A Finite Element Approach to the Two-dimensional Vibrational Schrödinger Equation and Its Application to the Hydrogen Bond

The finite element method was examined in relation to the two-dimensional vibrational Schrödinger equation. Some boundary conditions were used because of the symmetry of the potential, resulting in a higher precision in the case of the symmetrical potential, where the harmonic oscillators and the symmetrical hydrogen bond without anharmonicity were examined satisfactorily. An application was made to the symmetrical hydrogen bond with an-harmonicity, where the precision was less for the higher levels. By a comparison of the calculated with the observed infrared spectra, the anharmonic potential constants for the assumed potential function were estimated.