We have examined the response of an exact and an MCSCF reference state to a general time-dependent field. The time development of both the exact and the MCSCF reference state have been parametrized in terms of explicit exponential time-dependent transformations. The time development has been determined by requiring the Ehrenfest theorem to be satisfied through each order in the interaction between the molecular system and the field. The response of the exact and the MCSCF reference state has been used to evaluate linear, quadratic, and cubic response functions. It has been shown how a large variety of molecular properties may be expressed in terms of these response functions. It has also been demonstrated that molecular properties containing the electric dipole operator may be expressed in equivalent forms involving the momentum operator both for the exact and the MCSCF state. The MCSCF response functions have been transformed to computationally attractive expressions which do not contain summation indices over intermediate states and which allow direct techniques to be straightforwardly applied.

The linear and quadratic response functions have been determined for a coupled cluster reference state. From the response functions, computationally tractable expressions have been derived for excitation energies, first- and second-order matrix transition elements, transition matrix elements between excited states, and second- and third-order frequency-dependent molecular properties.

Coupled cluster singles and doubles linear response (CCLR) calculations have been carried out for excitation energies and dipole transition strengths for the lowest excitations in LiH, CH+, and C4 and the results compared with the results from a CI-like approach to equation of motion coupled cluster (EOMCC) . The transition strengths are similar in the two approaches for single molecule calculations on small systems. However, the CCLR approach gives size-intensive dipole transition strengths, while the EOMCC formalism does not. Thus, EOMCC calculations can give unphysically dipole transition strengths, e.g., in EOMCC calculations on a sequence of noninteracting LiH systems we obtained a negative dipole strength for the lowest totally symmetric dipole allowed transition for 19 or more noninteracting LiH systems. The CCLR approach is shown to be a very attractive "black box" approach for the calculation of transition moments.

A gauge origin independent formalism for the calculation of molecular magnetic properties is presented. Origin independence is obtained by using London’s gauge invariant atomic orbitals, expanding the second quantization Hamiltonian in the external magnetic field and nuclear magnetic moments, and using the resulting expansion terms as perturbation operators in response function calculations. To ensure orthonormality of the molecular orbitals, a field-dependent symmetrical orthonormalization is employed. In this way the gauge dependence of the London orbitals is transferred to the Hamiltonian. The resulting perturbation operators may be used to calculate magnetic properties from any approximate ab initio wave function.

Articles you may be interested inSign change of the Soret coefficient of poly(ethylene oxide) in water/ethanol mixtures observed by thermal diffusion forced Rayleigh scattering Static hyperpolarizability of the water dimer and the interaction hyperpolarizability of two water molecules Absolute signs of hyperpolarizabilities in the liquid stateThe experimental work by Levine and Bethea ͓J. Chem. Phys. 65, 2429 ͑1976͔͒ and by Ward and Miller ͓Phys. Rev. A 19, 826 ͑1979͔͒ on the hyperpolarizability of solvated water and water in the gas phase, respectively, showed a very substantial effect of the solvent on the measured hyperpolarizability. The sign of the hyperpolarizability of solvated water changed compared to gas phase and the numerical value increased by a factor of 1.5. This article presents a theoretical investigation of the solvent effects of the hyperpolarizabilities and their frequency dispersions for liquid water using the continuum, semicontinuum, and supermolecular models. Calculations involving the semicontinuum and supermolecular models give the sign change of the hyperpolarizabilities, indicating that the hydrogen bonds and the static dipole interaction have substantial impact on the hyperpolarizability of liquid water. Hyperpolarizabilities calculated by the supermolecular approach are about one third of those calculated by the semi-continuum model. The continuum and semicontinuum models involve a recent implementation of a quantum mechanical reaction field response method.