The molecular electron density distribution meeting place of X-ray diffraction and quantum chemistry intermediate - between theory and experiment

Quantum chemistry and the concepts used daily in chemistry are increasingly growing apart. Among the concepts that are able to bridge the gap between theory and experimental practice, electron density distribution has an important place. The study of this distribution has led to new developments in theory, including Hellmann-Feynman theory and the density functional theory. The possibilities and limitations of these methods are discussed. Various ways of analysing the electron density distribution are presented and discussed. X-ray diffraction enables us to ¿observe¿ the electron density distribution and electrostatic properties. Experimental results are compared with the results of quantum chemical calculations. It is shown that even intermolecular interaction is observable with this method. Problems in determining ionic charges are seen to be inherent in the method

The electron density distribution in the hydrogen bond. A quantum chemical and crystallographic study

With the help of Hartree—Fock—Slater calculations in which very large basis sets are employed, the polarisation of the water molecule by an electric field is explored. The various features in the electron density distribution are encountered again in the long hydrogen bond in the water dimer, showing that polarisation is the main effect. In short hydrogen bonds, exchange repulsion is shown to be equally important.\ud \ud The quality of the computational method is tested by comparing the results of the calculation of the electron density distribution in the crystal of α-oxalic acid dihydrate with the results of accurate X-ray diffraction measurements. By using models in which subsequently covalent bonding, hydrogen bonding and the electrostatic crystalline field are included, the effects of the various components are explored. Only the full theoretical model gives excellent agreement with the experiment, showing the quality of the model and the sensitivity of the experiment

Electrostatic Molecular Interaction from X-ray Diffraction Data. II. Test on Theoretical Pyrazine Data

In a previous paper [Moss & Feil (1981). Acta Cryst. A37, 414-421] a method was reported to calculate the electrostatic potential and the electrostatic interaction energy from single-crystal X-ray diffraction data. The method was applied to experimental pyrazine data; however, owing to the relatively low quality of the data, the results were inconclusive. In the present paper the results are presented of a model study in which the method has been applied to the analysis of ideal error-free diffraction data calculated from a theoretical wavefunction. The molecular quadrupole moments and the electrostatic interaction energies of two pyrazine molecules thus obtained are in very good agreement with the corresponding results derived directly from the wavefunction. Thus the proposed method may be used to determine the long-range electrostatic component of molecular interactions from highly accurate X-ray diffraction data

Electrostatic Molecular Interaction from X-ray Diffraction Data. I. Development of the Method; Test on Pyrazine

Electrostatic interaction is often an important part of the total interaction between molecules. It depends on the electron density distribution in the participating molecules, which can, in principle, be determined by X-ray diffraction methods. A method is described to calculate the electrostatic interaction between two nonpenetrating molecules by adding the pair-wise interaction between the constituent atoms. The molecular electron density distribution is expressed in terms of the densities corresponding with spherical atoms and deformations according to Hirshfeld's method. The electrostatic interaction between the various deformation densities is replaced by the interaction between the atomic multipole moments corresponding with the deformation densities. Application of the method to pyrazine, C4H4N2, showed qualitative agreement with results based on quantum-chemical calculations

A theoretical study of elastic X-ray scattering

Bragg X-ray scattering intensities are defined as scattering by the thermodynamic average electron-charge density. Purely elastic, kinematic X-ray scattering by a target in thermal equilibrium is always larger than Bragg scattering. At low temperatures, the elastic scattering becomes Bragg scattering. For large molecules, such as a crystal, at ordinary temperatures the elastic and Bragg scattering differ in a relative sense by O(N-1), where N is the number of vibrational degrees of freedom. For most practical cases the Bragg scattering is essentially the same as purely elastic scattering of X-rays

Electron-density-based calculations of intermolecular energy: case of urea

The intermolecular interaction energy in crystalline urea has been calculated both from diffraction data and from the Hartree-Fock crystalline electron-density distribution, using a modified atom-atom approximation scheme. The electrostatic part of this energy has been calculated from the atomic multipole moments, obtained by adjustment of the multipole model to experimental X-ray and to theoretical Hartree-Fock structure amplitudes. To obtain the induction energy, multipole moments were calculated from structure amplitudes for the crystalline electron density and from those that refer to the electron density of a superposition of isolated molecules. This worked well for the calculation of the interaction energy from Hartree-Fock data (6% difference from the sublimation-energy value), but not for the interaction energy from experimental data, where the moments of the superposition have to come from Hartree-Fock calculations: the two sets of multipole moments are far too different. The uncertainty of the phases of the structure amplitudes, combined with systematic errors in the theoretical data and noise in the experimental values, may account for the discrepancies. The nature of the different contributions to intermolecular interactions for urea is examined

Does the link between dissociation and cognitive inhibition in dissociative identity disorder generalize to other conditions characterised by traumatic dissociation: A study of Troubles-related PTSD

The electron-density distribution in urea, CO(NH2)2, was studied by high-precision single-crystal X-ray diffraction analysis at 148 (1) K. An experimental correction for TDS was applied to the X-ray intensities. Rmerge(F2) = 0.015. The displacement parameters agree quite well with results from neutron diffraction. The deformation density was obtained by refinement of 145 unique low-order reflections with the Hansen & Coppens [Acta Cryst. (1978), A34, 909-921] multipole model, resulting in R = 0.008, wR = 0.011 and S = 1.09. Orbital calculations were carried out applying different potentials to account for correlation and exchange: Hartree-Fock (HF), density-functional theory/local density approximation (DFT/LDA) and density-functional theory/generalized gradient approximation (DFT/GGA). Extensive comparisons of the deformation densities and structure factors were made between the results of the various calculations and the outcome of the refinement. The agreement between the experimental and theoretical results is excellent, judged by the deformation density and the structure factors [wR(HF) = 0.023, wR(DFT) = 0.019] and fair with respect to the results of a topological analysis. Density-functional calculations seem to yield slightly better results than Hartree-Fock calculations