Dual-Functional Tamm–Dancoff Approximation: A Convenient Density Functional Method that Correctly Describes S₁/S₀ Conical Intersections

Abstract

Time-dependent Kohn-Sham density functional theory has been used successfully to compute vertical excitation energies, especially for large molecular systems. However, the lack of double excitation character in the excited amplitudes produced by linear response in the adiabatic approximation holds it back from broader applications in photochemistry; for example, it shows (3N - 7)-dimensional conical intersection seams (where N is the number of atoms) between ground and excited states, although the correct dimensionality is 3N - 8. In this letter, we present a new, conceptually simple, easy-to-implement, and easy-to-use way to employ time-dependent Kohn-Sham density functional theory that has global accuracy comparable with the conventional single-functional version and that recovers the double cone topology of the potential energy surfaces at S/S conical intersection seams. The new method is called the dual-functional Tamm-Dancoff approximation (DF-TDA).

Hole–hole Tamm–Dancoff-approximated density functional theory: A highly efficient electronic structure method incorporating dynamic and static correlation

“…Methods of this type include rangeseparated wavefunction/DFT methods, [20][21] multiconfigurational pair-density functional theory [22][23] (MC-PDFT), and combinations of DFT and configuration interaction, [24][25] such as in DFT/MRCI. [26][27] Alternative approaches attempt to incorporate multireference character directly in the DFT formalism by using an unconventional reference 28 or appealing to ensemble densities.…”

A comparison of methods for theoretical photochemistry: Applications, successes and challenges

“…4). However, improvements to TD-DFT, such as long range corrections, dispersion corrections and, most recently, the Dual-Functional Tamm-Dancoff Approximation, 153 has meant that are they are starting to rival multireference in accuracy even for excited state potential energy surfaces. More generally, TD-DFT has become routine for the prediction of absorption and emission spectra, and in most cases provides qualitatively if not quantitatively useful results.…”

“…Often it is able to qualitatively explain experimental results, but does have failures and is rarely used for quantitative studies. However, new developments such as Truhlar's Dual-Functional Tamm-Dancoff Approximation 153 show enormous promise in raising the accuracy of TD-DFT to that of equivalent multireference methods, but at a fraction of the cost. At the other extreme, Grimme's Simplified Tamm-Dancoff Approximation has recently been shown to reproduce standard TD-DFT at a fraction of the cost, allowing systems with 1000s of atoms to be studied.…”

Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor

“…[26] neglects the deexcitation operators (as in the Tamm-Dancoff approximation [37,38]), which limits its application to systems for which this approximation is valid (e.g., far from conical intersections, see, for instance, Ref. [39]). In this work, we will restrict our excitation operator basis to single (α = 1) and double (α = 2) excitations such that E…”