Benchmark Computations of Nearly Degenerate Singlet and Triplet states of N-heterocyclic Chromophores : II. Density-based Methods

In this paper we demonstrate the performance of several density-based methods in predicting the inversion of S₁ and T₁ states of a few N-heterocyclic fused ring molecules (popularly known as INVEST molecules) with an eye to identify a well performing but cheap preliminary screening method. Both conventional LR-TDDFT and ΔSCF methods (namely MOM, SGM, ROKS) are considered for excited state computations using exchange-correlation (XC) functionals from different rungs of the Jacob's ladder. A well-justified systematism is observed in the performance of the functionals when compared against FICMRCISD and/or EOM-CCSD, with the most important feature being the capture of spin-polarization in presence of correlation. A set of functionals with the least mean absolute error (MAE) is proposed for both the approaches, LR-TDDFT and ΔSCF, which can be cheaper alternatives for computations on synthesizable larger derivatives of the templates studied here. We have based our findings on extensive studies of three cyclazine-based molecular templates, with additional studies on a set of six related templates. Previous benchmark studies for subsets of the functionals were conducted against the DLPNO-STEOM-CCSD, which resulted in an inadequate evaluation due to deficiencies in the benchmark theory. The role of exact-exchange, spin-contamination and spin-polarization in the context of DFT comes to the forefront in our studies and supports the numerical evaluation of XC functionals for these applications. Suitable connections are drawn to two and three state exciton models which identify the minimal physics governing the interactions in these molecules.