Classical and Mexican hat-type potential energy curve for the hydrogen molecule from a confined Kratzer oscillator

Abstract

We review harmonic oscillator theory for closed, stable quantum systems. The H2 potential energy curve (PEC) of Mexican hat-type, calculated with a confined Kratzer oscillator, is better than the Rydberg–Klein–Rees (RKR) H2 PEC. Compared with QM, the theory of chemical bonding is simplified, since a confined Kratzer oscillator can also lead to the long sought for universal function, once called the Holy Grail of Molecular Spectroscopy. This is validated by reducing PECs for different bonds H2, HF, I2, N2 and O2 to a single one. The equal probability for H2, originating either from [Formula: see text] or [Formula: see text], is quantified with a Gauss probability density function. At the Bohr scale, a confined harmonic oscillator behaves properly at the extremes of bound two-nucleon quantum systems.