Intracule Densities Research Articles

Elastic, inelastic and total cross sections for X-ray and electron scattering from molecular silane

Elastic, inelastic and total cross sections for X-ray and electron scattering calculated using high quality SCF molecular wavefunctions for silane (SiH4) are presented. The effects of basis set choice and free rotation on these cross sections are investigated. The effect of molecular binding and various other trends and systematics in the cross sections have been examined with the help of difference functions obtained by subtracting the appropriate independent atom model (IAM) cross section from the molecular cross section. The probability density for the interelectronic distance (radial intracule density) is obtained and analysed.

The evaluation of extracule and intracule densities in the first-row hydrides, LiH, BeH, BH, CH, NH, OH and FH, from self-consistent field molecular orbital wavefunctions

Extracule (centre of mass) and intracule (relative motion) pair densities are reported for the electronic ground states of the first-row hydrides, LiH, BeH, BH, CH, NH, OH and FH. For each type of two-particle coordinate and for each molecule, the radial, longitudinal and transverse densities are evaluated from self-consistent field molecular orbital wavefunctions constructed from 3-21G Gaussian basis sets. The radial intracule density I(r), the longitudinal intracule density L(i)(z) and the longitudinal extracule density L(e)(Z) evolve systematically from double maxima functions in LiH to single maximum functions in FH, whereas the extracule radial density E(R), the transverse extracule density T(i)(b) and the transverse extracule density T(e) (B) exhibit a single maximum in every case. These observations are explained in terms of the ionic character of the bond, the number of electron pairs, the probable orientations of the interelectronic vectors and the orientation of the vectors describing the centre of mass of an electron pair.

Scattering of fast electrons and X‐rays from molecules: CH4 and C2H2

AbstractSelf‐consistent‐field (SCF) wave functions are used to calculate cross sections for the elastic and inelastic scattering of fast electrons and x‐rays from CH4 and C2H2 molecules. The effects of basis set choice and free rotation on these cross sections are investigated. The utility of an approximate scheme to correct SCF inelastic cross sections for the effects of electron correlation is examined. The probability density for the interelectronic distance, or radial intracule density, is obtained and discussed.

Intracule densities and electron correlation in the hydrogen molecule

The spherically averaged intracule density I(r) is calculated with minimal and split-valence basis sets in the ground state of the hydrogen molecule. Restricted Hartree-Fock calculations indicate a high probability of interelectronic distances (r) of the order of 1 au as the internuclear separation (R) goes to infinity due to the incorrect dissociation of H2. The inadequacy of the restricted Hartree-Fock I(r) at large R is further illustrated by calculating (1/r) as a function of R. Configuration interaction calculations are shown to yield the correct qualitative form for I(r) at large R and when combined with the Hartree-Fock results yield the approximate Coulomb hole in H2 as a function of internuclear separation. Explicit formulae for the evaluation of I(r) and its moments with s-type Gaussian basis functions are included.

Scattering of fast electrons and X-rays from CO2 molecules

Self-consistent field (SCF) wave functions for CO2 are used to calculate cross sections for the elastic and inelastic scattering of fast electrons and x-rays from CO2 molecules. The effects of basis set choice and free rotation on these cross sections are investigated. The utility of an approximate scheme to correct SCF inelastic cross sections for the effects of electron correlation is examined. The probability density for the interelectronic distance, or radial intracule density, is obtained as a by-product.

Charge densities and two-electron intracules for the low-lying excited states of the helium-like ions

Spherically averaged one-electron charge densities rho (r) and two-electron intracule functions h(u) are computed for the 23S, 21S, 23P and 21P states of the helium-like ions from He to Mg10+. The distributions, based on correlated wavefunctions containing explicit dependence on the interelectronic separation, are expected to be the most accurate ones available. Interesting qualitative results obtained from a graphical analysis include the non-monotonicity of rho (r) in the 21S states of He, Li+ and Be2+, the absence of shell structure in the radial charge densities D(r) of the 23P and 21P states of the highly charged ions, and the absence of an intra-K-shell maximum in the radial intracule densities P(u) for the 21P states.

Anisotropic electronic intracule densities for diatomics

AbstractThe electronic intracule density, a three‐dimensional contraction of the spinless electron pair density, is the probability density function for an interelectronic vector. A computationally efficient algorithm for the evaluation of the basic two‐electron intracule integral for GTOs is presented. In order to provide an initial understanding of the topography of intracule distributions, anisotropic intracule densities for the X1Σ ground states of the H2 and N2 molecules are reported and analyzed.