Comparative Study of Two Approaches for Solving the Torsional Schrödinger Equation: Fourier Grid Hamiltonian Method and Hamiltonian Diagonalization Method

Abstract

In this study, we have compared the computational performance of two methods implemented to solve the Schrödinger equation for intramolecular torsional motions. The first approach is the Fourier grid Hamiltonian (FGH) operator method, which is based on fragmentation of the total torsional Hamiltonian into kinetic energy part, which is diagonal in momentum representation, and the potential energy part, diagonal in coordinate representation. The second approach is the standard diagonalization technique, based on variational principle of quantum mechanics. Torsional energy eigenvalues are further used to compute the torsional correlation times in the framework of BPP (Bloembergen-Purcell-Pound) approach. The results show that diagonalization technique performs much faster than the FGH algorithm. Besides that, the convergence of eigenvalues with the number of basis functions appears to be achieved faster with Hamiltonian diagonalization.