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

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.