Comparison of methods for solving the vibrational Schrödinger equation in the course of sequential Monte-Carlo-quantum mechanical treatment of hydroxide ion hydration

Abstract

Three numerical methods were applied to compute the anharmonic O–H stretching vibrational frequencies of the free and aqueous hydroxide ion on the basis of one-dimensional vibrational potential energies computed at various levels of theory: i) simple Hamiltonian matrix diagonalization technique, based on representation of the vibrational potential in Simons-Parr-Finlan (SPF) coordinates, ii) Numerov algorithm and iii) Fourier grid Hamiltonian method (FGH). Considering the Numerov algorithm as a reference method, the diagonalization technique performs remarkably well in a very wide range of frequencies and frequency shifts (up to 300 cm–1). FGH method, on the other hand, though showing a very good performance as well, exhibits more significant (and non-uniform) discrepancies with the Numerov algorithm, even for rather modest frequency shifts.

Keywords

• hydroxide ion
• ionic water solutions
• solvation
• hydrogen bonds
• intermolecular interactions
• anharmonic o–h vibrational frequency shifts
• monte-carlo simulation
• fourier grid
• hamiltonian method
• numerov algorithm
• diagonalization of hamiltonian matrix