research papers
Validation of experimental chargedensity
strategies: when do we overfit?^{a}Institut für Anorganische Chemie, Universität Göttingen, Tammannstraße 4, Göttingen 37077, Germany
^{*}Correspondence email: rherbst@shelx.uniac.gwdg.de
A crossvalidation method is supplied to judge between various strategies in multipole k different refinements. These distributions can be used for further error diagnostics, e.g. to detect erroneously defined parameters or incorrectly determined reflections. Visualization tools show the variation in the parameters. These different refinements also provide rough estimates for the standard deviation of topological parameters.
procedures. Its application enables straightforward detection of whether the of additional parameters leads to an improvement in the model or an overfitting of the given data. For all tested data sets it was possible to prove that the multipole parameters of atoms in comparable chemical environments should be constrained to be identical. In an automated approach, this method additionally delivers parameter distributions ofKeywords: charge density; crossvalidation; error detection; R_{free}; refinement strategies.
1. Introduction
Although Philip Coppens (2005) wrote that `Charge densities [have] come of age', experimental chargedensity studies still depend heavily on the amount and quality of the measured data. Additionally, there is no published investigation of whether or not the of all possible parameters might lead to overfitting of the data, because the old benchmark of the `independent atom model' (IAM), which should not run below the 10:1 datatoparameter ratio to keep the problem sufficiently overdetermined, is hardly violated even with a demanding chargedensity investigation. In a routine IAM only nine parameters, three positional and six anisotropic displacement parameters, are necessary to model the structure, while in a multipole (MM) via the Hansen–Coppens formalism (Hansen & Coppens, 1978) many more parameters are needed to describe the asphericity of the electron density distribution
Here, the density is divided into a core density, a spherical valence density and an aspherical valence density. The parameters κ and κ′ are used to describe the expansion and contraction of the density. This approach requires up to 27 (= 25 + 2) additional parameters per atom for multipole populations up to the hexadecapole level, and the κ and κ′ parameters. Some of the parameters are highly correlated, like the monopole population and the κ parameter of one particular atom. The valence density is mainly described by loworder data, but to derive proper thermal displacement parameters highresolution lowtemperature data are needed. Due to the development of more intense Xray sources, more sensitive area detectors and improved cryogenic crystal cooling techniques, the data quality has improved significantly so that even an anharmonic description of the thermal motion is increasingly reported in the literature (see e.g. Dos Santos et al., 2016; Poulain et al., 2014; Domagała et al., 2014), requiring even more parameters per atom. In experimental chargedensity investigations, highresolution data up to at least 1.0 Å^{−1} in sin(θ)/λ are necessary. Therefore, the datatoparameter ratio is usually higher than for a routine IAM This ratio alone might suggest that overfitting is not of any concern in experimental chargedensity determinations. However, this is not necessarily true because not all reflections contribute to all parameters equally, e.g. only the loworder reflections determine the valence density. Consequently, the increasing number of parameters might result in a significant drop in the R value without improving the model. A statistical method to detect that phenomenon is crossvalidation. In this modelvalidation technique, a sample population of data is divided into complementary subsets. One subset (the `training' or `work' set) is used to derive a model, while the other is used to validate the model (the `validation' or `test' set). In macromolecular crystallography this is known as the R_{free} concept (Brünger, 1992, 1997). Here, the measured data are divided into a work set (often 95–90% of all data) and a test set (the remaining 5–10%). The model is refined against the work set, while the test set is never used for but only to calculate an R value, the R_{free} value. Adding parameters will lead to a decrease in R_{work}, but only sensible added parameters will also decrease R_{free}. An increasing R_{free} is an unerring sign of overfitting. After determination of all sensible parameters, a final can then be performed against all data.
In chargedensity investigations, the following points need to be addressed:
(i) To adjudicate on overfitting, just the differences in R_{free} and R_{work} after introducing more parameters are monitored. Hence, we are not interested in their absolute values, which is different to the approach of protein crystallographers.
(ii) Determination of R_{work} and R_{free} in different resolution shells can be helpful because different regions of are of varying importance for different kinds of parameter.
(iii) The number of reflections in the validation set can be crucial. If the number is too small, the standard deviation of R_{free} is too large. The standard deviation of the free R value is given approximately by R_{free}/(2n)^{1/2} (Tickle et al., 2000), where n is the number of reflections in the test set. As the R values, and especially the differences in the R values, are very small, this standard deviation is normally too high to provide a conclusive answer from a single R_{free} value. If n is too large, the completeness of the training set is too small, leading to biased models. In statistics, this is solved by kfold crossvalidation, which means that the sample is divided into k subsets. One subset is used as a test set, while the other k − 1 sets give the model. This process is repeated k times with a different subset as the test set. Hence, all data are used for both model deriving and validation. For a chargedensity analysis this means that e.g. 20 test sets are produced. Every reflection is considered once in a test set and otherwise in the work set. This method was previously employed to validate the weighting of restraints (Paul et al., 2011; Zarychta et al., 2011) but should also be valid to judge e.g. constraints, as the program XD (Volkov et al., 2006) does not offer the opportunity to introduce restraints. A final is then of course employed against all available data. Out of the k different refinements the mean values 〈ΔR_{free}〉 can be calculated. Instead of checking 〈ΔR_{free}〉, a new value R_{cross} is defined that takes into account all test sets of all k refinements. Here, all differences between F_{o} and F_{c} for all reflections as validation reflections are used, therefore it is the R_{free} for all reflections as validation
A similar procedure has recently been described for macromolecules (Luebben & Gruene, 2015).
(iv) Normally the test set is chosen randomly, but caution is to be advised in noncentrosymmetric space groups or if pseudosymmetry is present, as the Friedel pairs cannot be considered to be independent observations. The Friedel pairs or pseudosymmetrically related reflections must be either both in the training set or both in the validation set.
(v) The validation set must be unbiased. That means it must never be used for the
unless the parameters are `shaken' before the crossvalidation starts.For the k different models, the distribution of each refined parameter v can be checked and compared with the value v_{total} including its s.u., s_{total}, derived from a against the complete data set. Model bias by omission of data can then be easily identified by outliers, e.g. values v_{i} that deviate by more than three times s_{total} from v_{total}. If all k refinements are independent, one should find a normal distribution with a mean value v_{mean} that is identical to v_{total}, and a standard deviation s_{mean} that equals s_{total} divided by a correction factor that can be derived from Cochran's theorem (Cochran & Wishart, 1934), e.g. 0.973 for ten test sets, 0.987 for 20 test sets and 0.995 for 50 test sets. However, as each uses (k − 1)/k × n_{d} reflections of the total n_{d} data, the refinements are not independent and therefore the expected standard deviation s_{mean} is smaller than s_{total}. As a converse argument, s_{mean} > s_{total} indicates problems in the refinement.
Subsequent to a ) parameters like the density ρ, Laplacian ∇^{2}ρ and ellipticity ∊ at the bond critical points should also be checked. Following the same arguments as above, we can estimate lower limits for the standard uncertainties of these sensitive values that are otherwise either entirely unavailable or include severe limitations (see the software manual for XD).
with no clear indication of overfitting, the distribution of topological QTAIM (quantum theory of atoms in molecules; Bader, 19902. Method
A Python script was developed that runs most of the required steps automatically. As input, it needs an IAM model including hydrogenatom positions, the XD master files (complete strategy), a parameter file and the data file. A stepwise addition of parameters, following the suggestions made in the XD manual, is highly recommended. Apart from convergence issues, a smaller step (e.g. smaller groups of parameters) supports the successful recognition of an overparameterization, along with the possibility of actually finding parameters that are likely to contribute to the overfitting of the data (see supporting information).
In this automatic process, the merged data set is first divided randomly into k (normally 20) different training and validation sets.
(i) For each training set as well as for the total data set the following steps are performed.
(a) In SHELXL (Sheldrick, 2008, 2015):
(1) Random shifts are applied to all coordinates and U_{ij} values;
(2) A highorder
of the heavyatom positional and anisotropic displacement parameters is performed to reduce bias;(3) A loworder
with fixed heavy atoms follows;(4) The residual density peaks are automatically assigned to hydrogen atom positions.
(b) In XD (Volkov et al., 2006) the full MM strategy is performed. In the first step the Hatom distances are adjusted to the neutron diffraction values (Allen & Bruno, 2010).
(c) For every step, a zerocycle calculation against the free sets (R_{free}) is performed.
(ii) R_{cross} is calculated by combining all xd.fco files of all validation sets for all steps.
(iii) Differences in 〈R_{work}〉 and R_{cross} are calculated for the individual steps and represented graphically.
(iv) In a second process, the distributions of all refined parameters of the k refinements with mean values v_{mean} and standard deviation s_{mean} are compared with the values of the against all data, v_{total}, and the estimated s_{total}, calculated by XD. Individual steps are selected for this comparison.
(a) To check for normal distribution, the Shapiro–Wilk test (Shapiro & Wilk, 1965) is performed for every parameter and the W and p values are given. (In this test two values, W and p, are calculated. W can be interpreted as a so has a value between 0 and 1. If the value is larger than a defined W_{crit}, the hypothesis of a normal distribution is accepted. p describes the probability of this particular sample distribution under the assumption of a normal distribution.)
(b) A complete list of all refined parameters is given, with v_{mean}, s_{mean}, v_{total}, s_{total}, W and p.
(c) Several tables for the diagnostics of outliers are given:
(1) A list of all parameters v_{i} with v_{total} − v_{i} > 3s_{total};
(2) A list of all parameters from the Shapiro–Wilk tests with a W value smaller than 0.905 or a p value smaller than 0.05, which means that the hypothesis of a normal distribution is refused with a significance level of 0.05;
(3) A list of all parameters with v_{total} − v_{mean}/s_{total} > 0.5;
(4) A list of all parameters with s_{mean} > s_{total};
(5) A summary of the number of outlier parameters per test set.
(d) For every parameter, a plot can be produced showing the against all data in grey and the distribution of the k refinements in red (see Fig. 4).
(e) To visualize the variation in electron density of the k refinements, an error cube is mapped on a density cube. A colourcoded overlay (e.g. transparent to red) of such an error cube on a density cube calculated from the full model will highlight regions of higher uncertainties (see Fig. 6). [A density cube is calculated for all k refinements and for the complete model using the XDPROP module. The standard deviation of every grid point is calculated considering all k density cubes. A new cube containing only the deviation of each respective grid point is written. This cube is plotted as a colourcoded overlay (e.g. as a gradient from transparent to red) on specified isosurface levels (1.0, 1.5, 2.0, 2.5) of the cube derived from the complete set of data. H atoms are automatically excluded from the calculation of the density cube because of their influence on the density combined with their unreliably determined positions that would add only a little information and clearly distract from the important parts.]
(v) Additionally, a routine can be started that runs XDPROP to search for bond critical points for all test sets at individually selectable steps of the whole strategy.
(a) Again, the distribution of the k refinements is compared with the against all data. From this distribution lower limits for standard deviations can be estimated.
(b) The Shapiro–Wilk values W and p are calculated.
This procedure will now be explicitly described for benchmark structure 1. Subsequently, benchmark structure 2 will be discussed much more briefly. Finally, some features of three additional structures will be presented to illustrate how this method can help to detect errors in the strategy or in the data. These features emphasize, among others, the need for chemical constraints to limit pole populations of chemically equivalent atoms. The structures themselves and their topological analyses are not within the scope of the current paper and will be discussed elsewhere.
3. Experimental
3.1. Benchmark structure 1
Data for 1 (Schwendemann et al., 2011; Fig. 1) were collected on a Bruker D8 threecircle goniometer equipped with a Bruker TXS30 Mo rotating anode with INCOATEC Helios mirror optics and an APEXII detector at 100 K. The compound crystallizes in with one molecule in the asymmetric unit.
The local coordinate systems were defined in such a way that the highest possible symmetry could be applied. This led to cylindrical symmetry for the H and F atoms and mirror symmetry for the ethyl and phenyl C atoms. For the paraC atoms even mm2 symmetry was adopted (for details see the supporting information). We constrained the pole population of chemically equivalent atoms to be identical (chemical constraints; for details see the supporting information). The two main questions we posed were:
(i) Can the
constraints be released without overfitting and would this add information to the model?(ii) Can the chemical constraints be released without overfitting and would this cause differences in the parameters concerning the constrained atoms?
3.1.1. Calculation of R_{cross}
The Friedel pairs were not merged because the structure crystallizes in a noncentrosymmetric
For all validation and training sets, it was ensured that both Friedel mates were in the same set.〈ΔR_{work}〉 and ΔR_{cross} were calculated for all data and for reflections on either side of sin(θ)/λ = 0.5 Å^{−1} to get a feeling for the influence of low and highorder reflections. Fig. 2 shows the results.
The first step in XD is refining multipole populations. Both 〈R_{work}〉 and R_{cross} drop significantly. For both residual values, the improvement is, as expected, larger from the loworder reflections compared with the highorder ones, because the valence density is mainly described by loworder reflections. The of the κ parameters has only a marginal effect on the R values but seems to improve the model slightly. Adding the monopole populations shows the expected effect: an improvement mainly from the loworder reflections. In addition, the following adjustments of displacement and positional parameters again do not indicate any overfitting. Here, a clear difference between low and highorder reflections is not expected. The adjustment of the Hatom positional parameters in a loworder followed by of all other parameters against all data is a major improvement and is, as expected, mainly due to the loworder reflections. The of κ′ shows only a marginal effect on the R values.
The next two steps concern the R values indicates neither a real model improvement nor clear overfitting. Although the changes are subtle, it seems that the highorder reflections unexpectedly contribute the most. Refining without any symmetry constraints, however, increases R_{cross} slightly, indicating overfitting of the data, although the total datatoparameter ratio of 27.0 still seems to be at the safe side, while the ratio of loworder data to the sum of monopole, multipole and κ parameter is only 5.1. Overfitting is even more evident when the chemical constraints for equivalent atoms are also abandoned. Even here, the datatoparameter ratio is still 16.7, while the ratio of loworder data to the sum of monopole, multipole and κ parameter is now only 2.5. Anyway, the residual density maps seem to be improved, because some peaks close to F atoms vanish. Although releasing constraints on the pole populations is overfitting, nevertheless the residual density still needs improvement. Hence, an anharmonic description of the thermal motion of these atoms was tested as an alternative, because we observe the typical positive and negative shashliklike density distribution (HerbstIrmer et al., 2013). Instead of releasing constraints, a with thirdorder Gram–Charlier coefficients for four F atoms was performed in two steps (see Fig. 3). First, the three fluorine atoms F33, F34 and F35 of one C_{6}F_{5} substituent and, in a second step, the paraF atom F24 of the second phenyl ring were anharmonically refined. Neither step shows any sign of overfitting and, as expected, the highorder reflections contribute the most. In the paper by HerbstIrmer et al. (2013) we have already investigated preliminary R_{free} tests to validate the of Gram–Charlier coefficients but came to the conclusion that the results were not clear. Now, the kfold crossvalidation and the differences in R_{cross} instead of 〈R_{free}〉 are much more decisive.
constraints. First, the of the F atoms is lowered from cylindrical to mirror plane symmetry. The small effect on theIt is important to note that several criteria must be fulfilled for a physically reasonable et al., 2013):
of anharmonic motion (HerbstIrmer(i) The residual density after harmonic supporting information).
shows a positive and negative shashliklike density distribution close to the atomic positions that vanishes after anharmonic (see the(ii) For each anharmonically refined atom, at least one Gram–Charlier coefficient is larger than three times its s.u. (see the supporting information).
(iii) Kuhs' rule (Kuhs, 1992) should be fulfilled (see the supporting information), at least for light elements like carbon and fluorine. [Kuhs introduced a rule for estimating the minimum data resolution for meaningful of anharmonic thermal parameters (Gram–Charlier coefficients) for each anisotropic atom: Q_{n} = 2n^{1/2}(2π)^{−1/2}(2ln2)^{1/2}〈u^{2}〉^{−1/2}.]
(iv) The probability density function (pdf) should be reasonable. Unfortunately, the graphical representations presented by HerbstIrmer et al. (2013) were obtained with a version of the program MoleCoolQt (Hübschle & Dittrich, 2011) that had a bug, producing wrong representations of the pdfs. Except for very strong anharmonic behaviour, normally no deviation from the harmonic ellipsoids is visible. However, the amount of negative density should be checked. For the two atoms F33 and F35 it is very small (lowest pdf values −0.87 and −0.34, respectively, and total integrated negative probability 0.000%), while for atoms F34 and F24 the lowest pdf values are −52.24 and −105.38, respectively, and the total integrated negative probabilities are 0.026 and 0.046%, respectively. These two atoms are chemically equivalent and therefore their monopole and multipole populations were constrained to be the same. Additionally, there is a high correlation between the Gram–Charlier coefficient C_{222} of atom F24 and the bonddirected dipole population of 90%, indicating that this anharmonic is not reasonable. Therefore only atom F34 should be refined anharmonically, while atom F24 stays harmonic. This improves the pdf for F34 considerably (lowest pdf value −1.06 and total integrated negative probability 0.000%). Now the highest correlation of 60–70% for the Gram–Charlier coefficent is to the positional parameters x, y and z, as described previously (HerbstIrmer et al., 2013).
This example emphasizes that a small drop in R_{cross} is a necessary, but by no means a sufficient, condition for a physically reasonable model. After the anharmonic of these three F atoms, we checked again the effect of lowering (see the supporting information). A reduction of cylindrical to mirror plane symmetry for the F atoms still does not indicate overfitting and has no significant effect on 〈R_{work}〉, but there is a slightly greater effect from the highorder reflection. As the influence on the residual density is also marginal [a drop in e_{gross} (Meindl & Henn, 2008) from 39 to 38.8 e Å^{−3}], we decided that the final strategy should maintain the abovementioned should keep all possible chemical constraints and should contain the anharmonic of the three F atoms.
3.1.2. Distribution of the refined parameters
To prevent model bias due to omission of reflections, we checked the distribution of parameters derived by the 20 different refinements. Fig. 4 shows two examples, in part (a) a parameter with all values within v_{total} ± s_{total} and in part (b) a parameter with one outlier.
For only nine out of 618 parameters of the final supporting information). Therefore, model bias due to omission of data can be excluded. Nine of the entire set of 14 outliers are octupole or hexadecapole populations of atoms C1 and C2. These atoms are refined without any or chemical constraints. Therefore, we increased the adopted in a new strategy: we now adopt m symmetry for atoms C1, N1 and B1, and mm2 symmetry for all phenyl C atoms. Additionally, we started refining the multipole population only up to the octupole level and added hexadecapole populations in a later step.
did we find one to three such outliers. The entire set of 14 deviations do not belong to one particular training set (for details see theFig. 5 shows the ΔR values for this stepwise The hexadecapole populations are first refined for all atoms besides C1, C2, B1 and N1, and then for all atoms. Then the three F atoms are refined anharmonically. In the next two steps no symmetry constraints are applied to atoms C1, B1 and N1, and afterwards the phenyl atoms are relaxed from mm2 to m symmetry. None of these steps seems to overfit. In the next step, the of the F atoms is changed from cylindrical to mirror plane symmetry. Again, no clear overfit is visible, but as before the highorder reflections seem to contribute the most. Releasing the and chemical constraints in the last two steps clearly overfits. Therefore, we decided to stop the strategy after step 17 with the symmetry reduction of the phenyl atoms to m symmetry. For this last nonoverfitting step there are only two parameters with v_{total} − v_{i} > 3s_{total} with a maximum value of 3.3s_{total}, and only seven parameters with s_{total} < s_{mean}. The largest (s_{mean} − s_{total})/s_{total} is 0.34. From the parameters describing the valence density (monopole and multipole populations and κ values), the hypothesis of a normal distribution is confirmed with a significance of 0.05 for 235 of the 255 parameters.
The idea presented in the following is based on the assumption that overfitted parameters are imprecisely determined and therefore lead to higher variations in the electron density described by them. A density cube at a relevant isosurface level will not be able to show that variation, as the model parameters do not directly reflect this uncertainty. A computational detour involving a set of density cubes calculated for all work sets allows calculation of the standard deviation of each density grid point (see §2). A colourcoded overlay (e.g. transparent to red) of such an error cube on a density cube (calculated from the full model) is able to highlight regions of higher uncertainties (Fig. 6). This error cube is related to the σ(ρ) cube, the calculation of which is implemented in XD, although it shows additional features not covered hitherto. As the Hatom positions are by far the least precisely determined parameters, their density will probably show severe features in the corresponding error cube.
Fig. 6 compares the variation in the electron density of the k refinements in an error cube mapped on a density cube (see §2) for the last reasonable step 17 (Fig. 6a), with step 20 (Fig. 6b) refining all possible multipoles. For step 17, the atoms with the highest variations are those that are refined with no constraints and no chemical constraints. Astonishingly, the of atom B1 seems to be very stable. In step 20 all atoms show relatively high variation.
3.1.3. Distribution of properties at bond critical points
With this ρ and ∇^{2}ρ in XD has some severe limitations, as mentioned in the manual. For the ellipticity ∊ no errors are provided. Nevertheless, an estimation of these errors would be useful. The distribution of k refinements can be used and, as previously described, the standard deviation derived from the distribution can be considered as a lower limit. The true error could be higher, because the k refinements are not independent. Table 1 shows a list of the properties at the bond critical points of the B—C and B—N bonds, comparing the final with the first without any or chemical constraints.
strategy, the distribution of properties at bond critical points can now be evaluated. The calculation of errors on

The following conclusions can be drawn:
(i) For all properties, the differences between the value derived from the v_{mean} − v_{total}/s_{total} < 0.6.
against all data and the mean value of the 20 refinements is insignificant, (ii) For the density ρ, the estimated for the against all data is slightly larger than the standard deviation of the distribution of the 20 refinements, s_{mean}/s_{total} < 1. The estimated is in the range 0.009–0.012 e Å^{−3}, or 1–1.5% of ρ. In an investigation using 13 different data sets of oxalic acid (Kamiński et al., 2014), the distribution has a standard deviation in the range 0.03–0.06 e Å^{−3} or 1.5–3.0%.
(iii) For the Laplacian ∇^{2}ρ, the estimated is much smaller than the standard deviation of the distribution, s_{mean}/s_{total} > 7.1. The standard deviations are between 0.3 and 0.6 e Å^{−5} i.e. 5–32% of v_{total}. In the abovementioned investigation (Kamiński et al., 2014), the standard deviation is between 1 and 7 e Å^{−5}, i.e. 6–28%.
(iv) For the ellipticity ∊, the standard deviation is between 0.009 and 0.02. In the work by Kamiński et al. (2014) it is between 0.01 and 0.04.
(v) Comparing the two refinements, most properties are very similar, but the Laplacian of the N—B bond changes from −0.94 to 1.86 e Å^{−5} and the ellipticity ∊ changes from 0.5 to 0.7. To investigate which step is mainly responsible for these differences, all properties were checked for several steps. The most important point seems to be the use of chemical constraints, agreeing with the greatest effect on R_{cross} (for details see the supporting information).
3.1.4. Influence of the number of test sets on the model
The influence of the number of training sets on the models was also checked. We repeated the R_{cross} is nearly identical for ten, 20 or 50 training sets (see the supporting information) but, as expected, for ten validation sets (more data left out) there are a higher number of outliers with v_{i} − v_{total} < 3s_{total}, while there are none for 50 validation sets. Accordingly, the standard deviations of the distributions shrink from ten to 50 validation sets. Here, we decided to use 20 sets, as this seems to be a sensible compromise between model bias and reasonable standard deviations.
using ten or 50 training sets, respectively (10% and 2% of data left out, respectively). The behaviour of3.1.5. Influence of Friedel mates on the model
We ensured that Friedel pairs are either both in the training set or both in the validation set because structure 1 crystallizes in a noncentrosymmetric To evaluate the impact of this treatment we performed the same but this time with randomly prepared training and validation sets without any special care for the Friedel pairs (see Fig. 7). Now overfitting is not that easy to detect. If we now check the feasibility of releasing the or chemical constraints, 〈R_{work}〉 responds in the familiar way but R_{cross} remains nearly unchanged. There is still an indication of overfitting if R_{mean} decreases much more than R_{cross}, but the picture is much less obscure with a proper treatment of the Friedel pairs. As they are not independent, neither is the model independent of a particular Friedel mate being present or not in the training set.
3.2. Benchmark structure 2
Data for structure 2 (Fig. 8) were collected on a Bruker D8 threecircle goniometer equipped with a Bruker TXS30 Mo rotating anode with INCOATEC Helios mirror optics and an APEXII detector at 100 K. The compound crystallizes in Pbca (Krause, 2017).
The local coordinate systems were defined so that the highest possible symmetry could be applied. This led to cylindrical symmetry for the H and S atoms, mirror symmetry for the methine C atoms and threefold symmetry for the methyl C atoms. For the anthracene C atoms mm2 symmetry was adopted. The pole populations of chemically equivalent atoms were constrained to be identical. The Catom multipole expansion was restricted to octupoles, while for S and P atoms hexadecapoles were employed. The strategy was similar to that of 1 (see the supporting information) and similar trends for the behaviour of R_{cross} are evident (see Fig. 9). The of the multipole populations improves 〈R_{work}〉 and R_{cross} significantly. Both values show an improvement that is greater from the loworder data compared with the highorder, which is in good agreement with expectations. The subsequent introduction of monopoles displays a similar picture. Next, adjustment of the displacement parameters does not show any sign of overfitting and is affected by both low and highorder reflections. The addition of positional parameters for nonhydrogen atoms does not need adjustment to the same extent here, indicating better starting parameters. With the density modelled, a new adjustment of the Hatom positions in step 6 leads to a drop in the lowresolution R value, which is again in good agreement with expectations.
The k parameters in step 8 stems predominantly from the lowresolution data. The introduction of hexadecapoles to the C atoms also shows an improvement from the loworder data. The same is found for the expansion from mm2 to m (in the plane) symmetry for the anthracene C atoms. However, on releasing the constraints, overfitting is indicated by a drop in 〈R_{work}〉 and an increase in R_{cross}, which is even more pronounced after the release of the constraints for equivalent atoms in step 14. The total datatoparameter ratio is still 24.2, but the ratio of loworder data to the monopole or multipole populations and the κ parameter is reduced to 3.1. Ultimately, we decided to stay with the more restricted model obtained after step 12. Here, the ratio of loworder data to the monopole or multipole populations and the κ parameter is still 13.0.
of the3.3. Constraints due to crystallographic symmetry
Atoms on special positions need constraints for the SHELXL these constraints are generated automatically, they need to be set manually in XD.
While in IAM programs likeCompound 3 (Fig. 10) crystallizes in Pnma with half a molecule in the (Jancik et al., 2017). Atoms P1, Cl1, Cl2 and N2 are located on a crystallographic mirror plane. Cylindrical symmetry was applied to the Cl atoms, and mm2 symmetry for the P and N atoms. All atoms of each element type were constrained to share the same monopole and multipole populations. Additional parameters were then added in a stepwise manner: multipole and monopole populations, and adjustment of U, xyz, κ and κ′. No step indicated any overfitting (see the supporting information). However, a typical residual density distribution, indicating anharmonic motion, was present. Hence thirdorder Gram–Charlier coefficients, first for the Cl atoms, then for the P atoms and finally for the N atoms, were introduced. No overfitting was visible and all performed tests for a reasonable of anharmonic motion were fulfilled (Jancik et al., 2017). Then the of the Cl atoms was released from cylindrical to mirror plane symmetry (datatoparameter ratio 44.3, loworder to monopole or multipole and κ parameter 8.7). Subsequently, in a similar fashion, the symmetry was lowered for the N and P atoms from mm2 to m (datatoparameter ratio still 41.2, loworder to monopole or multipole and κ parameter 6.4). The release of all chemical constraints for all atoms followed (datatoparameter ratio 28.7, loworder to monopole or multipole and κ parameter 4.9). Finally, all symmetry constraints for all atoms on general positions were released (datatoparameter ratio 24.7, loworder to monopole or multipole and κ parameter 3.7). While the release of the contraints for the N and P atoms has only a small effect on the R values, the release of both chemical and constraints for all atoms on general positions increases R_{cross}, clearly indicating overfitting.
In a first trial, the constraints for the Gram–Charlier coefficients for the atoms on special positions were mistakenly left unset. The impact on ΔR_{cross} was imperceptible, but this error could easily be identified by inspection of the distribution of values of the k refinements (see Fig. 11). Of course, such an error also leads to convergence problems, but the parameter distribution is able to identify the problematic parameters quickly.
3.4. Outlier detection
Structure 4 (Stute et al., 2012; Fig. 12) crystallizes in P2_{1}/n with one molecule in the asymmetric unit.
In this structure, the check of the parameter distribution identified all outliers with v_{total} − v_{i} > 3s_{total} (for details see the supporting information) as belonging to only three test sets. Two of these sets showed much higher R_{free} values than all other sets (see Fig. 13).
Careful inspection of these two validation sets showed that in both there is one very strong loworder reflection with F_{o} << F_{c} found by inspection of the DRK plots (Zhurov et al., 2008; Zavodnik et al., 1999) (see the supporting information). These two reflections are overexposed. Strong loworder reflections have a large effect on the multipole populations, so an inaccurate determination of such reflections is highly problematic. Since these reflections are omitted from these two training sets, the derived parameter sets from these two training sets are not outliers but proper values. An omission of these two reflections lowers the completeness in this important loworder range but improves the model indicated by a more reasonable parameter distribution (see as an example Fig. 14b).
3.5. Chemical constraints
In all our tested structures, we observed the release of chemical constraints to result in serious overfitting. Recently, we published the chargedensity investigation of a silylone (Niepötter et al., 2014). In this structure, an Si atom is coordinated by two identical cAAC (cyclic alkyl amino carbene) ligands. We found that the two Si—C bonds differ significantly in both length and ellipticity. Therefore, we anticipated that the release of chemical constraints is necessary for a proper modelling of this structure (for details of the R_{cross} procedure see the supporting information). However, unexpectedly, only the release of the constraints of the Si atom proved necessary to describe the differences in the two Si—C bonds. In contrast, the release of the chemical constraints of the two complete carbene ligands showed severe signs of overfitting, further emphasizing chemical constraints to be important in stabilizing a multipole at least for data sets to a resolution of 0.5–0.4 Å.
4. Conclusions
The presented method of crossvalidation is a valid tool in multipole R_{free} in macromolecular crystallography (Brünger, 1992, 1997) or the new R_{complete} concept (Luebben & Gruene, 2015), this method is not interested in absolute R_{cross} values but in the progress of R_{cross} along the strategy. For a reasonable not only must the normal R values decrease but also the R_{cross} value. Investigating several structures with this approach, we noticed the following general aspects:
Although the number of data in a highresolution data set is high enough to achieve a global datatoparameter ratio larger than 1:10 or even 1:20, even when all possible multipole parameters up to the hexadecapole level are refined, it has to be considered that not all reflections contribute equally to all multipole parameters. The information about the valence density is mainly gained from the relatively few loworder reflections. Therefore, the simple global datatoparameter rule of thumb is not sufficient to decide on the advisable number of parameters. In contrast with the well established(i) It helps to start with very high symmetry defined only by next neighbours.
(ii) Lowering these symmetry constraints often does not improve the model significantly. Normally it is sufficient to release these constraints for only a few atoms. Any unexpected large drop in R_{cross} is suspicious and helps to detect mistakes in the definition of the local coordinate system or the assumed local symmetry.
(iii) Release of all chemical constraints clearly causes overfitting in all investigated structures.
(iv) Unfortunately, XD does not offer restraints. However, using restraints instead of constraints could be a further improvement of the model (Paul et al., 2011; Zarychta et al., 2011). A protocol for oriented local atomic axes is explained in detail by Domagała & Jelsch (2008).
Additional to validation of the
strategy, analysis of the parameter distribution provides access to further causes of defects. Overlooking the necessary constraints required by can easily be prevented. Inaccurately determined strong loworder reflections that bias the derived parameters can be easily identified.The k different refinements also provide a distribution of the topological properties, leading to a rough estimate for the standard deviations of these parameters.
Supporting information
https://doi.org/10.1107/S2052252517005103/lc5072sup1.cif
DOI:fcf data for 1. DOI: https://doi.org/10.1107/S2052252517005103/lc50721sup2.hkl
fcf data for 2. DOI: https://doi.org/10.1107/S2052252517005103/lc50722sup3.hkl
Supplementary tables and figures. DOI: https://doi.org/10.1107/S2052252517005103/lc5072sup4.pdf
For all compounds, data collection: APEX2 v2012.2. Cell
SAINT V8.30C for 1_shelx, 1_xd; SAINT V8.37A for 2_shelx, 2_xd. Data reduction: SAINT V8.30C for 1_shelx, 1_xd; SAINT V8.37A for 2_shelx, 2_xd. Program(s) used to solve structure: SHELXT(G.M.Sheldrick,Acta Cryst.(2015)A71,38) for 1_shelx, 1_xd; SHELXT 2014/5 (Sheldrick, 2014) for 2_shelx, 2_xd. Program(s) used to refine structure: SHELXL2016/6 (Sheldrick, 2016) for 1_shelx, 1_xd, 2_shelx; Volkov et al., (2006) for 2_xd. For all compounds, molecular graphics: XP Version 5.1; software used to prepare material for publication: XP Version 5.1.C_{24}H_{18}BF_{10}N  D_{x} = 1.615 Mg m^{−}^{3} 
M_{r} = 521.20  Mo Kα radiation, λ = 0.71073 Å 
Tetragonal, P42_{1}c  Cell parameters from 8098 reflections 
a = 22.206 (3) Å  θ = 2.6–49.1° 
c = 8.692 (2) Å  µ = 0.16 mm^{−}^{1} 
V = 4286.1 (15) Å^{3}  T = 100 K 
Z = 8  Block, colorless 
F(000) = 2112  0.10 × 0.09 × 0.09 mm 
Bruker Smart APEX II Ultra diffractometer  19346 reflections with I > 2σ(I) 
Radiation source: BRUKER Rotating Anode  R_{int} = 0.041 
ω scans  θ_{max} = 49.2°, θ_{min} = 1.3° 
Absorption correction: multiscan SADABS 2015/1  h = −47→47 
T_{min} = 0.928, T_{max} = 0.971  k = −46→46 
404587 measured reflections  l = −18→18 
21597 independent reflections 
Refinement on F^{2}  Hydrogen site location: inferred from neighbouring sites 
Leastsquares matrix: full  Hatom parameters constrained 
R[F^{2} > 2σ(F^{2})] = 0.030  w = 1/[σ^{2}(F_{o}^{2}) + (0.0489P)^{2} + 0.0917P] where P = (F_{o}^{2} + 2F_{c}^{2})/3 
wR(F^{2}) = 0.084  (Δ/σ)_{max} = 0.001 
S = 1.12  Δρ_{max} = 0.51 e Å^{−}^{3} 
21597 reflections  Δρ_{min} = −0.25 e Å^{−}^{3} 
327 parameters  Absolute structure: Flack x determined using 8376 quotients [(I+)(I)]/[(I+)+(I)] (Parsons, Flack and Wagner, Acta Cryst. B69 (2013) 249259). 
0 restraints  Absolute structure parameter: −0.03 (3) 
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. 
x  y  z  U_{iso}*/U_{eq}  
N1  0.73830 (2)  0.51095 (2)  0.37910 (5)  0.01034 (5)  
B1  0.75169 (3)  0.52441 (3)  0.56972 (7)  0.01079 (7)  
C1  0.82116 (2)  0.50713 (3)  0.52843 (6)  0.01245 (7)  
H1A  0.846977  0.542449  0.506464  0.015*  
H1B  0.840401  0.480104  0.604519  0.015*  
C2  0.79872 (2)  0.47494 (2)  0.38502 (6)  0.01141 (6)  
H2  0.788807  0.432608  0.414986  0.014*  
C3  0.83693 (3)  0.47216 (2)  0.24174 (6)  0.01284 (7)  
C4  0.88063 (3)  0.51575 (3)  0.20902 (8)  0.01630 (8)  
H4  0.886656  0.548338  0.278129  0.020*  
C5  0.91536 (3)  0.51172 (4)  0.07596 (9)  0.02081 (11)  
H5  0.944715  0.541686  0.054466  0.025*  
C6  0.90720 (4)  0.46384 (4)  −0.02584 (8)  0.02268 (12)  
H6  0.930487  0.461449  −0.117312  0.027*  
C7  0.86477 (4)  0.41963 (4)  0.00732 (8)  0.02061 (11)  
H7  0.859428  0.386647  −0.060950  0.025*  
C8  0.83011 (3)  0.42363 (3)  0.14046 (7)  0.01619 (8)  
H8  0.801502  0.393056  0.162823  0.019*  
C9  0.74312 (3)  0.56601 (2)  0.28002 (6)  0.01298 (7)  
H9A  0.782759  0.584948  0.299476  0.016*  
H9B  0.711842  0.594982  0.313336  0.016*  
C10  0.73660 (3)  0.55650 (3)  0.10712 (7)  0.01851 (9)  
H10A  0.767876  0.528704  0.071275  0.028*  
H10B  0.740905  0.595193  0.054031  0.028*  
H10C  0.696818  0.539479  0.084903  0.028*  
C11  0.68641 (3)  0.47198 (3)  0.33416 (7)  0.01371 (7)  
H11A  0.684582  0.437255  0.405426  0.016*  
H11B  0.693848  0.455994  0.229554  0.016*  
C12  0.62563 (3)  0.50366 (3)  0.33529 (9)  0.01928 (10)  
H12A  0.618016  0.520320  0.437863  0.029*  
H12B  0.593895  0.474731  0.309272  0.029*  
H12C  0.625845  0.536316  0.259457  0.029*  
C13  0.74496 (2)  0.59298 (2)  0.63759 (6)  0.01058 (6)  
C14  0.70447 (2)  0.63917 (2)  0.60470 (6)  0.01176 (6)  
C15  0.70615 (3)  0.69567 (2)  0.67317 (7)  0.01316 (7)  
C16  0.74840 (3)  0.70805 (3)  0.78583 (6)  0.01430 (7)  
C17  0.78845 (3)  0.66311 (3)  0.82659 (6)  0.01367 (7)  
C18  0.78640 (2)  0.60791 (2)  0.75232 (6)  0.01192 (6)  
C19  0.71483 (2)  0.47761 (2)  0.68230 (6)  0.01201 (6)  
C20  0.73789 (3)  0.42301 (3)  0.73780 (6)  0.01451 (7)  
C21  0.71089 (4)  0.38950 (3)  0.85408 (7)  0.01773 (9)  
C22  0.65755 (4)  0.40895 (3)  0.91887 (7)  0.01869 (10)  
C23  0.63125 (3)  0.46129 (3)  0.86467 (8)  0.01780 (9)  
C24  0.65998 (3)  0.49360 (3)  0.74971 (7)  0.01412 (7)  
F14  0.65961 (2)  0.63126 (2)  0.50179 (5)  0.01574 (6)  
F15  0.66653 (2)  0.73833 (2)  0.63231 (6)  0.01857 (7)  
F16  0.74989 (3)  0.76149 (2)  0.85550 (6)  0.02063 (8)  
F17  0.82815 (2)  0.67254 (2)  0.94020 (5)  0.01959 (7)  
F18  0.82690 (2)  0.56711 (2)  0.80126 (5)  0.01659 (6)  
F20  0.78896 (2)  0.39950 (2)  0.68118 (6)  0.02022 (8)  
F21  0.73641 (3)  0.33875 (2)  0.90582 (6)  0.02569 (10)  
F22  0.63184 (3)  0.37764 (3)  1.03277 (6)  0.02743 (11)  
F23  0.57935 (3)  0.48065 (3)  0.92432 (8)  0.02757 (11)  
F24  0.63130 (2)  0.54419 (2)  0.70519 (6)  0.01877 (7) 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
N1  0.01126 (12)  0.01008 (12)  0.00968 (12)  −0.00041 (10)  −0.00024 (10)  −0.00035 (10) 
B1  0.01145 (17)  0.01110 (17)  0.00984 (16)  0.00017 (14)  0.00035 (14)  −0.00064 (13) 
C1  0.01123 (15)  0.01451 (17)  0.01161 (15)  0.00100 (13)  −0.00017 (12)  −0.00137 (13) 
C2  0.01225 (15)  0.01161 (14)  0.01038 (14)  0.00080 (12)  0.00121 (12)  −0.00036 (12) 
C3  0.01379 (16)  0.01329 (16)  0.01143 (15)  0.00195 (13)  0.00237 (13)  0.00001 (13) 
C4  0.01522 (18)  0.0168 (2)  0.01693 (19)  0.00058 (15)  0.00397 (16)  0.00170 (16) 
C5  0.0185 (2)  0.0231 (3)  0.0209 (2)  0.00345 (19)  0.00828 (19)  0.0057 (2) 
C6  0.0240 (3)  0.0272 (3)  0.0169 (2)  0.0092 (2)  0.0091 (2)  0.0035 (2) 
C7  0.0257 (3)  0.0221 (2)  0.01401 (19)  0.0077 (2)  0.00478 (19)  −0.00206 (17) 
C8  0.0197 (2)  0.01564 (18)  0.01327 (17)  0.00313 (16)  0.00263 (16)  −0.00208 (15) 
C9  0.01595 (18)  0.01171 (15)  0.01130 (15)  0.00062 (13)  0.00033 (13)  0.00127 (12) 
C10  0.0236 (2)  0.0207 (2)  0.01126 (16)  0.00315 (19)  −0.00050 (17)  0.00285 (16) 
C11  0.01416 (17)  0.01282 (16)  0.01416 (17)  −0.00193 (13)  −0.00148 (14)  −0.00216 (14) 
C12  0.01339 (18)  0.0197 (2)  0.0248 (3)  −0.00107 (16)  −0.00350 (18)  −0.0019 (2) 
C13  0.01096 (14)  0.01078 (14)  0.01000 (13)  −0.00056 (11)  0.00058 (11)  −0.00109 (11) 
C14  0.01092 (14)  0.01186 (15)  0.01249 (15)  −0.00003 (12)  0.00081 (12)  −0.00166 (12) 
C15  0.01326 (16)  0.01108 (15)  0.01513 (17)  0.00036 (13)  0.00316 (14)  −0.00174 (13) 
C16  0.01786 (19)  0.01180 (16)  0.01323 (16)  −0.00334 (14)  0.00320 (14)  −0.00326 (13) 
C17  0.01571 (18)  0.01447 (17)  0.01082 (15)  −0.00424 (14)  0.00012 (13)  −0.00223 (13) 
C18  0.01287 (15)  0.01282 (15)  0.01008 (13)  −0.00128 (13)  −0.00011 (12)  −0.00060 (12) 
C19  0.01407 (16)  0.01169 (15)  0.01026 (14)  −0.00047 (13)  0.00112 (12)  −0.00018 (12) 
C20  0.0193 (2)  0.01264 (16)  0.01158 (16)  0.00084 (15)  0.00132 (14)  0.00102 (13) 
C21  0.0271 (3)  0.01345 (17)  0.01267 (17)  −0.00213 (18)  0.00128 (17)  0.00189 (14) 
C22  0.0270 (3)  0.0161 (2)  0.01293 (17)  −0.00758 (19)  0.00477 (18)  −0.00034 (15) 
C23  0.0194 (2)  0.0168 (2)  0.0172 (2)  −0.00554 (17)  0.00663 (17)  −0.00230 (16) 
C24  0.01424 (17)  0.01362 (17)  0.01451 (17)  −0.00210 (14)  0.00280 (15)  −0.00074 (14) 
F14  0.01232 (12)  0.01725 (14)  0.01764 (14)  0.00206 (11)  −0.00322 (11)  −0.00331 (12) 
F15  0.01686 (15)  0.01358 (13)  0.02528 (18)  0.00427 (11)  0.00281 (13)  −0.00180 (13) 
F16  0.0295 (2)  0.01278 (13)  0.01956 (16)  −0.00394 (14)  0.00330 (15)  −0.00655 (12) 
F17  0.02197 (17)  0.02233 (17)  0.01448 (14)  −0.00653 (14)  −0.00438 (13)  −0.00417 (13) 
F18  0.01769 (14)  0.01813 (15)  0.01394 (12)  0.00282 (12)  −0.00438 (11)  −0.00059 (11) 
F20  0.02397 (18)  0.01716 (15)  0.01954 (16)  0.00744 (14)  0.00495 (14)  0.00432 (13) 
F21  0.0408 (3)  0.01606 (16)  0.02022 (18)  0.00214 (17)  0.00136 (19)  0.00721 (14) 
F22  0.0410 (3)  0.0226 (2)  0.01865 (17)  −0.0116 (2)  0.01085 (19)  0.00293 (15) 
F23  0.0237 (2)  0.0260 (2)  0.0330 (3)  −0.00421 (17)  0.0171 (2)  −0.00224 (19) 
F24  0.01430 (14)  0.01618 (14)  0.02584 (18)  0.00163 (12)  0.00488 (13)  0.00142 (13) 
N1—C11  1.4929 (7)  C14—C15  1.3892 (7) 
N1—C9  1.4994 (7)  C15—F15  1.3407 (7) 
N1—C2  1.5628 (7)  C15—C16  1.3838 (9) 
N1—B1  1.7096 (8)  C16—F16  1.3328 (7) 
B1—C1  1.6297 (8)  C16—C17  1.3829 (9) 
B1—C13  1.6398 (8)  C17—F17  1.3401 (7) 
B1—C19  1.6454 (8)  C17—C18  1.3860 (8) 
C1—C2  1.5208 (8)  C18—F18  1.3456 (7) 
C2—C3  1.5081 (8)  C19—C24  1.3976 (8) 
C3—C8  1.3997 (8)  C19—C20  1.4018 (8) 
C3—C4  1.3998 (9)  C20—F20  1.3419 (8) 
C4—C5  1.3930 (9)  C20—C21  1.3909 (9) 
C5—C6  1.3951 (13)  C21—F21  1.3391 (9) 
C6—C7  1.3909 (13)  C21—C22  1.3809 (11) 
C7—C8  1.3927 (9)  C22—F22  1.3377 (8) 
C9—C10  1.5246 (9)  C22—C23  1.3835 (11) 
C11—C12  1.5220 (9)  C23—F23  1.3349 (9) 
C13—C14  1.3936 (8)  C23—C24  1.3857 (9) 
C13—C18  1.3969 (7)  C24—F24  1.3480 (8) 
C14—F14  1.3504 (7)  
C11—N1—C9  112.18 (4)  C15—C14—C13  124.03 (5) 
C11—N1—C2  112.00 (4)  F15—C15—C16  119.48 (5) 
C9—N1—C2  112.01 (4)  F15—C15—C14  120.47 (5) 
C11—N1—B1  119.28 (4)  C16—C15—C14  120.04 (5) 
C9—N1—B1  113.68 (4)  F16—C16—C17  120.68 (6) 
C2—N1—B1  84.73 (3)  F16—C16—C15  121.01 (6) 
C1—B1—C13  112.59 (4)  C17—C16—C15  118.30 (5) 
C1—B1—C19  116.95 (4)  F17—C17—C16  119.93 (5) 
C13—B1—C19  109.10 (4)  F17—C17—C18  120.21 (6) 
C1—B1—N1  84.84 (4)  C16—C17—C18  119.84 (5) 
C13—B1—N1  119.67 (4)  F18—C18—C17  115.22 (5) 
C19—B1—N1  112.30 (4)  F18—C18—C13  120.41 (5) 
C2—C1—B1  88.91 (4)  C17—C18—C13  124.34 (5) 
C3—C2—C1  120.78 (5)  C24—C19—C20  113.19 (5) 
C3—C2—N1  118.47 (4)  C24—C19—B1  121.50 (5) 
C1—C2—N1  93.89 (4)  C20—C19—B1  124.70 (5) 
C8—C3—C4  118.65 (5)  F20—C20—C21  115.00 (5) 
C8—C3—C2  119.34 (5)  F20—C20—C19  121.26 (5) 
C4—C3—C2  121.97 (5)  C21—C20—C19  123.74 (6) 
C5—C4—C3  120.54 (6)  F21—C21—C22  119.29 (6) 
C4—C5—C6  120.23 (7)  F21—C21—C20  120.79 (7) 
C7—C6—C5  119.64 (6)  C22—C21—C20  119.92 (6) 
C6—C7—C8  120.09 (7)  F22—C22—C21  120.36 (7) 
C7—C8—C3  120.80 (6)  F22—C22—C23  120.56 (7) 
N1—C9—C10  116.51 (5)  C21—C22—C23  119.08 (6) 
N1—C11—C12  114.51 (5)  F23—C23—C22  120.19 (6) 
C14—C13—C18  113.37 (5)  F23—C23—C24  120.72 (7) 
C14—C13—B1  131.95 (5)  C22—C23—C24  119.09 (6) 
C18—C13—B1  114.66 (4)  F24—C24—C23  114.90 (5) 
F14—C14—C15  114.90 (5)  F24—C24—C19  120.21 (5) 
F14—C14—C13  121.07 (5)  C23—C24—C19  124.89 (6) 
C_{24}H_{18}BF_{10}N  D_{x} = 1.615 Mg m^{−}^{3} 
M_{r} = 521.20  Mo Kα radiation, λ = 0.71073 Å 
Tetragonal, P42_{1}c  Cell parameters from 8098 reflections 
a = 22.206 (3) Å  θ = 2.6–49.1° 
c = 8.692 (2) Å  µ = 0.16 mm^{−}^{1} 
V = 4286.1 (15) Å^{3}  T = 100 K 
Z = 8  Block, colorless 
F(000) = 2112  0.10 × 0.09 × 0.09 mm 
Bruker Smart APEX II Ultra diffractometer  19346 reflections with I > 2σ(I) 
Radiation source: BRUKER Rotating Anode  R_{int} = 0.041 
ω scans  θ_{max} = 49.2°, θ_{min} = 1.3° 
Absorption correction: multiscan SADABS 2015/1  h = −47→47 
T_{min} = 0.928, T_{max} = 0.971  k = −46→46 
404587 measured reflections  l = −18→18 
21597 independent reflections 
Refinement on F^{2}  Hatom parameters constrained 
Leastsquares matrix: full  ' w2 = 1/[s^{2}(F_{o}^{2})]' 
R[F^{2} > 2σ(F^{2})] = 0.018  (Δ/σ)_{max} = 0.001 
wR(F^{2}) = 0.016  Δρ_{max} = 0.30 e Å^{−}^{3} 
S = 1.10  Δρ_{min} = −0.23 e Å^{−}^{3} 
20737 reflections  Absolute structure: Flack x determined using 8376 quotients [(I+)(I)]/[(I+)+(I)] (Parsons, Flack and Wagner, Acta Cryst. B69 (2013) 249259). 
618 parameters  Absolute structure parameter: −0.03 (3) 
0 restraints 
x  y  z  U_{iso}*/U_{eq}  
F(22)  0.826859 (6)  0.567098 (6)  0.801390 (12)  0.021  
F(23)  0.828166 (7)  0.672509 (5)  0.940220 (17)  0.024  
F(24)  0.749861 (5)  0.761563 (9)  0.855557 (16)  0.025  
F(25)  0.666509 (6)  0.738352 (6)  0.632345 (14)  0.023  
F(26)  0.659555 (6)  0.631275 (5)  0.501802 (15)  0.020  
F(32)  0.788978 (7)  0.399533 (5)  0.681213 (14)  0.025  
F(33)  0.736321 (13)  0.338764 (13)  0.90565 (3)  0.030  
F(34)  0.631798 (13)  0.377609 (13)  1.03259 (4)  0.032  
F(35)  0.579318 (14)  0.480595 (11)  0.92421 (3)  0.032  
F(36)  0.631308 (5)  0.544167 (6)  0.705155 (14)  0.023  
N(1)  0.738276 (8)  0.510918 (8)  0.37901 (2)  0.015  
C(1)  0.821143 (9)  0.507108 (9)  0.52838 (2)  0.017  
C(2)  0.798720 (9)  0.474980 (9)  0.38496 (2)  0.016  
C(3)  0.686396 (8)  0.472032 (8)  0.334067 (19)  0.019  
C(4)  0.625660 (8)  0.503612 (8)  0.33512 (2)  0.024  
C(5)  0.743079 (7)  0.566012 (8)  0.28001 (2)  0.018  
C(6)  0.736609 (8)  0.556540 (8)  0.10727 (2)  0.023  
C(11)  0.836898 (8)  0.472154 (8)  0.24180 (2)  0.018  
C(12)  0.880624 (8)  0.515723 (9)  0.20898 (2)  0.021  
C(13)  0.915406 (9)  0.511728 (11)  0.07601 (3)  0.026  
C(14)  0.907218 (10)  0.463900 (9)  −0.02590 (3)  0.027  
C(15)  0.864743 (10)  0.419543 (10)  0.00732 (2)  0.025  
C(16)  0.830121 (9)  0.423620 (9)  0.14049 (2)  0.021  
C(21)  0.744941 (7)  0.592987 (8)  0.637502 (18)  0.015  
C(22)  0.786415 (7)  0.607899 (8)  0.752331 (19)  0.017  
C(23)  0.788456 (8)  0.663106 (8)  0.826657 (19)  0.018  
C(24)  0.748368 (7)  0.708093 (9)  0.785898 (19)  0.019  
C(25)  0.706097 (8)  0.695748 (8)  0.67313 (2)  0.018  
C(26)  0.704451 (7)  0.639175 (7)  0.604678 (19)  0.017  
C(31)  0.714866 (8)  0.477614 (8)  0.682257 (19)  0.017  
C(32)  0.737918 (8)  0.423083 (8)  0.737745 (19)  0.019  
C(33)  0.710942 (10)  0.389436 (8)  0.85399 (2)  0.022  
C(34)  0.657472 (9)  0.408874 (8)  0.91900 (2)  0.023  
C(35)  0.631152 (9)  0.461276 (9)  0.86465 (2)  0.023  
C(36)  0.659926 (8)  0.493656 (8)  0.74951 (2)  0.019  
B(1)  0.751686 (8)  0.524439 (8)  0.56965 (2)  0.015  
H(1A)  0.846149  0.547366  0.498003  0.02073 (3)  
H(1B)  0.849685  0.480102  0.60257  0.02073 (3)  
H(2)  0.784218  0.429646  0.413164  0.01952 (3)  
H(3A)  0.686187  0.435031  0.415589  0.02230 (3)  
H(3B)  0.695806  0.453308  0.221303  0.02230 (3)  
H(4A)  0.623262  0.539335  0.250176  0.03604 (5)  
H(4B)  0.615649  0.522104  0.447796  0.03604 (5)  
H(4C)  0.591466  0.470787  0.304829  0.03604 (5)  
H(5A)  0.786275  0.586107  0.307719  0.02141 (3)  
H(5B)  0.707919  0.596695  0.317011  0.02141 (3)  
H(6A)  0.739564  0.600865  0.055292  0.03483 (5)  
H(6B)  0.692692  0.539122  0.075433  0.03483 (5)  
H(6C)  0.771055  0.52782  0.057732  0.03483 (5)  
H(12)  0.8883  0.552359  0.287591  0.02530 (3)  
H(13)  0.949182  0.545052  0.05089  0.03067 (4)  
H(14)  0.933892  0.461587  −0.12908  0.03283 (5)  
H(15)  0.858457  0.382173  −0.06983  0.03043 (4)  
H(16)  0.797812  0.388984  0.166593  0.02514 (3) 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
F(22)  0.02235 (4)  0.02294 (4)  0.01843 (4)  0.00242 (4)  −0.00418 (4)  −0.00055 (4) 
F(23)  0.02695 (5)  0.02696 (6)  0.01947 (4)  −0.00660 (4)  −0.00402 (5)  −0.00417 (4) 
F(24)  0.03395 (7)  0.01791 (5)  0.02420 (5)  −0.00404 (4)  0.00344 (4)  −0.00628 (5) 
F(25)  0.02163 (4)  0.01840 (4)  0.03002 (6)  0.00392 (5)  0.00284 (4)  −0.00197 (4) 
F(26)  0.01724 (4)  0.02175 (5)  0.02249 (4)  0.00205 (3)  −0.00287 (4)  −0.00313 (4) 
F(32)  0.02907 (6)  0.02183 (5)  0.02419 (5)  0.00712 (4)  0.00462 (5)  0.00431 (4) 
F(33)  0.04507 (7)  0.02114 (5)  0.02493 (6)  0.00173 (5)  0.00136 (5)  0.00701 (4) 
F(34)  0.04518 (7)  0.02751 (6)  0.02343 (5)  −0.01183 (5)  0.01003 (6)  0.00250 (6) 
F(35)  0.02915 (6)  0.03037 (6)  0.03750 (7)  −0.00469 (5)  0.01673 (5)  −0.00215 (5) 
F(36)  0.01893 (4)  0.02114 (5)  0.03019 (5)  0.00132 (4)  0.00473 (4)  0.00120 (4) 
N(1)  0.01597 (7)  0.01511 (7)  0.01426 (6)  −0.00040 (6)  −0.00023 (6)  −0.00029 (6) 
C(1)  0.01590 (7)  0.01941 (7)  0.01651 (7)  0.00083 (6)  −0.00046 (6)  −0.00132 (6) 
C(2)  0.01747 (7)  0.01605 (7)  0.01527 (7)  0.00072 (6)  0.00132 (6)  −0.00040 (6) 
C(3)  0.01940 (7)  0.01758 (6)  0.01876 (7)  −0.00186 (5)  −0.00144 (5)  −0.00208 (5) 
C(4)  0.01812 (7)  0.02443 (7)  0.02951 (8)  −0.00113 (6)  −0.00338 (6)  −0.00204 (6) 
C(5)  0.02054 (7)  0.01644 (6)  0.01654 (6)  0.00031 (5)  0.00017 (5)  0.00108 (5) 
C(6)  0.02817 (8)  0.02549 (7)  0.01600 (7)  0.00309 (6)  −0.00060 (6)  0.00283 (5) 
C(11)  0.01863 (6)  0.01796 (7)  0.01628 (6)  0.00169 (6)  0.00269 (6)  −0.00014 (6) 
C(12)  0.02000 (7)  0.02154 (7)  0.02172 (7)  0.00010 (6)  0.00434 (6)  0.00140 (6) 
C(13)  0.02321 (8)  0.02774 (9)  0.02573 (8)  0.00309 (7)  0.00857 (7)  0.00540 (8) 
C(14)  0.02864 (8)  0.03155 (11)  0.02189 (8)  0.00861 (9)  0.00945 (8)  0.00347 (7) 
C(15)  0.03039 (8)  0.02688 (8)  0.01881 (7)  0.00730 (8)  0.00525 (7)  −0.00238 (7) 
C(16)  0.02453 (7)  0.02023 (7)  0.01809 (6)  0.00271 (6)  0.00315 (6)  −0.00235 (6) 
C(21)  0.01590 (6)  0.01533 (6)  0.01500 (5)  −0.00062 (5)  0.00015 (5)  −0.00143 (5) 
C(22)  0.01774 (6)  0.01759 (6)  0.01496 (5)  −0.00134 (5)  −0.00048 (5)  −0.00088 (5) 
C(23)  0.02045 (6)  0.01888 (6)  0.01583 (5)  −0.00402 (5)  0.00001 (5)  −0.00232 (5) 
C(24)  0.02241 (7)  0.01646 (6)  0.01827 (6)  −0.00291 (5)  0.00271 (6)  −0.00320 (5) 
C(25)  0.01830 (6)  0.01554 (6)  0.02001 (6)  0.00022 (5)  0.00263 (5)  −0.00209 (5) 
C(26)  0.01582 (6)  0.01626 (6)  0.01746 (6)  0.00046 (5)  0.00038 (5)  −0.00182 (5) 
C(31)  0.01896 (6)  0.01633 (6)  0.01525 (6)  −0.00037 (5)  0.00146 (5)  0.00029 (5) 
C(32)  0.02420 (7)  0.01717 (6)  0.01679 (6)  0.00097 (5)  0.00152 (5)  0.00163 (5) 
C(33)  0.03150 (8)  0.01838 (6)  0.01745 (6)  −0.00216 (6)  0.00167 (6)  0.00218 (5) 
C(34)  0.03126 (8)  0.02072 (7)  0.01818 (7)  −0.00697 (7)  0.00492 (6)  0.00005 (6) 
C(35)  0.02436 (7)  0.02154 (7)  0.02184 (7)  −0.00541 (6)  0.00678 (6)  −0.00194 (6) 
C(36)  0.01889 (6)  0.01826 (6)  0.01940 (6)  −0.00181 (5)  0.00324 (6)  −0.00072 (5) 
B(1)  0.01598 (7)  0.01570 (7)  0.01479 (7)  0.00019 (6)  0.00048 (6)  −0.00061 (6) 
F(22)—C(22)  1.3451 (2)  C(6)—H(6C)  1.0850 (2) 
F(23)—C(23)  1.3400 (2)  C(11)—C(12)  1.4001 (3) 
F(24)—C(24)  1.3332 (3)  C(11)—C(16)  1.3999 (3) 
F(25)—C(25)  1.3392 (2)  C(12)—C(13)  1.3929 (3) 
F(26)—C(26)  1.3507 (2)  C(12)—H(12)  1.0760 (2) 
F(32)—C(32)  1.3418 (2)  C(13)—C(14)  1.3949 (3) 
F(33)—C(33)  1.3362 (4)  C(13)—H(13)  1.0760 (2) 
F(34)—C(34)  1.3349 (4)  C(14)—C(15)  1.3940 (3) 
F(35)—C(35)  1.3330 (4)  C(14)—H(14)  1.0760 (3) 
F(36)—C(36)  1.3456 (2)  C(15)—C(16)  1.3925 (3) 
C(1)—C(2)  1.5201 (3)  C(15)—H(15)  1.0760 (2) 
C(1)—B(1)  1.6296 (3)  C(16)—H(16)  1.0760 (2) 
C(1)—H(1A)  1.0850 (2)  C(21)—C(22)  1.3979 (2) 
C(1)—H(1B)  1.0850 (2)  C(21)—C(26)  1.3935 (2) 
C(2)—C(11)  1.5070 (3)  C(21)—B(1)  1.6393 (2) 
C(2)—H(2)  1.0850 (2)  C(22)—C(23)  1.3865 (2) 
C(3)—C(4)  1.5202 (3)  C(23)—C(24)  1.3842 (3) 
C(3)—H(3A)  1.0850 (2)  C(24)—C(25)  1.3846 (2) 
C(3)—H(3B)  1.0850 (2)  C(25)—C(26)  1.3905 (2) 
C(4)—H(4A)  1.0850 (2)  C(31)—C(32)  1.4003 (2) 
C(4)—H(4B)  1.0850 (2)  C(31)—C(36)  1.3989 (2) 
C(4)—H(4C)  1.0850 (2)  C(31)—B(1)  1.6455 (3) 
C(5)—C(6)  1.5229 (3)  C(32)—C(33)  1.3921 (2) 
C(5)—H(5A)  1.0850 (2)  C(33)—C(34)  1.3840 (3) 
C(5)—H(5B)  1.0850 (2)  C(34)—C(35)  1.3852 (3) 
C(6)—H(6A)  1.0850 (2)  C(35)—C(36)  1.3881 (2) 
C(6)—H(6B)  1.0850 (2)  
C(2)—C(1)—B(1)  88.932 (14)  C(11)—C(16)—C(15)  120.90 (2) 
C(2)—C(1)—H(1A)  110.781 (16)  C(11)—C(16)—H(16)  119.299 (19) 
C(2)—C(1)—H(1B)  114.793 (16)  C(15)—C(16)—H(16)  119.80 (2) 
B(1)—C(1)—H(1A)  110.082 (15)  C(22)—C(21)—C(26)  113.387 (17) 
B(1)—C(1)—H(1B)  123.542 (16)  C(22)—C(21)—B(1)  114.623 (15) 
H(1A)—C(1)—H(1B)  107.522 (17)  C(26)—C(21)—B(1)  131.971 (15) 
C(1)—C(2)—C(11)  120.823 (17)  F(22)—C(22)—C(21)  120.444 (15) 
C(1)—C(2)—H(2)  110.329 (16)  F(22)—C(22)—C(23)  115.216 (15) 
C(11)—C(2)—H(2)  108.354 (16)  C(21)—C(22)—C(23)  124.312 (17) 
C(4)—C(3)—H(3A)  109.976 (15)  F(23)—C(23)—C(22)  120.168 (17) 
C(4)—C(3)—H(3B)  110.676 (15)  F(23)—C(23)—C(24)  119.954 (15) 
H(3A)—C(3)—H(3B)  107.493 (16)  C(22)—C(23)—C(24)  119.859 (17) 
C(3)—C(4)—H(4A)  112.131 (16)  F(24)—C(24)—C(23)  120.699 (15) 
C(3)—C(4)—H(4B)  111.211 (15)  F(24)—C(24)—C(25)  120.977 (16) 
C(3)—C(4)—H(4C)  108.031 (16)  C(23)—C(24)—C(25)  118.315 (19) 
H(4A)—C(4)—H(4B)  109.116 (17)  F(25)—C(25)—C(24)  119.509 (16) 
H(4A)—C(4)—H(4C)  106.960 (16)  F(25)—C(25)—C(26)  120.511 (16) 
H(4B)—C(4)—H(4C)  109.263 (16)  C(24)—C(25)—C(26)  119.975 (18) 
C(6)—C(5)—H(5A)  111.042 (15)  F(26)—C(26)—C(21)  121.079 (15) 
C(6)—C(5)—H(5B)  108.124 (14)  F(26)—C(26)—C(25)  114.836 (15) 
H(5A)—C(5)—H(5B)  108.186 (15)  C(21)—C(26)—C(25)  124.084 (17) 
C(5)—C(6)—H(6A)  106.233 (15)  C(32)—C(31)—C(36)  113.271 (17) 
C(5)—C(6)—H(6B)  112.674 (15)  C(32)—C(31)—B(1)  124.726 (16) 
C(5)—C(6)—H(6C)  113.950 (15)  C(36)—C(31)—B(1)  121.397 (15) 
H(6A)—C(6)—H(6B)  105.756 (15)  F(32)—C(32)—C(31)  121.317 (15) 
H(6A)—C(6)—H(6C)  108.986 (16)  F(32)—C(32)—C(33)  114.848 (16) 
H(6B)—C(6)—H(6C)  108.838 (16)  C(31)—C(32)—C(33)  123.834 (18) 
C(2)—C(11)—C(12)  121.979 (18)  F(33)—C(33)—C(32)  120.96 (2) 
C(2)—C(11)—C(16)  119.406 (19)  F(33)—C(33)—C(34)  119.161 (19) 
C(12)—C(11)—C(16)  118.58 (2)  C(32)—C(33)—C(34)  119.875 (19) 
C(11)—C(12)—C(13)  120.64 (2)  F(34)—C(34)—C(33)  120.41 (2) 
C(11)—C(12)—H(12)  120.195 (19)  F(34)—C(34)—C(35)  120.59 (2) 
C(13)—C(12)—H(12)  119.16 (2)  C(33)—C(34)—C(35)  118.99 (2) 
C(12)—C(13)—C(14)  120.21 (2)  F(35)—C(35)—C(34)  120.147 (19) 
C(12)—C(13)—H(13)  120.74 (2)  F(35)—C(35)—C(36)  120.71 (2) 
C(14)—C(13)—H(13)  119.05 (2)  C(34)—C(35)—C(36)  119.131 (19) 
C(13)—C(14)—C(15)  119.65 (2)  F(36)—C(36)—C(31)  120.294 (16) 
C(13)—C(14)—H(14)  119.60 (2)  F(36)—C(36)—C(35)  114.895 (16) 
C(15)—C(14)—H(14)  120.76 (2)  C(31)—C(36)—C(35)  124.805 (18) 
C(14)—C(15)—C(16)  119.99 (2)  C(1)—B(1)—C(21)  112.642 (14) 
C(14)—C(15)—H(15)  120.24 (2)  C(1)—B(1)—C(31)  116.872 (14) 
C(16)—C(15)—H(15)  119.77 (2)  C(21)—B(1)—C(31)  109.109 (13) 
C_{20}H_{23}PS  D_{x} = 1.291 Mg m^{−}^{3} 
M_{r} = 326.41  Mo Kα radiation, λ = 0.71073 Å 
Orthorhombic, Pbca  Cell parameters from 9781 reflections 
a = 10.9323 (7) Å  θ = 2.7–52.2° 
b = 14.5698 (10) Å  µ = 0.28 mm^{−}^{1} 
c = 21.0910 (14) Å  T = 99 K 
V = 3359.4 (4) Å^{3}  Block, yellow 
Z = 8  0.12 × 0.11 × 0.10 mm 
F(000) = 1392 
Bruker Smart APEX II Ultra diffractometer  15462 reflections with I > 2σ(I) 
Radiation source: BRUKER Rotating Anode  R_{int} = 0.025 
ω scans  θ_{max} = 52.2°, θ_{min} = 1.9° 
Absorption correction: multiscan SADABS2016/2  h = −24→24 
T_{min} = 0.885, T_{max} = 0.929  k = −32→32 
222190 measured reflections  l = −46→46 
19329 independent reflections 
Refinement on F^{2}  0 restraints 
Leastsquares matrix: full  Hydrogen site location: inferred from neighbouring sites 
R[F^{2} > 2σ(F^{2})] = 0.024  Hatom parameters constrained 
wR(F^{2}) = 0.090  w = 1/[σ^{2}(F_{o}^{2}) + (0.0508P)^{2} + 0.0744P] where P = (F_{o}^{2} + 2F_{c}^{2})/3 
S = 1.11  (Δ/σ)_{max} = 0.007 
19329 reflections  Δρ_{max} = 0.60 e Å^{−}^{3} 
203 parameters  Δρ_{min} = −0.27 e Å^{−}^{3} 
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. 
x  y  z  U_{iso}*/U_{eq}  
P1  0.43671 (2)  0.29822 (2)  0.56327 (2)  0.00922 (2)  
S1  0.60402 (2)  0.33080 (2)  0.53581 (2)  0.01521 (2)  
C1  0.40206 (3)  0.31454 (2)  0.64870 (2)  0.01034 (4)  
C2  0.30308 (3)  0.26463 (2)  0.67638 (2)  0.01075 (4)  
C4  0.11899 (3)  0.16839 (3)  0.66988 (2)  0.01492 (5)  
H4  0.058349  0.139171  0.644711  0.018*  
C3  0.20688 (3)  0.22113 (2)  0.64096 (2)  0.01242 (4)  
H3  0.204017  0.229091  0.596281  0.015*  
C6  0.20005 (3)  0.20333 (3)  0.77300 (2)  0.01496 (5)  
H6  0.195897  0.198935  0.817888  0.018*  
C5  0.11708 (3)  0.15670 (3)  0.73686 (2)  0.01648 (5)  
H5  0.058972  0.117058  0.756143  0.020*  
C9  0.46281 (3)  0.36539 (2)  0.75644 (2)  0.01249 (4)  
C8  0.37449 (3)  0.30767 (2)  0.78264 (2)  0.01384 (4)  
H8  0.369591  0.301534  0.827413  0.017*  
C7  0.29318 (3)  0.25872 (2)  0.74445 (2)  0.01205 (4)  
C10  0.54052 (4)  0.41836 (3)  0.79718 (2)  0.01576 (5)  
H10  0.532674  0.412301  0.841845  0.019*  
C11  0.62554 (4)  0.47733 (3)  0.77299 (2)  0.01712 (5)  
H11  0.677982  0.510914  0.800405  0.021*  
C12  0.63443 (4)  0.48772 (3)  0.70613 (2)  0.01678 (5)  
H12  0.690985  0.530669  0.689118  0.020*  
C13  0.56309 (3)  0.43705 (2)  0.66565 (2)  0.01450 (5)  
H13  0.571264  0.446018  0.621240  0.017*  
C14  0.47650 (3)  0.37091 (2)  0.68854 (2)  0.01117 (4)  
C15  0.41687 (3)  0.17399 (2)  0.54644 (2)  0.01192 (4)  
H15  0.331068  0.156393  0.557495  0.014*  
C16  0.43759 (4)  0.15348 (3)  0.47599 (2)  0.01605 (5)  
H16A  0.519861  0.173469  0.463738  0.024*  
H16C  0.376730  0.186496  0.450617  0.024*  
H16B  0.429444  0.087369  0.468551  0.024*  
C17  0.50405 (4)  0.11832 (3)  0.58809 (2)  0.01940 (6)  
H17A  0.486521  0.130758  0.632838  0.029*  
H17C  0.588664  0.135782  0.578596  0.029*  
H17B  0.492851  0.052749  0.579522  0.029*  
C18  0.31688 (3)  0.36258 (2)  0.51945 (2)  0.01225 (4)  
H18  0.243807  0.321749  0.515231  0.015*  
C19  0.35876 (4)  0.38913 (3)  0.45265 (2)  0.01911 (6)  
H19A  0.432669  0.426977  0.455445  0.029*  
H19B  0.293831  0.423951  0.431486  0.029*  
H19C  0.376578  0.333465  0.428258  0.029*  
C20  0.27772 (4)  0.44846 (3)  0.55624 (2)  0.01955 (6)  
H20A  0.245183  0.430371  0.597694  0.029*  
H20B  0.214382  0.481141  0.532330  0.029*  
H20C  0.348555  0.488766  0.562210  0.029* 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
P1  0.00966 (3)  0.00933 (3)  0.00867 (3)  −0.00075 (2)  0.00098 (2)  −0.00078 (2) 
S1  0.01136 (3)  0.01617 (3)  0.01811 (4)  −0.00326 (2)  0.00435 (2)  −0.00375 (2) 
C1  0.01183 (9)  0.01038 (8)  0.00880 (8)  −0.00040 (7)  0.00017 (7)  −0.00053 (7) 
C2  0.01143 (9)  0.01123 (9)  0.00958 (8)  0.00031 (7)  0.00080 (7)  0.00003 (7) 
C4  0.01242 (10)  0.01699 (12)  0.01534 (11)  −0.00203 (8)  0.00165 (8)  −0.00001 (9) 
C3  0.01142 (9)  0.01434 (10)  0.01149 (9)  −0.00088 (8)  0.00079 (7)  −0.00042 (8) 
C6  0.01548 (11)  0.01714 (12)  0.01227 (10)  −0.00029 (9)  0.00285 (8)  0.00252 (8) 
C5  0.01480 (11)  0.01863 (13)  0.01600 (11)  −0.00226 (9)  0.00318 (9)  0.00265 (10) 
C9  0.01581 (10)  0.01208 (9)  0.00958 (8)  0.00048 (8)  −0.00150 (8)  −0.00077 (7) 
C8  0.01701 (11)  0.01531 (11)  0.00920 (9)  0.00022 (9)  0.00000 (8)  0.00019 (8) 
C7  0.01340 (10)  0.01293 (10)  0.00983 (8)  0.00075 (8)  0.00114 (7)  0.00080 (7) 
C10  0.02043 (13)  0.01572 (11)  0.01114 (9)  −0.00081 (10)  −0.00372 (9)  −0.00173 (8) 
C11  0.02093 (13)  0.01564 (12)  0.01478 (11)  −0.00247 (10)  −0.00493 (10)  −0.00240 (9) 
C12  0.02077 (13)  0.01437 (11)  0.01520 (11)  −0.00526 (10)  −0.00252 (10)  −0.00138 (9) 
C13  0.01903 (12)  0.01251 (10)  0.01196 (10)  −0.00426 (9)  −0.00104 (9)  −0.00057 (8) 
C14  0.01384 (10)  0.01010 (8)  0.00956 (8)  −0.00033 (7)  −0.00105 (7)  −0.00057 (7) 
C15  0.01332 (10)  0.01044 (9)  0.01200 (9)  −0.00067 (7)  0.00129 (8)  −0.00182 (7) 
C16  0.01854 (13)  0.01643 (12)  0.01318 (10)  −0.00112 (9)  0.00189 (9)  −0.00490 (9) 
C17  0.02619 (16)  0.01329 (11)  0.01871 (13)  0.00420 (11)  −0.00341 (12)  −0.00006 (10) 
C18  0.01270 (9)  0.01309 (10)  0.01097 (9)  −0.00054 (8)  0.00020 (7)  0.00197 (7) 
C19  0.02249 (15)  0.02290 (15)  0.01195 (10)  0.00001 (12)  0.00153 (10)  0.00518 (10) 
C20  0.02356 (15)  0.01691 (13)  0.01817 (13)  0.00773 (11)  0.00076 (11)  0.00065 (10) 
P1—C1  1.8565 (3)  C11—H11  0.9500 
P1—C15  1.8572 (3)  C12—C13  1.3719 (5) 
P1—C18  1.8573 (3)  C12—H12  0.9500 
P1—S1  1.9765 (2)  C13—C14  1.4345 (5) 
C1—C2  1.4285 (4)  C13—H13  0.9500 
C1—C14  1.4292 (4)  C15—C17  1.5290 (5) 
C2—C3  1.4373 (4)  C15—C16  1.5325 (5) 
C2—C7  1.4423 (4)  C15—H15  1.0000 
C4—C3  1.3732 (5)  C16—H16A  0.9800 
C4—C5  1.4230 (5)  C16—H16C  0.9800 
C4—H4  0.9500  C16—H16B  0.9800 
C3—H3  0.9500  C17—H17A  0.9800 
C6—C5  1.3658 (5)  C17—H17C  0.9800 
C6—C7  1.4319 (5)  C17—H17B  0.9800 
C6—H6  0.9500  C18—C19  1.5310 (5) 
C5—H5  0.9500  C18—C20  1.5334 (5) 
C9—C8  1.3946 (5)  C18—H18  1.0000 
C9—C10  1.4338 (5)  C19—H19A  0.9800 
C9—C14  1.4421 (4)  C19—H19B  0.9800 
C8—C7  1.3955 (5)  C19—H19C  0.9800 
C8—H8  0.9500  C20—H20A  0.9800 
C10—C11  1.3647 (6)  C20—H20B  0.9800 
C10—H10  0.9500  C20—H20C  0.9800 
C11—C12  1.4215 (5)  
C1—P1—C15  106.649 (14)  C12—C13—C14  121.82 (3) 
C1—P1—C18  105.929 (14)  C12—C13—H13  119.1 
C15—P1—C18  108.335 (15)  C14—C13—H13  119.1 
C1—P1—S1  116.260 (11)  C1—C14—C13  124.34 (3) 
C15—P1—S1  106.626 (11)  C1—C14—C9  119.51 (3) 
C18—P1—S1  112.682 (12)  C13—C14—C9  116.11 (3) 
C2—C1—C14  118.92 (3)  C17—C15—C16  111.19 (3) 
C2—C1—P1  119.08 (2)  C17—C15—P1  109.54 (2) 
C14—C1—P1  121.87 (2)  C16—C15—P1  110.98 (2) 
C1—C2—C3  124.49 (3)  C17—C15—H15  108.3 
C1—C2—C7  119.61 (3)  C16—C15—H15  108.3 
C3—C2—C7  115.86 (3)  P1—C15—H15  108.3 
C3—C4—C5  121.21 (3)  C15—C16—H16A  109.5 
C3—C4—H4  119.4  C15—C16—H16C  109.5 
C5—C4—H4  119.4  H16A—C16—H16C  109.5 
C4—C3—C2  121.86 (3)  C15—C16—H16B  109.5 
C4—C3—H3  119.1  H16A—C16—H16B  109.5 
C2—C3—H3  119.1  H16C—C16—H16B  109.5 
C5—C6—C7  121.20 (3)  C15—C17—H17A  109.5 
C5—C6—H6  119.4  C15—C17—H17C  109.5 
C7—C6—H6  119.4  H17A—C17—H17C  109.5 
C6—C5—C4  118.99 (3)  C15—C17—H17B  109.5 
C6—C5—H5  120.5  H17A—C17—H17B  109.5 
C4—C5—H5  120.5  H17C—C17—H17B  109.5 
C8—C9—C10  119.82 (3)  C19—C18—C20  110.06 (3) 
C8—C9—C14  119.94 (3)  C19—C18—P1  112.00 (2) 
C10—C9—C14  120.24 (3)  C20—C18—P1  110.92 (2) 
C9—C8—C7  121.36 (3)  C19—C18—H18  107.9 
C9—C8—H8  119.3  C20—C18—H18  107.9 
C7—C8—H8  119.3  P1—C18—H18  107.9 
C8—C7—C6  119.89 (3)  C18—C19—H19A  109.5 
C8—C7—C2  119.75 (3)  C18—C19—H19B  109.5 
C6—C7—C2  120.36 (3)  H19A—C19—H19B  109.5 
C11—C10—C9  121.22 (3)  C18—C19—H19C  109.5 
C11—C10—H10  119.4  H19A—C19—H19C  109.5 
C9—C10—H10  119.4  H19B—C19—H19C  109.5 
C10—C11—C12  118.98 (3)  C18—C20—H20A  109.5 
C10—C11—H11  120.5  C18—C20—H20B  109.5 
C12—C11—H11  120.5  H20A—C20—H20B  109.5 
C13—C12—C11  121.40 (3)  C18—C20—H20C  109.5 
C13—C12—H12  119.3  H20A—C20—H20C  109.5 
C11—C12—H12  119.3  H20B—C20—H20C  109.5 
C_{20}H_{23}PS  D_{x} = 1.291 Mg m^{−}^{3} 
M_{r} = 326.41  Mo Kα radiation, λ = 0.71073 Å 
Orthorhombic, Pbca  Cell parameters from 9781 reflections 
a = 10.932 (2) Å  θ = 2.7–52.2° 
b = 14.570 (2) Å  µ = 0.28 mm^{−}^{1} 
c = 21.091 (3) Å  T = 99 K 
V = 3359.4 (9) Å^{3}  Block, yellow 
Z = 8  0.12 × 0.11 × 0.10 mm 
F(000) = 1392 
Bruker Smart APEX II Ultra diffractometer  15462 reflections with I > 2σ(I) 
Radiation source: BRUKER Rotating Anode  R_{int} = 0.025 
ω scans  θ_{max} = 52.2°, θ_{min} = 1.9° 
Absorption correction: multiscan SADABS2016/2  h = −24→24 
T_{min} = 0.885, T_{max} = 0.929  k = −32→32 
222190 measured reflections  l = −46→46 
19329 independent reflections 
Refinement on F^{2}  0 restraints 
Leastsquares matrix: full  Hydrogen site location: inferred from neighbouring sites 
R[F^{2} > 2σ(F^{2})] = 0.018  Hatom parameters constrained 
wR(F^{2}) = 0.016  ' w2 = 1/[s^{2}(F_{o}^{2})]' 
S = 1.20  (Δ/σ)_{max} < 0.001 
18435 reflections  Δρ_{max} = 0.22 e Å^{−}^{3} 
332 parameters  Δρ_{min} = −0.20 e Å^{−}^{3} 
x  y  z  U_{iso}*/U_{eq}  
S(1)  0.604030 (3)  0.330802 (3)  0.535802 (2)  0.015  
P(1)  0.436726 (3)  0.298216 (2)  0.563275 (2)  0.009  
C(1)  0.402036 (13)  0.314540 (9)  0.648694 (7)  0.010  
C(2)  0.303081 (13)  0.264624 (9)  0.676372 (6)  0.011  
C(3)  0.206907 (13)  0.221082 (9)  0.640947 (7)  0.012  
C(4)  0.119010 (13)  0.168349 (10)  0.669895 (7)  0.015  
C(5)  0.117016 (14)  0.156675 (11)  0.736838 (7)  0.016  
C(6)  0.200110 (14)  0.203308 (10)  0.773012 (7)  0.015  
C(7)  0.293180 (13)  0.258724 (9)  0.744461 (7)  0.012  
C(8)  0.374461 (14)  0.307695 (10)  0.782637 (7)  0.014  
C(9)  0.462788 (13)  0.365439 (10)  0.756440 (7)  0.012  
C(10)  0.540525 (15)  0.418287 (10)  0.797177 (7)  0.016  
C(11)  0.625718 (15)  0.477389 (11)  0.772952 (7)  0.017  
C(12)  0.634569 (15)  0.487663 (10)  0.706141 (7)  0.017  
C(13)  0.563095 (14)  0.437053 (10)  0.665667 (7)  0.015  
C(14)  0.476514 (13)  0.370879 (9)  0.688534 (6)  0.011  
C(15)  0.416881 (13)  0.173961 (10)  0.546454 (6)  0.012  
C(16)  0.437598 (14)  0.153514 (10)  0.475988 (7)  0.016  
C(17)  0.504184 (16)  0.118305 (10)  0.588112 (8)  0.019  
C(18)  0.316860 (13)  0.362555 (10)  0.519445 (6)  0.012  
C(19)  0.358729 (15)  0.389095 (11)  0.452680 (7)  0.019  
C(20)  0.277762 (15)  0.448357 (11)  0.556255 (7)  0.020  
H(3)  0.197651  0.232378  0.590422  0.01490 (2)  
H(4)  0.049147  0.136662  0.640804  0.01786 (3)  
H(5)  0.048275  0.113192  0.758399  0.01965 (3)  
H(6)  0.197779  0.2016  0.824333  0.01794 (3)  
H(8)  0.36641  0.302111  0.83367  0.01655 (3)  
H(10)  0.52779  0.410203  0.847793  0.01894 (3)  
H(11)  0.684501  0.517412  0.803676  0.02053 (3)  
H(12)  0.698036  0.537317  0.686702  0.02031 (3)  
H(13)  0.570857  0.44906  0.615153  0.01743 (3)  
H(15)  0.322198  0.15507  0.558131  0.01430 (2)  
H(16A)  0.526384  0.17641  0.460509  0.02409 (3)  
H(16B)  0.431018  0.080369  0.469457  0.02409 (3)  
H(16C)  0.369336  0.185059  0.446309  0.02409 (3)  
H(17A)  0.487181  0.129244  0.63784  0.02905 (4)  
H(17B)  0.49115  0.046477  0.578123  0.02905 (4)  
H(17C)  0.597858  0.135302  0.577517  0.02905 (4)  
H(18)  0.240258  0.313953  0.516063  0.01472 (2)  
H(19A)  0.439974  0.430751  0.455154  0.02875 (4)  
H(19B)  0.28732  0.428366  0.430283  0.02875 (4)  
H(19C)  0.378086  0.330325  0.423378  0.02875 (4)  
H(20A)  0.240305  0.431831  0.602084  0.02943 (4)  
H(20B)  0.2097  0.483589  0.528494  0.02943 (4)  
H(20C)  0.353903  0.494179  0.563184  0.02943 (4) 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
S(1)  0.011368 (13)  0.016133 (15)  0.018203 (15)  −0.003237 (11)  0.004317 (11)  −0.003787 (12) 
P(1)  0.009546 (12)  0.009326 (12)  0.008771 (12)  −0.000740 (10)  0.001024 (10)  −0.000802 (10) 
C(1)  0.01180 (5)  0.01046 (5)  0.00875 (4)  −0.00066 (4)  0.00035 (4)  −0.00068 (4) 
C(2)  0.01140 (5)  0.01136 (5)  0.00927 (4)  −0.00019 (4)  0.00088 (4)  −0.00004 (4) 
C(3)  0.01121 (5)  0.01485 (5)  0.01118 (5)  −0.00124 (4)  0.00082 (4)  −0.00049 (4) 
C(4)  0.01237 (5)  0.01736 (6)  0.01492 (5)  −0.00259 (5)  0.00161 (4)  0.00019 (4) 
C(5)  0.01464 (6)  0.01898 (6)  0.01552 (5)  −0.00268 (5)  0.00311 (5)  0.00255 (5) 
C(6)  0.01543 (5)  0.01734 (6)  0.01207 (5)  −0.00069 (5)  0.00273 (4)  0.00265 (4) 
C(7)  0.01325 (5)  0.01324 (5)  0.00958 (5)  0.00037 (4)  0.00122 (4)  0.00078 (4) 
C(8)  0.01682 (6)  0.01548 (6)  0.00907 (5)  −0.00036 (5)  0.00001 (4)  0.00002 (4) 
C(9)  0.01593 (5)  0.01209 (5)  0.00929 (4)  −0.00004 (4)  −0.00149 (4)  −0.00077 (4) 
C(10)  0.02058 (6)  0.01593 (6)  0.01085 (5)  −0.00142 (5)  −0.00376 (4)  −0.00161 (4) 
C(11)  0.02105 (6)  0.01584 (6)  0.01443 (6)  −0.00319 (5)  −0.00488 (5)  −0.00224 (4) 
C(12)  0.02114 (6)  0.01479 (5)  0.01484 (6)  −0.00582 (5)  −0.00260 (5)  −0.00147 (4) 
C(13)  0.01926 (6)  0.01257 (5)  0.01174 (5)  −0.00476 (5)  −0.00110 (4)  −0.00057 (4) 
C(14)  0.01383 (5)  0.01016 (5)  0.00940 (4)  −0.00072 (4)  −0.00108 (4)  −0.00062 (4) 
C(15)  0.01327 (5)  0.01044 (5)  0.01203 (5)  −0.00066 (4)  0.00134 (4)  −0.00198 (4) 
C(16)  0.01842 (6)  0.01649 (6)  0.01326 (5)  −0.00103 (5)  0.00200 (4)  −0.00511 (4) 
C(17)  0.02615 (7)  0.01323 (6)  0.01872 (6)  0.00434 (5)  −0.00330 (5)  0.00001 (5) 
C(18)  0.01259 (5)  0.01309 (5)  0.01112 (5)  −0.00053 (4)  0.00021 (4)  0.00206 (4) 
C(19)  0.02267 (7)  0.02280 (7)  0.01203 (5)  0.00011 (5)  0.00147 (5)  0.00533 (5) 
C(20)  0.02364 (7)  0.01688 (6)  0.01833 (6)  0.00791 (5)  0.00080 (5)  0.00061 (5) 
S(1)—P(1)  1.9764 (1)  C(11)—H(11)  1.0830 (2) 
P(1)—C(1)  1.8564 (2)  C(12)—C(13)  1.3722 (2) 
P(1)—C(15)  1.8575 (1)  C(12)—H(12)  1.0830 (2) 
P(1)—C(18)  1.8575 (2)  C(13)—C(14)  1.4346 (2) 
C(1)—C(2)  1.4283 (2)  C(13)—H(13)  1.0830 (1) 
C(1)—C(14)  1.4293 (2)  C(15)—C(16)  1.5326 (2) 
C(2)—C(3)  1.4374 (2)  C(15)—C(17)  1.5298 (2) 
C(2)—C(7)  1.4427 (2)  C(15)—H(15)  1.0990 (1) 
C(3)—C(4)  1.3735 (2)  C(16)—H(16A)  1.0770 (2) 
C(3)—H(3)  1.0830 (1)  C(16)—H(16B)  1.0770 (1) 
C(4)—C(5)  1.4223 (2)  C(16)—H(16C)  1.0770 (2) 
C(4)—H(4)  1.0830 (2)  C(17)—H(17A)  1.0770 (2) 
C(5)—C(6)  1.3671 (2)  C(17)—H(17B)  1.0770 (2) 
C(5)—H(5)  1.0830 (2)  C(17)—H(17C)  1.0770 (2) 
C(6)—C(7)  1.4317 (2)  C(18)—C(19)  1.5303 (2) 
C(6)—H(6)  1.0830 (2)  C(18)—C(20)  1.5324 (2) 
C(7)—C(8)  1.3953 (2)  C(18)—H(18)  1.0990 (2) 
C(8)—C(9)  1.3948 (2)  C(19)—H(19A)  1.0770 (2) 
C(8)—H(8)  1.0830 (2)  C(19)—H(19B)  1.0770 (2) 
C(9)—C(10)  1.4329 (2)  C(19)—H(19C)  1.0770 (2) 
C(9)—C(14)  1.4422 (2)  C(20)—H(20A)  1.0770 (2) 
C(10)—C(11)  1.3675 (2)  C(20)—H(20B)  1.0770 (2) 
C(10)—H(10)  1.0830 (2)  C(20)—H(20C)  1.0770 (2) 
C(11)—C(12)  1.4203 (2)  
S(1)—P(1)—C(1)  116.282 (5)  C(12)—C(13)—C(14)  121.850 (13) 
S(1)—P(1)—C(15)  106.631 (5)  C(12)—C(13)—H(13)  118.722 (14) 
S(1)—P(1)—C(18)  112.686 (5)  C(14)—C(13)—H(13)  119.405 (13) 
C(1)—P(1)—C(15)  106.640 (6)  C(1)—C(14)—C(9)  119.537 (12) 
C(1)—P(1)—C(18)  105.915 (6)  C(1)—C(14)—C(13)  124.346 (13) 
C(15)—P(1)—C(18)  108.325 (7)  C(9)—C(14)—C(13)  116.067 (12) 
P(1)—C(1)—C(2)  119.088 (10)  P(1)—C(15)—C(16)  110.941 (9) 
P(1)—C(1)—C(14)  121.855 (11)  P(1)—C(15)—C(17)  109.515 (10) 
C(2)—C(1)—C(14)  118.923 (13)  P(1)—C(15)—H(15)  108.137 (10) 
C(1)—C(2)—C(3)  124.492 (12)  C(16)—C(15)—C(17)  111.205 (12) 
C(1)—C(2)—C(7)  119.604 (12)  C(16)—C(15)—H(15)  107.927 (11) 
C(3)—C(2)—C(7)  115.864 (12)  C(17)—C(15)—H(15)  109.033 (12) 
C(2)—C(3)—C(4)  121.841 (13)  C(15)—C(16)—H(16A)  111.526 (12) 
C(2)—C(3)—H(3)  120.845 (13)  C(15)—C(16)—H(16B)  107.849 (12) 
C(4)—C(3)—H(3)  117.197 (13)  C(15)—C(16)—H(16C)  112.226 (12) 
C(3)—C(4)—C(5)  121.259 (13)  H(16A)—C(16)—H(16B)  109.143 (13) 
C(3)—C(4)—H(4)  118.686 (14)  H(16A)—C(16)—H(16C)  108.426 (13) 
C(5)—C(4)—H(4)  120.040 (13)  H(16B)—C(16)—H(16C)  107.558 (12) 
C(4)—C(5)—C(6)  118.973 (13)  C(15)—C(17)—H(17A)  111.911 (13) 
C(4)—C(5)—H(5)  119.830 (14)  C(15)—C(17)—H(17B)  108.674 (13) 
C(6)—C(5)—H(5)  121.163 (14)  C(15)—C(17)—H(17C)  110.618 (13) 
C(5)—C(6)—C(7)  121.183 (14)  H(17A)—C(17)—H(17B)  108.147 (14) 
C(5)—C(6)—H(6)  122.055 (14)  H(17A)—C(17)—H(17C)  109.398 (14) 
C(7)—C(6)—H(6)  116.747 (14)  H(17B)—C(17)—H(17C)  107.978 (14) 
C(2)—C(7)—C(6)  120.370 (13)  P(1)—C(18)—C(19)  111.991 (10) 
C(2)—C(7)—C(8)  119.745 (13)  P(1)—C(18)—C(20)  110.875 (10) 
C(6)—C(7)—C(8)  119.883 (13)  P(1)—C(18)—H(18)  104.162 (10) 
C(7)—C(8)—C(9)  121.380 (14)  C(19)—C(18)—C(20)  110.088 (12) 
C(7)—C(8)—H(8)  118.903 (15)  C(19)—C(18)—H(18)  109.329 (12) 
C(9)—C(8)—H(8)  119.688 (14)  C(20)—C(18)—H(18)  110.243 (12) 
C(8)—C(9)—C(10)  119.813 (13)  C(18)—C(19)—H(19A)  110.150 (13) 
C(8)—C(9)—C(14)  119.904 (13)  C(18)—C(19)—H(19B)  108.725 (13) 
C(10)—C(9)—C(14)  120.278 (13)  C(18)—C(19)—H(19C)  112.698 (13) 
C(9)—C(10)—C(11)  121.216 (14)  H(19A)—C(19)—H(19B)  108.639 (14) 
C(9)—C(10)—H(10)  117.152 (15)  H(19A)—C(19)—H(19C)  108.289 (14) 
C(11)—C(10)—H(10)  121.624 (14)  H(19B)—C(19)—H(19C)  108.248 (13) 
C(10)—C(11)—C(12)  118.911 (13)  C(18)—C(20)—H(20A)  112.231 (13) 
C(10)—C(11)—H(11)  121.307 (15)  C(18)—C(20)—H(20B)  107.824 (13) 
C(12)—C(11)—H(11)  119.764 (14)  C(18)—C(20)—H(20C)  111.032 (13) 
C(11)—C(12)—C(13)  121.450 (14)  H(20A)—C(20)—H(20B)  109.378 (14) 
C(11)—C(12)—H(12)  119.316 (13)  H(20A)—C(20)—H(20C)  108.099 (14) 
C(13)—C(12)—H(12)  119.227 (14)  H(20B)—C(20)—H(20C)  108.195 (14) 
Acknowledgements
We thank the Fonds der Chemischen Industrie and the Danish National Research Foundation (DNRF93) funded Center for Materials Crystallography (CMC) for financial support. We thank Daniel Kratzert, University of Freiburg, for the data collection of structures 1, 2 and 4.
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