ωB2PLYP and ωB2GPPLYP: The First Two Double-Hybrid Density Functionals with Long-Range Correction Optimized for Excitation Energies

Abstract

Double-hybrid density functionals are currently the most accurate density functionals for ground-state properties and electronic excitations. Nevertheless, the lack of a long-range correction scheme makes them unreliable when it comes to long-range excitations. For this reason, we propose the first two time-dependent double-hybrid functionals with correct asymptotic long-range behavior named ωB2PLYP and ωB2GPPLYP. Herein, we demonstrate their excellent performance and show that they are the most accurate and robust time-dependent density functional theory methods for electronic excitation energies. They provide a balanced description of local-valence, Rydberg, and charge-transfer states. They are also able to tackle the difficult first two transitions in polycyclic aromatic hydrocarbons and show very promising results in a preliminary study on transition-metal compounds, exemplified for titanium dioxide clusters. This work shows that double hybrids can be systematically improved also for excitation energies, and further work in this field is warranted.

Organic molecules with inverted gaps between first excited singlet and triplet states and appreciable fluorescence rates

“…Several efficient approaches were compared against benchmark methods for molecules 1 and 2 (Scheme 1). Table 1 shows the results of several computational excited state techniques of varying computational cost including two particularly efficient families of methods that include double excitations, namely double-hybrid TD-DFAs [68][69][70][71] (ωB2PLYP 41 ) and spin-flip TD-DFAs 60,61 (SA-SF-PBE50 [60][61][62][63][64][65] ). Using ωB2PLYP, we could estimate vibrational contributions to the singlet-triplet gap by performing excited singlet and triplet geometry optimizations.…”

“…22,116 Therefore, refined models accounting for double excitations are required to describe the low-energy excited electronic states of INVEST emitters appropriately. TD-DFAs need to be double-hybrid or higher in their rung 41,122 or have to be used as spin-flip variant with a well-behaved triplet state as reference. 123 Accordingly, a four-state model has been proposed as minimal model to describe the low-energy excited states of INVEST molecules.…”

On the Performances of Density Functionals for Open Shell First-Row Transition Metal Compounds

“…All calculations were performed with the ORCA 4.2.0 program 26,27 . Totally 19 functionals were tested: PBE-D3BJ 28,29 , BP86-D3BJ 30,31 , TPSS-D3BJ 32 , M06L-D3 33 , MN15L 34 , TPSSh-D3BJ 35 , SCAN-D3BJ 36 , B3LYP-D3BJ 37 , PBE0-D3BJ 38 , M06-D3 33 44 , wB2PGLYP 45 , PWPB95-D3BJ 46 . In contrast to most benchmark studies that geometries were optimized at a fixed level, in this work all geometries were optimized with the corresponding functional in combination with the def2-TZVP basis set 47 , unless especially noted.…”

An Analysis of Recent BLYP and PBE-Based Range-Separated Double-Hybrid Density Functional Approximations for Main-Group Thermochemistry, Kinetics and Noncovalent Interactions

“…In this study, we focus on the applicability of six recently developed RS-DHDFs to ground-state thermochemistry, kinetics and noncovalent interactions. These six RS-DHDFs are ωB2PLYP, 42 ωB2GP-PLYP, their variants ωB2PLYP18 42 and ωB2GP-PLYP18, 42 as well as RSX-0DH 43 and RSX-QIDH. 44 The semi-empirical methods ωB2PLYP and ωB2GP-PLYP are based on Becke-88 45 (B) exchange and Lee-Yang-Parr 46 (LYP) correlation and were parametrized by our group for electronic excitation energies.…”

“…44 The semi-empirical methods ωB2PLYP and ωB2GP-PLYP are based on Becke-88 45 (B) exchange and Lee-Yang-Parr 46 (LYP) correlation and were parametrized by our group for electronic excitation energies. 42 They were shown to be some of the most accurate and robust timedependent DFT methods for vertical singlet-singlet and singlet-triplet excitations, including local valence, Rydberg and charge-transfer transitions. 42,[47][48][49] The value of the range-separation parameter ω is 0.30 bohr −1 for ωB2PLYP and 0.27 bohr −1 for ωB2GP-PLYP, which is similar to many RS hybrids.…”