Higher-order SCF response functions in a quasi-energy formulation

Abstract

This thesis is concerned with computer modelling of molecules interacting with electromagnetic radiation (light, radio waves, etc.), static electric and magnetic fields (in the laboratory), as well as approximate treatments of the motions of the molecules' atomic nuclei (vibration). Compared to interactions between electrons or between electron and nucleus, these interactions are small, and well approximated by perturbation theory.

Perturbation of isolated molecules in their ground state by time-dependent electromagnetic fields is known as 'response theory' (response functions), and permits study of both ground and excited states. For the 'self-consistent field' (SCF) class of electronic structure models, which includes the popular Kohn-Sham DFT models, this thesis presents a full hierachy of new formulas for response functions.

Although there are several equivalent formulas for a given response function, one specific is typically preferable due to computational considerations. The derived formulas are expressed in terms of the atomic-orbital (AO) density matrix, and take into account time- and perturbation dependence of the AOs, such as magnetic-field-dependent 'London AOs' or 'gauge-including AOs', which are employed to obtain gauge-origin independent results with improved basis set convergence.

The density matrix has an advantage over the more common molecular orbital (MO) parameterization in that it typically decays rapidly with the distance between atoms. For large molecules one may therefore truncate the density matrix. This can lead to great computational savings.

We formulate response theory by applying perturbation theory to 'Floquet theory' (sometimes called optical Bloch equations), which is a semi-classical quantum field theory. The central quantity in Floquet theory is the 'quasi-energy', and this is therefore the 'quasi-energy formalism' of response theory.

We have implemented the response function formulas in a local version of the DALTON quantum chemistry program, and demonstrate applications to the Cotton-Mouton birefringence, coherent anti-Stokes Raman scattering, electric-field-gradient induced birefringence, and to the vibrational corrections to hyperpolarizabilities.