## 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.