Anharmonic vibrational wave functions, infrared band intensities, and dipole moments of water

A new and simple method to expand the anharmonic vibrational wave functions with respect to the harmonic oscillator wave functions is proposed. The coefficients of the expansion are given as matrix elements of the S function of the contact transformation in the perturbation theory and the explicit expressions of these coefficients are given within the approximation to the second order in λ. As an example of the expansion, the wave functions of water molecules were calculated and applied to the calculation of infrared band intensities and average values of dipole moments in several states.