Direct quantal fitting of the molecular potential energy function from experimental data

Abstract

The vibration and rotation of the nuclei of diatomic molecules can be determined using a fully quantum treatment. In the past, approximate semi-classical techniques have often been used, in part due to the difficulty in modeling diatomic potential energy functions and in part due to the effort required for non-linear least-squares fitting. This thesis outlines the process that obtains a potential energy curve from experimental data using a fully quantum technique. The design and implementation of the potential energy curves incorporates physical constraints such as the long range asymptotic behaviour as well as specification and optimization of the minimum point. A concept from quantum defect theory is also used to aid in the modeling of the potential. This uses a smooth, easily-fitted curve, a quantum defect, that inherently includes the dramatic features of the potential energy at very short bond lengths. An analytic form for the wavefunction for long bond lengths is also developed. This analytic form allows for direct calculation of observables at long range that involve little numerical error and provides boundary conditions which are used to find values of the wavefunction more accurately at shorter