Revised M11 Exchange-Correlation Functional for Electronic Excitation Energies and Ground-State Properties

Abstract

The ability of Kohn−Sham density functional theory (KS-DFT) to accurately predict various types of electronic excitation energies with (necessarily approximate) exchangecorrelation functionals faces several challenges. Chief among these is that valence excitations are usually inherently multiconfigurational and therefore best treated by functionals with local exchange, whereas Rydberg and charge-transfer excitations are often better treated with nonlocal exchange. The question arises regarding whether one can optimize a functional such that all three kinds of excitations (valence, Rydberg, and charge transfer, including long-range charge transfer) are treated in a balanced and accurate way. The goal of the present work is to try to answer that question and then to optimize a functional with the best possible balanced behavior. Of the variety of functional types available, we choose to use a range-separated hybrid meta functional for the following reasons: (i) Range separation allows the percentage of Hartree−Fock (HF) exchange to change with interelectronic separation, and therefore, one can have 100% HF exchange at large interelectronic separations, which gives good performance for long-range charge-transfer excitations, while the range separation allows one to simultaneously have smaller values of HF exchange at small and intermediate interelectronic separations, giving good performance for valence and Rydberg excitations. (ii) Meta functionals allow one to obtain better accuracy with high HF exchange than is possible with functionals whose local part depends only on spin densities and their gradients. This work starts with the range-separated hybrid meta functional M11 and reoptimizes it (with strong smoothness restraints) against electronic excitation energies and ground-state properties to obtain a new functional called revM11 that gives good performance for all three types of electronic excitations and at the same time gives very good predictions across the board for ground-state properties.

Double hybrids and time‐dependent density functional theory: An implementation and benchmark on charge transfer excited states

“…Overall from the analysis of our data, we can conclude that DHs represent a good alternative to adjusted range separated hybrids for the treatment of intramolecular charge transfer excitations provided that the double correction is correctly included. Indeed excitation energies of 3.8 eV, 3.4 eV, 3.0 eV, and 2.7 eV were reported for Aryl‐TCNE (Aryl = benzene, toluene, o‐xylene, naphthalene, respectively) by Baer and collaborators using the BNL functional and of 3.9 eV, by Truhlar and collaborators, using the revM11 functional in the case of the benzene‐TCNE system …”

Empirical Double‐Hybrid Density Functional Theory: A ‘Third Way’ in Between WFT and DFT

“…In addition, we realized that double hybrids inherit some of the slow basis set convergence of correlated WFT [48] 3.76 0.74 0.41 0.82 0.89 0.90 1.9 ωB97X-V 3.96 1.02 0.56 1.07 0.73 0.58 2.0 ωB97X-D3 [48] 4.39 1.08 0.49 0.92 0.88 1.01 2.3 CAM-B3LYP-D3 [31] 5. 32 1.13 0.88 1.26 1.24 0.81 2.4 c LC-ωPBEh-D3 [49] 5.49 1.32 0.95 1.24 1.13 0.84 -revM11 [50] 5.73 1.12 0.76 1.28 1.61 0.95 2.7 b M11 [51] 6.42 0.96 0.57 1.10 2.54 1.25 2.7 CAM-QTP00-D3 [52,53] 6. 48 1.65 1.08 1.28 1.28 1.20 4.5…”

Dual‐hybrid direct random phase approximation and second‐order screened exchange with nonlocal van der Waals correlations for noncovalent interactions

“…The performances of the dRPA75‐NL, SOSEX75‐NL, and dRPA75 methods have also been assessed against the PEC4 dataset with the def2‐QZVPP basis set directly. The PEC4 dataset consists of four potential energy curves of the Ne 2 , Ar 2 , Kr 2 , and KrHe dimers.…”

“…The set 22 (S22), set 66 (S66), noncovalent complexation energies of 31 complexes (NCCE31), set of 23 open‐shell noncovalent systems (O23), and potential energy curves of four rare gas dimers (Ne 2 , Ar 2 , Kr 2 , and KrHe) (PEC4) were used to assess the performances of the dRPA75‐NL and SOSEX75‐NL methods. As the well‐known S22 dataset, the S66 dataset was also constructed by the Hobza group .…”