Sigrid D. Peyerimhoff

Geometry of Molecules. I. Wavefunctions for Some Six‐ and Eight‐Electron Polyhydrides

Potential surfaces have been investigated for BH2+, BH2−, NH2+, BeH2, BH3, CH3+, and BeH3− by means of LC (Hartree—Fock) AO MO SCF wavefunctions. One‐electron‐energy‐versus‐angle diagrams were determined for these AH2 and AH3 molecules, and comparison with the widely used empirical diagrams of Walsh demonstrates a quantitative similarity between them. In addition, mathematical inequalities are derived relating changes in the sum of one‐electron energies with angle to changes in the total energy with angle. Aided by these expressions, we are able to make direct connection between Walshs qualitative rules and the physically well‐defined ab initio solutions.

Geometry of Molecules. III. F2O, Li2O, FOH, LiOH

LC (Hartree—Fock) AO MO SCF calculations have been carried out for F2O, Li2O, FOH, and LiOH. Correlation diagrams showing the variation of orbital energies with internuclear angle have been constructed and demonstrated to be the theoretical counterparts to previous empirical correlation diagrams given by Mulliken and Walsh. Consideration of mathematical inequalities arising from the Hartree—Fock equations emphasizes the geometry‐determining nature of the orbital‐energy sum; at the same time such an investigation relates the fact that the sum of orbital energies does not have a minimum for the equilibrium linear configurations of Li2O and LiOH to the highly ionic character of these systems.

Geometry of Molecules. II. Diborane and Ethane

The diborane molecule has been investigated in its equilibrium D2h geometry, in the D3d (ethane) structure, and three intermediate configurations. Charge‐contour diagrams show that the electron distribution between the boron nuclei is considerably less concentrated than in the boron—bridge‐hydrogen bonds. Calculations for ethane in both equilibrium and bridged‐hydrogen configurations show that the carbon p functions of C2H6 play a much greater role in molecular binding than those of boron in B2H6 and this fact explains their different geometry.

MRD-CI Method for the Study of Low-Lying Electronic States. Application to Second-Row Molecular Ions of Type AH2+, AH+, AB+, and HAB+

From the point of view of the Schodinger equation the theoretical description of molecular ions is not essentially different than that for neutral systems. The corresponding Hamiltonian operator simply needs to be approximately adjusted to reflect the number of electrons in the ionic species and the problem is reduced to obtaining the associated eigenvectors and eigenvalues theore of to a suitably good approximation. Furthermore for molecules containing relatively light atoms there is good reason to believe that a non-relativistic approach to electronic structure calculations suffices in virtually all types of applications, and thus a purely electrostatic Hamiltonian operator is all that is required. In addition in most situations the Born-Oppenheimer Approximation can be safely assumed in such calculations, which is to say the nuclear and electronic motion can be treated in a basically uncoupled manner (the field of fixed or clamped nuclei). In this case the nuclear kinetic energy is temporarily ignored in the calculations and the first step in the overall treatment is to solve the so-called electronic Schrodinger equation for a series of fixed nuclear conformations (clamped-nuclei approximation).