Full Implementation, Optimization, and Evaluation of a Range-Separated Local Hybrid Functional with Wide Accuracy for Ground and Excited States

Abstract

We report the first full and efficient implementation of range-separated local hybrid functionals (RSLHs) into the TURBOMOLE program package. This enables the computation of ground-state energies and nuclear gradients as well as excitation energies. Regarding the computational effort, RSLHs scale like regular local hybrid functionals (LHs) with system or basis set size and increase timings by a factor of 2–3 in total. An advanced RSLH, ωLH22t, has been optimized for atomization energies and reaction barriers. It is an extension of the recent LH20t local hybrid and is based on short-range PBE and long-range HF exchange-energy densities, a pig2 calibration function to deal with the gauge ambiguity of exchange-energy densities, and reoptimized B95c correlation. ωLH22t has been evaluated for a wide range of ground-state and excited-state quantities. It further improves upon the already successful LH20t functional for the GMTKN55 main-group energetics test suite, and it outperforms any global hybrid while performing close to the top rung-4 functional, ωB97M-V, for these evaluations when augmented by D4 dispersion corrections. ωLH22t performs excellently for transition-metal reactivity and provides good balance between delocalization errors and left–right correlation for mixed-valence systems, with a somewhat larger bias toward localized states compared to LH20t. It approaches the accuracy of the best local hybrids to date for core, valence singlet and triplet, and Rydberg excitation energies while improving strikingly on intra- and intermolecular charge-transfer excitations, comparable to the most successful range-separated hybrids available.

Accurate Ionization Potentials, Electron Affinities, and Band Gaps from the ωLH22t Range-Separated Local Hybrid Functional: No Tuning Required

“…ωLH22t has been implemented into the TURBOMOLE program package for electronic structure calculations, using efficient seminumerical integration techniqes for the integrals based on the exact-exchange (EXX) energy density. − In the current V7.7 release of the code it can be accessed by custom user input. Details on this, as well as on implementation, optimization, and performance can be found in ref , and further explanations on the underlying LH approach can also be found in the literature. − Here we provide a short summary of the salient aspects.…”

“…ωLH22t has been implemented into the TURBOMOLE program package for electronic structure calculations, using efficient seminumerical integration techniqes for the integrals based on the exact-exchange (EXX) energy density. − In the current V7.7 release of the code it can be accessed by custom user input. Details on this, as well as on implementation, optimization, and performance can be found in ref , and further explanations on the underlying LH approach can also be found in the literature. − Here we provide a short summary of the salient aspects. The general functional form is given by E XC RSLH = E normalX ex + prefix∫ ( 1 − a false( boldr false) ) ( e X DFA , SR , ω false( boldr false) − e X ex , SR , ω false( boldr false) + G false( boldr false) ) normald boldr + E normalC DFA where E normalX ex is the (full-range) EXX energy, a denotes a local mixing function (LMF) determining the position-dependent short-range (SR) EXX admixture, normale …”

“…Energies for the latter are competitive with those for RSHs and a clear improvement over LHs, while ωLH22t shares the good performances of related LHs for core, Rydberg, and triplet-valence excitations. In the current RSLH implementation, the cost of a calculation is at most a factor of 2–3 higher than for an RSH using the same settings to run the seminumerical computations as for a GH or RSH (giving closely comparable numerical accuracy). This margin may even become lower due to ongoing code improvements.…”

Locally Range-Separated Local Hybrid Functionals – The Next Level on the Hybrid Functional Ladder

“…However, it provides a qualitatively correct exactexchange admixture in the different regions in real-space and thus has been used in several of the more recently developed LH functionals. 9,97 While the recently proposed LMF model by Holzer and Franzke 90 within their TMHF functional also violates these two constraints, its behavior in core regions in contrast to the t-LMF is qualitatively wrong due to almost vanishing exact-exchange contributions, despite containing more empirical parameters. For the sake of simplicity, this new LMF model thus has not been considered in this work.…”

“…However, local hybrids are not able to provide the correct asymptotic XC potential 95 and thus accurate long-range charge-transfer excitations. 23 More recent developments include the combination of local hybrids with conventional range-separated hybrid functionals (range-separate local hybrids, RSLHs) 96,97 as well as efforts to mimic strong correlation effects 98,99 similar to the B05 family of functionals, 37,38 which essentially can be viewed as a special form of local hybrid functionals. A more comprehensive summary of local hybrids can be found in a recent review.…”