  0.0525  
H2  −0.305 (2)  0.099 (2)  0.730 (7)  0.0525 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
Si1  0.0149 (16)  0.038 (3)  0.0168 (17)  −0.0011 (14)  −0  −0 
Si2  0.0105 (12)  0.0412 (19)  0.0166 (12)  −0.0014 (9)  −0.0013 (10)  −0.0024 (14) 
Al1  0.0125 (12)  0.038 (2)  0.0205 (14)  0.0019 (10)  0.0004 (12)  0.0007 (14) 
Na1  0.0216 (19)  0.056 (3)  0.029 (2)  0.0015 (15)  −0.0015 (18)  −0.004 (2) 
O1  0.0155 (19)  0.060 (4)  0.016 (2)  0.0031 (18)  0.0049 (18)  −0.001 (2) 
O2  0.022 (2)  0.049 (3)  0.021 (2)  0.0013 (18)  0.001 (2)  −0.003 (2) 
O3  0.0139 (18)  0.035 (3)  0.027 (2)  0.0003 (14)  −0.0032 (19)  −0.001 (2) 
O4  0.013 (2)  0.047 (3)  0.038 (3)  −0.0042 (17)  0.001 (2)  0.008 (3) 
O5  0.0122 (19)  0.057 (4)  0.022 (2)  0.0029 (18)  −0.0058 (18)  0.001 (2) 
O6  0.029 (3)  0.071 (5)  0.031 (3)  0.000 (3)  −0.002 (3)  0.001 (3) 
H1  0.035211  0.084898  0.037356  0.000318  −0.00225  0.001636 
H2  0.035211  0.084898  0.037356  0.000318  −0.00225  0.001636 
Si1—O1  1.627 (6)  Al1—O2  1.751 (10) 
Si1—O1^{i}  1.627 (6)  Al1—O3  1.740 (7) 
Si1—O2  1.601 (7)  Al1—O4  1.757 (8) 
Si1—O2^{i}  1.601 (7)  Al1—O5  1.751 (7) 
Si2—Al1^{ii}  3.111 (6)  Na1—Na1^{vii}  3.671 (11) 
Si2—Al1^{iii}  3.046 (5)  Na1—Na1^{viii}  3.671 (11) 
Si2—Na1^{iv}  3.065 (8)  Na1—O3^{ix}  2.517 (9) 
Si2—Na1^{iii}  3.589 (7)  Na1—O3^{x}  2.626 (10) 
Si2—O1  1.642 (9)  Na1—O4  2.353 (8) 
Si2—O3^{iii}  1.623 (6)  Na1—O5^{ix}  2.401 (10) 
Si2—O4^{iv}  1.616 (9)  Na1—O6  2.370 (12) 
Si2—O5^{ii}  1.607 (8)  Na1—O6^{vii}  2.399 (12) 
Al1—Na1  3.553 (6)  Na1—H2^{vii}  2.67 (4) 
Al1—Na1^{v}  3.099 (8)  O6—H1  0.96 (2) 
Al1—Na1^{vi}  3.867 (8)  O6—H2  0.96 (4) 
O1—Si1—O1^{i}  110.0 (3)  Si2^{xii}—Na1—O5^{ix}  21.26 (19) 
O1—Si1—O2  109.0 (3)  Si2^{xii}—Na1—O6  91.2 (3) 
O1—Si1—O2^{i}  108.5 (3)  Si2^{xii}—Na1—O6^{vii}  125.9 (3) 
O1^{i}—Si1—O2  108.5 (3)  Si2^{xii}—Na1—H2^{vii}  142.3 (10) 
O1^{i}—Si1—O2^{i}  109.0 (3)  Al1—Na1—Al1^{ix}  97.13 (19) 
O2—Si1—O2^{i}  111.8 (4)  Al1—Na1—Al1^{x}  105.34 (17) 
Al1^{ii}—Si2—Al1^{iii}  108.46 (17)  Al1—Na1—Na1^{vii}  112.8 (2) 
Al1^{ii}—Si2—Na1^{iv}  116.7 (3)  Al1—Na1—Na1^{viii}  112.3 (2) 
Al1^{ii}—Si2—Na1^{iii}  54.54 (15)  Al1—Na1—O3^{ix}  126.3 (3) 
Al1^{ii}—Si2—O1  107.6 (3)  Al1—Na1—O3^{x}  88.2 (2) 
Al1^{ii}—Si2—O3^{iii}  130.9 (3)  Al1—Na1—O4  25.6 (2) 
Al1^{ii}—Si2—O4^{iv}  92.5 (3)  Al1—Na1—O5^{ix}  65.42 (18) 
Al1^{ii}—Si2—O5^{ii}  23.1 (3)  Al1—Na1—O6  123.2 (3) 
Al1^{iii}—Si2—Na1^{iv}  78.51 (16)  Al1—Na1—O6^{vii}  92.6 (3) 
Al1^{iii}—Si2—Na1^{iii}  64.14 (13)  Al1—Na1—H2^{vii}  98.2 (10) 
Al1^{iii}—Si2—O1  109.6 (3)  Al1^{ix}—Na1—Al1^{x}  156.9 (2) 
Al1^{iii}—Si2—O3^{iii}  26.0 (2)  Al1^{ix}—Na1—Na1^{vii}  69.1 (2) 
Al1^{iii}—Si2—O4^{iv}  127.4 (3)  Al1^{ix}—Na1—Na1^{viii}  126.6 (2) 
Al1^{iii}—Si2—O5^{ii}  86.7 (3)  Al1^{ix}—Na1—O3^{ix}  34.15 (17) 
Na1^{iv}—Si2—Na1^{iii}  130.9 (2)  Al1^{ix}—Na1—O3^{x}  169.9 (3) 
Na1^{iv}—Si2—O1  129.7 (3)  Al1^{ix}—Na1—O4  121.3 (3) 
Na1^{iv}—Si2—O3^{iii}  58.9 (3)  Al1^{ix}—Na1—O5^{ix}  34.23 (18) 
Na1^{iv}—Si2—O4^{iv}  49.2 (3)  Al1^{ix}—Na1—O6  86.7 (3) 
Na1^{iv}—Si2—O5^{ii}  120.8 (4)  Al1^{ix}—Na1—O6^{vii}  104.7 (4) 
Na1^{iii}—Si2—O1  93.8 (3)  Al1^{ix}—Na1—H2^{vii}  123.4 (10) 
Na1^{iii}—Si2—O3^{iii}  90.1 (3)  Al1^{x}—Na1—Na1^{vii}  96.7 (2) 
Na1^{iii}—Si2—O4^{iv}  145.1 (4)  Al1^{x}—Na1—Na1^{viii}  48.47 (16) 
Na1^{iii}—Si2—O5^{ii}  32.8 (3)  Al1^{x}—Na1—O3^{ix}  123.3 (2) 
O1—Si2—O3^{iii}  107.4 (5)  Al1^{x}—Na1—O3^{x}  22.08 (16) 
O1—Si2—O4^{iv}  108.8 (5)  Al1^{x}—Na1—O4  81.7 (3) 
O1—Si2—O5^{ii}  109.4 (4)  Al1^{x}—Na1—O5^{ix}  168.2 (3) 
O3^{iii}—Si2—O4^{iv}  107.3 (4)  Al1^{x}—Na1—O6  85.5 (3) 
O3^{iii}—Si2—O5^{ii}  111.2 (4)  Al1^{x}—Na1—O6^{vii}  69.5 (3) 
O4^{iv}—Si2—O5^{ii}  112.6 (5)  Al1^{x}—Na1—H2^{vii}  48.6 (10) 
Si2^{xi}—Al1—Si2^{xii}  142.9 (2)  Na1^{vii}—Na1—Na1^{viii}  128.9 (2) 
Si2^{xi}—Al1—Na1  129.4 (2)  Na1^{vii}—Na1—O3^{ix}  45.7 (2) 
Si2^{xi}—Al1—Na1^{v}  70.61 (17)  Na1^{vii}—Na1—O3^{x}  116.7 (3) 
Si2^{xi}—Al1—Na1^{vi}  119.79 (15)  Na1^{vii}—Na1—O4  126.5 (3) 
Si2^{xi}—Al1—O2  105.7 (3)  Na1^{vii}—Na1—O5^{ix}  93.8 (3) 
Si2^{xi}—Al1—O3  124.9 (3)  Na1^{vii}—Na1—O6  121.1 (3) 
Si2^{xi}—Al1—O4  94.3 (3)  Na1^{vii}—Na1—O6^{vii}  39.4 (3) 
Si2^{xi}—Al1—O5  21.1 (3)  Na1^{vii}—Na1—H2^{vii}  54.8 (10) 
Si2^{xii}—Al1—Na1  65.37 (13)  Na1^{viii}—Na1—O3^{ix}  116.4 (3) 
Si2^{xii}—Al1—Na1^{v}  75.12 (16)  Na1^{viii}—Na1—O3^{x}  43.3 (2) 
Si2^{xii}—Al1—Na1^{vi}  50.96 (13)  Na1^{viii}—Na1—O4  89.2 (3) 
Si2^{xii}—Al1—O2  107.2 (3)  Na1^{viii}—Na1—O5^{ix}  126.5 (3) 
Si2^{xii}—Al1—O3  24.15 (18)  Na1^{viii}—Na1—O6  40.0 (3) 
Si2^{xii}—Al1—O4  90.2 (3)  Na1^{viii}—Na1—O6^{vii}  116.7 (3) 
Si2^{xii}—Al1—O5  125.2 (3)  Na1^{viii}—Na1—H2^{vii}  96.1 (10) 
Na1—Al1—Na1^{v}  128.7 (2)  O3^{ix}—Na1—O3^{x}  144.1 (3) 
Na1—Al1—Na1^{vi}  109.34 (17)  O3^{ix}—Na1—O4  151.9 (4) 
Na1—Al1—O2  92.6 (3)  O3^{ix}—Na1—O5^{ix}  68.2 (3) 
Na1—Al1—O3  89.4 (2)  O3^{ix}—Na1—O6  84.7 (3) 
Na1—Al1—O4  35.4 (3)  O3^{ix}—Na1—O6^{vii}  85.0 (4) 
Na1—Al1—O5  143.9 (4)  O3^{ix}—Na1—H2^{vii}  97.8 (10) 
Na1^{v}—Al1—Na1^{vi}  62.45 (19)  O3^{x}—Na1—O4  62.9 (3) 
Na1^{v}—Al1—O2  130.8 (3)  O3^{x}—Na1—O5^{ix}  146.1 (4) 
Na1^{v}—Al1—O3  54.3 (3)  O3^{x}—Na1—O6  83.2 (4) 
Na1^{v}—Al1—O4  119.3 (4)  O3^{x}—Na1—O6^{vii}  83.6 (3) 
Na1^{v}—Al1—O5  50.5 (3)  O3^{x}—Na1—H2^{vii}  63.8 (10) 
Na1^{vi}—Al1—O2  80.9 (3)  O4—Na1—O5^{ix}  87.8 (3) 
Na1^{vi}—Al1—O3  34.6 (3)  O4—Na1—O6  112.2 (4) 
Na1^{vi}—Al1—O4  140.7 (3)  O4—Na1—O6^{vii}  93.6 (3) 
Na1^{vi}—Al1—O5  100.2 (3)  O4—Na1—H2^{vii}  90.1 (10) 
O2—Al1—O3  110.1 (5)  O5^{ix}—Na1—O6  93.6 (4) 
O2—Al1—O4  109.9 (4)  O5^{ix}—Na1—O6^{vii}  116.8 (4) 
O2—Al1—O5  112.5 (4)  O5^{ix}—Na1—H2^{vii}  137.3 (10) 
O3—Al1—O4  110.6 (4)  O6—Na1—O6^{vii}  141.2 (4) 
O3—Al1—O5  104.5 (4)  O6—Na1—H2^{vii}  126.3 (10) 
O4—Al1—O5  109.1 (5)  O6^{vii}—Na1—H2^{vii}  20.9 (10) 
Si2^{xiii}—Na1—Si2^{xii}  98.60 (18)  Si1—O1—Si2  145.2 (4) 
Si2^{xiii}—Na1—Al1  56.25 (14)  Si1—O2—Al1  142.6 (5) 
Si2^{xiii}—Na1—Al1^{ix}  152.6 (2)  Si2^{xii}—O3—Al1  129.8 (4) 
Si2^{xiii}—Na1—Al1^{x}  50.53 (13)  Si2^{xii}—O3—Na1^{v}  128.3 (4) 
Si2^{xiii}—Na1—Na1^{vii}  124.2 (2)  Si2^{xii}—O3—Na1^{vi}  89.1 (3) 
Si2^{xiii}—Na1—Na1^{viii}  66.9 (2)  Al1—O3—Na1^{v}  91.6 (3) 
Si2^{xiii}—Na1—O3^{ix}  169.6 (3)  Al1—O3—Na1^{vi}  123.4 (4) 
Si2^{xiii}—Na1—O3^{x}  31.96 (15)  Na1^{v}—O3—Na1^{vi}  91.0 (3) 
Si2^{xiii}—Na1—O4  31.3 (2)  Si2^{xiii}—O4—Al1  138.0 (4) 
Si2^{xiii}—Na1—O5^{ix}  118.5 (3)  Si2^{xiii}—O4—Na1  99.4 (3) 
Si2^{xiii}—Na1—O6  102.1 (4)  Al1—O4—Na1  118.9 (5) 
Si2^{xiii}—Na1—O6^{vii}  84.8 (3)  Si2^{xi}—O5—Al1  135.7 (5) 
Si2^{xiii}—Na1—H2^{vii}  71.9 (10)  Si2^{xi}—O5—Na1^{v}  125.9 (4) 
Si2^{xii}—Na1—Al1  50.49 (11)  Al1—O5—Na1^{v}  95.3 (3) 
Si2^{xii}—Na1—Al1^{ix}  54.85 (14)  Na1—O6—Na1^{viii}  100.6 (4) 
Si2^{xii}—Na1—Al1^{x}  146.9 (2)  Na1—O6—H1  113 (3) 
Si2^{xii}—Na1—Na1^{vii}  112.8 (2)  Na1—O6—H2  127 (3) 
Si2^{xii}—Na1—Na1^{viii}  113.9 (2)  Na1^{viii}—O6—H1  114 (3) 
Si2^{xii}—Na1—O3^{ix}  89.0 (2)  Na1^{viii}—O6—H2  96 (3) 
Si2^{xii}—Na1—O3^{x}  124.9 (3)  H1—O6—H2  104 (4) 
Si2^{xii}—Na1—O4  69.2 (2)  Na1^{viii}—H2—O6  63 (2) 
Symmetry codes: (i) −x, −y, z; (ii) x, y, z−1; (iii) x+1/4, −y+1/4, z−3/4; (iv) −x, −y, z−1; (v) x+1/4, −y+1/4, z+1/4; (vi) −x−1/4, y+1/4, z−1/4; (vii) −x−1/2, −y, z−1/2; (viii) −x−1/2, −y, z+1/2; (ix) x−1/4, −y+1/4, z−1/4; (x) −x−1/4, y−1/4, z+1/4; (xi) x, y, z+1; (xii) x−1/4, −y+1/4, z+3/4; (xiii) −x, −y, z+1. 
D—H···A  D—H  H···A  D···A  D—H···A 
O6—H1···O1^{xiv}  0.96 (2)  2.16 (4)  3.009 (11)  146 (4) 
O6—H2···O2^{xii}  0.96 (4)  1.95 (4)  2.884 (12)  163 (4) 
Symmetry codes: (xii) x−1/4, −y+1/4, z+3/4; (xiv) x−1/2, y, z+1/2. 
Funding information
This research was supported by the Czech Science Foundation, project No. 2105926X. AS and HC acknowledge funding by the H2020 ITN project NanED, grant agreement No. 956099. CzechNanoLab project LM2023051 funded by MEYS CR is acknowledged for financial support of the measurements at LNSM Research Infrastructure.
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