The analysis of polarization effects on the interelectronic separations in the atoms and molecules of the G1 test set

摘要

We have calculated the differences between kinetic, nuclear attraction, and two-electron energies as well as the position intracules, P(u), for 56 molecules and 17 atoms contained in the G1 test set, using basis sets differing in their degree of polarization. The calculations were performed using an unrestricted Hartree-Fock wave function that was expanded using the 6-31G, 6-31G(d,p), 6-31G(3d,3p), 6-31G(3df,3pd), 6-311G, 6-311G(d,p), 6-311G(3d,3p), 6-311G(3df,3pd), 6-311++G, 6-311++G(d,p), 6-311++G(3d,3p), and 6-311++G(3df,3pd) basis sets. In addition to these Pople basis sets, the Dunning's cc-pVDZ and cc-pVTZ bases as well as the non-polarized portions of these basis sets were used. We observe a consistent contraction of electron pairs (as measured by the distribution in P(u)) as the number of polarization functions is increased beyond zero in molecular systems. This contraction is related to an increase in the electron density in the internuclear bonding regions of molecules as the wave functions are polarized. We note that the increased flexibility in the polarized basis set allows for a more accurate description of the chemical bond and is energetically favorable due to an increased level of attraction to the nuclei (despite the obvious increase in electronic repulsion energy). Because of the increase in electron density in internal regions of the molecule (at the expense of electron density depletions in outer regions), the probability of observing electrons closer together (i.e., at smaller u) increases due to the relationship between P(u) and its Coulomb component, J(u).In the context of intracule functional theory, intracules are probability densities that describe the relative properties of electron pairs. This article describes the so-called basis antihole through position intracule and electron density studies of the G1 test set of atoms and molecules, and in doing so it defines important connections between intracule functional theory and the electron density.