An approximate molecular orbital method

Abstract

An approximate molecular orbital method is developed for hydrogen and first row elements at the minimum basis set level. Although the basis set consists of only valence Orbitals, the explicitly ignored inner shell is accommodated through pseudopotentials. The one center one electron terms are evaluated from atomic spectra. The two and three center one electron terms are exactly calculated. The two electron Coulomb matrix is evaluated rapidly in a mixed representation using a simple projection overlap. The two electron exchange matrix is estimated in a symmetrically orthogonalized set, with simple empirical corrections. The resulting method executes approximately as rapidly as does the popular INDO method. The model is applied to molecules up to the size of adenine, C5N5H5. Where comparison can be made with minimum basis set STO calculations, the method reproduces occupied molecular orbital eigenvalues, electron densities, and calculated bond distances to within a rms error of 0.03 a.u. The virtual molecular orbital eigenvalues are generally also within ±0.03 a.u., with the notable exceptions of homonuclear diatomic molecules. A simple empirical scheme allows calculation of experimental bonding energies with a rms error of ∼20 kcal in a study of 22 polyatomic molecules, and the results appear consistent enough to develop a bond energy additivity scheme such as devised by Pauling. Analysis is made of the several approximations used in the model. Copyright © 1975 American Institute of Physics.