Cubic Response Theory and the Electromagnetic Properties of Ground and Excited States

Abstract: This thesis is devoted to the study of analytical response theory up to third order and its application to electromagnetic properties of ground and excited states. Computationally tractable expressions for the cubic response function for SCF and MCSCF wave functions have been derived and implemented in a computer code. The implementation includes several strategies that allow cubic response calculations for accurate wave functions with large active spaces. Several types of so-called direct techniques, the use of integral screening, and parallel algorithms enable large-scale SCF cubic response calculations. The quadratic and cubic response functions have also been implemented in a self-consistent reaction field model to simulate equilibrium and non-equilibrium solvation.A large number of frequency-dependent electric and magnetic properties are directly related to the cubic response function, including several multi-photon processes, such as three-photon absorption and two-photon absorption between excited states, can be obtained through various residues of the cubic response function. From one of the residues, second-order properties of excited states may be obtained without the explicit determination of the excited state wave function. This new approach to excited-state properties—and inparticular the use of a single-determinant reference state—has been investigated for a variety of molecules. The results support this approach, both in comparison with linear response calculations applied to the excited state and in comparison with experimental data where available.The second hypermagnetizability, related to the Cotton-Mouton effect, has been calculated for noble gas atoms, HF, H20, NH3, CH4, and 02 . Frequency-dependent perturbations of electric, magnetic, and quadrupole type have been applied in the first calculation of circular dichroism for electric field induced second harmonic generation—the effect is predicted to be small but measurable.The applicability of the response code for large systems has been demonstrated by the calculation of the polarizability, second hyperpolarizability and magnetizability for the fullerenes, C60, C70 , and C84 . The second hyperpolarizability has also been calculated for oligomeric sequences of different polymers, including polyacenes, cis-, trans- and diphenyl-polyenes.The equilibrium and non-equilibrium reaction field models have been applied in calculations of hyperpolarizability depolarization ratios and excited state polarizabilities of nitroanilines in solution.Triplet spectra and phosphorescence of the nitrogen molecule and short polyenes have been studied with linear and quadratic response theory.