electronic reprint Journal of
Applied Crystallography ISSN 0021-8898
WinXPRO: a program for calculating crystal and molecular properties using multipole parameters of the electron density Adam Stash and Vladimir Tsirelson
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J. Appl. Cryst. (2002). 35, 371–373
Stash and Tsirelson
WinXPRO
computer programs Journal of
Applied Crystallography ISSN 0021-8898
Received 20 June 2001 Accepted 18 February 2002
WinXPRO: a program for calculating crystal and molecular properties using multipole parameters of the electron density Adam Stasha and Vladimir Tsirelsonb* a Karpov Institute of Physical Chemistry, ul. Vorontsovo pole 10, 103064 Moscow, Russia, and bMendeleev University of Chemical Technology, Miusskaya Sq. 9, Moscow 125047, Russia. Correspondence e-mail:
[email protected]
# 2002 International Union of Crystallography Printed in Great Britain ± all rights reserved
The computer program WinXPRO enables the calculation of crystal and molecular properties using the multipole parameters of the electron density. The list of properties includes the electron density and its topological and electric ®eld characteristics, the local kinetic and potential energies, the electron localization function, and the effective crystal potential. WinXPRO works under the Windows operating system and can utilize any existing graphics program to display output.
1. Introduction
2. Program specification
As a result of recent advances in instrumentation (Boese et al., 1999; Bolotovsky et al., 1995; Graafsma et al., 1997; Martin & Pinkerton, 1998; Ivanov et al., 1999) and experimental data treatment techniques (Tsirelson & Ozerov, 1996), accurate X-ray diffraction analysis has become an effective tool in the study of the physical and chemical properties of solids that depend on the electron density distribution. The reconstruction of the electron density from X-ray diffraction intensities corrected for absorption, thermal diffuse scattering, multiple scattering and extinction is normally implemented by the multipole structural model (Hirshfeld, 1971; Stewart, 1976; Hansen & Coppens, 1978; Parini et al., 1985). The model (quasi)static electron density, in spite of the limited resolution and incomplete thermal deconvolution, is close to the `true' quantum-mechanical one, tr(r), derived from ®rst principles. Moreover, the model electron density exhibits the same set of critical points as tr(r), provided that accurate experimental data and physically correct structural models are used (Kapphahn et al., 1988, 1989; Tsirelson et al., 1998). Therefore, it can be considered to be a homeomorphic image of the `true' tr (Tsirelson, 1996). As a result, not only valence or deformation maps, but also the topological features of the electron density, such as the Laplacian of the electron density, its gradient ®eld and characteristics of the critical points (Bader, 1990), can the calculated using the model electron density (Tsirelson et al., 2000). The electrostatic potential (Stewart, 1979; Varnek et al., 1981; Su & Coppens, 1992), dipole and quadrupole molecular moments (Spackman, 1992), electric ®eld gradient at nuclear positions (Tsirelson et al., 1987; Brown & Spackman, 1994; Su & Coppens, 1996) and the electrostatic intermolecular energy (Suponitsky et al., 1999) can be calculated as well. Recently, the local kinetic, potential and exchange energies and effective crystal potentials (Tsirelson, 2002) and electron localization function (Tsirelson & Stash, 2002) were also calculated by combining the model electron density and formulae of density functional theory. Existing computer programs that can calculate some of the properties mentioned above (Ghermani et al., 1992; Koritsansky et al., 1995; Stewart et al., 1998; Souhassou & Blessing, 1999) work, as a rule, under Unix-type operating systems. We have developed the program WinXPRO to allow the calculation of these properties on the Windows platform.
Running under Windows, WinXPRO requires at least 8 Mbytes of RAM on a computer with a 586 processor or better. WinXPRO has a graphical user interface (GUI). The input information consists of the list of the mulipole electron density parameters obtained by the Hansen & Coppens (1978) formalism and corresponding symmetry data. The input ®le may be constructed automatically from the parameter and symmetry ®les of MOLLY (Hansen, 1991; Protas, 1995) and XD (Koritsansky et al., 1995). The atomic (molecular) cluster used in the calculation is speci®ed by indication of the distance from a given atom/point or by the choice of some spatial volume. Any number of molecules within this cluster can be included in the calculation; in other words, the properties of a single molecule or some group of molecules may be modelled. The existing version of WinXPRO is designed for a maximal cluster consisting of 250 atoms. The results of calculations are presented as output ®les containing numerical characteristics and/or data ®les with information necessary for the graphical display of two-dimensional surfaces (x, y, P) or three-dimensional images (x, y, z, P) (here x, y, z are spatial coordinates and P is the property to be represented). The pictures can be displayed by any existing graphics program. The list of the characteristics calculated by WinXPRO is as follows. (i) Total, core, valence and deformation electron densities. (ii) Laplacian of the electron density. (iii) Electrostatic potential distribution. (iv) Gradient ®eld of the electron density and electrostatic potential. (v) Local kinetic, potential and electronic energies calculated under different approximations of the density functional formalism. (vi) Critical points in the electron density, electrostatic potential, the Laplacian of the electron density and local energies. (vii) Electron localization function. (viii) Local electronic exchange density under different approximations. (ix) Dirac±Slater exchange potential. (x) Fermi momentum distribution. (xi) Electric ®eld gradients at nuclear positions. (xii) Dipole and quadrupole molecular moments. (xiii) Potential-derived atomic charges.
J. Appl. Cryst. (2002). 35, 371±373
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computer programs
Figure 3
Figure 1
Electrostatic (lower left) and effective (upper right) potentials in the (100) plane of a cubic MgO crystal calculated with parameters of the multipole model ®tted to experimentally extinction-corrected structure factors (Stash et al., 2002). The effective potential consists of the electrostatic part plus the Slater±Dirac exchange potential vx = ÿ(1/)[32(r)]1/3 (atomic units are used). Positive lines are solid; contour intervals are 2, 4, 8 10n (ÿ3 < n < 3). Areas of the negative effective crystal potential correspond to regions of the maximal electron depletion in the (100) plane of MgO. The map demonstrates that electrons are concentrated in atomic basins of MgO and re¯ects the close-shell atomic interactions in this crystal.
Gradient vector ®eld of the electrostatic potential, '(r), in crystalline urea calculated with the multipole parameters of Zavodnik et al. (1999). Recalling that the classic force acting on the electron at r is F(r) = |e|r'(r), we can see that the map shows the atomic-like regions within which the electrons are electrostatically attracted by corresponding nuclei. These regions, therefore, re¯ect the balance of the Coulomb atom±atom interactions in urea. Note that only the nearestneighbouring atomic pairs (including intermolecular contacts) are explicitly connected by the pairs of gradient lines in the r'(r) ®eld. In general, a network of the `atom±atom interactions' realising the transmission of the Coulomb interactions through a crystal is a speci®c property of each compound.
(xiv) Estimated standard deviations in the electron density and Laplacian of the electron density. In addition, these characteristics can be calculated for a promolecule or a procrystal. The combination of functions, for example, the calculation of the total effective potential, which is the sum of the electrostatic and exchange potentials (Fig. 1), is also provided for. WinXPRO has been tested by comparison of the results with those from XD calculations (Zhurova, 2001). The energy density distributions were compared with results of quantum-chemical calculations by Hartree±Fock methods (Tsirelson & Yakovlev, 2002). Some illustrations of the results obtained with WinXPRO are shown in Figs. 1, 2 and 3.
3. Documentation and availability Information regarding the algorithms used in WinXPRO and the distribution details can found at the Web site http://stash.chat.ru. Note that some modi®ed subroutines from early versions of LSPROP (Howard & Mallinson, 1993), XPRO/DOS (Ivanov, Abramov & Tsirelson, 1997) and AIMPAC (Biegler-Koenig et al., 1982) have been used in WinXPRO.
Figure 2
Electron localization function (r) (Savin et al., 1992) in the (100) plane of solid molecular chlorine Cl2 (space group Cmca, Z = 4; each molecule possesses a crystallographic inversion centre and lies in a mirror perpendicular to the a axis; molecules form molecular layers parallel to the bc plane). The (r) function is de®ned by (r) = (1 + 2)ÿ1 with = gs/gTF; gs = (3/10)(32)2/35/3(r) ÿ (1/9)|r(r)|2/(r) + (1/6)r2(r) (Tsirelson & Stash, 2002), while gTF is the Tomas± Fermi kinetic energy density, g = (3/10)(32)2/35/3(r); (r) is the electron density. The (r) function ranges from 0 to 1; (r) values close to 1 denote the regions of maximal concentration of the electron pairs. The picture reveals the atomic shell structure and demonstrates that the lone-pair electron concentrations of Cl atoms provide a speci®c mutual arrangement of the molecular units Cl2, minimizing the molecular interactions in the (100) plane of the crystal. As a result, the short Ê , indicated by the dashed lines, nearest-neighbour intermolecular contacts of 3.28 A which realise the `key-lock interactions', take place in the solid molecular chlorine. Only lines corresponding to values of > 0.5 are shown (the interval is 0.05). Multipole parameters according to Stevens (1979) have been used in calculation.
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We thank Professor R. F. W. Bader and Dr P. Mallinson for providing us with the AIMPAC and LSPROP Fortran codes and permission to use them, and Dr E. A. Zhurova for testing WinXPRO. The contributions of Drs Yu. Abramov and Yu. Ivanov are gratefully acknowledged.
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