The use of effective core potentials in Hirshfeld atom refinement: making quantum crystallography faster in NoSpherA2

Kleemiss, F.; Meurer, F.; Shenderovich, I.G.; Bodensteiner, M.

doi:10.1107/S1600576725000901

research papers

JOURNAL OF
APPLIED
CRYSTALLOGRAPHY

ISSN: 1600-5767

Volume 58| Part 2| April 2025| Pages 374-382

https://doi.org/10.1107/S1600576725000901

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The use of effective core potentials in Hirshfeld atom refinement: making quantum crystallography faster in NoSpherA2

Florian Kleemiss,^a,^b ^* Florian Meurer,^b Ilya G. Shenderovich ^b and Michael Bodensteiner ^b

^aInstitute of Inorganic Chemistry, RWTH Aachen University, Landoltweg 1a, 52074 Aachen, Germany, and ^bFakultät für Chemie und Pharmazie, Universität Regensburg, Universitätsstraße 31, 93040 Regensburg, Germany
^*Correspondence e-mail: florian.kleemiss@ac.rwth-aachen.de

Edited by K. Wozniak, Warsaw University, Poland (Received 18 October 2024; accepted 31 January 2025; online 7 March 2025)

This article is part of a collection of articles on Quantum Crystallography, and commemorates the 100th anniversary of the development of Quantum Mechanics.

The refinement of structural models against X-ray diffraction data benefits significantly from employing non-spherical scattering factors in terms of precision and accuracy. Tailor-made scattering factors are available from quantum chemical calculations of the electron density using routine calculation packages. In this process, heavy elements in particular pose a difficulty due to their large numbers of electrons which are not involved in chemical bonding. An elegant way to circumvent this is by using effective core potentials. This work presents an approach for the treatment of these missing electrons in advanced structural refinement methods, such as Hirshfeld atom refinement. It also provides examples and benchmarks demonstrating up to a twofold reduction in refinement time without compromising on accuracy.

Keywords: quantum crystallography; Hirshfeld atom refinement; effective core potentials; NoSpherA2; heavy elements.

CCDC references: 2386372; 2386374

1. Introduction

The use of non-spherical scattering factors, for example those obtained by the method of (transferable) multipole models (Hansen & Coppens, 1978 ; Jha et al., 2023 ; Rybicka et al., 2022 ; Dittrich et al., 2013 ; Domagała et al., 2012 ) or Hirshfeld atom refinement (HAR) (Capelli et al., 2014 ; Fugel et al., 2018 ; Woińska et al., 2016 ; Ruth et al., 2022 ), improves the overall quality and certainty of information about a structure obtainable from diffraction data. HAR can accurately and precisely locate hydrogen atoms in light element structures from X-ray data, comparably to neutron diffraction experiments (Woińska et al., 2016; Novelli et al., 2021 ). Previous studies show that refining hydrogen atoms becomes more challenging for heavier elements (Kleemiss et al., 2021 ; Woińska et al., 2021 , 2023 ). During the calculations required to obtain non-spherical form factors for the refinement, a significant amount of time is spent calculating orbital coefficients using relativistic Hamiltonians for orbitals that show comparatively small deformation, as shown below. The increased time required for wavefunction-based refinement techniques is one of the drawbacks compared with multipole-based techniques, which this work will attempt to address for heavy elements, where the effect is most pronounced.

Within the framework of HAR, the atomic form factor for a scattering vector k is obtained from an electron density calculated for a molecule ρ(r), for example by ab initio calculations, applying the Hirshfeld weighting scheme relying on spherical neutral atomic electron densities ( $[{\rho _{\rm A,0}}]$ ) and subsequent Fourier transformation:

$[{f_{\rm HAR}}\left({\bf k} \right) = \int {w_{\rm A}}\left({\bf r} \right)\rho \left({\bf r} \right) \exp{(2\pi kr)} \, {\rm d}{\bf r}, \eqno(1)]$

where

$[{w_{\rm A}}\left({\bf r} \right) = {{{\rho _{\rm A,0}}\left({\bf r} \right)} \over {\sum \nolimits_i {\rho _{i,0}}\left({\bf r} \right)}}.]$

This is in contrast to the independent atom model, where atomic spherically averaged wavefunctions are used to parameterize a set of Gaussian functions as a fit to the form factors.

It has been shown that relativistic effects on the non-spherical scattering factors of atoms are most pronounced in the close vicinity of the core of heavier elements and can potentially affect neighbouring atoms in the structure (Bučinský et al., 2016 ; Podhorský et al., 2021 ). In addition, effects like electron correlation show similar or even more significant effects close to these heavy atoms, as shown in the work of Bučinský et al. (2016). Therefore, neglecting the impact of relativistic Hamiltonians would introduce considerable errors into the refinement (Bučinský et al., 2016). However, quantum chemical calculations that consider these effects analytically during the calculation are time consuming. Therefore, different levels of approximations are available within standard software packages. In this work, we will compare the results of refinements using three approaches of scalar relativistic calculations: the zeroth-order relativistic approximation (ZORA) (van Lenthe et al., 1993 , 1994 ), the infinite-order relativistic approximation (IORA) (Dyall & van Lenthe, 1999 ) and the Douglas–Kroll–Hess second-order Hamiltonian (DKH) (Hess, 1985 ; Wolf et al., 2002 , 2004 ).

A different approach to tackling this issue in quantum chemical calculations is the application of effective core potentials (ECPs). These were introduced to mimic the effect of the core electrons on the valence shell without explicitly calculating the electrons modelled by the potential (Kahn & Goddard, 1968 ; Kahn et al., 1976 ; Flores-Moreno et al., 2006 ). This allows comparable accuracy of theoretical calculations with much less computational effort.

ECPs are often defined in conjunction with a matching optimized basis set and parameterized by a few key features that characterize the potential:

(i) the number of electrons modelled by the ECP;

(ii) a series of contracted Gaussian functions with ranging angular momenta that model the potential exhibited by the defined number of core electrons that are not explicitly calculated;

(iii) the maximum angular momentum of the ECP expansion.

A problem arises when using this approach to calculate the form factor of atoms within the framework of HAR similar to equation (1): all electrons contribute to the scattering, and the omitted electrons require a treatment that compensates for the missed scattering power in the core regions of heavier elements during the modelling procedure.

Recently, we introduced a model for spherical scattering factors of atoms based on Slater-type orbitals (Kleemiss et al., 2024 ). The calculation of contributions to the form factor in this approach is based on the summation of all occupied orbitals, which allows the calculation of individual form factors of subsets of orbitals. Using this approach, it is possible to calculate independently the missing scattering contribution from the core electrons and generate complete form factors.

However, the total electron density obtained would be incorrect if the atomic densities were combined with the valence density obtained by an ECP-based calculation, since the nodal behaviour of the ECP valence orbitals is incorrect (Dolg & Cao, 2024 ). The electron density of the remaining orbitals [ $[{\rho _{\rm ECP}}\left({\bf r} \right)]$ ] is too low in the near-core region but too high in the mid-distance region, and only becomes reliable at the actual valence distance. This inadequacy in electron density is an intrinsic property of the ECP approach. To visualize this effect, the radial distribution function of the electron density of the valence orbitals of an all-electron calculation [ $[{\rho _{\rm val}}\left({\bf r} \right)]$ ] of Rb, the first element in the periodic table with an ECP in the def2 family, and the calculation of the density resulting from an ECP calculation are plotted in Fig. 1. Only the orbitals of the all-electron calculation that are also included in the ECP basis, i.e. removing the 28 lowest energy unrestricted orbitals, were used. This visualization follows the argumentation of Dolg & Cao (2024).

Figure 1
Difference in radial electron distribution function of 3s, 3p, 3d, 4s, 4p and 5s valence orbitals for Rb using def2-TZVPP (Leininger et al., 1996

; Peterson et al., 2003

; Weigend & Ahlrichs, 2005

; Gulde et al., 2012

; Dolg et al., 1989

; Andrae et al., 1990

) (blue), using an all-electron relativistic Jorge-TZVP-DKH calculation (orange) and the difference between the two distributions (green, dashed) against distance from the nucleus on a logarithmic scale.

To account for these differences, we propose a correction function that introduces the density difference of the missing nodal lobes of the valence orbitals to reconstruct correctly the total electron density for calculations of scattering factors.

In this work, we compare electron densities and scattering factors obtained by all-electron calculations using the aforementioned relativistic approximations and ECPs with added calculated core form factors, alongside their application to example heavy element X-ray diffraction structures. A comparison of the calculation times is also included to see if a trade off between time and accuracy might be justified.

2. Computation of correction functions and form factors

Depending on the explicit formulation of the ECP, varying valence electron densities and nodal behaviours are obtained. Different correction functions must be used for these different core approaches. Most calculations using ECPs can be divided into small-core and large-core calculations, according to the number of electrons modelled by the ECP. The flexibility of small-core potentials, where the ECP models fewer electrons, compromises the accuracy of the calculation results and the time required to perform them. Therefore, this work will focus on calculating the correction functions and form factors of small-core functions of the def2 family. However, the framework can easily be extended to other core sizes. This family of basis sets has defined ECP parameters from atoms between Rb and Rn (37 ≤ Z ≤ 86).

The fit was performed using Gaussian functions centred on the atomic position. The resulting expressions as a function of the fit parameter vectors a and b and the distance to the atomic position r are

$[\Delta \rho ({\bf a}, {\bf b}, r) = \sum \limits_i {a_i} \, \exp{( - {b_i} \, {r^2})} . \eqno(2)]$

To obtain the parameter vectors a and b, a target function t was defined. To ensure the accuracy of the result in terms of the electron density, the radial electron distribution of increasing moments and the overall number of electrons being conserved, this function was chosen as

$[\eqalignno{ t\left({\bf a}, {\bf b}\right) = & \, \left[ \int\limits_{0}^{\infty} \Delta \rho \left({\bf a}, {\bf b}, r\right) {r}^{2} \, {\rm d}r \right ]^{2} \cr & \, + \left \{ {{\int \nolimits_{0}^{\infty} \left [ \rho_{\rm ECP} \left(r\right) - \rho_{\rm val} \left(r\right) + \Delta \rho \left({\bf a}, {\bf b}, r\right) \right ] {r}^{2} \ {\rm d}r} \over {\int \nolimits_{0}^{\infty} \left [ \rho_{\rm ECP} \left(r\right) - \rho_{\rm val} \left(r\right) \right ] {r}^{2} \, {\rm d}r}} \right \}^{2} \cr & \, + \left \{ {{\int \nolimits_{0}^{\infty} \left [ \rho_{\rm ECP} \left(r\right) - \rho_{\rm val} \left(r\right) + \Delta \rho \left({\bf a}, {\bf b}, r\right) \right ] r \ {\rm d}r} \over {\int \nolimits_{0}^{\infty} \left [ \rho_{\rm ECP} \left(r\right) - \rho_{\rm val} \left(r\right) \right ] r \, {\rm d}r}} \right \}^{2} \cr & \, + \left \{ {{\int \nolimits_{0}^{\infty} \left [ \rho_{\rm ECP} \left(r\right) - \rho_{\rm val} \left(r\right) + \Delta \rho \left({\bf a}, {\bf b}, r\right) \right ] \ {\rm d}r} \over {\int \nolimits_{0}^{\infty} \left [ \rho_{\rm ECP} \left(r\right) - \rho_{\rm val} \left(r\right) \right ] \ {\rm d}r}} \right \}^{2}. &(3)}]$

The minimization of this objective function t can be considered as a simultaneous least-squares minimization of the electron density difference and its higher moments between $[\rho_{\rm ECP} \left(r \right) + \Delta \rho \left({\bf a}, {\bf b}, r \right)]$ and $[\rho_{\rm val} \left(r \right)]$ under the restraint that the number of electrons should be conserved. The latter is why the first integral is introduced over the entire radial correction function $[\Delta \rho \left({\bf a}, {\bf b}, r \right)]$ . Technically, the integrals were evaluated by numerical integration using fixed-step radial grids with a step size of 0.00008 bohr in a range of $[0\ \lt \ r \le 20]$ bohr.

The calculation of spherically averaged electron densities from a non-symmetric wavefunction was implemented in NoSpherA2 (Kleemiss et al., 2021), employing averaging on an iteratively growing angular grid for a set of radial points until a predefined convergence criterion of a relative difference between steps of less than 10⁻⁴ is reached. These calculations were performed on unrestricted ground-state wavefunctions with all electrons obtained using ORCA (Version 5.0.4; Neese et al., 2020 ) on a level of theory of IORA-MP2/Jorge-TZVP-DKH with finite nucleus approximations and picture change effects taken into account, including spin-orbit coupling (Neese et al., 2020; Barros et al., 2010 ; Camiletti et al., 2008 ; Campos & Jorge, 2013 ; Campos et al., 2017 ; Canal Neto et al., 2005 ; De Oliveira et al., 2018 ; Machado et al., 2009 ; Martins et al., 2016 ).

An initial minimization of the target function t [equation (3)] was performed using random initial values for the parameter vectors a and b employing the `minimize' function in the Python module SciPy (Virtanen et al., 2020 ). To ensure that the resulting parameters were not just local minima in the parameter space of this fit, a subsequent differential evolution search as implemented in SciPy was performed. We consider this approach crucial, because the parameters are highly correlated and a simple minimization would not be able to find the optimal parameters. The parameters for the search were chosen within bounds for $[{a_i}, \, {b_i}]$ to an interval based on the first values found in the minimum, resulting in a range of $[[ 0.5 a_i, \, 3 a_i ] \semi [ 0.3 b_i, \, 3 b_i ]]$ , respectively. The sample size for each generation was 15 per parameter, setting the convergence tolerance to 1 × 10⁻³ and the maximum number of generations to 10⁶. This tolerance was chosen because the error function can be understood as a relative error of the three moments of the initial difference between the all-electron and ECP-based calculations. This was judged to be sufficiently accurate, with an error of less than 0.33% on average over all moments of the electron density. If features of the difference function were not correctly included, as judged by plotting fits similar to Figs. 1 and 2, an additional entry was added to the parameters and the fitting routine was repeated.

This procedure was applied to all elements with (37 ≤ Z ≤ 86). The resulting function $[\Delta \rho \left({\bf a}, {\bf b}, r \right)]$ was plotted against the original differences $[\rho_{\rm ECP} - \rho_{\rm valence}]$ and the electron densities of the valence orbitals ( $[\rho_{\rm ECP}, \rho_{\rm valence})]$ themselves. The final plots are shown in Fig. 2. It was not possible to achieve this convergence limit for all elements within the available computational limits of the local resources. Future updates may improve the errors achieved (see Table S1 in the supporting information). The values obtained are included in the source code of NoSpherA2 and used when ECP-based calculations are performed.

The resulting functions can compensate for the error in nodal behaviour when evaluating the electron density at a given point to calculate atomic form factors, or can be used to calculate directly the contributions to the form factor. The form factor resulting from the correction function can be calculated according to the procedure described in the supporting information of our previous work (Kleemiss et al., 2024):

$[\eqalignno{ f_{\rm correction} \left [ {{\sin (\theta)} \over {\lambda}} \right ] & = {2 \over {[\sin (\theta)/\lambda]}} \int \limits_0^\infty \!\!\Delta \rho \left ( {\bf a}, {\bf b}, r \right ) \, r \sin \left [ 2\pi {{\sin (\theta)} \over {\lambda}} \, r \right ] \, {\rm d}r \cr & = \sum \limits_i {a_i} \sqrt { {{\pi^3} \over {b_i^3}}} \exp \left \{ - {{ [\sin (\theta)/\lambda]^2} \over {4 b_i}} \right \} . &(4)}]$

Using equation (4), an overall form factor for an atom of a quantum chemical calculation employing ECPs can be obtained according to a construction of e.g. Hirshfeld atoms, supplementing the missing information from the Slater function-based orbitals (Kleemiss et al., 2024) on the basis of atomic wavefunctions from Koga et al. (1999 , 2000 ) corresponding to the core that was omitted in the quantum chemical calculation and the correction functions according to equation (3):

$[f = f_{\rm HAR} + f_{\rm Slater \, core} + f_{\rm correction} . \eqno(5)]$

Any source of atomically partitioned valence densities could be adopted with this approach. However, the use of Hirshfeld atoms has proven to be accurate and robust (Woińska et al., 2023; Ruth et al., 2022; Chodkiewicz et al., 2020 ).

3. Implementation in NoSpherA2

Several relativistic approximations are available in quantum chemical software packages such as, for example, ORCA, pySCF or Tonto (Neese et al., 2020; Jayatilaka & Grimwood, 2003 ; Sun et al., 2018 ). Within this study, we will focus on implementations available in ORCA. Therefore, the selection of a scalar relativistic DKH Hamiltonian has been extended by a possible choice between ZORA, DKH and IORA. The selection is automatically applied during the generation of input files and the calculations are performed accordingly. Instructions for manual control are given in the supporting information.

The choice of using an ECP is included in the selection of a basis set when a heavy element is present in the structure: the def2 family of basis sets (Leininger et al., 1996 ; Peterson et al., 2003 ; Weigend & Ahlrichs, 2005 ; Gulde et al., 2012 ; Dolg et al., 1989 ; Andrae et al., 1990 ) has been included for elements up to Rn. Heavier elements will require a different basis set, since the def2 family is not parameterized for elements heavier than Rn.

Note that a combination of ECPs with a scalar relativistic Hamiltonian is unreasonable, since the relativistic effect is already taken into account by the coefficients of the potentials.

When calculating the scattering factors from a wavefunction given to NoSpherA2, the additional command line keyword -ECP will enable two additional steps during the calculation:

(i) inclusion of core electron densities for atoms with ECPs from the Slater densities as implemented previously (Kleemiss et al., 2024), and

(ii) addition of the correction function for atoms with ECPs, both in the calculation of the statistics of the non-spherical density printed after partitioning and in the calculation of the form factors.

An integer number given as a command line argument can be used to select different modes to switch between, corresponding to predefined sets of ECPs. Mode (i) defines all atoms according to the ECPs present in the def2 family of basis sets. Further modes are planned to extend this to additional basis sets, but this is not implemented at present. An updated table summarizing the available modes is printed using the -help command.

The complete form factors are printed to the resulting .tsc/.tscb file, so no additional steps are required to calculate the structure factors.

4. Results and discussion

The resulting fitting functions, the corresponding scattering factors and the performance of the resulting electron densities relative to an all-electron atomic density are given in the following subsection, followed by the application to experimental diffraction data sets from gold-, iodine- and mercury-containing molecules.

4.1. Comparison of ECP valence electron densities and all-electron valence densities

The electron densities obtained by a calculation on a level of theory of unrestricted PBE0/def2-TZVP for Rb, I, Au and Hg atoms in their respective ground states are shown in Fig. 2. Table S1 shows the size of the parameter vectors for the elements used, the minimum and maximum exponents in the vector b, and the minimum value of t obtained.

Figure 2
Plots of radial electron density from the def2 wavefunction ρ_ECP(r) (blue), valence electron density from the relativistic Jorge wavefunction ρ_val(r) (orange), the difference between these densities (green, dotted) and the fitted correction function of the difference (red, dashed) for the elements (a) Rb, (b) I, (c) Au and (d) Hg on a double logarithmic scale shifted up by an absolute value of 5 to allow logarithmic plotting. Insets contain the absolute difference between the correction function and the density difference to be fitted (blue, dashed).

The plotted electron densities (Fig. 2) show how the application of the correction function can introduce nodal behaviour similar to an all-electron calculation. Once these correction parameters are determined, no significant additional time is required to calculate the form factors compared with the Hirshfeld atoms. However, the calculation of Hirshfeld atoms from all-electron wavefunctions takes longer because the radial grids around the atomic core have to be more precise, and therefore the Fourier transform has to be performed on more grid points.

In most cases, the major contribution to the overall timing of HAR will still be the quantum chemical calculation itself. The timings of refinements using both approaches are compared in Section 4.3.

4.2. Comparison of scattering factors derived from ECP wavefunctions and all-electron calculations

The scattering factors were calculated using the same program as for the spherically averaged electron density, exchanging the function call for the electron density with that for the scattering factors and calculating the sets of spherically averaged valence scattering factors f_ECP, f_val from the exact wavefunctions used for the electron density plots in Fig. 2. The resulting scattering factors were supplemented by the correction scattering factor applying equation (4) and are plotted in Fig. 3. The correction functions are almost indistinguishable from the difference between the all-electron calculation and the ECP-based results. This confirms that the fit was successful in real space and can compensate for the differences between the nodal behaviour of the calculated orbitals in reciprocal space. An enlarged plot of the difference between the target difference and the fit is shown in an inset for each plot.

Figure 3
Plots of spherical scattering factor from the def2 wavefunction ρ_ECP(r) (blue) and from the valence orbitals of the relativistic Jorge wavefunction ρ_val(r) (orange), the difference between these scattering factors (green, dotted), and the fitted correction scattering factors obtained by the fitted density (red, dashed) for the elements (a) Rb, (b) I, (c) Au and (d) Hg. Insets contain the difference between the correction function scattering factors and those derived by the valence atoms to be fitted (blue, dashed).

However, the differences between the two curves, as shown in the insets of Fig. 3, are relatively small compared with the absolute values of the valence scattering factors at low resolution (orange and blue), so the ratio between the correction function and the overall scattering factor, including all electrons of the wavefunction calculated using scalar relativistic methods, is plotted in Fig. 4. The relative contribution of the valence orbitals to the overall scattering factor is highest in the low-resolution region. In contrast, the contribution of the scattering factor obtained by the correction functions is highest at higher resolution. This observation is not surprising, given the reciprocal relationship between the expansion of the functions with the highest correction coefficients corresponding to the highest values of b_i, yielding the most contracted electron density closest to the atomic core. The same behaviour is observed for the scattering factors of the core orbitals, which have the most significant contribution relative to the highest-resolution reflections.

Figure 4
Plots of ratios between correction spherical scattering factor and all-electron scattering factor from the relativistic calculation (blue) and between the valence scattering factor and the all-electron scattering factors (orange) for the elements (a) Rb, (b) I, (c) Au and (d) Hg.

4.3. Comparison of refinement results and performance obtained by ECP basis sets and all-electron relativistic NoSpherA2-HAR

To test the performance of the ECP basis in combination with the core densities obtained by the Slater-type densities and the calculated correction functions, a series of high-quality high-resolution data sets were collected on three compounds containing iodine, gold and mercury using Mo Kα radiation: (dppm)Au₂Br₂ (McAuliffe et al., 1979 ), [(OPPh₃)₂H][AuI₄] and [(dppe)₂Hg][PF₆]₂ [dppm is bis(diphenylphosphino)methane, dppe is 1,2-bis(diphenylphosphino)ethane]. Details of their synthesis and crystallization are given in the supporting information. The data collection statistics for these data sets are summarized in Table 1. Refinements using both the ECP and the all-electron densities were performed with NoSpherA2 (Kleemiss et al., 2021) using r2SCAN (Furness et al., 2020a ,b ) in all cases. No relativistic correction was included for the ECP-based calculations, and the def2-TZVP basis set (Weigend & Ahlrichs, 2005; Gulde et al., 2012) was used. For the all-electron calculations, the Jorge-TZVP-DKH basis set (Campos & Jorge, 2013; Barros et al., 2010; Machado et al., 2009; Camiletti et al., 2008; Canal Neto et al., 2005; De Oliveira et al., 2018; Martins et al., 2016; Campos et al., 2017) was chosen, in combination with the possible permutations of the relativistic approximations. All calculations were performed using ORCA Version 5.0.4 on a desktop computer with 12 cores on a Threadripper 5965WX with 256 GB of memory, with grid accuracy set to `Normal' and the convergence set to `NormalConv' without a solvation model. The required computation times using the different levels of theory and relativistic approximations are summarized in Table 2.

Table 1
Crystallographic data for (dppm)Au₂Br₂, [(OPPh₃)₂H][AuI₄] and [(dppe)₂Hg][PF₆]₂

Compound name	(dppm)Au₂Br₂	[(OPPh₃)₂H][AuI₄]	[(dppe)₂Hg][PF₆]₂
Sum formula	C₂₅H₂₂Au₂Br₂P₂	C₃₆H₃₀AuI₄O₂P₂	C₅₂H₄₈F₁₂HgP₆
Space group	C2/c	$[P{\overline 1}]$	P1
a (Å)	31.0668 (7)	9.23767 (5)	9.9613 (1)
b (Å)	7.30892 (3)	10.52981 (5)	11.6741 (2)
c (Å)	18.3076 (4)	10.54412 (7)	11.9272 (2)
α (°)	90	102.0929 (5)	102.495 (1)
β (°)	142.559 (5)	112.8397 (6)	107.125 (1)
γ (°)	90	90.4679 (4)	96.849 (1)
V (Å³)	2527.2 (3)	919.677 (10)	1268.99 (4)
Z	4	1	1
Z′	0.5	1	1
No. of reflections measured	134667	323488	271959
No. of merged reflections	6793	30754	33734
d_min (Å)	0.58	0.50	0.54
〈I/σ(I)〉	61.6	57.3	43.0
R_int (%)	4.12	3.50	3.53
Average multiplicity	19.82	10.52	8.06
CCDC Refcode of IAM results	2385139	2386374	2386372

Table 2
Comparison of timings rounded to seconds (wavefunction calculation/partitioning) for different models of (dppm)Au₂Br₂, [(OPPh₃)₂H][AuI₄] and [(dppe)₂Hg][PF₆]₂

Level of theory	(dppm)Au₂Br₂	[(OPPh₃)₂H][AuI₄]	[(dppe)₂Hg](PF₆)₂
DKH2-r2SCAN/Jorge-TZVP-DKH	100/53	72/10	621/62
ZORA-r2SCAN/Jorge-TZVP-DKH	61/53	63/10	266/63
IORA-r2SCAN/Jorge-TZVP-DKH	96/52	122/10	318/63
r2SCAN/def2-TZVP	46/49	37/9	165/57
No. of atoms with ECPs	2	5	1

The speedup observed when using ECPs is most evident in the wavefunction calculation (def2-TZVP versus Jorge-TZVP-DKH in Table 2). Compared with DKH2-based calculations, significant speedup can also be observed when using ZORA or IORA. In the case of [(dppe)₂Hg](PF₆)_2, a speedup of a factor of 2.33 was observed. Even with only one atom bearing electrons modelled by an ECP, as in [(dppe)₂Hg](PF₆)₂, an additional speedup of a factor of 1.62 can be observed when comparing ZORA and def2-ECP-based calculations. In the case of the gold-based compounds, the speedup between DKH2 and ZORA is less pronounced (factors of 1.63 and 1.14, respectively), but the presence of more atoms bearing ECPs leads to speedups from ZORA compared with ECPs with factors of 1.34 and 1.69, respectively.

The calculation of the scattering factors still requires elaborate numerical integration grids for ECPs – for Au/Hg, the atomic grids for all-electron calculations have 10580/11018 points; the def2-based grids only need 6262/6372 gridpoints – which reduces the time required for the observed cases by only a few milliseconds to seconds in the best case.

All refinements are compared in terms of the R values R₁ and wR₂, the highest and lowest residual density present in the unit cell, and e_gross as a measure of integrated residual density (Meindl & Henn, 2008 ) in Table 3. A visualization of the complete fractal dimension plots is shown in Figs. S1–S3. The refinements are nearly identical, with only the refinements of (dppm)Au₂Br₂ showing a slightly more symmetric distribution of the minimum and maximum residual density around 0. There is no systematic improvement or disadvantage to the use of ECPs in refining the systems studied.

Table 3
Comparison of residual density, R values and e_gross refinement results

Level of theory	Min/max residual density†	e_gross‡	R₁/wR₂
[(dppe)₂Hg][PF₆]₂
DKH2-r2SCAN/Jorge-TZVP-DKH	−1.3752/1.2489	28.9306	0.0171/0.0312
ZORA-r2SCAN/Jorge-TZVP-DKH	−1.3773/1.2495	28.9363	0.0171/0.0312
IORA-r2SCAN/Jorge-TZVP-DKH	−1.3816/1.2535	28.8395	0.0171/0.0316
r2SCAN/def2-TZVP	−1.3830/1.2588	28.9110	0.0171/0.0311
[(OPPh₃)₂H][AuI₄]
DKH2-r2SCAN/Jorge-TZVP-DKH	−1.6629/3.1812	37.0742	0.0256/0.0662
ZORA-r2SCAN/Jorge-TZVP-DKH	−1.6757/3.1850	37.0802	0.0256/0.0657
IORA-r2SCAN/Jorge-TZVP-DKH	−1.6602/3.1779	37.0491	0.0256/0.0659
r2SCAN/def2-TZVP	−1.6668/3.1943	37.1950	0.0256/0.0663
(dppm)Au₂Br₂
DKH2-r2SCAN/Jorge-TZVP-DKH	−0.8233/0.9923	143.3873	0.0165/0.0258
ZORA-r2SCAN/Jorge-TZVP-DKH	−0.8191/0.9974	143.3642	0.0165/0.0258
IORA-r2SCAN/Jorge-TZVP-DKH	−0.8381/0.9741	143.0681	0.0165/0.0257
r2SCAN/def2-TZVP	−0.8593/0.9586	143.1639	0.0165/0.0256

†Residual densities were obtained using a grid point separation of 0.1 Å rather than the default grids after refinements in Olex2 to get a more detailed evaluation of residual density values.
‡According to the definition of Meindl & Henn (2008

5. Conclusion

The zeroth-order relativistic approximation is the best choice for the tested systems when using all-electron basis sets. While the difference from the results obtained by other all-electron methods is marginal, the improvement in timing is sometimes almost a factor of 2. Therefore, the default relativistic treatment for ORCA with all-electron basis sets in NoSpherA2 was changed to ZORA and will be reported in the CIFs created automatically by NoSpherA2.

Our results clearly show that the refinement of structures containing heavy elements can benefit considerably from using ECPs in terms of computational effort required, without any significant loss of accuracy compared with results obtained after HAR using all-electron basis sets. The speedup depends on the number of heavy elements in the calculated wavefunction, so larger structures with multiple heavy element atoms benefit the most. Similar refinement statistics and residual density maps are obtained when comparing the results of the two approaches. Therefore, the use of ECPs is generally recommended, as it saves time and computational resources without compromising refinement accuracy or quality.

Supporting information

CCDC references: 2386372; 2386374

Link https://doi.org/10.5281/zenodo.13789873
Raw data (including frames) of dppm(AuBr)2

Link https://doi.org/10.5281/zenodo.13790193
Raw data (including frames) of [(dppe)2Hg][PF6]2

Link https://doi.org/10.5281/zenodo.13790014
Raw data (including frames) of [(Ph3PO)2H][AuI4]

Link https://doi.org/10.5281/zenodo.13951060
ZIP archive including CIFs with processed intensities and calculated intensities, structural model and fit parameters, and tscb files required for reproduction of the refinement results

Crystal structure: contains datablocks dppe2HgPF62_IAM, Ph3PO2HAuI4_IAM. DOI: https://doi.org/10.1107/S1600576725000901/woz5004sup1.cif

Additional information and figures, including fractal dimension plots and synthesis conditions, plots of density error for all elements, and deformation density comparisons between all-electron and ECP calculations. DOI: https://doi.org/10.1107/S1600576725000901/woz5004sup2.pdf

Computing details top

(dppe2HgPF62_IAM) top

Crystal data top

C₅₂H₄₈HgP₄·2(F₆P)	Z = 1
M_r = 1287.39	F(000) = 637.301
Triclinic, P1	D_x = 1.685 Mg m⁻³
a = 9.9613 (1) Å	Mo Kα radiation, λ = 0.71073 Å
b = 11.6741 (2) Å	Cell parameters from 52349 reflections
c = 11.9272 (2) Å	θ = 2.2–52.8°
α = 102.495 (1)°	µ = 3.30 mm⁻¹
β = 107.125 (1)°	T = 100 K
γ = 96.849 (1)°	Block, clear yellow
V = 1268.99 (4) Å³	0.16 × 0.12 × 0.08 mm

Data collection top

XtaLAB Synergy R, DW system, HyPix-Arc 150 diffractometer	61739 independent reflections
Radiation source: Rotating-anode X-ray tube, Rigaku (Mo) X-ray Source	56135 reflections with I ≥ 2u(I)
Mirror monochromator	R_int = 0.0000
Detector resolution: 10.0000 pixels mm^-1	θ_max = 54.6°, θ_min = 2.2°
ω scans	h = −22→22
Absorption correction: gaussian CrysAlisPro 1.171.43.93a (Rigaku Oxford Diffraction, 2023) Numerical absorption correction based on gaussian integration over a multifaceted crystal model Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.	k = −26→26
T_min = 0.702, T_max = 0.989	l = −27→27
61739 measured reflections

Refinement top

Refinement on F²	92 constraints
Least-squares matrix: full	H-atom parameters constrained
R[F² > 2σ(F²)] = 0.031	w = 1/[σ²(F_o²) + (0.0232P)² + 0.297P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.056	(Δ/σ)_max = −0.001
S = 1.00	Δρ_max = 2.95 e Å⁻³
61739 reflections	Δρ_min = −4.70 e Å⁻³
666 parameters	Absolute structure: Hooft, R.W.W., Straver, L.H., Spek, A.L. (2010). J. Appl. Cryst., 43, 665-668.
3 restraints	Absolute structure parameter: −0.0030 (5)

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Hg01	0.356549 (9)	0.404870 (8)	0.596890 (7)	0.010793 (19)
P002	0.14667 (3)	0.25695 (3)	0.60258 (3)	0.01059 (4)
P003	0.07164 (4)	0.42123 (3)	0.06015 (3)	0.01774 (5)
P004	0.48840 (3)	0.30833 (3)	0.46743 (3)	0.01070 (4)
P005	0.58705 (3)	0.42410 (3)	0.77603 (3)	0.01197 (4)
P006	0.21020 (3)	0.55738 (3)	0.63182 (3)	0.01137 (4)
P007	0.65741 (4)	0.90864 (3)	0.62295 (3)	0.01748 (5)
F008	−0.03517 (17)	0.40818 (16)	−0.07378 (12)	0.0391 (4)
F009	0.66385 (12)	0.92689 (10)	0.76153 (9)	0.02613 (18)
F00B	0.74950 (13)	1.04220 (10)	0.65708 (12)	0.0317 (2)
F00D	0.51324 (11)	0.96139 (11)	0.59456 (10)	0.02798 (19)
C00E	0.69519 (12)	0.56620 (11)	0.87543 (11)	0.01459 (15)
F00F	0.80189 (12)	0.85683 (11)	0.65081 (11)	0.0293 (2)
F00G	0.04680 (19)	0.27829 (11)	0.03452 (13)	0.0420 (3)
F00H	0.65017 (13)	0.89095 (11)	0.48371 (10)	0.0299 (2)
C00I	0.62056 (12)	0.25940 (11)	0.58082 (10)	0.01417 (15)
H00a	0.57149 (12)	0.19626 (11)	0.60678 (10)	0.01700 (18)*
H00b	0.68908 (12)	0.22516 (11)	0.54430 (10)	0.01700 (18)*
F00K	0.09795 (13)	0.56301 (10)	0.08478 (12)	0.0318 (2)
C00L	0.04048 (12)	0.47001 (10)	0.62498 (11)	0.01451 (15)
H00c	−0.02258 (12)	0.44194 (10)	0.53898 (11)	0.01741 (18)*
H00d	−0.00737 (12)	0.52336 (10)	0.66999 (11)	0.01741 (18)*
C00M	0.29558 (12)	0.65134 (10)	0.78528 (10)	0.01312 (14)
C00N	0.67046 (14)	0.34665 (12)	0.33687 (12)	0.01712 (18)
H00N	0.66210 (14)	0.26221 (12)	0.31650 (12)	0.0205 (2)*
C00O	0.17235 (11)	0.14760 (10)	0.68899 (10)	0.01251 (14)
C00P	0.70194 (11)	0.36506 (12)	0.69166 (10)	0.01512 (16)
H00e	0.74541 (11)	0.42985 (12)	0.66415 (10)	0.01814 (19)*
H00f	0.78062 (11)	0.33903 (12)	0.74691 (10)	0.01814 (19)*
C00R	0.05567 (12)	0.36102 (10)	0.67738 (10)	0.01376 (15)
H00g	0.11040 (12)	0.38900 (10)	0.76550 (10)	0.01651 (18)*
H00h	−0.04072 (12)	0.31827 (10)	0.66772 (10)	0.01651 (18)*
C00S	0.41359 (17)	0.06160 (12)	0.35566 (13)	0.0210 (2)
H00S	0.47722 (17)	0.05111 (12)	0.42795 (13)	0.0253 (3)*
C00T	−0.09880 (12)	0.09101 (10)	0.44568 (10)	0.01475 (15)
H00T	−0.10603 (12)	0.06946 (10)	0.51637 (10)	0.01770 (19)*
C00U	0.08505 (12)	0.12431 (11)	0.75757 (11)	0.01520 (16)
H00U	0.01188 (12)	0.16859 (11)	0.76212 (11)	0.01824 (19)*
C00V	0.52273 (15)	0.18000 (13)	1.01824 (12)	0.0202 (2)
H00V	0.50854 (15)	0.13031 (13)	1.06882 (12)	0.0243 (2)*
C00W	0.72484 (15)	0.59222 (12)	1.00112 (11)	0.01895 (19)
H00W	0.68719 (15)	0.53560 (12)	1.03601 (11)	0.0227 (2)*
F00X	0.1805 (2)	0.43416 (15)	0.19232 (11)	0.0565 (5)
F00Y	0.19996 (13)	0.41770 (13)	0.00480 (14)	0.0395 (3)
C010	0.46274 (13)	0.34086 (12)	0.92827 (11)	0.01668 (17)
H010	0.40653 (13)	0.40025 (12)	0.91644 (11)	0.0200 (2)*
F011	−0.05815 (18)	0.42416 (15)	0.11148 (16)	0.0480 (4)
C012	0.24397 (19)	−0.02165 (17)	0.15290 (16)	0.0273 (3)
H012	0.19235 (19)	−0.08924 (17)	0.08693 (16)	0.0328 (4)*
C013	0.01374 (11)	0.18127 (10)	0.45534 (10)	0.01232 (14)
C014	0.07645 (15)	0.73853 (11)	0.56688 (12)	0.01798 (18)
H014	0.04949 (15)	0.74284 (11)	0.63751 (12)	0.0216 (2)*
C015	0.75027 (14)	0.65055 (13)	0.82468 (12)	0.01937 (19)
H015	0.72760 (14)	0.63415 (13)	0.73894 (12)	0.0232 (2)*
C016	0.24833 (16)	0.64014 (12)	0.88252 (12)	0.0197 (2)
H016	0.16300 (16)	0.58527 (12)	0.86883 (12)	0.0236 (2)*
C017	0.15773 (12)	0.65503 (10)	0.53540 (10)	0.01427 (15)
C019	0.39531 (12)	0.17615 (10)	0.34598 (10)	0.01327 (14)
C01A	0.30095 (15)	0.19152 (13)	0.23990 (11)	0.01921 (19)
H01A	0.28839 (15)	0.26956 (13)	0.23362 (11)	0.0230 (2)*
C01C	0.19526 (16)	0.64673 (14)	0.43069 (12)	0.0209 (2)
H01C	0.24925 (16)	0.58915 (14)	0.40875 (12)	0.0250 (2)*
C01D	0.07513 (18)	0.80878 (14)	0.39103 (13)	0.0248 (3)
H01D	0.04916 (18)	0.86268 (14)	0.34273 (13)	0.0298 (3)*
C01E	0.30377 (14)	−0.00273 (12)	0.74851 (12)	0.01820 (18)
H01E	0.37908 (14)	−0.04518 (12)	0.74665 (12)	0.0218 (2)*
C01F	0.42041 (12)	0.73342 (11)	0.80579 (10)	0.01483 (15)
H01F	0.45303 (12)	0.74047 (11)	0.73987 (10)	0.01780 (18)*
C01G	0.83829 (16)	0.75856 (13)	0.89967 (15)	0.0232 (2)
H01G	0.87826 (16)	0.81461 (13)	0.86544 (15)	0.0278 (3)*
C01H	−0.19977 (14)	0.03316 (12)	0.33241 (11)	0.01779 (18)
H01H	−0.27578 (14)	−0.02815 (12)	0.32574 (11)	0.0213 (2)*
C01I	0.1527 (2)	0.72384 (16)	0.35838 (14)	0.0271 (3)
H01I	0.1771 (2)	0.71818 (16)	0.28637 (14)	0.0326 (3)*
C01J	0.03528 (17)	0.81523 (13)	0.49421 (13)	0.0220 (2)
H01J	−0.02008 (17)	0.87203 (13)	0.51511 (13)	0.0264 (3)*
C01L	0.62369 (15)	0.16398 (13)	0.95968 (12)	0.01933 (19)
H01L	0.67746 (15)	0.10278 (13)	0.96976 (12)	0.0232 (2)*
C01N	0.32728 (19)	0.71000 (14)	0.99963 (12)	0.0244 (3)
H01N	0.29669 (19)	0.70155 (14)	1.06621 (12)	0.0293 (3)*
C01O	0.21550 (15)	−0.02675 (12)	0.81545 (12)	0.01851 (19)
H01O	0.23023 (15)	−0.08612 (12)	0.85872 (12)	0.0222 (2)*
C01P	0.64635 (13)	0.23721 (12)	0.88634 (11)	0.01652 (17)
H01P	0.71618 (13)	0.22667 (12)	0.84727 (11)	0.0198 (2)*
F01Q	0.56512 (12)	0.77596 (9)	0.58890 (10)	0.02745 (19)
C01R	0.22554 (17)	0.09232 (16)	0.14362 (13)	0.0259 (3)
H01R	0.16138 (17)	0.10256 (16)	0.07145 (13)	0.0311 (3)*
C01S	−0.07978 (15)	0.15584 (14)	0.23777 (11)	0.0206 (2)
H01S	−0.07416 (15)	0.17840 (14)	0.16713 (11)	0.0247 (3)*
C01T	0.60645 (16)	0.52450 (12)	0.43835 (13)	0.0202 (2)
H01T	0.55351 (16)	0.56106 (12)	0.48560 (13)	0.0242 (2)*
C01U	0.45056 (18)	0.79197 (15)	1.01944 (13)	0.0222 (2)
H01U	0.50364 (18)	0.83961 (15)	1.09944 (13)	0.0267 (3)*
C01V	0.56591 (11)	0.32620 (10)	0.87051 (10)	0.01314 (14)
C01W	0.69686 (19)	0.59457 (13)	0.39868 (16)	0.0260 (3)
H01W	0.70684 (19)	0.67914 (13)	0.42010 (16)	0.0312 (3)*
C01X	0.80999 (17)	0.70167 (13)	1.07530 (13)	0.0239 (2)
H01X	0.82885 (17)	0.72005 (13)	1.16072 (13)	0.0286 (3)*
C01Y	−0.18956 (15)	0.06506 (12)	0.22857 (11)	0.01919 (19)
H01Y	−0.25792 (15)	0.02457 (12)	0.15124 (11)	0.0230 (2)*
C01Z	0.44269 (15)	0.26846 (13)	1.00291 (12)	0.0201 (2)
H01Z	0.37424 (15)	0.27956 (13)	1.04337 (12)	0.0241 (2)*
C022	0.77231 (16)	0.54069 (14)	0.32787 (14)	0.0228 (2)
H022	0.83381 (16)	0.58881 (14)	0.30116 (14)	0.0274 (3)*
C023	0.59414 (12)	0.40050 (10)	0.40831 (10)	0.01325 (14)
C024	0.86730 (17)	0.78384 (13)	1.02508 (15)	0.0248 (3)
H024	0.92654 (17)	0.85763 (13)	1.07636 (15)	0.0297 (3)*
C025	0.02187 (14)	0.21355 (13)	0.35086 (11)	0.01715 (18)
H025	0.09721 (14)	0.27525 (13)	0.35711 (11)	0.0206 (2)*
C027	0.75863 (18)	0.41691 (16)	0.29569 (15)	0.0197 (2)
H027	0.80910 (18)	0.38052 (16)	0.24596 (15)	0.0237 (3)*
C029	0.49663 (14)	0.80457 (12)	0.92246 (12)	0.01831 (18)
H029	0.58001 (14)	0.86170 (12)	0.93608 (12)	0.0220 (2)*
C02A	0.28144 (12)	0.08344 (11)	0.68445 (11)	0.01505 (16)
H02A	0.34038 (12)	0.09880 (11)	0.63750 (11)	0.01806 (19)*
C3	0.10609 (14)	0.03579 (12)	0.81912 (11)	0.01748 (18)
H3	0.04525 (14)	0.01812 (12)	0.86384 (11)	0.0210 (2)*
C4	0.3377 (2)	−0.03746 (13)	0.25844 (15)	0.0275 (3)
H4	0.3501 (2)	−0.11566 (13)	0.26424 (15)	0.0330 (3)*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Hg01	0.00842 (3)	0.01265 (3)	0.01185 (3)	0.002655 (18)	0.004644 (18)	0.002240 (19)
P002	0.00996 (9)	0.01085 (10)	0.01166 (9)	0.00190 (7)	0.00468 (7)	0.00295 (7)
P003	0.01872 (12)	0.02185 (14)	0.01518 (12)	0.00591 (11)	0.00727 (10)	0.00672 (10)
P004	0.01115 (9)	0.01188 (10)	0.01051 (9)	0.00298 (8)	0.00520 (7)	0.00324 (7)
P005	0.00957 (9)	0.01579 (11)	0.01029 (9)	0.00235 (8)	0.00337 (7)	0.00284 (8)
P006	0.01124 (9)	0.01089 (10)	0.01248 (10)	0.00270 (8)	0.00486 (8)	0.00250 (8)
P007	0.01944 (13)	0.01766 (13)	0.02227 (14)	0.00737 (10)	0.01216 (11)	0.01006 (11)
F008	0.0339 (6)	0.0541 (9)	0.0208 (5)	0.0134 (6)	−0.0027 (5)	0.0062 (5)
F009	0.0358 (5)	0.0268 (4)	0.0216 (4)	0.0114 (4)	0.0141 (4)	0.0088 (3)
F00B	0.0318 (5)	0.0203 (4)	0.0495 (7)	0.0030 (4)	0.0223 (5)	0.0113 (4)
F00D	0.0242 (4)	0.0371 (5)	0.0349 (5)	0.0169 (4)	0.0161 (4)	0.0198 (4)
C00E	0.0132 (4)	0.0151 (4)	0.0139 (4)	0.0021 (3)	0.0027 (3)	0.0036 (3)
F00F	0.0253 (4)	0.0333 (5)	0.0374 (5)	0.0172 (4)	0.0146 (4)	0.0134 (4)
F00G	0.0678 (9)	0.0224 (5)	0.0431 (7)	0.0078 (5)	0.0287 (7)	0.0098 (5)
F00H	0.0393 (6)	0.0369 (5)	0.0268 (4)	0.0152 (4)	0.0211 (4)	0.0171 (4)
C00I	0.0133 (3)	0.0176 (4)	0.0137 (4)	0.0056 (3)	0.0059 (3)	0.0051 (3)
F00K	0.0343 (5)	0.0225 (4)	0.0401 (6)	0.0072 (4)	0.0145 (5)	0.0074 (4)
C00L	0.0116 (3)	0.0130 (4)	0.0196 (4)	0.0032 (3)	0.0064 (3)	0.0035 (3)
C00M	0.0147 (3)	0.0120 (4)	0.0133 (3)	0.0031 (3)	0.0057 (3)	0.0031 (3)
C00N	0.0194 (4)	0.0175 (4)	0.0186 (4)	0.0036 (4)	0.0122 (4)	0.0048 (3)
C00O	0.0121 (3)	0.0132 (4)	0.0124 (3)	0.0020 (3)	0.0039 (3)	0.0044 (3)
C00P	0.0105 (3)	0.0224 (5)	0.0133 (4)	0.0040 (3)	0.0054 (3)	0.0043 (3)
C00R	0.0131 (3)	0.0139 (4)	0.0163 (4)	0.0030 (3)	0.0083 (3)	0.0032 (3)
C00S	0.0304 (6)	0.0133 (4)	0.0187 (5)	0.0029 (4)	0.0076 (4)	0.0041 (3)
C00T	0.0154 (4)	0.0141 (4)	0.0136 (4)	0.0002 (3)	0.0036 (3)	0.0042 (3)
C00U	0.0135 (3)	0.0183 (4)	0.0149 (4)	0.0022 (3)	0.0056 (3)	0.0059 (3)
C00V	0.0219 (5)	0.0225 (5)	0.0180 (5)	0.0028 (4)	0.0077 (4)	0.0082 (4)
C00W	0.0216 (5)	0.0173 (5)	0.0139 (4)	0.0010 (4)	0.0019 (3)	0.0028 (3)
F00X	0.0800 (11)	0.0542 (9)	0.0211 (5)	0.0397 (8)	−0.0094 (6)	0.0031 (5)
F00Y	0.0277 (5)	0.0452 (7)	0.0592 (8)	0.0163 (5)	0.0285 (5)	0.0168 (6)
C010	0.0159 (4)	0.0204 (5)	0.0164 (4)	0.0047 (3)	0.0083 (3)	0.0054 (3)
F011	0.0566 (8)	0.0515 (8)	0.0626 (9)	0.0157 (7)	0.0511 (8)	0.0229 (7)
C012	0.0246 (6)	0.0257 (7)	0.0237 (6)	−0.0035 (6)	0.0090 (5)	−0.0067 (5)
C013	0.0124 (3)	0.0127 (3)	0.0124 (3)	0.0021 (3)	0.0050 (3)	0.0032 (3)
C014	0.0221 (5)	0.0153 (4)	0.0172 (4)	0.0066 (4)	0.0062 (4)	0.0046 (3)
C015	0.0184 (4)	0.0200 (5)	0.0197 (5)	0.0021 (4)	0.0054 (4)	0.0073 (4)
C016	0.0256 (5)	0.0165 (4)	0.0166 (4)	−0.0019 (4)	0.0115 (4)	0.0006 (3)
C017	0.0158 (4)	0.0137 (4)	0.0134 (4)	0.0029 (3)	0.0045 (3)	0.0041 (3)
C019	0.0145 (3)	0.0133 (4)	0.0122 (3)	0.0015 (3)	0.0059 (3)	0.0025 (3)
C01A	0.0203 (5)	0.0223 (5)	0.0131 (4)	0.0069 (4)	0.0035 (3)	0.0020 (3)
C01C	0.0258 (5)	0.0231 (5)	0.0173 (4)	0.0062 (4)	0.0104 (4)	0.0074 (4)
C01D	0.0305 (6)	0.0198 (5)	0.0200 (5)	0.0008 (5)	0.0008 (5)	0.0096 (4)
C01E	0.0201 (5)	0.0167 (4)	0.0201 (5)	0.0062 (4)	0.0069 (4)	0.0078 (4)
C01F	0.0146 (4)	0.0151 (4)	0.0148 (4)	0.0022 (3)	0.0052 (3)	0.0039 (3)
C01G	0.0212 (5)	0.0183 (5)	0.0283 (6)	0.0008 (4)	0.0055 (4)	0.0082 (4)
C01H	0.0175 (4)	0.0168 (4)	0.0152 (4)	−0.0020 (3)	0.0021 (3)	0.0039 (3)
C01I	0.0353 (7)	0.0293 (7)	0.0190 (5)	0.0040 (6)	0.0095 (5)	0.0113 (5)
C01J	0.0256 (6)	0.0160 (5)	0.0224 (5)	0.0062 (4)	0.0031 (4)	0.0069 (4)
C01L	0.0208 (5)	0.0200 (5)	0.0184 (4)	0.0060 (4)	0.0059 (4)	0.0074 (4)
C01N	0.0343 (7)	0.0217 (5)	0.0152 (4)	−0.0027 (5)	0.0115 (5)	0.0005 (4)
C01O	0.0220 (5)	0.0169 (4)	0.0166 (4)	0.0023 (4)	0.0049 (4)	0.0071 (3)
C01P	0.0150 (4)	0.0200 (5)	0.0162 (4)	0.0057 (3)	0.0062 (3)	0.0054 (3)
F01Q	0.0338 (5)	0.0205 (4)	0.0309 (5)	0.0006 (3)	0.0167 (4)	0.0067 (3)
C01R	0.0228 (5)	0.0316 (7)	0.0155 (5)	0.0055 (5)	0.0020 (4)	−0.0039 (4)
C01S	0.0219 (5)	0.0258 (6)	0.0127 (4)	−0.0003 (4)	0.0050 (4)	0.0060 (4)
C01T	0.0258 (5)	0.0141 (4)	0.0243 (5)	0.0029 (4)	0.0138 (4)	0.0052 (4)
C01U	0.0267 (6)	0.0204 (6)	0.0145 (5)	−0.0005 (5)	0.0055 (4)	−0.0009 (4)
C01V	0.0120 (3)	0.0154 (4)	0.0118 (3)	0.0023 (3)	0.0042 (3)	0.0028 (3)
C01W	0.0328 (7)	0.0159 (5)	0.0335 (7)	0.0007 (5)	0.0180 (6)	0.0077 (5)
C01X	0.0273 (6)	0.0187 (5)	0.0175 (5)	0.0004 (4)	−0.0008 (4)	0.0018 (4)
C01Y	0.0199 (5)	0.0203 (5)	0.0134 (4)	−0.0005 (4)	0.0023 (3)	0.0032 (3)
C01Z	0.0205 (5)	0.0249 (6)	0.0182 (4)	0.0040 (4)	0.0105 (4)	0.0073 (4)
C022	0.0231 (5)	0.0239 (6)	0.0234 (5)	−0.0019 (4)	0.0108 (4)	0.0096 (4)
C023	0.0143 (3)	0.0137 (4)	0.0132 (3)	0.0020 (3)	0.0067 (3)	0.0041 (3)
C024	0.0214 (5)	0.0171 (5)	0.0281 (6)	−0.0001 (4)	0.0003 (5)	0.0033 (4)
C025	0.0176 (4)	0.0203 (5)	0.0138 (4)	−0.0004 (4)	0.0065 (3)	0.0055 (4)
C027	0.0191 (5)	0.0252 (6)	0.0193 (6)	0.0023 (4)	0.0119 (5)	0.0082 (5)
C029	0.0171 (4)	0.0172 (4)	0.0175 (4)	0.0012 (4)	0.0039 (3)	0.0018 (3)
C02A	0.0150 (4)	0.0148 (4)	0.0171 (4)	0.0042 (3)	0.0063 (3)	0.0055 (3)
C3	0.0182 (4)	0.0204 (5)	0.0145 (4)	0.0007 (4)	0.0057 (3)	0.0071 (3)
C4	0.0382 (8)	0.0148 (5)	0.0267 (6)	−0.0012 (5)	0.0128 (6)	0.0002 (4)

Geometric parameters (Å, º) top

Hg01—P002	2.5750 (3)	C012—H012	0.9500
Hg01—P004	2.4847 (3)	C012—C01R	1.388 (3)
Hg01—P005	2.5822 (3)	C012—C4	1.393 (3)
Hg01—P006	2.4748 (3)	C013—C025	1.3989 (16)
P002—C00O	1.8026 (11)	C014—H014	0.9500
P002—C00R	1.8340 (11)	C014—C017	1.3984 (17)
P002—C013	1.8161 (11)	C014—C01J	1.3911 (18)
P003—F008	1.6007 (14)	C015—H015	0.9500
P003—F00G	1.6048 (13)	C015—C01G	1.395 (2)
P003—F00K	1.5922 (12)	C016—H016	0.9500
P003—F00X	1.5920 (12)	C016—C01N	1.3935 (19)
P003—F00Y	1.6028 (11)	C017—C01C	1.3930 (17)
P003—F011	1.5859 (12)	C019—C01A	1.3980 (17)
P004—C00I	1.8313 (11)	C01A—H01A	0.9500
P004—C019	1.7999 (11)	C01A—C01R	1.3904 (19)
P004—C023	1.8055 (11)	C01C—H01C	0.9500
P005—C00E	1.8134 (12)	C01C—C01I	1.395 (2)
P005—C00P	1.8340 (11)	C01D—H01D	0.9500
P005—C01V	1.8056 (12)	C01D—C01I	1.388 (3)
P006—C00L	1.8375 (11)	C01D—C01J	1.390 (2)
P006—C00M	1.8079 (11)	C01E—H01E	0.9500
P006—C017	1.8030 (12)	C01E—C01O	1.3932 (19)
P007—F009	1.6011 (10)	C01E—C02A	1.3896 (17)
P007—F00B	1.6132 (11)	C01F—H01F	0.9500
P007—F00D	1.6034 (10)	C01F—C029	1.3893 (17)
P007—F00F	1.6002 (10)	C01G—H01G	0.9500
P007—F00H	1.6073 (11)	C01G—C024	1.393 (2)
P007—F01Q	1.6056 (11)	C01H—H01H	0.9500
C00E—C00W	1.3956 (17)	C01H—C01Y	1.3956 (18)
C00E—C015	1.4006 (19)	C01I—H01I	0.9500
C00I—H00a	0.9900	C01J—H01J	0.9500
C00I—H00b	0.9900	C01L—H01L	0.9500
C00I—C00P	1.5334 (17)	C01L—C01P	1.3931 (18)
C00L—H00c	0.9900	C01N—H01N	0.9500
C00L—H00d	0.9900	C01N—C01U	1.389 (2)
C00L—C00R	1.5383 (17)	C01O—H01O	0.9500
C00M—C016	1.3987 (16)	C01O—C3	1.388 (2)
C00M—C01F	1.3998 (16)	C01P—H01P	0.9500
C00N—H00N	0.9500	C01P—C01V	1.3969 (17)
C00N—C023	1.4011 (15)	C01R—H01R	0.9500
C00N—C027	1.3935 (19)	C01S—H01S	0.9500
C00O—C00U	1.3993 (15)	C01S—C01Y	1.3905 (19)
C00O—C02A	1.3986 (16)	C01S—C025	1.3923 (18)
C00P—H00e	0.9900	C01T—H01T	0.9500
C00P—H00f	0.9900	C01T—C01W	1.3953 (19)
C00R—H00g	0.9900	C01T—C023	1.3950 (17)
C00R—H00h	0.9900	C01U—H01U	0.9500
C00S—H00S	0.9500	C01U—C029	1.393 (2)
C00S—C019	1.3955 (17)	C01W—H01W	0.9500
C00S—C4	1.396 (2)	C01W—C022	1.389 (2)
C00T—H00T	0.9500	C01X—H01X	0.9500
C00T—C013	1.4036 (15)	C01X—C024	1.387 (2)
C00T—C01H	1.3914 (16)	C01Y—H01Y	0.9500
C00U—H00U	0.9500	C01Z—H01Z	0.9500
C00U—C3	1.3929 (17)	C022—H022	0.9500
C00V—H00V	0.9500	C022—C027	1.392 (2)
C00V—C01L	1.392 (2)	C024—H024	0.9500
C00V—C01Z	1.388 (2)	C025—H025	0.9500
C00W—H00W	0.9500	C027—H027	0.9500
C00W—C01X	1.3947 (19)	C029—H029	0.9500
C010—H010	0.9500	C02A—H02A	0.9500
C010—C01V	1.4029 (15)	C3—H3	0.9500
C010—C01Z	1.3917 (18)	C4—H4	0.9500

P004—Hg01—P002	112.536 (12)	C01R—C012—H012	119.82 (9)
P005—Hg01—P002	111.620 (11)	C4—C012—H012	119.82 (10)
P005—Hg01—P004	85.078 (11)	C4—C012—C01R	120.36 (15)
P006—Hg01—P002	84.953 (11)	C00T—C013—P002	120.30 (8)
P006—Hg01—P004	147.170 (12)	C025—C013—P002	120.19 (8)
P006—Hg01—P005	115.128 (12)	C025—C013—C00T	119.51 (10)
C00O—P002—Hg01	122.69 (4)	C017—C014—H014	120.17 (7)
C00R—P002—Hg01	100.45 (4)	C01J—C014—H014	120.17 (9)
C00R—P002—C00O	104.99 (5)	C01J—C014—C017	119.65 (12)
C013—P002—Hg01	115.10 (4)	H015—C015—C00E	119.91 (7)
C013—P002—C00O	106.86 (5)	C01G—C015—C00E	120.18 (13)
C013—P002—C00R	104.47 (5)	C01G—C015—H015	119.91 (9)
F00G—P003—F008	90.21 (9)	H016—C016—C00M	120.23 (7)
F00K—P003—F008	89.74 (8)	C01N—C016—C00M	119.54 (12)
F00K—P003—F00G	179.23 (7)	C01N—C016—H016	120.23 (8)
F00X—P003—F008	178.86 (10)	C014—C017—P006	118.60 (9)
F00X—P003—F00G	89.79 (9)	C01C—C017—P006	120.96 (10)
F00X—P003—F00K	90.25 (8)	C01C—C017—C014	120.43 (11)
F00Y—P003—F008	88.28 (8)	C00S—C019—P004	122.29 (9)
F00Y—P003—F00G	89.26 (8)	C01A—C019—P004	117.50 (9)
F00Y—P003—F00K	89.97 (7)	C01A—C019—C00S	120.21 (11)
F00Y—P003—F00X	90.59 (10)	H01A—C01A—C019	120.08 (7)
F011—P003—F008	90.24 (9)	C01R—C01A—C019	119.85 (13)
F011—P003—F00G	90.66 (8)	C01R—C01A—H01A	120.08 (9)
F011—P003—F00K	90.11 (8)	H01C—C01C—C017	120.35 (8)
F011—P003—F00X	90.89 (10)	C01I—C01C—C017	119.30 (14)
F011—P003—F00Y	178.52 (9)	C01I—C01C—H01C	120.35 (9)
C00I—P004—Hg01	99.68 (4)	C01I—C01D—H01D	119.91 (8)
C019—P004—Hg01	118.66 (4)	C01J—C01D—H01D	119.91 (9)
C019—P004—C00I	106.13 (5)	C01J—C01D—C01I	120.19 (13)
C023—P004—Hg01	118.95 (4)	C01O—C01E—H01E	120.06 (8)
C023—P004—C00I	104.48 (5)	C02A—C01E—H01E	120.06 (7)
C023—P004—C019	106.89 (5)	C02A—C01E—C01O	119.87 (12)
C00E—P005—Hg01	123.61 (4)	H01F—C01F—C00M	119.98 (6)
C00P—P005—Hg01	99.83 (4)	C029—C01F—C00M	120.05 (11)
C00P—P005—C00E	103.63 (6)	C029—C01F—H01F	119.98 (7)
C01V—P005—Hg01	113.11 (4)	H01G—C01G—C015	120.17 (9)
C01V—P005—C00E	107.66 (6)	C024—C01G—C015	119.66 (14)
C01V—P005—C00P	107.06 (5)	C024—C01G—H01G	120.17 (9)
C00L—P006—Hg01	103.90 (4)	H01H—C01H—C00T	119.95 (7)
C00M—P006—Hg01	107.74 (4)	C01Y—C01H—C00T	120.10 (11)
C00M—P006—C00L	108.00 (5)	C01Y—C01H—H01H	119.95 (7)
C017—P006—Hg01	124.58 (4)	C01D—C01I—C01C	120.38 (14)
C017—P006—C00L	104.65 (5)	H01I—C01I—C01C	119.81 (9)
C017—P006—C00M	107.04 (5)	H01I—C01I—C01D	119.81 (8)
F00B—P007—F009	90.04 (6)	C01D—C01J—C014	120.01 (14)
F00D—P007—F009	89.74 (6)	H01J—C01J—C014	120.00 (9)
F00D—P007—F00B	89.38 (6)	H01J—C01J—C01D	120.00 (9)
F00F—P007—F009	90.56 (6)	H01L—C01L—C00V	119.82 (8)
F00F—P007—F00B	90.22 (7)	C01P—C01L—C00V	120.37 (12)
F00F—P007—F00D	179.51 (6)	C01P—C01L—H01L	119.82 (8)
F00H—P007—F009	179.60 (6)	H01N—C01N—C016	119.86 (8)
F00H—P007—F00B	89.84 (7)	C01U—C01N—C016	120.29 (13)
F00H—P007—F00D	89.88 (6)	C01U—C01N—H01N	119.86 (8)
F00H—P007—F00F	89.82 (6)	H01O—C01O—C01E	119.90 (8)
F01Q—P007—F009	89.94 (6)	C3—C01O—C01E	120.19 (11)
F01Q—P007—F00B	179.75 (7)	C3—C01O—H01O	119.90 (7)
F01Q—P007—F00D	90.37 (6)	H01P—C01P—C01L	120.16 (8)
F01Q—P007—F00F	90.03 (6)	C01V—C01P—C01L	119.68 (11)
F01Q—P007—F00H	90.18 (6)	C01V—C01P—H01P	120.16 (7)
C00W—C00E—P005	121.10 (10)	C01A—C01R—C012	120.03 (15)
C015—C00E—P005	119.14 (10)	H01R—C01R—C012	119.99 (9)
C015—C00E—C00W	119.75 (11)	H01R—C01R—C01A	119.99 (9)
H00a—C00I—P004	109.57 (4)	C01Y—C01S—H01S	120.12 (7)
H00b—C00I—P004	109.57 (3)	C025—C01S—H01S	120.12 (8)
H00b—C00I—H00a	108.1	C025—C01S—C01Y	119.77 (12)
C00P—C00I—P004	110.41 (8)	C01W—C01T—H01T	120.15 (9)
C00P—C00I—H00a	109.57 (6)	C023—C01T—H01T	120.15 (7)
C00P—C00I—H00b	109.57 (6)	C023—C01T—C01W	119.70 (12)
H00c—C00L—P006	108.58 (4)	H01U—C01U—C01N	119.87 (8)
H00d—C00L—P006	108.58 (4)	C029—C01U—C01N	120.26 (13)
H00d—C00L—H00c	107.6	C029—C01U—H01U	119.87 (8)
C00R—C00L—P006	114.74 (8)	C010—C01V—P005	117.61 (9)
C00R—C00L—H00c	108.58 (6)	C01P—C01V—P005	122.64 (8)
C00R—C00L—H00d	108.58 (6)	C01P—C01V—C010	119.75 (11)
C016—C00M—P006	123.44 (9)	H01W—C01W—C01T	119.99 (9)
C01F—C00M—P006	116.46 (8)	C022—C01W—C01T	120.02 (13)
C01F—C00M—C016	119.97 (10)	C022—C01W—H01W	119.99 (8)
C023—C00N—H00N	119.99 (7)	H01X—C01X—C00W	119.80 (9)
C027—C00N—H00N	119.99 (9)	C024—C01X—C00W	120.39 (14)
C027—C00N—C023	120.02 (13)	C024—C01X—H01X	119.80 (9)
C00U—C00O—P002	121.89 (9)	C01S—C01Y—C01H	120.31 (11)
C02A—C00O—P002	118.24 (8)	H01Y—C01Y—C01H	119.85 (7)
C02A—C00O—C00U	119.86 (10)	H01Y—C01Y—C01S	119.85 (7)
C00I—C00P—P005	112.89 (7)	C010—C01Z—C00V	120.01 (12)
H00e—C00P—P005	109.01 (4)	H01Z—C01Z—C00V	120.00 (8)
H00e—C00P—C00I	109.01 (6)	H01Z—C01Z—C010	120.00 (8)
H00f—C00P—P005	109.01 (4)	H022—C022—C01W	119.69 (8)
H00f—C00P—C00I	109.01 (6)	C027—C022—C01W	120.61 (12)
H00f—C00P—H00e	107.8	C027—C022—H022	119.69 (8)
C00L—C00R—P002	112.43 (7)	C00N—C023—P004	119.12 (9)
H00g—C00R—P002	109.11 (4)	C01T—C023—P004	120.76 (9)
H00g—C00R—C00L	109.11 (6)	C01T—C023—C00N	120.03 (11)
H00h—C00R—P002	109.11 (4)	C01X—C024—C01G	120.24 (13)
H00h—C00R—C00L	109.11 (6)	H024—C024—C01G	119.88 (9)
H00h—C00R—H00g	107.8	H024—C024—C01X	119.88 (9)
C019—C00S—H00S	120.22 (7)	C01S—C025—C013	120.42 (11)
C4—C00S—H00S	120.22 (10)	H025—C025—C013	119.79 (7)
C4—C00S—C019	119.56 (14)	H025—C025—C01S	119.79 (8)
C013—C00T—H00T	120.06 (6)	C022—C027—C00N	119.60 (14)
C01H—C00T—H00T	120.06 (7)	H027—C027—C00N	120.20 (9)
C01H—C00T—C013	119.89 (10)	H027—C027—C022	120.20 (8)
H00U—C00U—C00O	120.21 (7)	C01U—C029—C01F	119.87 (12)
C3—C00U—C00O	119.59 (11)	H029—C029—C01F	120.07 (7)
C3—C00U—H00U	120.21 (7)	H029—C029—C01U	120.07 (8)
C01L—C00V—H00V	119.93 (8)	C01E—C02A—C00O	120.12 (11)
C01Z—C00V—H00V	119.93 (8)	H02A—C02A—C00O	119.94 (6)
C01Z—C00V—C01L	120.14 (12)	H02A—C02A—C01E	119.94 (7)
H00W—C00W—C00E	120.14 (8)	C01O—C3—C00U	120.34 (11)
C01X—C00W—C00E	119.73 (13)	H3—C3—C00U	119.83 (7)
C01X—C00W—H00W	120.14 (9)	H3—C3—C01O	119.83 (7)
C01V—C010—H010	119.98 (7)	C012—C4—C00S	120.00 (15)
C01Z—C010—H010	119.98 (8)	H4—C4—C00S	120.00 (10)
C01Z—C010—C01V	120.04 (12)	H4—C4—C012	120.00 (10)

P002—C00O—C00U—C3	177.65 (9)	C00N—C027—C022—C01W	−1.2 (2)
P002—C00O—C02A—C01E	−179.21 (9)	C00O—C00U—C3—C01O	1.82 (14)
P002—C00R—C00L—P006	−57.17 (7)	C00O—C02A—C01E—C01O	1.22 (14)
P002—C013—C00T—C01H	−179.71 (10)	C00S—C019—C01A—C01R	−0.25 (15)
P002—C013—C025—C01S	−179.99 (11)	C00S—C4—C012—C01R	0.1 (2)
P004—C00I—C00P—P005	65.71 (7)	C00T—C013—C025—C01S	−0.74 (14)
P004—C019—C00S—C4	179.69 (12)	C00T—C01H—C01Y—C01S	−0.90 (17)
P004—C019—C01A—C01R	−179.55 (11)	C00U—C3—C01O—C01E	−1.02 (15)
P004—C023—C00N—C027	−176.64 (11)	C00V—C01L—C01P—C01V	−0.77 (16)
P004—C023—C01T—C01W	175.44 (13)	C00V—C01Z—C010—C01V	−1.33 (16)
P005—C00E—C00W—C01X	179.13 (12)	C00W—C01X—C024—C01G	1.08 (19)
P005—C00E—C015—C01G	−177.51 (11)	C010—C01V—C01P—C01L	−0.18 (13)
P005—C01V—C010—C01Z	−179.50 (10)	C012—C01R—C01A—C019	0.01 (19)
P005—C01V—C01P—C01L	−179.41 (10)	C013—C025—C01S—C01Y	−0.38 (16)
P006—C00M—C016—C01N	174.92 (13)	C014—C017—C01C—C01I	0.95 (15)
P006—C00M—C01F—C029	−176.64 (9)	C014—C01J—C01D—C01I	1.71 (18)
P006—C017—C014—C01J	179.69 (10)	C015—C01G—C024—C01X	0.54 (19)
P006—C017—C01C—C01I	−179.99 (12)	C016—C01N—C01U—C029	−0.3 (2)
C00E—C00W—C01X—C024	−1.11 (17)	C017—C01C—C01I—C01D	0.66 (17)
C00E—C015—C01G—C024	−2.13 (16)	C01C—C01I—C01D—C01J	−2.0 (2)
C00M—C016—C01N—C01U	1.28 (18)	C01F—C029—C01U—C01N	−1.13 (17)
C00M—C01F—C029—C01U	1.59 (15)	C01H—C01Y—C01S—C025	1.20 (17)
C00N—C023—C01T—C01W	−1.09 (15)	C01T—C01W—C022—C027	0.1 (2)

(Ph3PO2HAuI4_IAM) top

Crystal data top

AuI₄·C₁₈H₁₆OP·C₁₈H₁₅OP	Z = 1
M_r = 1262.18	F(000) = 581.500
Triclinic, P1	D_x = 2.279 Mg m⁻³
a = 9.23767 (5) Å	Mo Kα radiation, λ = 0.71073 Å
b = 10.52981 (5) Å	Cell parameters from 80913 reflections
c = 10.54412 (7) Å	θ = 2.4–63.4°
α = 102.0929 (5)°	µ = 7.47 mm⁻¹
β = 112.8397 (6)°	T = 100 K
γ = 90.4679 (4)°	Block, clear violet
V = 919.68 (1) Å³	0.17 × 0.12 × 0.09 mm

Data collection top

XtaLAB Synergy R, DW system, HyPix-Arc 150 diffractometer	54692 independent reflections
Radiation source: Rotating-anode X-ray tube, Rigaku (Mo) X-ray Source	43904 reflections with I ≥ 2u(I)
Mirror monochromator	R_int = 0.0000
Detector resolution: 10.0000 pixels mm^-1	θ_max = 60.1°, θ_min = 2.2°
ω scans	h = −22→22
Absorption correction: gaussian CrysAlisPro 1.171.43.93a (Rigaku Oxford Diffraction, 2023) Numerical absorption correction based on gaussian integration over a multifaceted crystal model Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.	k = −25→25
T_min = 0.422, T_max = 0.812	l = −25→25
54692 measured reflections

Refinement top

Refinement on F²	60 constraints
Least-squares matrix: full	H atoms treated by a mixture of independent and constrained refinement
R[F² > 2σ(F²)] = 0.034	w = 1/[σ²(F_o²) + (0.0527P)² + 0.4064P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.094	(Δ/σ)_max = 0.009
S = 0.98	Δρ_max = 3.68 e Å⁻³
54692 reflections	Δρ_min = −2.53 e Å⁻³
535 parameters	Absolute structure: Hooft, R.W.W., Straver, L.H., Spek, A.L. (2010). J. Appl. Cryst., 43, 665-668.
6 restraints	Absolute structure parameter: 0.360 (8)

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Au01	0.998183 (2)	0.111198 (2)	0.496043 (2)	0.01480 (3)
I002	0.770424 (5)	0.234329 (5)	0.347244 (5)	0.02251 (6)
I003	1.177137 (5)	0.186543 (5)	0.378138 (5)	0.02289 (7)
I004	0.818513 (5)	0.035878 (5)	0.613806 (5)	0.02322 (7)
I005	1.225539 (5)	−0.012638 (5)	0.645060 (5)	0.02354 (7)
P006	0.74727 (4)	0.61177 (4)	0.69614 (4)	0.01138 (7)
P007	0.24812 (4)	0.61098 (4)	0.29547 (4)	0.01142 (7)
C008	0.5507 (2)	0.28410 (19)	0.7341 (2)	0.0218 (4)
H008	0.5094 (2)	0.19894 (19)	0.6769 (2)	0.0262 (4)*
O00A	0.63829 (13)	0.60540 (13)	0.54241 (12)	0.0161 (2)
O00B	0.35716 (13)	0.61704 (13)	0.44913 (12)	0.0165 (2)
C00C	0.22415 (18)	0.45137 (16)	0.18503 (17)	0.0135 (2)
C00D	0.3410 (2)	0.2588 (2)	0.1163 (2)	0.0250 (4)
H00D	0.4305 (2)	0.2113 (2)	0.1290 (2)	0.0300 (5)*
C00E	0.05817 (17)	0.65147 (17)	0.28770 (16)	0.0131 (2)
C00F	0.6095 (2)	0.37401 (18)	0.68248 (19)	0.0184 (3)
H00F	0.6081 (2)	0.35050 (18)	0.58994 (19)	0.0221 (4)*
C00G	1.1418 (2)	0.42463 (19)	0.7369 (2)	0.0194 (3)
H00G	1.1824 (2)	0.34652 (19)	0.7614 (2)	0.0232 (4)*
C00H	0.0645 (2)	0.27463 (18)	−0.0083 (2)	0.0211 (4)
H00H	−0.0351 (2)	0.23780 (18)	−0.0803 (2)	0.0253 (4)*
C00J	0.5523 (2)	0.31851 (19)	0.8696 (2)	0.0219 (4)
H00J	0.5119 (2)	0.25668 (19)	0.9046 (2)	0.0262 (4)*
C00K	0.32412 (18)	0.72318 (16)	0.22468 (17)	0.0135 (2)
C00L	0.3830 (2)	0.7795 (2)	0.0380 (2)	0.0223 (4)
H00L	0.3832 (2)	0.7563 (2)	−0.0539 (2)	0.0267 (5)*
C00M	0.1957 (2)	0.20592 (19)	0.0102 (2)	0.0233 (4)
H00M	0.1861 (2)	0.12250 (19)	−0.0499 (2)	0.0280 (5)*
C00N	0.6727 (2)	0.53370 (18)	0.90338 (17)	0.0165 (3)
H00N	0.7146 (2)	0.61856 (18)	0.96110 (17)	0.0198 (3)*
C00O	1.2276 (2)	0.5077 (2)	0.7001 (2)	0.0199 (3)
H00O	1.3260 (2)	0.4855 (2)	0.6975 (2)	0.0239 (4)*
C00P	0.99580 (19)	0.45527 (18)	0.73830 (19)	0.0166 (3)
H00P	0.93619 (19)	0.39770 (18)	0.76236 (19)	0.0200 (3)*
C00Q	0.3562 (2)	0.38141 (18)	0.2044 (2)	0.0193 (3)
H00Q	0.4557 (2)	0.41728 (18)	0.2772 (2)	0.0232 (4)*
C00R	0.00000 (19)	0.76763 (17)	0.25349 (19)	0.0164 (3)
H00R	0.05995 (19)	0.82521 (17)	0.22978 (19)	0.0197 (3)*
C00S	0.6391 (2)	0.84229 (19)	0.7872 (2)	0.0195 (3)
H00S	0.5396 (2)	0.80702 (19)	0.7139 (2)	0.0234 (4)*
C00T	0.3221 (2)	0.68843 (19)	0.08797 (18)	0.0173 (3)
H00T	0.2796 (2)	0.60374 (19)	0.03001 (18)	0.0207 (3)*
C00U	0.0785 (2)	0.39750 (18)	0.07843 (19)	0.0177 (3)
H00U	−0.0114 (2)	0.44474 (18)	0.06493 (19)	0.0213 (4)*
C00V	0.67102 (18)	0.49959 (16)	0.76691 (16)	0.0131 (2)
C00W	0.6129 (2)	0.4433 (2)	0.95421 (19)	0.0206 (3)
H00W	0.6133 (2)	0.4665 (2)	1.04642 (19)	0.0247 (4)*
C00X	−0.17502 (19)	0.5987 (2)	0.32497 (19)	0.0190 (3)
H00X	−0.23462 (19)	0.5419 (2)	0.34989 (19)	0.0228 (4)*
C00Y	0.7998 (2)	1.0169 (2)	0.9815 (2)	0.0239 (4)
H00Y	0.8093 (2)	1.1004 (2)	1.0414 (2)	0.0286 (5)*
C00Z	−0.1459 (2)	0.7985 (2)	0.2543 (2)	0.0202 (3)
H00Z	−0.1866 (2)	0.8766 (2)	0.2296 (2)	0.0243 (4)*
C010	0.9176 (2)	0.82483 (18)	0.91372 (19)	0.0180 (3)
H010	1.0073 (2)	0.77724 (18)	0.92733 (19)	0.0216 (4)*
C011	−0.03070 (19)	0.56574 (18)	0.32198 (18)	0.0165 (3)
H011	0.00752 (19)	0.48590 (18)	0.34296 (18)	0.0198 (3)*
C012	1.02622 (19)	0.65661 (19)	0.66993 (18)	0.0168 (3)
H012	0.98794 (19)	0.73644 (19)	0.64897 (18)	0.0201 (3)*
C013	0.6544 (2)	0.9637 (2)	0.8752 (2)	0.0246 (4)
H013	0.5648 (2)	1.0111 (2)	0.8627 (2)	0.0296 (5)*
C014	0.3859 (2)	0.84834 (18)	0.30919 (19)	0.0178 (3)
H014	0.3881 (2)	0.87164 (18)	0.40200 (19)	0.0213 (4)*
C015	0.93767 (17)	0.57109 (17)	0.70409 (17)	0.0134 (2)
C016	0.9315 (2)	0.9478 (2)	1.0002 (2)	0.0222 (4)
H016	1.0312 (2)	0.9847 (2)	1.0722 (2)	0.0266 (4)*
C017	0.4434 (2)	0.9040 (2)	0.1220 (2)	0.0223 (4)
H017	0.4842 (2)	0.9655 (2)	0.0869 (2)	0.0268 (4)*
C018	1.1706 (2)	0.6238 (2)	0.66693 (19)	0.0194 (3)
H018	1.2303 (2)	0.6806 (2)	0.64220 (19)	0.0232 (4)*
C019	0.77089 (19)	0.77146 (17)	0.80653 (17)	0.0142 (2)
C01A	−0.2326 (2)	0.7145 (2)	0.2916 (2)	0.0199 (3)
H01A	−0.3311 (2)	0.7365 (2)	0.2941 (2)	0.0238 (4)*
C6	0.4444 (2)	0.93891 (19)	0.2569 (2)	0.0217 (4)
H6	0.4849 (2)	1.02437 (19)	0.3136 (2)	0.0260 (4)*
H00A	0.534 (5)	0.608 (5)	0.524 (5)	0.035 (11)*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Au01	0.01541 (4)	0.01384 (4)	0.01551 (4)	0.00066 (3)	0.00663 (3)	0.00327 (3)
I002	0.01917 (13)	0.02343 (13)	0.02532 (13)	0.00395 (10)	0.00748 (10)	0.00907 (11)
I003	0.02219 (14)	0.02764 (17)	0.02223 (13)	−0.00039 (12)	0.01175 (11)	0.00719 (11)
I004	0.02409 (17)	0.02660 (16)	0.02213 (13)	0.00000 (12)	0.01214 (11)	0.00652 (11)
I005	0.01909 (13)	0.02487 (15)	0.02615 (14)	0.00287 (11)	0.00806 (11)	0.00667 (12)
P006	0.00782 (15)	0.01442 (17)	0.01150 (16)	0.00087 (12)	0.00355 (12)	0.00274 (13)
P007	0.00779 (15)	0.01463 (17)	0.01132 (16)	0.00092 (12)	0.00355 (12)	0.00242 (13)
C008	0.0241 (10)	0.0151 (7)	0.0293 (10)	−0.0007 (6)	0.0147 (8)	0.0032 (7)
O00A	0.0094 (4)	0.0259 (7)	0.0121 (4)	0.0020 (4)	0.0030 (3)	0.0046 (4)
O00B	0.0098 (4)	0.0265 (7)	0.0122 (5)	0.0023 (4)	0.0032 (4)	0.0044 (4)
C00C	0.0126 (6)	0.0134 (6)	0.0146 (6)	0.0011 (4)	0.0054 (5)	0.0034 (5)
C00D	0.0254 (10)	0.0190 (8)	0.0322 (12)	0.0059 (7)	0.0144 (9)	0.0036 (8)
C00E	0.0088 (5)	0.0170 (6)	0.0130 (5)	0.0019 (4)	0.0041 (4)	0.0028 (5)
C00F	0.0184 (7)	0.0153 (7)	0.0212 (8)	−0.0019 (5)	0.0099 (6)	−0.0001 (6)
C00G	0.0134 (7)	0.0187 (7)	0.0244 (9)	0.0054 (5)	0.0066 (6)	0.0035 (7)
C00H	0.0244 (9)	0.0156 (7)	0.0183 (8)	−0.0028 (6)	0.0046 (7)	0.0013 (6)
C00J	0.0222 (9)	0.0196 (8)	0.0283 (10)	0.0005 (7)	0.0126 (8)	0.0101 (7)
C00K	0.0107 (5)	0.0145 (6)	0.0156 (6)	0.0001 (4)	0.0062 (5)	0.0024 (5)
C00L	0.0238 (10)	0.0264 (10)	0.0182 (8)	−0.0023 (7)	0.0092 (7)	0.0070 (7)
C00M	0.0322 (12)	0.0148 (7)	0.0240 (9)	0.0009 (7)	0.0138 (9)	0.0015 (7)
C00N	0.0170 (7)	0.0183 (7)	0.0132 (6)	−0.0024 (5)	0.0057 (5)	0.0024 (5)
C00O	0.0114 (6)	0.0255 (9)	0.0222 (8)	0.0041 (6)	0.0075 (6)	0.0024 (7)
C00P	0.0120 (6)	0.0168 (7)	0.0208 (7)	0.0030 (5)	0.0062 (5)	0.0043 (6)
C00Q	0.0147 (7)	0.0176 (7)	0.0239 (8)	0.0035 (5)	0.0071 (6)	0.0022 (6)
C00R	0.0113 (6)	0.0166 (7)	0.0199 (7)	0.0016 (5)	0.0050 (5)	0.0033 (6)
C00S	0.0153 (7)	0.0186 (7)	0.0248 (9)	0.0041 (6)	0.0090 (6)	0.0034 (7)
C00T	0.0170 (7)	0.0195 (7)	0.0148 (6)	−0.0030 (6)	0.0064 (5)	0.0030 (6)
C00U	0.0163 (7)	0.0164 (7)	0.0176 (7)	0.0001 (5)	0.0041 (6)	0.0032 (6)
C00V	0.0108 (5)	0.0143 (6)	0.0133 (6)	0.0000 (4)	0.0046 (4)	0.0019 (5)
C00W	0.0220 (9)	0.0234 (9)	0.0182 (8)	−0.0025 (7)	0.0090 (7)	0.0069 (7)
C00X	0.0108 (6)	0.0279 (9)	0.0194 (7)	0.0018 (6)	0.0071 (5)	0.0058 (7)
C00Y	0.0314 (12)	0.0157 (7)	0.0249 (10)	0.0008 (7)	0.0136 (9)	0.0008 (7)
C00Z	0.0126 (6)	0.0207 (8)	0.0250 (9)	0.0039 (6)	0.0067 (6)	0.0017 (7)
C010	0.0166 (7)	0.0162 (7)	0.0162 (7)	−0.0001 (5)	0.0023 (6)	0.0020 (6)
C011	0.0114 (6)	0.0217 (8)	0.0186 (7)	0.0023 (5)	0.0068 (5)	0.0078 (6)
C012	0.0116 (6)	0.0227 (8)	0.0179 (7)	0.0017 (5)	0.0067 (5)	0.0072 (6)
C013	0.0244 (10)	0.0179 (8)	0.0323 (11)	0.0055 (7)	0.0140 (9)	0.0017 (8)
C014	0.0190 (8)	0.0153 (6)	0.0194 (7)	−0.0014 (5)	0.0105 (6)	−0.0006 (5)
C015	0.0090 (5)	0.0171 (6)	0.0143 (6)	0.0019 (4)	0.0045 (4)	0.0039 (5)
C016	0.0250 (10)	0.0181 (8)	0.0183 (8)	−0.0023 (7)	0.0048 (7)	0.0011 (6)
C017	0.0229 (9)	0.0195 (8)	0.0278 (10)	0.0003 (7)	0.0122 (8)	0.0085 (7)
C018	0.0123 (6)	0.0279 (10)	0.0199 (8)	0.0011 (6)	0.0081 (6)	0.0065 (7)
C019	0.0126 (6)	0.0150 (6)	0.0152 (6)	0.0016 (5)	0.0058 (5)	0.0034 (5)
C01A	0.0111 (6)	0.0273 (9)	0.0198 (8)	0.0032 (6)	0.0064 (6)	0.0020 (7)
C6	0.0235 (9)	0.0142 (7)	0.0288 (10)	−0.0024 (6)	0.0139 (8)	0.0012 (7)

Geometric parameters (Å, º) top

Au01—I002	2.6275 (1)	C00N—C00V	1.402 (2)
Au01—I003	2.6258 (1)	C00N—C00W	1.390 (3)
Au01—I004	2.6299 (1)	C00O—H00O	0.9500
Au01—I005	2.6309 (1)	C00O—C018	1.393 (3)
P006—O00A	1.5270 (12)	C00P—H00P	0.9500
P006—C00V	1.7922 (18)	C00P—C015	1.397 (2)
P006—C015	1.7880 (16)	C00Q—H00Q	0.9500
P006—C019	1.7908 (17)	C00R—H00R	0.9500
P007—O00B	1.5272 (12)	C00R—C00Z	1.392 (2)
P007—C00C	1.7898 (16)	C00S—H00S	0.9500
P007—C00E	1.7840 (16)	C00S—C013	1.383 (3)
P007—C00K	1.7912 (18)	C00S—C019	1.402 (2)
C008—H008	0.9500	C00T—H00T	0.9500
C008—C00F	1.387 (3)	C00U—H00U	0.9500
C008—C00J	1.393 (3)	C00W—H00W	0.9500
O00A—H00A	0.91 (4)	C00X—H00X	0.9500
C00C—C00Q	1.399 (2)	C00X—C011	1.391 (2)
C00C—C00U	1.393 (2)	C00X—C01A	1.392 (3)
C00D—H00D	0.9500	C00Y—H00Y	0.9500
C00D—C00M	1.387 (3)	C00Y—C013	1.389 (3)
C00D—C00Q	1.393 (3)	C00Y—C016	1.391 (3)
C00E—C00R	1.400 (3)	C00Z—H00Z	0.9500
C00E—C011	1.405 (2)	C00Z—C01A	1.399 (3)
C00F—H00F	0.9500	C010—H010	0.9500
C00F—C00V	1.402 (2)	C010—C016	1.392 (3)
C00G—H00G	0.9500	C010—C019	1.401 (2)
C00G—C00O	1.384 (3)	C011—H011	0.9500
C00G—C00P	1.394 (2)	C012—H012	0.9500
C00H—H00H	0.9500	C012—C015	1.401 (2)
C00H—C00M	1.385 (3)	C012—C018	1.391 (2)
C00H—C00U	1.392 (3)	C013—H013	0.9500
C00J—H00J	0.9500	C014—H014	0.9500
C00J—C00W	1.395 (3)	C014—C6	1.396 (3)
C00K—C00T	1.404 (2)	C016—H016	0.9500
C00K—C014	1.399 (2)	C017—H017	0.9500
C00L—H00L	0.9500	C017—C6	1.390 (3)
C00L—C00T	1.395 (3)	C018—H018	0.9500
C00L—C017	1.390 (3)	C01A—H01A	0.9500
C00M—H00M	0.9500	C6—H6	0.9500
C00N—H00N	0.9500

I003—Au01—I002	89.2766 (19)	H00R—C00R—C00E	120.08 (10)
I004—Au01—I002	90.6233 (19)	C00Z—C00R—C00E	119.84 (18)
I004—Au01—I003	179.8981 (17)	C00Z—C00R—H00R	120.08 (12)
I005—Au01—I002	179.810 (2)	C013—C00S—H00S	120.11 (11)
I005—Au01—I003	90.8917 (19)	C019—C00S—H00S	120.11 (10)
I005—Au01—I004	89.208 (2)	C019—C00S—C013	119.77 (17)
C00V—P006—O00A	110.84 (7)	C00L—C00T—C00K	119.34 (17)
C015—P006—O00A	108.92 (7)	H00T—C00T—C00K	120.33 (10)
C015—P006—C00V	109.22 (8)	H00T—C00T—C00L	120.33 (11)
C019—P006—O00A	112.03 (8)	C00H—C00U—C00C	120.13 (17)
C019—P006—C00V	107.76 (8)	H00U—C00U—C00C	119.94 (10)
C019—P006—C015	108.00 (8)	H00U—C00U—C00H	119.94 (11)
C00C—P007—O00B	111.97 (8)	C00F—C00V—P006	118.32 (13)
C00E—P007—O00B	108.92 (7)	C00N—C00V—P006	121.95 (13)
C00E—P007—C00C	107.89 (7)	C00N—C00V—C00F	119.72 (16)
C00K—P007—O00B	110.94 (7)	C00N—C00W—C00J	119.90 (18)
C00K—P007—C00C	107.83 (8)	H00W—C00W—C00J	120.05 (12)
C00K—P007—C00E	109.21 (8)	H00W—C00W—C00N	120.05 (11)
C00F—C008—H008	119.95 (11)	C011—C00X—H00X	119.85 (12)
C00J—C008—H008	119.95 (11)	C01A—C00X—H00X	119.85 (11)
C00J—C008—C00F	120.09 (17)	C01A—C00X—C011	120.30 (18)
H00A—O00A—P006	116 (3)	C013—C00Y—H00Y	120.02 (12)
C00Q—C00C—P007	118.82 (12)	C016—C00Y—H00Y	120.02 (11)
C00U—C00C—P007	121.47 (13)	C016—C00Y—C013	119.95 (18)
C00U—C00C—C00Q	119.69 (16)	H00Z—C00Z—C00R	120.07 (12)
C00M—C00D—H00D	119.83 (12)	C01A—C00Z—C00R	119.86 (18)
C00Q—C00D—H00D	119.83 (11)	C01A—C00Z—H00Z	120.07 (11)
C00Q—C00D—C00M	120.34 (19)	C016—C010—H010	120.12 (11)
C00R—C00E—P007	121.47 (13)	C019—C010—H010	120.12 (11)
C011—C00E—P007	118.29 (13)	C019—C010—C016	119.76 (17)
C011—C00E—C00R	120.20 (15)	C00X—C011—C00E	119.50 (17)
H00F—C00F—C008	120.00 (11)	H011—C011—C00E	120.25 (10)
C00V—C00F—C008	120.00 (17)	H011—C011—C00X	120.25 (12)
C00V—C00F—H00F	120.00 (11)	C015—C012—H012	120.24 (10)
C00O—C00G—H00G	119.92 (11)	C018—C012—H012	120.24 (12)
C00P—C00G—H00G	119.92 (12)	C018—C012—C015	119.53 (18)
C00P—C00G—C00O	120.15 (18)	C00Y—C013—C00S	120.58 (18)
C00M—C00H—H00H	119.94 (11)	H013—C013—C00S	119.71 (11)
C00U—C00H—H00H	119.94 (11)	H013—C013—C00Y	119.71 (12)
C00U—C00H—C00M	120.13 (17)	H014—C014—C00K	120.05 (10)
H00J—C00J—C008	119.85 (11)	C6—C014—C00K	119.90 (16)
C00W—C00J—C008	120.30 (18)	C6—C014—H014	120.05 (11)
C00W—C00J—H00J	119.85 (12)	C00P—C015—P006	121.55 (13)
C00T—C00K—P007	121.66 (13)	C012—C015—P006	118.21 (13)
C014—C00K—P007	118.29 (13)	C012—C015—C00P	120.20 (15)
C014—C00K—C00T	120.05 (16)	C010—C016—C00Y	120.16 (17)
C00T—C00L—H00L	119.78 (11)	H016—C016—C00Y	119.92 (11)
C017—C00L—H00L	119.78 (12)	H016—C016—C010	119.92 (11)
C017—C00L—C00T	120.44 (19)	H017—C017—C00L	119.85 (12)
C00H—C00M—C00D	120.04 (18)	C6—C017—C00L	120.31 (19)
H00M—C00M—C00D	119.98 (12)	C6—C017—H017	119.85 (11)
H00M—C00M—C00H	119.98 (11)	C012—C018—C00O	120.08 (18)
C00V—C00N—H00N	120.00 (10)	H018—C018—C00O	119.96 (11)
C00W—C00N—H00N	120.00 (11)	H018—C018—C012	119.96 (12)
C00W—C00N—C00V	119.99 (16)	C00S—C019—P006	119.17 (13)
H00O—C00O—C00G	119.81 (11)	C010—C019—P006	121.04 (13)
C018—C00O—C00G	120.39 (16)	C010—C019—C00S	119.77 (16)
C018—C00O—H00O	119.81 (11)	C00Z—C01A—C00X	120.28 (16)
H00P—C00P—C00G	120.19 (12)	H01A—C01A—C00X	119.86 (11)
C015—C00P—C00G	119.62 (18)	H01A—C01A—C00Z	119.86 (11)
C015—C00P—H00P	120.19 (10)	C017—C6—C014	119.95 (17)
C00D—C00Q—C00C	119.67 (16)	H6—C6—C014	120.02 (11)
H00Q—C00Q—C00C	120.16 (10)	H6—C6—C017	120.02 (11)
H00Q—C00Q—C00D	120.16 (11)

P006—C00V—C00F—C008	179.42 (14)	C00D—C00M—C00H—C00U	0.8 (3)
P006—C00V—C00N—C00W	−179.70 (15)	C00E—C00R—C00Z—C01A	1.1 (2)
P006—C015—C00P—C00G	177.07 (14)	C00E—C011—C00X—C01A	1.2 (2)
P006—C015—C012—C018	−176.18 (13)	C00F—C00V—C00N—C00W	−0.3 (2)
P006—C019—C00S—C013	177.59 (17)	C00G—C00O—C018—C012	−0.3 (2)
P006—C019—C010—C016	−178.38 (16)	C00G—C00P—C015—C012	−0.6 (2)
P007—C00C—C00Q—C00D	−177.84 (17)	C00J—C00W—C00N—C00V	0.4 (2)
P007—C00C—C00U—C00H	178.21 (16)	C00K—C00T—C00L—C017	−0.8 (2)
P007—C00E—C00R—C00Z	−177.28 (14)	C00K—C014—C6—C017	−1.0 (2)
P007—C00E—C011—C00X	176.20 (13)	C00L—C017—C6—C014	0.6 (2)
P007—C00K—C00T—C00L	−179.91 (15)	C00O—C018—C012—C015	−1.1 (2)
P007—C00K—C014—C6	−179.21 (14)	C00P—C015—C012—C018	1.59 (19)
C008—C00F—C00V—C00N	0.0 (2)	C00R—C00Z—C01A—C00X	−1.4 (2)
C008—C00J—C00W—C00N	−0.3 (2)	C00S—C013—C00Y—C016	0.0 (3)
C00C—C00Q—C00D—C00M	−0.2 (2)	C00S—C019—C010—C016	0.0 (2)
C00C—C00U—C00H—C00M	−0.6 (2)	C00Y—C016—C010—C019	0.8 (3)

Acknowledgements

F. Kleemiss is immensely thankful for discussions with Christoph Bannwarth, Arne Lüchow and Michael Dolg about the correction functions. Open access funding enabled and organized by Projekt DEAL.

Funding information

F. Kleemiss acknowledges funding by the DFG within the Walter Benjamin Scheme of the DFG (grant No. KL 3500/1-1). F. Meurer acknowledges funding by the Studienstiftung des deutschen Volkes.

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Volume 58| Part 2| April 2025| Pages 374-382

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research papers\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

The use of effective core potentials in Hirshfeld atom refinement: making quantum crystallography faster in NoSpherA2

1. Introduction

2. Computation of correction functions and form factors

3. Implementation in NoSpherA2

4. Results and discussion

4.1. Comparison of ECP valence electron densities and all-electron valence densities

4.2. Comparison of scattering factors derived from ECP wavefunctions and all-electron calculations

4.3. Comparison of refinement results and performance obtained by ECP basis sets and all-electron relativistic NoSpherA2-HAR

5. Conclusion

Supporting information

Acknowledgements

Funding information

References

research papers