Solution of Schrödinger Equation for Simple Diatomic Molecules Using One-Parameter 1s Slater-Type Orbitals Wave Function

Abstract

The Schrödinger equation for simple homonuclear and heteronuclear diatomic molecules is analytically solved using one-parameter Slater-type orbitals (STOs) to approximate the electronic wave function within a molecular orbital (MO)-like approach. The resulting total energies, equilibrium bond lengths, potential curves, and electron densities are presented in detail. Calculations using a selected orbital exponent accurately reproduce results from standard methods. Furthermore, the optimization of the orbital exponent allows for a more accurate representation of the electronic wave function, leading to the improved results of the total energy and the equilibrium bond length, as well as minimal computational cost. Seen in the heteronuclear diatomic molecule, the use of the one-parameter STOs allows the transformation of the heteronuclear problem into the homonuclear one, revealing the electron repulsion effect on the orbital exponent parameter.