Donald R. Whitman

Optimized Gaussian Basis SCF Wavefunctions for First‐Row Atoms

Optimum atomic Gaussian‐type‐function bases for self‐consistent‐field calculations are reported for B, C, N, O, and F, with from two to eight s functions and from one to four p functions. Orbital energies and coefficients are presented for the (3s1p), (5s2p), and (7s3p) bases for each atom, and the functions are shown to yield lower atomic energies than previously proposed Gaussian bases of the same size.

Constrained‐Variation Method in Molecular Quantum Mechanics. Application to Lithium Hydride

A general method is developed for calculating wavefunctions by minimizing the energy subject to the constraints of theoretically or experimentally known moments. The method is applied to a valence‐bond type configuration‐interaction wavefunction for LiH. An extremely small sacrifice in energy results when the wavefunction is constrained to fit the experimental dipole moment exactly. The expectation values of other physical properties are calculated both for the free‐variation function and the constrained‐variation function with the constrained‐variation function yielding improved predictions for the diamagnetic shielding, diamagnetic susceptibility, and electric field gradient at the lithium nucleus. In addition, it exhibits better gauge invariance of the total susceptibility as well as improved adherence to the Hellmann—Feynman condition. New predictions of other properties which have not been determined experimentally are also calculated, including the electric quadrupole moment.

Quantum Mechanical Calculation of Molecular Radii. I. Hydrides of Elements of Periodic Groups IV through VII

The fraction of the total electron density within a sphere having the empirical van der Waals radius is calculated for the atoms of eight elements, using Hartree‐Fock atomic wavefunctions. The sphere is found to contain 97%–99% of the electron density, indicating that such calculations correlate well with atomic sizes. The procedure is extended to eight hydride molecules of the type AHn, with molecular size determined by the radius of the 98% contour as computed from published one‐center SCF molecular wave‐functions. The predicted molecular radii agree well with experimental values and support the usefulness of this method for describing effective molecular size.

Computer Assignment Technique for Analysis of High‐Resolution NMR Spectra

A computer assignment technique for calculating chemical shifts and spin coupling constants from experimental high‐resolution proton magnetic resonance spectra is described. The observed spectral lines are assigned to transitions within the energy‐level diagram in a manner consistent with equal‐spacing and intensity‐sum rules. Experimental eigenvalues are calculated and introduced into equations derived from the spin Hamiltonian secular determinant in analytical form and in the diagonal experimentally observed form. These equations are implicit in the chemical shifts and spin coupling constants and in general must be solved by numerical methods although in some cases explicit solutions are found. The technique is applied to the 60 Mc spectrum of o‐dichlorobenzene to obtain the results δ=15.23 cps, J12=8.17 cps, J23=7.44 cps, J13=1.61 cps, and J14=0.36 cps.

Constrained‐Variation Method Applied to Helium‐Atom Wavefunctions

The constrained‐variation method is applied to helium‐atom wavefunctions, using precise Pekeris values of electron moments both as constraints and as tests of the effectiveness of the method. The conclusions support the basic premise that constrained‐variation wavefunctions may better represent the true electron densities in a system than do the corresponding free‐variation functions.

MO-SCF calculations for B2O3

The results of ab-initio molecular self-consistent field calculations with atomic optimized Gaussian bases are reported for the B2O3 molecule. These distinguish between several plausible structures and yield a V-shaped structure as the minimum energy geometry.