Hole-Hole Tamm-Dancoff-Approximated Density Functional Theory: A Highly Efficient Electronic Structure Method Incorporating Dynamic and Static Correlation
The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field (CASSCF) methods are deficient in their ability to describe dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we describe the hole-hole Tamm- Dancoff approximated (hh-TDA) density functional theory method, which is closely related to the previously established particle-particle random phase approximation (pp-RPA) and its TDA variant (pp-TDA). In hh-TDA, the N-electron electronic states are obtained through double annihilations starting from a doubly anionic (N+2 electron) reference state. In this way, hh-TDA treats ground and excited states on equal footing, thus allowing for conical intersections to be correctly described. The treatment of dynamic correlation is introduced through the use of commonly-employed density functional approximations to the exchange-correlation potential. hh-TDA appears to be a promising candidate to efficiently treat the photochemistry of organic and biochemical systems that involve several low-lying excited states – particularly those with both low-lying pipi* and npi* states where inclusion of dynamic correlation is essential to describe the relative energetics. In contrast to the existing literature on pp-TDA, we employ a functional- dependent choice for the response kernel in pp- and hh-TDA, which closely resembles the response kernels occurring in linear response and collinear spin-flip TDDFT.