Calculating the ground state energy of hydrogen molecules and helium hydride ions using Bohr’s quantum theory

Abstract

Molecular composition and chemical bonding have always been the fundamental basics in computing chemistry. As the helium hydride ion has been proven to be widespread in the Universe, it has once again ignited interest in this substance. To understand its composition, such as getting the ground state energy and chemical bonds length of the helium hydride ion, one needs to solve the Schrödinger equation based on quantum mechanics and the variational method. However, such methods are not intuitive for non-related field researchers. In this paper, Bohr’s semi-classical quantum model is first used to explain the formation of the bonds’ length, and to calculate the ground state energy of hydrogen molecules. Then, such methods are extended to the helium hydride ion. Our model gives a comparably accurate result compared with the results from variational methods. Furthermore, the physical picture of this method is straightforward, and is suitable for intuitively explaining the formation of hydrogen molecules and helium hydride ions.

Few-electron atoms with linear Bohr–Sommerfeld electron paths

“…We may also invert the question and starting from the accurate ground-state energy, calculate the value of 1/d needed to bring the semiclassical value in agreement with the exact one. 3 Naturally, we have lim…”

“…While the semiclassical Bohr model of the atom is lacking in the very fundamental sense that it predicts non-spherical atoms (the atoms, or at the very least the hydrogen atom and singleelectron ions, are flat discs), it is still 'correct enough' to predict chemical bonding, as has been shown under different assumptions both with pedagogical [1][2][3] and more technical aims [4,5] and already by Bohr himself who predicted a stable H 2 molecule with a very reasonable binding energy [6,7]. In hindsight, one problem with Bohr's approach is that the circular orbits, even in the isolated atom, correspond to a state of unphysically high angular momentum.…”