Vladimir G. Tsirelson

WinXPRO: a program for calculating crystal and molecular properties using multipole parameters of the electron density

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 field 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.

Multipole analysis of the electron density in triphylite, LiFePO4, using X-ray diffraction data

The electron density distribution and 3d-orbital electron occupancies for the Fe atom in synthetic triphylite, LiFePO 4 , have been analysed using single-crystal X-ray diffraction data measured at T=298 K with Mo Kα (λ=0.71069 A) radiation to a resolution corresponding to (sin θ max /λ)=1.078 A -1 . Measurements of 3265 reflections gave 944 unique data [R int (I)=0.036] with I>2σ(I). For an atomic multipole density model fitted by least-squares methods R(F)=0.0174 for all unique reflections. The Fe atom 3d-orbital occupancies have been derived from the multipole population coefficients using point-group-specific relations

The chemical bond and atomic displacements in SrTiO3 from X-ray diffraction analysis

The deformation electron-density (dynamic Fourier) maps and the anharmonicity of atomic displacements in strontium titanate, SrTiO 3 (Gram-Charlier model), were studied by high-precision single-crystal X-ray diffraction analysis at 145(1) and 296(2) K. Space group Pm3m, cubic, λ(Mo Kα) = 0.71069 A, Z = 1, F(000) = 84, T = 145 (1)K, a = 3.8996(5)A, V = 59.30(2)A 3 , D x = 5.138(2) g cm -3 , μ = 26.778 mm -1 , R = 0.0063, wR = 0.0040, S = 1.05 for 131 unique reflections and T = 296(2)K, a = 3.901(1)A, V = 59.36(5)A 3 , D x = 5.133(4) g cm -3 , μ = 26.700 mm -1 , R = 0.0071, wR = 0.0050, S = 1.40 for 109 unique reflections. Strong anharmonicity of the atomic displacements was observed for all atoms at 145 K and for Ti and O atoms at 296 K. These are explained by a model in which electronic instability in the TiO 6 octahedron leads to a displacement of the Ti atom from the center of the octahedron, and the lattice instability resulting from the consequent stretching of the Sr-O bonds leads to a rotation of the octahedra. Both distortions show only short-range order at the temperature studies, but show indications of freezing out as the temperature is lowered towards the rotational phase transition at 106 K. The experimental dynamic Fourier deformation electron-density maps and the Hirshfeld atomic charges were calculated

Topological definition of crystal structure: determination of the bonded interactions in solid molecular chlorine

The heavier halide molecules form layered crystals indicative of the presence of a specific directed intermolecular interaction. It is shown that this interaction within the crystal can be defined and characterized using the topology of the electron density within the theory of atoms in crystals. It is also shown that its presence in the crystal and the resulting geometry of the layered structure can be predicted in terms of the topology of the Laplacian distribution of an isolated Cl2 molecule, as it relates to the definition of Lewis acid and base sites within the valence shell of an atom. The generality of the definition of both primary and secondary interactions in terms of the topology of the electron density is demonstrated for all types of crystal. The electron density of solid molecular chlorine was determined by fitting the experimental X-ray structure factors and by theoretical calculation and its topology determined. Each Cl atom is found to be linked by bond paths, lines of maximum electron density, to twelve other atoms in the crystal: to four atoms in the same layer parallel to the bc plane, one of which defines the intramolecular bond of the Cl2 group, to six atoms in the four neighbouring molecules lying in the same stack parallel to the b axis and to two atoms in molecules situated in a neighbouring stack.

Determination of the electron localization function from electron density

Approximate determination of electron localization function (ELF) from electron density and its first and second derivatives is described. It is demonstrated that the second-order gradient expansion of the kinetic energy density yields the modified ELF, which exhibits all the features characterizing electron pairing. Calculations based on the accurate electron densities derived from X-ray diffraction data carried out for crystalline magnesium oxide, chlorine and urea: they demonstrate that the ELF reveals important peculiarities of crystal architecture.

Intermolecular hydrogen bond energies in crystals evaluated using electron density properties: DFT computations with periodic boundary conditions

The hydrogen bond (H‐bond) energies are evaluated for 18 molecular crystals with 28 moderate and strong OH···O bonds using the approaches based on the electron density properties, which are derived from the B3LYP/6‐311G** calculations with periodic boundary conditions. The approaches considered explore linear relationships between the local electronic kinetic Gb and potential Vb densities at the H···O bond critical point and the H‐bond energy EHB. Comparison of the computed EHB values with the experimental data and enthalpies evaluated using the empirical correlation of spectral and thermodynamic parameters (Iogansen, Spectrochim. Acta Part A 1999, 55, 1585) enables to estimate the accuracy and applicability limits of the approaches used. The Vb−EHB approach overestimates the energy of moderate H‐bonds (EHB < 60 kJ/mol) by ∼20% and gives unreliably high energies for crystals with strong H‐bonds. On the other hand, the Gb−EHB approach affords reliable results for the crystals under consideration. The linear relationship between Gb and EHB is basis set superposition error (BSSE) free and allows to estimate the H‐bond energy without computing it by means of the supramolecular approach. Therefore, for the evaluation of H‐bond energies in molecular crystals, the Gb value can be recommended to be obtained from both density functional theory (DFT) computations with periodic boundary conditions and precise X‐ray diffraction experiments.

The mapping of electronic energy distributions using experimental electron density

It is demonstrated that the approximate kinetic energy density calculated using the second-order gradient expansion with parameters of the multipole model fitted to experimental structure factors reproduces the main features of this quantity in a molecular or crystal position space. The use of the local virial theorem provides an appropriate derivation of approximate potential energy density and electronic energy density from the experimental (model) electron density and its derivatives. Consideration of these functions is not restricted by the critical points in the electron density and provides a comprehensive characterization of bonding in molecules and crystals.

X-ray and Electron Diffraction Study of MgO

Precise X-ray and high-energy transmission electron diffraction methods were used for the study of electron density and electrostatic potential in MgO crystals. The structure amplitudes were determined and their accuracy estimated using ab initio Hartree-Fock structure amplitudes as criteria. The electrostatic potential distributions, reconstructed using Fourier series from both X-ray and electron diffraction data, are in satisfactory mutual agreement and are similar to the theory. They, however, suffer from restricted experimental resolution and, therefore, the reconstruction of the electrostatic potential via an analytical structural model is preferable. The model of electron density was adjusted to X-ray experimental structure amplitudes and those calculated by the Hartree-Fock method. The electrostatic potential, deformation electron density and the Laplacian of the electron density were calculated with this model. The critical points in both experimental and theoretical model electron densities were found and compared with those for procrystals from spherical atoms and ions. A disagreement concerning the type of critical point at (,,0) in the area of low, near-uniform electron density is observed. It is noted that topological analysis of the electron density in crystals can be related with a close-packing concept.

Cl···Cl Interactions in Molecular Crystals: Insights from the Theoretical Charge Density Analysis

The structure, IR harmonic frequencies and intensities of normal vibrations of 20 molecular crystals with the X-Cl···Cl-X contacts of different types, where X = C, Cl, and F and the Cl···Cl distance varying from ~3.0 to ~4.0 Å, are computed using the solid-state DFT method. The obtained crystalline wave functions have been further used to define and describe quantitatively the Cl···Cl interactions via the electron-density features at the Cl···Cl bond critical points. We found that the electron-density at the bond critical point is almost independent of the particular type of the contact or hybridization of the ipso carbon atom. The energy of Cl···Cl interactions, E(int), is evaluated from the linking E(int) and local electronic kinetic energy density at the Cl···Cl bond critical points. E(int) varies from 2 to 12 kJ/mol. The applicability of the geometrical criterion for the detection of the Cl···Cl interactions in crystals with two or more intermolecular Cl···Cl contacts for the unique chlorine atom is not straightforward. The detection of these interactions in such crystals may be done by the quantum-topological analysis of the periodic electron density.

A topological analysis of electron density and chemical bonding in cyclophosphazenes PnNnX2n (X = H, F, Cl; N = 2, 3, 4)

The restricted Hartree-Fock method was used to determine the cycle size effects on the geometric parameters of several inorganic templates, cyclophosphazenes PnNnX2n (X = H, F, Cl; n = 2, 3, 4). A topological analysis of local electronic properties at the electron density critical points of bonds allowed us to quantitatively characterize the chemical bond in cyclophosphazenes and its dependence on the cycle size and substituents at phosphorus. The calculated distributions of the electron density Laplacian and electron pair localization functions revealed the special features of the electronic structure of the nitrogen and phosphorus atoms. These results explain the nature of noncovalent interactions between the P atoms of one cyclophosphazene molecule and the N atoms of the other.