Development of non-born-Oppenheimer methods for ground and excited state molecular properties

Abstract

The nuclear-electronic orbital (NEO) method is a multicomponent approach that allows the quantum mechanical treatment of electrons and specified protons on the same quantum mechanical level. NEO does not make the Born-Oppenheimber approximation between electrons and select protons, and therefore has great potential in applications to non-Born-Oppenheimer processes such as proton-coupled electron transfer (PCET). Additionally, NEO can also capture nuclear quantum effects such as zero-point energy and proton delocalization in a direct and efficient manner. This dissertation describes the development of NEO methods for calculating both ground and excited state molecular properties. For the ground state, a general multicomponent embedding scheme is developed and tested within the NEO framework to obtain nuclear densities. Machinery is also presented for identifying the character and stability of NEO self-consistent field (SCF) solutions, allowing the differentiation between minima and saddle points. For excited states, the linear response multicomponent time-dependent density functional theory (TDDFT) is derived and implemented within the NEO framework. The results for nuclear vibrational excitations of interest corresponding to single or multiple protons calculated with NEO-TDDFT are accurate when the method is used in conjunction with large nuclear and electronic basis sets. Lastly, a scheme is presented for coupling proton vibrational excitation energies calculated with NEO-TDDFT to the normal modes associated with the other nuclei. This scheme, denoted NEO-DFT(V), thereby allows for full molecular vibrational frequencies to be calculated. These NEO methods provide the foundation for a wide range of applications, especially those involving non-Born-Oppenheimber processes or nuclear quantum effects.