On exact calculation of response properties of oscillators in static electric field: a fourier grid Hamiltonian approach. I. One-dimensional systems

Abstract

The Fourier grid Hamiltonian method is used to calculate the response properties of different types of 1-d (one-dimensional) quantum oscillators in a uniform static electric field. The calculations are potentially exact. Excepting the harmonic oscillator, the other model oscillators studied are seen to possess nonlinear polarizabilities. In general, the polarizabilities are not monotonic functions of appropriate vibrational quantum numbers. The exact nature of this vibrational-state dependence of polarizabilities is shown to depend on the type of mechanical anharmonicity in which the nuclei move and the nature of electrical anharmonicity characterizing the field-oscillator coupling. The large vibrational contribution to nonlinear polarizabilities often predicted for real diatomics could therefore originate from the mechanical and electrical anharmonicities of the potential in which the nuclei move when placed in a static electric field.