Implementation of an NDDO/CI/SOS approach for second-order hyperpolarizabilities

Abstract

We report the implementation of the sum-over-states (SOS) formalism for neglect of diatomic differential overlap (NDDO) Hamiltonians Austin model 1 (AM1), parametric method 3 (PM3), and modified neglect of differential overlap (MNDO) for calculation of third-order nonlinear optical properties into the program package VAMP and its application to third harmonic generation (THG). Extensive comparisons between THG experimental data and published MOPAC/FF to VAMP/PECI/SOS and AMPAC/FF calculated values were carried out in gas phase and in solvent for a data set of 236 compounds of the general type DπA and conjugated π systems. Great care was taken to derive the global minimum conformers, yielding significant deviations of the geometries derived by the three Hamiltonians. The data set therefore gives an overview of the shortcomings and strengths of the semiempirical methods. Here, the implementations of solvent effects in both semiempirical packages are especially problematic in the case of elongated molecules, so a threshold for molecular globularity had to be defined to eliminate erroneous data. The correlation statistics presented for γ are in acceptable agreement for the whole data set as for all experimentally well-defined substance classes with scalable correlation slopes smaller than unity. The data become more reliable for large γ, probably due to more precise experimental values. Inclusion of solvent effects raises the polarizabilities of the molecules consistently. These results enable us to qualitatively predict trends for small as well as large second-order polarizabilities, to derive scaling functions for quantitative predictions, and to calculate experimentally nonaccessible tensor elements of γ. The SOS formalism even allows us to obtain insights into the frequency dependence of second-order hyperpolarizability effects beyond THG. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 727–760, 2000