Ionic Kratzer bond theory and vibrational levels for achiral covalent bond HH

TL;DR

This paper introduces an ionic Kratzer bond theory for H2, deriving vibrational levels and bond energy from first principles, achieving high accuracy comparable to advanced quantum methods.

Contribution

It presents a novel ionic Kratzer oscillator model that accurately predicts H2 vibrational levels and bond energy from fundamental constants, surpassing traditional methods.

Findings

Bond energy within 0.08% of experimental value

Vibrational levels within 0.02% accuracy

Outperforms Dunham oscillator by 30 times

Abstract

A dihydrogen Hamiltonian reduces to the Sommerfeld-Kratzer-potential, adapted for field quantization according to old-quantum theory. Constants omega_e, k_e and r_e needed for the H_2 vibrational system derive solely from hydrogen mass m_H. For H_2, a first principles ionic Kratzer oscillator returns the covalent bond energy within 0,08 % and all levels within 0,02 %, 30 times better than the Dunham oscillator and as accurate as early ab initio QM.