Extraordinary Basic Functions in Valence Theory

Abstract

It is pointed out that, provided kinetic energies are properly computed, one may use functions which are continuous with piecewise continuous first derivatives as trial variation functions in quantum-mechanical calculations of molecular electronic wave functions. As a simple example, a function of the type A exp[−(Z<r<+Z>r>)]is shown to be a good alternative to the conventional Eckart function for the helium atom. A rather more detailed study of helium is carried out to illustrate the use of individual lobes of real hydrogenlike atomic orbitals as an extended basic set of functions for molecular calculations. Implications for the general problem of correlation energies in atoms and molecules are discussed, and it is shown that a rationalization of the lowered electronic repulsions employed in modern pi-electron theory is provided by the supposition that pi electrons tend to move in opposite rather than the same lobes of pi orbitals.