Initial convergence of the perturbation series expansion for vibrational nonlinear optical properties

Ab initio Hartree–Fock and MP2 calculations of the longitudinal (hyper)polarizability—including the static electronic, static zero-point vibrational average (ZPVA), and pure vibrational (static and dynamic) contributions—have been carried out on a set of seven typical medium size conjugated nonlinear optical (NLO) molecules. The ZPVA is obtained through first-order in mechanical plus electrical anharmonicity. Based on physical “nuclear relaxation” considerations the individual (square bracket) terms that contribute to the pure vibrational (hyper)polarizability are then taken into account through third-, fourth-, or fifth-order depending upon the type of term. In order to carry out the correlated treatment, field-induced coordinates and a special finite field technique are utilized. Correlation leads to very substantial differences in the absolute and relative values of the various contributions. In comparison to the electronic term the ZPVA correction is usually small but in one case is over two-thirds as large. On the other hand, both static and dynamic pure vibrational contributions are commonly of a magnitude that is comparable to, or are larger than, the electronic term. The higher-order pure vibration terms are often large. For dynamic processes they can be almost as important as the lowest-order terms; for static (hyper)polarizabilities they can be more important. Thus, for typical NLO molecules, the initial convergence behavior of the perturbation series in mechanical and electrical anharmonicity requires further investigation.