Relativistic Two-Component Particle-Particle Tamm-Dancoff Approximation

With the recent introduction of the particle particle random-phase and Tamm-Dancoff approximations to ab initio theory, routine queries of traditionally difficult systems, such as diradicals and doubly excited states, have been made possible. However, although a wealth of inquiry has been directed to investigating these methods, the current formulations have been restricted to spin-collinear systems, leaving the methods incapable of treating noncollinearity and spin orbit relativistic effects in excited states. In this work, we extend the particle particle Tamm-Dancoff approximation to suit two-component Hamiltonians to explicitly treat relativistic effects in excited states. After reviewing the theory and computational implementation, we demonstrate the accuracy of this extension by evaluating the fine structure splittings some of atomic and molecular systems.