Moving beyond molecular orbitals with reduced density matrices: Applications to chemiluminescent molecules and strong-field atomic processes

The single-electron picture is a prevalent picture used to describe the behavior of atoms and molecules. In molecular orbital theory, single-electron functions (orbitals) are responsible for the bonding and properties of molecules. The single active electron approximation models the interaction of atoms and intense laser fields by considering only the electron in the highest occupied molecular orbital. For the cases we will present and many others, many-electron effects which transcend the single-electron picture influence the reactions and dynamics of the systems. We employ the reduced density matrix (RDM) as a tool for understanding and quantifying correlated behavior. In particular, the two-electron RDM (2-RDM), which is obtained by integrating the N-2 degrees of freedom of electrons 3 through N from the density matrix &PSgr;&PSgr;*, contains the relevant information for determining the electronic structure of atoms and molecules. This is because the electronic structure problem is dependent on the pairwise Coulombic interaction of electrons. In the first part of the dissertation, we apply methods which directly calculate the 2-RDM without the N-electron wavefunction to systems which include arynes, vinylidene carbenes, and a chemiluminescent dioxetanone decomposition reaction related to the firefly luciferin system. In the second part of the dissertation, we turn our focus to describing atoms in intense laser fields using the ion density matrix (IDM). The IDM reduces the strong-field density by combining electronic excitations depending on their orbital of origin. We develop and apply the time-dependent configuration interaction singles (TDCIS) method for application to strong-field atomic problems. We use the TDCIS method to calculate IDM elements for Ar and Kr undergoing high harmonic generation (HHG), a highly nonlinear non-perturbative strong-field process, and for Xe ionized by an attosecond pulse.