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Hole-Hole Tamm-Dancoff-Approximated Density Functional Theory: A Highly Efficient Electronic Structure Method Incorporating Dynamic and Static Correlation

revised on 17.06.2020 and posted on 18.06.2020 by Christoph Bannwarth, Jimmy K. Yu, Edward G. Hohenstein, Todd J. Martínez

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 neglect much of the dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we revisit hole-hole Tamm-Dancoff approximated (hh-TDA) density functional theory for this purpose. The hh-TDA method is the hole-hole counterpart to the more established particle-particle TDA (pp-TDA) method, both of which are derived from the particle-particle random phase approximation (pp-RPA). 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. We show that hh-TDA is 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 and pp-RPA, 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.


AMOS program of the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, and Biosciences Division and by the Department of Energy, Laboratory Directed Research and Development program at SLAC National Accelerator Laboratory, under contract DE-AC02-76SF00515.

Leopoldina Fellowship Program (Project No. LPDS 2018-09)


Email Address of Submitting Author


Stanford University



ORCID For Submitting Author


Declaration of Conflict of Interest

Todd J. Martínez is a co-founder of PetaChem, LLC.

Version Notes

Updated literature discussion on pp-RPA, pp-TDA, and hh-TDA in the introduction. Added a new section on unbound orbitals and added supplemental data to the SI (equivalence of pp-TDA & hh-TDA to Full CI for H2 with STO-3G, ethylene states described with pp-TDA and hh-TDA and different functionals, basis set dependency).