Cross-sections of (a) , (b) , and (c) (right panel) taken through the bonding axis at an internuclear distance of 3.7 Å. The white dots show the location of the Na+ nuclei.
Slices of the numerically calculated for (left panels) and fits of these slices (right panels) to Eq. (12) . Slices were taken through the bonding axis with internuclear spacings of (a) 2.5 Å, (b) 3.7 Å, and (c) 5.0 Å, and all axis labels are in atomic units. The white dots show the location of the Na+ nuclei.
Bond length (R) coordinate dependence (points) of the fitting parameters (a) and (b) from Eq. (12) , which themselves are fit to (a) twelfth-order and (b) thirteenth-order polynomials, respectively (solid curves), plotted in atomic units.
Gas-phase potential energy surfaces of the system calculated from MQC MD simulations with a frozen core pseudopotential (blue hexagons), our coordinate-dependent pseudopotential (orange squares) and from fixed-point RHF calculations of the LUMO of (green circles) and UHF calculations of the HOMO of (black stars) using GAUSSIAN 03.
Charge densities for calculated from MQC simulations employing (a) a frozen core approximation pseudopotential, (b) our coordinate-dependent pseudopotential (CDP), and (c) one generated from an unrestricted Hartree-Fock calculation using GAUSSIAN 03. The electron density increases from the blue to the red contours, and the purple contour marks zero effective charge density. Calculations were performed at a bond distance of 3.50 Å and slices were taken through the bonding axis. The white dots show the location of the Na+ nuclei.
Fitting function ξfit and corresponding parameter functions x (where x represents the general functional form for each of the eight fitting parameters for ξfit) for the coordinate-dependent pseudopotential for the bonding electron of . R is the internuclear distance in atomic units.
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