Molecular response to electromagnetic fields - static or optical - within a framework of perturbation theory diverges close to resonance with molecular transitionen energies, and need work-around solutions for real-valued response functions. This licentiate thesis deals with nonlinear response, with focus being on cubic polarizaibilities, and outlines the underlying mathematics for exact-state and approximatestate, complex-valued response functions applicable to quantum chemical computation. Such a complex-valued response theory is commonly known as dampedresponse theory, for which the response functions consists of a real and an imaginary component, each of them representing various spectroscopies in nature. In addition to the mathematics, the formulas have been implemented in the quantum chemical package DALTON, and several tests determining the integrity of the implementation has been conducted.
The fourth and final major part of the thesis is concerned with applied nonlinear response theory, including not only cubic response functions, but also quadratic and linear response functions, some of which are of the more exotic character. Three spectroscopies have been investigated for small and medium-sized organic molecules and the neon atom: two-photon absorption (TPA), Jones birefringence (JB), and magnetic circular dichroism (MCD).
The TPA part is a simple demonstration of capability of the damped cubic response code, for which neon is the example system. Perfect agreement is shown for the Ehrenfest approach and an independent implementation based on the quasienergy formalism.
JB is an optical eect in which induced refractive anisotropy, by means of external electric and magnetic static elds, results in ellipticity of linearly polarized light beams. This part mainly discuss implications from a paper which the current author took part in. The paper ultimately attempts to indentify the general observable strength of the effect, and coincidentaly pin-point some particular system suitable for experiments. Among other finds, JB is found to be correlated to the electric dipole moment, and for monosubstituted benzenes, the para-Hammett constant.
Finally, MCD is discussed based on three papers in which the present author is included. The elegant MCD solution to broad absorption peaks, for which it is desired to distinguish individual states, is demonstrated on adenine and three additional purine derivatives. A drawn out debate regarding relative stability of certain low-lying states could be settled by this method. Furthermore, appropriate description of solvation environment in conjunction with the exchange-correlation functionals B3LYP and CAM-B3LYP is investigated on purine and pyrimidine derivatives. CAM-B3LYP is found to be superior in terms of general prole shapes, while results regarding solvation model are rather inconclusive, although the results suggests some level of solvation model is appropriate, such as a polarizable continuum model or explicit solvation molecules.