Assessing the Tamm–Dancoff approximation, singlet–singlet, and singlet–triplet excitations with the latest long-range corrected double-hybrid density functionals

Abstract

We continue our work on the long-range corrected double-hybrid density functionals (LC-DHDFs) ωB2PLYP and ωB2GP-PLYP that we developed in the context of time-dependent (TD) Density Functional Theory (DFT) to enable the robust description of singlet–singlet excitations [M. Casanova-Páez, M. B. Dardis, and L. Goerigk, J. Chem. Theory Comput. 15, 4735 (2019)]. In our initial study, we only assessed the impact of a LC on BLYP-based DHDFs, and herein, we extend our understanding by providing the first test of PBE-based LC-DHDFs within the established TD-DHDF scheme. Moreover, this study is one of few that provides a direct comparison between TD-DHDFs and their faster Tamm–Dancoff-approximation variants (TDA-DHDFs). Most importantly, this is the first TDA-DHDF study since Grimme and Neese’s TDA-B2PLYP [J. Chem. Phys. 127, 154116 (2007)] and the first work on TD-DHDFs that addresses singlet–triplet excitations. We show how the difference between TD-DHDFs and TDA-DHDFs is often negligible for singlet–singlet excitations, but how one has to apply TDA-DHDFs for triplet excitations. For both excitation types, the LC is beneficial to the BLYP-based DHDFs, but detrimental to the PBE-based ones. For local-valence and Rydberg excitations, ωB2PLYP and ωB2GP-PLYP as well as the global DHDF PBE-QIDH can be recommended. If a transition exhibits charge-transfer character, ωB2PLYP and ωB2GP-PLYP should be applied. An analysis of the gaps between the first singlet and triplet excited states of our systems revealed that there is room for further improvements to reach better robustness. Until that goal has been achieved, we recommend ωB2PLYP and ωB2GP-PLYP as some of the currently best TDA-DFT methods.

A Simple Range-Separated Double-Hybrid Density Functional Theory for Excited States

“…The reference energies were calculated at the CCSDT-3 level using the cc-pVDZ basis sets. Another compilation of CT excitations was presented by Goerigk and co-workers, 83 which contains relatively standard organic molecules. The reference energies were obtained at different levels of theory, detailed information can be found in ref ( 83 ).…”

“…Another compilation of CT excitations was presented by Goerigk and co-workers, 83 which contains relatively standard organic molecules. The reference energies were obtained at different levels of theory, detailed information can be found in ref ( 83 ). As it can be assumed that the former CT set is a more challenging compilation, we only briefly discuss the results regarding the latter.…”

“… Error measures for the calculated excitation energies for the SG test set 56 using the aug-cc-pVTZ basis sets with the corresponding auxiliary bases. The PBE-QIDH, B2(GP)PLYP, ωB2(GP)PLYP, CAM-B3LYP, and ωB97X values were taken from ref ( 83 ), while the CCSD results come from ref ( 56 ). …”

“…The excitation energies for the additional CT test set proposed by Goerigk and co-workers 83 were also assessed. As could be assumed, these excitations are less challenging for TDA-TDDFT calculations.…”

“… 77 − 80 The connection between the fraction of the exact exchange in the RS XC energy and the optimal range-separation parameter for the nonempirical functionals was presented by Adamo et al 78 Later, it was demonstrated that these parameters are in line with the results obtained by relying on the so-called optimally tuned procedure. 79 The only excited-state RS-DH approach proposed 81 and carefully benchmarked 82 , 83 recently by Goerigk and co-workers also originated from this scheme.…”