Calculation of vibrational dynamic hyperpolarizabilities for H2O, CO2, and NH3

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Abstract
Dynamic vibrational first and second hyperpolarizabilities, applicable to a number of nonlinear optical processes, have been calculated for H2O, CO2, and NH3 at a typical laser frequency. As a percentage of their electronic counterparts, they range from being very small to being on the order of 20–30 %. The static values have also been calculated and are much larger. The calculations were based on perturbation theory and required knowledge of (a) first and second derivatives of the electrical properties(dipole moment,polarizability, and first hyperpolarizability functions) with respect to the normal coordinates, and (b) the harmonic and first anharmonic force constants. These were found at both the SCF and MP2 levels of approximation. In most cases electron correlation has a marked effect on the vibrational hyperpolarizabilities. Anharmonicity contributions are relatively small except for the static case and for the dc‐Kerr effect.