Calculation and electronic description of molecular quadratic hyperpolarizabilities employing the ZINDO-SOS quantum chemical formalism. Chromophore architecture and substituent effects

To understand the second-order nonlinear optical response of molecular chromophores, we have developed and applied a formalism based on the use of perturbation theoretic (sum-over-states) methods using an uncorrelated (single determinant) ground state. When this method is used with a semi-empirical INDO/S Hamiltonian, it affords calculational results that are in excellent systematic agreement with experimental observations on a wide variety of organic and organometallic chromophores. Perhaps more importantly, the sum-over-states formulation permits understanding of the nonlinear response in terms of the nature of the excited states, interstate transitions, and changes in localization and dipole moment character. This paper presents calculations on a series of substituted organics, revealing several important regularities. (1) The nonlinear response increases substantially with the increasing size of conjugating groups between donor and acceptor ends. (2) Generally, increased polarity in the ground state results in increased nonlinear response. (3) Two-level models offer qualitative guidance in many, but not all, situations. Three-level corrections to two-level terms generally scale straightforwardly, being roughly one-half the value the two-level terms. (4) For most donor-acceptor π organics, major variations arise in second-order properties from the nature of the acceptor moiety, since donor characteristics are largely dominated by the π electron centre to which the electron donating group is attached. Insights are obtained into why highly-polarizable second-row substituents are generally less effective than first-row substituents in β enhancement and into suggested design characteristics for improving the β response of molecular chromophores. Hammett substituents parameters are at best limited qualitative aids in chromophore design.