Exploration of the Effects of Bond Length on the Potential Energy Curves for Diatomic Compounds

By  Ramsey Cotton and Ashley Summers

Faculty mentor: Leanna Giancarlo

Bond dissociation energy (BDE) is the unique energy required to break a bond in a molecule into its respective atoms or molecular fragments. In this study, the theories behind harmonic and anharmonic oscillators, which address BDE of diatomic molecules, were employed to relate the length of a bond to its corresponding potential energy. A computational chemistry program was utilized to investigate the potential energies of diatomic hydrogen (H₂), bromine (Br₂), and hydrogen bromide (HBr). The diatomic molecules were found to obey Hooke’s law for harmonic oscillation at low energies, but as the energy increased with stretching the bond, deviations were observed due to anharmonicity because the restoring force was inequivalent to the displacement force. Instead of a harmonic parabolic shape, the potential energy curve followed a Morse potential function, approaching an asymptote representing the dissociation of the molecule into its constituent atoms at increased energies. The equilibrium bond length of dihydrogen was found to be approximately 75 pm, with an error of 1.16% from the literature value, 74.14 pm.¹ Despite the accuracy of the computed bond length, the BDE for H₂ was elucidated to be 1025 kJ/mol using the computational program, with a 135 % error from the literature value of 436 kJ/mol.¹ In this presentation, an overview of these theories, the experimentation, and the major results will be provided for H₂ and the other diatomic molecules. 

References: 

1. Engel, T. Vibrational and Rotational Spectroscopy of Diatomic Molecules. In Quantum Chemistry & Spectroscopy, 4th ed.; Pearson, 2019; pp 171-200. 

We hereby declare that we have neither given nor received unauthorized help on this work.