How Beneficial Is the Explicit Account of Doubly-Excited Configurations in Linear Response Theory?

Abstract

In different branches of time-dependent density functional theory (TDDFT), the static and dynamic electron correlation enters in different ways. The standard spin-conserving linear response (LR-TDDFT) methodology includes explicitly the contributions of the singly-excited configurations; however, it relies on an implicit account of the electron correlation through an (approximate) exchange-correlation (XC) functional. In the mixed-reference spin-flip TDDFT (MRSF-TDDFT), a number of doubly-excited (DE) configurations are explicitly included in the description of their response states. Here, the importance of the explicit account of DE is investigated for the lowest four excited singlet states of all-trans-polyenes up to C24H26. For the optically bright 1B u + state, the DE contribution in MRSF-TDDFT approaches 10% with the increasing system size. For the optically dark 2A g – state, the DE contribution increases from ca. 13% (C4H6) to nearly 30% (C24H26). An even more considerable DE contribution (∼50%) is observed in the higher 1B u – states. As LR-TDDFT misses these contributions entirely, its ability to accurately describe the excited states is limited by the XC functional. The hybrid XC functionals with a small fraction of the exact exchange, e.g., B3LYP, may mimic certain effects of DE through the self-interaction error (SIE). However, the description of the 1B u + state by LR-TDDFT remains poor. On the other hand, MRSF-TDDFT can flexibly take an implicit (through the XC functional) and an explicit (through DE) account of the electron correlation, which enables a more balanced description of various types of the excited states regardless of their character, thus reducing the chances of failure.

Spin-Flip TDDFT for Photochemistry

“…The same optimization procedure applied to LR-TDDFT lands on C HFX = 0.2 as the optimal value, corresponding to B3LYP. 128 This observation further corroborates the idea that 50% HFX is close to optimal for collinear spin-flip methods.…”

Relief of excited-state antiaromaticity enables the smallest red emitter

“…MRSF-TDDFT is capable of producing the correct double-cone topology of the intersections and describing the geometry of the lowest-energy conical intersections and their relative energies with accuracy matching that of the best multireference wavefunction ab initio methods 39 . BH&HLYP functional was employed to provide the best performance of the MRSF methodology as verified by previous benchmarking studies 40 , 41 . The potential energy surfaces (PESs) were constructed by the recently reported geodesic interpolation method 55 , which reformulates the problem of existing interpolation methods by searching the geodesic curve on the Riemannian manifold.…”

“…For this purpose, we employed the mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT; MRSF for brevity) method developed recently by us 38 , 39 . Unlike conventional DFT or linear-response TDDFT (LR-TDDFT), MRSF-TDDFT provides the exact dimensionality of conical intersections, describes strongly correlated ground and excited systems, and eliminates spin contamination inherent in other SF methods 40 , 41 . Using the computed structures (see Supplementary Tables 4 – 6 for energies; Supplementary Figs.…”

Fast and Accurate Computation of Nonadiabatic Coupling Matrix Elements Using the Truncated Leibniz Formula and Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory

“…As MRSF obtains all the singlet states from spin-flip orbital transitions generated for the triplet reference state, it can properly introduce the multireference characteristics into the response states, both ground and excited, as well as the coupling between the ground and excited electronic states necessary for obtaining the correct topology of CIs. , The particular advantage of MRSF before the usual SF-TDDFT is that it eliminates the notorious spin-contamination of the response electronic states . In addition, MRSF can flexibly take an implicit (through the XC functional) and an explicit (through both singly and some important doubly exited configurations) account of electron correlation, thus allowing for a balanced description of the dynamic and static electron correlation. Hence, MRSF is a practical and accurate method for general use.…”