An Exploration of Theoretical Spectra

Abstract

This thesis presents an exploration of theoretical spectra, both in their creation andinterpretation, with a focus on coupled cluster methods and an emphasis on the importance of relativistic effects. Throughout this work the X2C Hamiltonian is utilized to produce the reference wavefunction, including both scalar relativistic effects and spin-orbit coupling variationally in the presented schemes. First, a relativistic equation-of-motion coupled-cluster with single and double excitations(X2C-EOM-CCSD) formalism is presented including a discussion of the massively parallelized implementation available in the ChronusQuatum software package. In order to evaluate the accuracy of X2C-EOM-CCSD, we compare calculated, experimental, and TDDFT results, looking at zero-field splitting values. In addition to calculating the excitation energies for this low energy region, the oscillator strength of each excitation is calculated. This enables the simulation of absorption spectra, the observation of which excited states are populated, and the comparison of other general spectral features in the low energy UV-Visible region in order to benchmark the accuracy. Additionally, a relativistic time-dependent equation-of-motion coupled-cluster with singleand double excitations (TD-EOM-CCSD) formalism is presented. Unlike other explicitly time-dependent quantum chemical methods, the present approach considers the time correlation function of the dipole operator, as opposed to the expectation value of the timedependent dipole moment. The accuracy of X2C-TD-EOM-CCSD is evaluated by comparing zero-field splitting in atomic absorption spectra of open-shell systems (Na, K, Mg+, and Ca+) with values obtained from experiment. In closed-shell species (Na+, K+, Mg2+, and Ca2+), singlet triplet mixing is observed in the X2C-TD-EOM-CC calculations, which results from the use of the X2C reference. The effects of the X2C reference are evaluated by comparing spectra derived from X2C-TD-EOM-CC calculations to those from TD-EOM-CC calculations using a complex generalized Hartree-Fock (C-GHF) reference. The interpretation of spectra is an arduous task that can be simplified with the use ofspectral analysis tools. The Python library, fasma, is presented as a tool to help simplify this problem. By breaking down spectra into angular momentum character or molecular orbital contributions, along with giving information about the excitation order of each transition, various regions of the spectra can be interpreted and features of interest can be quickly identified. While keeping ease of use in mind, this library also allows extensive customization of analysis by the user through the quantity of information from electronic structure calculations that is made into easily accessible Python objects.