Singlet‐Triplet Excited‐State Inversion in Heptazine and Related Molecules: Assessment of TD‐DFT and ab initio Methods

Abstract

We have investigated the origin of the S1‐T1 energy levels inversion for heptazine, and other N‐doped π‐conjugated hydrocarbons, leading thus to an unusually negative singlet‐triplet energy gap (ΔEST<0 ). Since this inversion might rely on substantial doubly‐excited configurations to the S1 and/or T1 wavefunctions, we have systematically applied multi‐configurational SA‐CASSCF and SC‐NEVPT2 methods, SCS‐corrected CC2 and ADC(2) approaches, and linear‐response TD‐DFT, to analyze if the latter method could also face this challenging issue. We have also extended the study to B‐doped π‐conjugated systems, to see the effect of chemical composition on the results. For all the systems studied, an intricate interplay between the singlet‐triplet exchange interaction, the influence of doubly‐excited configurations, and the impact of dynamic correlation effects, serves to explain the ΔEST<0 values found for most of the compounds, which is not predicted by TD‐DFT.

Triangular boron carbon nitrides: an unexplored family of chromophores with unique properties for photocatalysis and optoelectronics

“…22 This inversion of S1/T1 energies was independently confirmed by calculations for the mono-aza phenalene [3.3.3]cyclazine, 23 referred to as cyclazine (Cz) in what follows, and other azaphenalenes. 24 It was pointed out that the S1/T1 inversion in Hz (by about 0.25 eV) appears to be very robust with respect to chemical modifications and oligomerization. 22 The origin of the S1/T1 inversion in Cz and Hz can be traced to the spatially nonoverlapping character of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) and the nearly pure HOMO-LUMO excitation character of the S1 and T1 wave functions, which results in an exceptionally small exchange integral.…”

Origin of The Failure of Density Functional Theories in Predicting Inverted Singlet-Triplet Gaps

“…In recent publications, computational studies have proposed several new molecules that can produce inverted singlet-triplet gaps (ΔEST <0). [10][11][12][13] Pollice et al identified computationally a set of organic chromophores that showed efficient TADF processes using equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) 17 as the method of choice for large-scale screening. 11 Sancho-Garcia and co-workers have suggested that small chemical modifications of the triangle derivatives can produce good candidates for inverted singlet-triplet gap using several correlated wave function methods.…”

“…11 Sancho-Garcia and co-workers have suggested that small chemical modifications of the triangle derivatives can produce good candidates for inverted singlet-triplet gap using several correlated wave function methods. 13 While many wave function-based electronic structure methods, such as configuration interaction singles with doubles correction (CIS(D)) 18 , EOM-CCSD 17 and similarity transformed equation-of-motion coupled-cluster singles and doubles (STEOM-CCSD) 19,20 , have correctly predicted inverted singlet-triplet gaps, one of the most widely used excited-state electronic structure method, linear response time-dependent density functional theory (LR-TDDFT) 21 has failed to predict the inversion of singlet-triplet gaps. Computational studies, in the past, pointed towards the inability of LR-TDDFT to incorporate double excitations by going beyond adiabatic approximation 22 as the source of this error.…”

Origin of The Failure of Density Functional Theories in Predicting Inverted Singlet-Triplet Gaps

“…7,8,9 Both theoretical and computational modeling has contributed significantly in finding efficient design principles for TADF materials. [10][11][12][13][14] Most TADF materials developed so far have small but positive ΔEST gaps as Hund's rule 15 predicts that the first excited state of a closed-shell molecule is a T1 state and the S1 excited state will always be higher in energy. However, some Ndoped triangulate molecules have been shown to violate Hund's rule by having inverted singlettriplet gaps (ΔEST < 0) .…”