Range-separated hybrid density functionals made simple

In this communication, we present a new and simple route to derive range-separated exchange (RSX) hybrid and double hybrid density functionals in a nonempirical fashion. In line with our previous developments [Brémond et al., J. Chem. Theory Comput. 14, 4052 (2018)], we show that by imposing an additional physical constraint to the exchange-correlation energy, i.e., by enforcing to reproduce the total energy of the hydrogen atom, we are able to generalize the nonempirical determination of the range-separation parameter to a family of RSX hybrid density functionals. The success of the resulting models is illustrated by an accurate modeling of several molecular systems and properties, like ionization potentials, particularly prone to the one- and many-electron self-interaction errors.E.B. thanks ANR (Agence Nationale de la Recherche) and CGI (Commissariat à l’Investissement d’Avenir) for their financial support for this work through Labex SEAM (Science and Engineering for Advanced Materials and devices) ANR 11 LABX 086, ANR 11 IDEX 05 02. The authors acknowledge the GENCI-CINES for HPC resources (Project Nos. AP010810360 and A0040810359)

Communication: Double-hybrid functionals from adiabatic-connection:The QIDH model

A new approach stemming from the adiabatic-connection (AC) formalism is proposed to derive parameter-free double-hybrid (DH) exchange-correlation functionals. It is based on a quadratic form that models the integrand of the coupling parameter, whose components are chosen to satisfy several well-known limiting conditions. Its integration leads to DHs containing a single parameter controlling the amount of exact exchange, which is determined by requiring it to depend on the weight of the MP2 correlation contribution. Two new parameter-free DHs functionals are derived in this way, by incorporating the non-empirical PBE and TPSS functionals in the underlying expression. Their extensive testing using the GMTKN30 benchmark indicates that they are in competition with state-of-the-art DHs, yet providing much better self-interaction errors and opening a new avenue towards the design of accurate double-hybrid exchange-correlation functionals departing from the AC integrand.J.C.S.G. and A.J.P.J. thank the “Ministerio de Educación y Ciencia” of Spain and the “European Regional Development Fund” through project CTQ2011-27253 for financial and computational support

Importance of Orbital Optimization for Double-Hybrid Density Functionals: Application of the OO-PBE-QIDH Model for Closed- and Open-Shell Systems

We assess here the reliability of orbital optimization for modern double-hybrid density functionals such as the parameter-free PBE-QIDH model. We select for that purpose a set of closed- and open-shell strongly and weakly bound systems, including some standard and widely used data sets, to show that orbital optimization improves the results with respect to standard models, notably for electronically complicated systems, and through first-order properties obtained as derivatives of the energy.This work is supported by the “Ministerio de Economía y Competitividad” of Spain and the “European Regional Development Fund” through project CTQ2014-55073-P

Quadratic integrand double-hybrid made spin-component-scaled

We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.A.J.P.J. and J.C.S.G. thank the “Ministerio de Economía y Competitividad” of Spain and the “European Regional Development Fund” through Project No. CTQ2014-55073-P for financial support

Tackling an accurate description of molecular reactivity with double-hybrid density functionals

In this communication, we assess a panel of 18 double-hybrid (DH) density functionals for the modeling of the thermochemistry and kinetics properties of an extended dataset of 449 organic chemistry reactions belonging to the BH9 database. We show that most of DHs provide a statistically robust performance to model barrier height and reaction energies in reaching the `chemical accuracy'. In particular, we show that nonempirical DHs like PBE0-DH and PBE-QIDH, or minimally parameterized alternatives like $\omega$B2PLYP and B2K-PLYP succeed to model accurately both properties in a balanced fashion. We demonstrate however that parameterized approaches like $\omega$B97X-2 or DSD-like DHs are more biased to only one of both properties.E.B. thanks ANR (Agence Nationale de la Recherche) and CGI (Commissariat à l’Investissement d’Avenir) for their financial support of this work through Labex SEAM (Science and Engineering for Advanced Materials and devices) ANR-10-LABX-096 and ANR-18-IDEX-0001. The authors acknowledge the GENCI-CINES for HPC resources (Projects A0100810359) just like the local P3MB HPC platform of Université de Paris (ANR-18-IDEX-0001). H.L. acknowledges the financial support from the China Scholarship Council (Grant 201908310062). A.J.P.J. and J.C.S.G. thank the Ministry of Science, Innovation, and Universities of Spain (PID2019-106114GB-I00)

Nonempirical Double-Hybrid Functionals: An Effective Tool for Chemists

Density functional theory (DFT) emerged in the last two decades as the most reliable tool for the description and prediction of properties of molecular systems and extended materials, coupling in an unprecedented way high accuracy and reasonable computational cost. This success rests also on the development of more and more performing density functional approximations (DFAs). Indeed, the Achilles’ heel of DFT is represented by the exchange-correlation contribution to the total energy, which, being unknown, must be approximated. Since the beginning of the 1990s, global hybrids (GH) functionals, where an explicit dependence of the exchange-correlation energy on occupied Kohn–Sham orbitals is introduced thanks to a fraction of Hartree–Fock-like exchange, imposed themselves as the most reliable DFAs for chemical applications. However, if these functionals normally provide results of sufficient accuracy for most of the cases analyzed, some properties, such as thermochemistry or dispersive interactions, can still be significantly improved. A possible way out is represented by the inclusion, into the exchange-correlation functional, of an explicit dependence on virtual Kohn–Sham orbitals via perturbation theory. This leads to a new class of functionals, called double-hybrids (DHs). In this Account, we describe our nonempirical approach to DHs, which, following the line traced by the Perdew–Burke–Ernzerhof approach, allows for the definition of a GH (PBE0) and a DH (QIDH) model. In such a way, a whole family of nonempirical functionals, spanning on the highest rungs of the Perdew’s quality scale, is now available and competitive with other—more empirical—DFAs. Discussion of selected cases, ranging from thermochemistry and reactions to weak interactions and excitation energies, not only show the large range of applicability of nonempirical DFAs, but also underline how increasing the number of theoretical constraints parallels with an improvement of the DFA’s numerical performances. This fact further consolidates the strong theoretical framework of nonempirical DFAs. Finally, even if nonempirical DH approaches are still computationally expensive, relying on the fact that they can benefit of all technical enhancements developed for speeding up post-Hartree–Fock methods, there is substantial hope for their near future routine application to the description and prediction of complex chemical systems and reactions.This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 648558)

Nonempirical (double‐hybrid) density functionals applied to atomic excitation energies: A systematic basis set investigation

We investigate here the lowest‐energy (spin‐conserving) excitation energies for the set of He‐Ne atoms, with the family of nonempirical PBE, PBE0, PBE0‐1/3, PBE0‐DH, PBE‐CIDH, PBE‐QIDH, and PBE0‐2 functionals, after employing a wide variety of basis sets systematically approaching the basis set limit: def2‐nVP(D), cc‐pVnZ, aug‐cc‐pVnZ, and d‐aug‐cc‐pVnZ. We find that an accuracy (ie, mean unsigned error) of 0.3 to 0.4 eV for time‐dependent density functional theory (DFT) atomic excitation energies can be robustly achieved with modern double‐hybrid methods, which are also stable with respect to the addition of a double set of diffuse functions, contrarily to hybrid versions, in agreement with recent findings employing sophisticated multiconfigurational DFT methods.L.H.M. acknowledges the “Instituto Universitario de Materiales (IUMA)” for a research internship. The work in Alicante is supported by the projects AICO/2018/175 from the Regional Government (GVA/FSE) and FIS2015-64222-C2-2-P from the “Ministerio de Ciencia, Innovación y Universidades”. E.B. thanks ANR (“Agence Nationale de la Recherche”) and CGI (“Commissariat à l'Investissement d'Avenir”) for financial support through Labex SEAM (Science and Engineering for Advanced Materials and devices) ANR 11 LABX 086, ANR 11 IDEX 05 02

Axial–equatorial equilibrium in substituted cyclohexanes: a DFT perspective on a small but complex problem

In Chemistry, complexity is not necessarily associated to large systems, as illustrated by the textbook example of axial–equatorial equilibrium in mono-substituted cyclohexanes. The difficulty in modelling such a simple isomerization is related to the need for reproducing the delicate balance between two forces, with opposite effects, namely the attractive London dispersion and the repulsive steric interactions. Such balance is a stimulating challenge for density-functional approximations and it is systematically explored here by considering 20 mono-substituted cyclohexanes. In comparison to highly accurate CCSD(T) reference calculations, their axial–equatorial equilibrium is studied with a large set of 48 exchange–correlation approximations, spanning from semilocal to hybrid to more recent double hybrid functionals. This dataset, called SAV20 (as Steric A-values for 20 molecules), allows to highlight the difficulties encountered by common and more original DFT approaches, including those corrected for dispersion with empirical potentials, the 6-31G*-ACP model, and our cost-effective PBE-QIDH/DH-SVPD protocol, in modeling these challenging interactions. Interestingly, the performance of the approaches considered in this contribution on the SAV20 dataset does not correlate with that obtained with other more standard datasets, such as S66, IDISP or NC15, thus indicating that SAV20 covers physicochemical features not already considered in previous noncovalent interaction benchmarks.Funded by the European Union (ERC, project MaMA, no. 101097351). E. B. gratefully acknowledges ANR (Agence Nationale de la Recherche) for the financial support of this work through the MoMoPlasm project (ANR-21-CE29-0003). He thanks also ANR and CGI (Commissariat à l’Investissement d’Avenir) for their financial support of this research through Labex SEAM (Science and Engineering for Advanced Materials and devices) ANR-10-LABX-096, ANR-18-IDEX-000. H. L. acknowledges financial support from the China Scholarship Council (grant no. 201908310062)

Communication: Accurate description of interaction energies and three-body effects in weakly bound molecular complexes by PBE-QIDH models

We apply a recently developed parameter-free double-hybrid density functional belonging to the quadratic-integrand double-hybrid model to calculate association energies (ΔE) and three-body effects (Δ3E) arising from intermolecular interactions in weakly bound supramolecular complexes (i.e., the dataset 3B-69). The model behaves very accurately for trimer association energies and is found to outperform widely used density functional approximations while approaching the accuracy of more costly ab initio methods for three-body effects. The results are further improved when we add some specific corrections for the remaining dispersion interactions, D3(BJ) or VV10 for two-body effects and Axilrod-Teller-Muto for three-body effects, leading to marginal deviations (less than 1 kcal/mol for ΔE and around 0.03–0.04 kcal/mol for Δ3E) with respect to benchmark results.We acknowledge the “Ministerio de Economía y Competitividad” of Spain and the “European Regional Development Fund” through the Project No. CTQ2014-55073-P

Partnering dispersion corrections with modern parameter-free double-hybrid density functionals

The PBE-QIDH and SOS1-PBE-QIDH double-hybrid density functionals are merged with a pair of dispersion corrections, namely the pairwise additive D3(BJ) and the non-local correlation functional VV10, leading to the corresponding dispersion-corrected models. The parameters adjusting each of the dispersion corrections to the functionals are obtained by fitting to well-established energy datasets (e.g. S130) used as a benchmark, giving rise to functionals spanning covalent and non-covalent binding forces. The application of the models to challenging systems out of the training set, like those comprising the L7 database of large supramolecular complexes, or the S66x8 dataset of stretched and elongated intermolecular distances, reveals the high accuracy of the coupling.JCSG and AJPJ thank the “Ministerio de Economía y Competitividad” of Spain and the “European Regional Development Fund” through project CTQ2014-55073-P