Dynamic Electron Density Research Articles

Dynamic electron transfers in B2H6 and Cu(PH3)2(BH4)

In order to investigate the coupling of molecular vibrations and electron distribution, dynamic electron transfers in B2H6 and Cu(PH3)2(BH4) are lated by using a new variational method. In both molecules, the dynamic electron density near bridging hydrogen atoms decreases to form the density valley by exciting specific vibrational modes. On the other hand, in both sides of the valley density hills grow up. For these molecules, similar contour maps are given by the modes with different symmetry which have large contribution of the bridging ligands. While the dynamic electron transfer of B2H6 arises in symmetric form, the vibrational modes of the Cu complex gives the asymmetric redistribution of the dynamic electron density. This is attributed to the difference of the symmetry between the two molecules.

Dynamic analysis of electron density in the course of the internal motion of molecular system

The general dynamic aspect of electron density of a molecular system is studied on the basis of the general equation of the electron orbital which is formulated for the dynamic study of electronic motion. The newly defined electron orbital incorporates the dynamics of molecular vibration into the electronic structures. In this scheme, the change of electron distribution caused by excitation of vibrational state is defined as the ‘‘dynamic electron transfer.’’ The dynamic electron density is found to have the remarkable ‘‘additive’’ property. The time-dependent aspect of the dynamic electron redistribution is also analyzed on the basis of the ‘‘coherent state.’’ The new method relates the classical vibrational amplitude to the quantum number of the vibrational state. As a preliminary application of the present treatment, the dynamic electron densities of H2, HD, HT, HF, and HCl molecules are calculated by use of ab initio molecular orbital method.

Deformationsdichteverteilung in Salzen komplexer Anionen I: X–N-Dichte in α-Calciumformiat bei 100 K und 296 K

Abstract Measurements of the deformation density in the formate group of α-Ca(HCOO)2 by the X – N-technique at 100 K and 296 K are presented. In addition to the usual corrections (profile analysis for background, absorption, extinction) a correction for thermal diffuse scattering was applied. This correction lowered the deformation density by about 5%. The oxygen lone pairs are observed at angles slightly less than 120° from the C – O bond axis indicating a sp2-hybridization of the oxygen. The experimental results agree fairly well with theoretical static and dynamic electron density calculations for the bonds. Some differences are observed, however, for the lone pair region.

Anharmonic contributions to dynamic electron densities caused by large librations of molecules

The effect of large librations of molecules on electron density distributions is investigated with the already published structures of β-NaN3, p-nitropyridine N-oxide and anthracene, and with some model calculations for C, N, O atoms. For this purpose, the temperature factor of the atom concerned is expanded with cumulants, and the smearing function of the nuclear positions and the dynamic electron density is calculated by an Edgeworth series. The results are represented as difference densities p(anharmonic) - p(harmonic) ≡ p(A - H) maps. For the end N atom in β-NaN3 at 295 K and for the C(7) atom in p-nitropyridine N-oxide at 30 K, these maps contain minima of 0.53 e Å-3 (N) and 0.22 e Å-3 [C(7)] in front of the nuclei, and maxima of 0.44 e Å-3 (N) and 0.21 e Å-3 [C(7)] behind the nuclei. Thus, due to large librations, the density is shifted from in front of the nuclei towards the back of the nuclei, as viewed from the centre of libration. The magnitude of the region of non-vanishing p(A - H) density largely depends on the magnitude of the atomic motions (temperature). With the end N (295 K) mentioned above the radius of this region around the nucleus is about 0.5 Å, and with C (7) about 0.2 Å. Apart from the temperature, the p(A - H) densities are essentially determined by the distance of the atom from the centre of libration, and by the ratio of the librational/translational contributions to the atomic motions. A procedure is described to estimate the extrema in the p(A - H) densities in an actual structure.