The focus of this thesis is in two main areas: computational approaches to heavy element thermochemistry and development of quantum electron-nuclear dynamic methods. Computational chemistry is important because it can be used to describe time-independent phenomena such as enthalpies of formation, geometries, activation energies, and much more. Furthermore, computational chemistry can describe many time-dependent phenomena as well such as electron-transfer rates, ionization effects, and ultrafast phenomena.Methodologies for time-independent phenomena are well-developed, though there is still more that needs to be understood about lower parts of the periodic table. Existing methods often miss an important aspect for the description of these elements; ranging from the incorporation of certain relativistic effects to the treatment of static and dynamic correlation. For time-dependent phenomena that involve strong electron-nuclear coupling, methods are much less developed and restricted to two-electron systems. Including a quantum treatment of both the nuclei and electrons is an immense challenge for larger systems. Developing a general and efficient method is of great interest as it would provide more theoretical insight in the growing attosecond science field. In this dissertation, time-independent methods for heavy elements, namely the actinides and lanthanides are investigated. As well, the development of a time-dependent method with a quantum description of electron-nuclear dynamics is presented.The overview is as follows, in Chapter 3 the performance of commonly used density functional theory (DFT) approaches are analyzed for a select set of lanthanide containing molecules. 22 different functionals were considered to gain insight on performance for prediction of thermochemical properties compared to experiment. for the prediction of enthalpies of formation and bond dissociation energies. The focus is specifically on determining the accuracy of relativistic effective core potentials for these lanthanide species. The set of lanthanides, termed Ln54 set, includes lanthanide oxides, fluorides, and chlorides with the lanthanide formally in the +1, +2, and +3 oxidation state.In Chapter 4, a similar analysis as for the lanthanides was done for a series of actinide compounds. A dataset for enthalpies of formation from experiment encompassing a set of 66 actinide species consisting of Th, U, Np, Pu, or Am with oxide, halide or both ligands was compiled and used as a gauge. The study was expanded to include a variety of approach that account for relativistic effects, which are important for heavy element species. In Chapter 5 the impact of spin-orbit effects on DFT calculations was considered for the lanthanide oxide subset of the Ln54 dataset (along with YbF and LuF). A number of methods are considered, including spin-orbit DFT (SO-DFT) and full four-component Diract-Hartree-Fock calculations for spin-orbit coupling.The following chapters 6, 7, and 8, development towards the multiconfigurational electron nuclear dynamics (MCEND) method and subsequent analysis of electron-nuclear dynamic effects. In Chapter 6 an overview of the motivation and methods for a quantum mechanical method for both electrons and nuclei is presented along with initial efforts on the method development. In Chapter 7the first published work of our recent MCEND work is detailed. In this chapter, the dynamics of H2and LiH in strong laser fields is studied and insight is gained about how the electron and nuclear motion are coupled. Analysis is done of excitation spectra and coherence properties of the electronic and nuclear wavefunctions. In Chapter 8 the performance of the MCEND method is detailed for the diatomics: H2, HeH+, BeH+, LiH, Li2, and N2. The ground-state equilibrium bond lengths and dipole moments, and time-dependent properties (electronic, vibrational, and high-harmonic spectra)are obtained with MCEND. The viability of MCEND is demonstrated, as well as the observation of nonadiabatic effects that arise in high-harmonic spectra, where electronic excitation displaces nuclear motion from equilibrium position. Isotope effects for H2 are also analyzed for the spectra. Lastly, the future directions of the research are discussed in Chapter 9.
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