Atomic Spectral-Product Representations of Molecular Electronic Structure: Metric Matrices and Atomic-Product Composition of Molecular Eigenfunctions

Authors

M. Ben-Nun, Robert Benny Gerber Festschrift
J. D. Mills, Air Force Research Laboratory
R. J. Hinde, University of Tennessee
C. L. Winstead, California Institute of Technology
J. A. Boatz, Air Force Research Laboratory
G. A. Gallup, University of Nebraska - Lincoln
P. W. Langhoff, University of CaliforniaFollow

Document Type

Article

Date of this Version

2009

Citation

J. Phys. Chem. A 2009, 113, 7687–7697

Comments

© 2009 American Chemical Society

This document is a U.S. government work and is not subject to copyright in the United States.

DOI: 10.1021/jp901427x

Abstract

Recent progress is reported in development of ab initio computational methods for the electronic structures of molecules employing the many-electron eigenstates of constituent atoms in spectral-product forms. The approach provides a universal atomic-product description of the electronic structure of matter as an alternative to more commonly employed valence-bond- or molecular-orbital-based representations. The Hamiltonian matrix in this representation is seen to comprise a sum over atomic energies and a pairwise sum over Coulombic interaction terms that depend only on the separations of the individual atomic pairs. Overall electron antisymmetry can be enforced by unitary transformation when appropriate, rather than as a possibly encumbering or unnecessary global constraint. The matrix representative of the antisymmetrizer in the spectralproduct basis, which is equivalent to the metric matrix of the corresponding explicitly antisymmetric basis, provides the required transformation to antisymmetric or linearly independent states after Hamiltonian evaluation. Particular attention is focused in the present report on properties of the metric matrix and on the atomic-product compositions of molecular eigenstates as described in the spectral-product representations. Illustrative calculations are reported for simple but prototypically important diatomic (H₂, CH) and triatomic (H₃, CH₂) molecules employing algorithms and computer codes devised recently for this purpose. This particular implementation of the approach combines Slater-orbital-based one- and two-electron integral evaluations, valence-bond constructions of standard tableau functions and matrices, and transformations to atomic eigenstateproduct representations. The calculated metric matrices and corresponding potential energy surfaces obtained in this way elucidate a number of aspects of the spectral-product development, including the nature of closure in the representation, the general redundancy or linear dependence of its explicitly antisymmetrized form, the convergence of the apparently disparate atomic-product and explicitly antisymmetrized atomic-product forms to a common invariant subspace, and the nature of a chemical bonding descriptor provided by the atomicproduct compositions of molecular eigenstates. Concluding remarks indicate additional studies in progress and the prognosis for performing atomic spectral-product calculations more generally and efficiently.