Modified Atoms-in-Molecules Model for Predicting Diatomic Ground- and Excited-State Potential-Energy Curves. I. LiH, BeH, and BH

Abstract

A model is proposed for the approximate calculation, starting with theoretical atoms‐in‐molecules‐like composite functions (or linear combinations of valence bond structures) of potential‐energy curves for ground and excited diatomic systems. The assumptions which define the model may be summarized as follows: (1) diatomic electronic eigenstates are represented by a linear combination of composite functions which, in their orbital approximation, are constructed from a common basis set of atomic orbitals; (2) all valence (or peel) orbitals associated with a given nucleus contain a common orbital exponent, which is a nonlinear variational parameter in the molecular calculation; (3) the total molecular energy is separated into its intra‐atomic and interatomic parts; (4) the intra‐atomic energy of a given atom (or ion) is separated into its core (inner‐shell) and peel (valence‐shell) contributions; (5) the peel energy of a given atom (or ion) in the molecule is estimated from the experimental peel energy of the isolated atom (or ion) modified by a semitheoretical function of the scaling factor (which, in effect, accounts for the energy change of the peel when its orbital exponent is revised from the optimum isolated atom value to the optimum molecular‐state value); (6) matrix elements over the interaction‐energy operator are approximated in a systematic manner. The model is applied to 17 electronic states of LiH, BeH, and BH, 10 of which have been observed experimentally. Dissociation and excitation energies of eight of the lower states are predicted with an average error of ±1913 cm⁻¹=±0.24 eV. The model is shown to be inappropriate for higher‐energy states containing Rydberg character; errors of +1 eV are encountered here. Fundamental vibrational frequencies for six of the lower states are predicted with an average error of ±324 cm⁻¹, and equilibrium internuclear distances for eight of the lower states are obtained on the average within 0.09 bohr ∼0.05 Å of experiment. Theoretical analyses in terms of atomic promotional energies, structure projections, orbital occupation numbers, and gross charge distributions are tabulated and discussed.