| For many decades, the field of chemical reaction dynamics has utilized computational methods that rely on potential energy surfaces that are constructed using stationary-state calculations. These methods are typically devoid of dynamical couplings between the electronic and nuclear degrees of freedom, a fact that can result in incorrect descriptions of dynamical processes. Often, non-adiabatic coupling expressions are included in these methodologies. The Electron-Nuclear Dynamics (END) formalism, in contrast, circumvents these deficiencies by calculating all intermolecular forces directly at each time step in the dynamics and by explicitly maintaining all electronic-nuclear couplings.; The purpose of this work is to offer two new frameworks for implementing electronic representations in dynamical calculations. Firstly, a new schema is proposed for developing atomic basis sets that are consistent with dynamical calculations. Traditionally, basis sets have been designed for use in stationary-state calculations of the structures and properties of molecules in their ground states. As a consequence of common construction techniques that utilize energy optimization methods, the unoccupied orbitals bear little resemblance to physical virtual atomic orbitals. We develop and implement a method for basis set construction that relies upon physical properties of atomic orbitals and that results in meaningful virtual orbitals. These basis sets are shown to provide a significant improvement in the accuracy of calculated dynamical properties such as charge transfer probabilities.; Secondly, the theoretical framework of END is expanded to incorporate a multi-configurational representation for electrons. This formalism, named Vector Hartree-Fock, is based in the theory of vector coherent states and utilizes a complete active space electronic representation. The Vector Hartree-Fock method is fully disclosed, with derivation of the equations of motion. The expressions for the equation of motion are derived in full and a plan for implementing the Vector Hartree-Fock formalism within the current ENDyne computer code is given. |
