Field-induced coordinates for the determination of dynamic vibrational nonlinear optical properties

The most important contribution to nonresonant vibrational nonlinear optical properties arises from nuclear relaxation (NR). In previous work a set of static field-induced vibrational coordinates (FICs) has been developed to simplify calculation of the NR contribution within the infinite optical frequency approximation. Although the number of FICs is small and independent of molecular size, these coordinates form a complete set. However, the infinite optical frequency approximation does not take into account the frequency dispersion, which we evaluate for three conjugated organic molecules that span a range of polarity and valence-bond/charge transfer characteristics. Our results show that dispersion can be significant and that, in such cases, frequency-dependent FICs (FD-FICs) are necessary for an adequate treatment. A complete, though still small, set of FD-FICs is presented for this purpose. Computational tests reveal that a reduced subset, together with an harmonic approximation, can be used to achieve high accuracy outside the infrared (IR) region. That subset is complete for the electro-optic and Pockels and Kerr effects though not for other common properties.