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

## DOI:

https://doi.org/10.20450/mjcce.2010.167## 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## 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.

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*Macedonian Journal of Chemistry and Chemical Engineering*,

*29*(2), 203–213. https://doi.org/10.20450/mjcce.2010.167

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