A novel method by which to calculate the near edge X-rayabsorption fine structure region of the X-ray absorption spectrum has been derived and implemented. By means of damped coupled cluster theory at coupled cluster levels CCS, CC2, CCSD and CCSDR(3), the spectra of neon and methane have been investigated. Using methods incorprating double excitations, the important relaxation effects maybe taken into account by simultaneous excitation of the core electron and relaxation of other electrons. An asymmetric Lanczos-chain driven approach has been utilized as a means to partially resolve the excitation space given by the coupled cluster Jacobian. The K-edge of the systems have been considered, and relativistic effects are estimated with use of the Douglas--Kroll scalar relativistic Hamiltonian. Comparisons have been made to results obtained with the four-component static-exchange approach and ionization potentials obtained by the {Delta}SCF-method. The appropriate basis sets by which to describe the core and excited states have been been determined.  The addition of core-polarizing functions and diffuse or Rydberg functions is important for this description. Scalar relativistic effects accounts for an increase in excitation energies due to the contraction of the 1s-orbital, and this increase is seen to be 0.88 eV for neon. The coupled cluster hierachy shows a trend of convergence towards the experimental spectrum, with an 1s -> 3p excitation energy for neon of an accuracy of 0.40 eV at a relativistic CCSDR(3) level of theory. Results obtained at the damped coupled cluster and STEX levels of theory, respectively, are seen to be in agreement, with a mere relative energy shift.

This thesis explores and expands upon theoretical means of quantifying a number of nonlinear spectroscopies, including two-photon absorption, resonant-inelastic x-ray scattering, Jones birefringence, and magnetic circular dichroism. On top of that, detailed information is given for the derivation and program implementation of damped cubic response functions. Complex-valued cubic response functions have been implemented in the quantum chemistry package DALTON, based on working equations formulated for an approximate-state wave function. An assessment of the implementation, such that for small frequencies the second-order hyperpolarizability should behave according to an analytic function that depends quadratically on the optical frequencies. It is demonstrated how two-photon absorption (TPA) can be described either through second-order transition moments or via the damped cubic response function. A few calculated TPA profiles are produced for a set of smaller molecules, in order to display the capability of the cubic response function in the x-ray frequency region. Resonance-inelastic x-ray scattering (RIXS) is explored in a similar manner as two-photon absorption. It is shown how the second-order hyperpolarizability can represent RIXS in the limit of intermediate-state and final-state resonances. Complications emerging from the complex dispersion of the hyperpolarizability are discussed. Moreover, linear birefringences, with focus on the Jones birefringence, are investigated for noble gases, monosubstituted benzenes, furan homologues, and a pure acetonitrile liquid. A linear relation between the Jones birefringence and the empirical para-Hammett constant as well as the permanent electric dipole moment is presented. Estimations of three linear birefringences --- Kerr, Cotton--Mouton, and Jones ---are obtained by averaging over a set of liquid snapshots. The Jones effect for acetonitrile turns out to be unusually large inmparison to the other two investigated linear birefringences. The final chapter of the thesis investigates magnetically induced circular dichroism (MCD). A question regarding relative stability of the first set of excited states for DNA-related molecular systems is resolved through MCD by exploiting the signed nature of circular dichroisms. Furthermore, to what extent solvent contributions affect MCD spectra is explored. The effect on uracil MCD spectrum due to thionation is studied, for which the degree of redshifting for systems 2-thiouracil and 4-thiouracil can be seen to be addative as compared to the 2,4-dithiouracil system. / <p>QC 20171129</p>