Development and Application of the Variational Two-Electron Reduced Density Matrix Complete Active Space Self-Consistent Field Method to Address the Electron Correlation Problem in Quantum Chemistry

The goal of this dissertation is to describe a series of developments and applications of the variational two-electron reduced density matrix (v2RDM-) complete active space self-consistent field (CASSCF) method to the electron correlation problem in electronic structure theory. The v2RDM-CASSCF method is a complete active space (CAS) method based on optimizing the two-electron reduced density matrix (2RDM). Since the 2RDM is a more compact object than the N-electron wavefunction, it is possible to formulate a CAS approach that scales polynomially, rather than exponentially, with respect to the size of the active space. For this reason, computer implementations of v2RDM-driven CASSCF are capable of treating active spaces much larger than the limit of current implementations of wavefunction-/configuration interaction (CI-) driven wavefunction CASSCF. The work described in this dissertation addresses three deficiencies of v2RDM-CASSCF: the lack of an analytic energy derivative code, the lack of an efficient code with which to compute excited states, and the lack of a method with which to correct the v2RDM-CASSCF energy for dynamical correlation. We develop analytic first derivatives of the v2RDM-CASSCF energy, and we show, in fact, that the expressions for the analytic first derivative of the energy are identical to those for CI-based CASSCF. For the excited state problem, we improve an approach by which excited states and excited state properties can be computed from the ground state 2RDM. Lastly, we develop a model for dynamical correlation for v2RDM-CASSCF references. With this model, energies computed at the v2RDM-CASSCF level of theory can be corrected to account for the effects of dynamical correlation.