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Kaupp M, Wodyński A, Arbuznikov AV, Fürst S, Schattenberg CJ. Toward the Next Generation of Density Functionals: Escaping the Zero-Sum Game by Using the Exact-Exchange Energy Density. Acc Chem Res 2024; 57:1815-1826. [PMID: 38905497 PMCID: PMC11223257 DOI: 10.1021/acs.accounts.4c00209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2024] [Revised: 05/29/2024] [Accepted: 06/03/2024] [Indexed: 06/23/2024]
Abstract
ConspectusKohn-Sham density functional theory (KS DFT) is arguably the most widely applied electronic-structure method with tens of thousands of publications each year in a wide variety of fields. Its importance and usefulness can thus hardly be overstated. The central quantity that determines the accuracy of KS DFT calculations is the exchange-correlation functional. Its exact form is unknown, or better "unknowable", and therefore the derivation of ever more accurate yet efficiently applicable approximate functionals is the "holy grail" in the field. In this context, the simultaneous minimization of so-called delocalization errors and static correlation errors is the greatest challenge that needs to be overcome as we move toward more accurate yet computationally efficient methods. In many cases, an improvement on one of these two aspects (also often termed fractional-charge and fractional-spin errors, respectively) generates a deterioration in the other one. Here we report on recent notable progress in escaping this so-called "zero-sum-game" by constructing new functionals based on the exact-exchange energy density. In particular, local hybrid and range-separated local hybrid functionals are discussed that incorporate additional terms that deal with static correlation as well as with delocalization errors. Taking hints from other coordinate-space models of nondynamical and strong electron correlations (the B13 and KP16/B13 models), position-dependent functions that cover these aspects in real space have been devised and incorporated into the local-mixing functions determining the position-dependence of exact-exchange admixture of local hybrids as well as into the treatment of range separation in range-separated local hybrids. While initial functionals followed closely the B13 and KP16/B13 frameworks, meanwhile simpler real-space functions based on ratios of semilocal and exact-exchange energy densities have been found, providing a basis for relatively simple and numerically convenient functionals. Notably, the correction terms can either increase or decrease exact-exchange admixture locally in real space (and in interelectronic-distance space), leading even to regions with negative admixture in cases of particularly strong static correlations. Efficient implementations into a fast computer code (Turbomole) using seminumerical integration techniques make such local hybrid and range-separated local hybrid functionals promising new tools for complicated composite systems in many research areas, where simultaneously small delocalization errors and static correlation errors are crucial. First real-world application examples of the new functionals are provided, including stretched bonds, symmetry-breaking and hyperfine coupling in open-shell transition-metal complexes, as well as a reduction of static correlation errors in the computation of nuclear shieldings and magnetizabilities. The newest versions of range-separated local hybrids (e.g., ωLH23tdE) retain the excellent frontier-orbital energies and correct asymptotic exchange-correlation potential of the underlying ωLH22t functional while improving substantially on strong-correlation cases. The form of these functionals can be further linked to the performance of the recent impactful deep-neural-network "black-box" functional DM21, which itself may be viewed as a range-separated local hybrid.
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Affiliation(s)
- Martin Kaupp
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Artur Wodyński
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Alexei V. Arbuznikov
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Susanne Fürst
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Caspar J. Schattenberg
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
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2
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Schattenberg C, Kaupp M. Implementation and First Evaluation of Strong-Correlation-Corrected Local Hybrid Functionals for the Calculation of NMR Shieldings and Shifts. J Phys Chem A 2024; 128:2253-2271. [PMID: 38456430 PMCID: PMC10961831 DOI: 10.1021/acs.jpca.3c08507] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2023] [Revised: 02/01/2024] [Accepted: 02/09/2024] [Indexed: 03/09/2024]
Abstract
Local hybrid functionals containing strong-correlation factors (scLHs) and range-separated local hybrids (RSLHs) have been integrated into an efficient coupled-perturbed Kohn-Sham implementation for the calculation of nuclear shielding constants. Several scLHs and the ωLH22t RSLH have then been evaluated for the first time for the extended NS372 benchmark set of main-group shieldings and shifts and the TM70 benchmark of 3d transition-metal shifts. The effects of the strong-correlation corrections have been analyzed with respect to the spatial distribution of the sc-factors, which locally diminish exact-exchange admixture at certain regions in a molecule. The scLH22t, scLH23t-mBR, and scLH23t-mBR-P functionals, which contain a "damped" strong-correlation factor to retain the excellent performance of the underlying LH20t functional for weakly correlated situations, tend to make smaller corrections to shieldings and shifts than the "undamped" scLH22ta functional. While the latter functional can also deteriorate agreement with the reference data in certain weakly correlated cases, it provides overall better performance, in particular for systems where static correlation is appreciable. This pertains only to a minority of systems in the NS372 main-group test set but to many more systems in the TM70 transition-metal test set, in particular for high-oxidation-state complexes, e.g., Cr(+VI) complexes and other systems with stretched bonds. Another undamped scLH, the simpler LDA-based scLH21ct-SVWN-m, also tends to provide significant improvements in many cases. The differences between the functionals and species can be rationalized on the basis of one-dimensional plots of the strong-correlation factors, augmented by isosurface plots of the fractional orbital density (FOD). Position-dependent exact-exchange admixture is thus shown to provide substantial flexibility in treating response properties like NMR shifts for both weakly and strongly correlated systems.
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Affiliation(s)
- Caspar
Jonas Schattenberg
- Research
Unit of Structural Chemistry & Computational Biophysics, Leibniz-Forschungsinstitut für Molekulare Pharmakologie
(FMP), Robert-Roessle-Str.
10, 13125 Berlin, Germany
| | - Martin Kaupp
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
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Schattenberg C, Wodyński A, Åström H, Sundholm D, Kaupp M, Lehtola S. Revisiting Gauge-Independent Kinetic Energy Densities in Meta-GGAs and Local Hybrid Calculations of Magnetizabilities. J Phys Chem A 2023; 127:10896-10907. [PMID: 38100678 PMCID: PMC10758120 DOI: 10.1021/acs.jpca.3c06244] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2023] [Revised: 10/27/2023] [Accepted: 11/08/2023] [Indexed: 12/17/2023]
Abstract
In a recent study [J. Chem. Theory Comput. 2021, 17, 1457-1468], some of us examined the accuracy of magnetizabilities calculated with density functionals representing the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA (mGGA), as well as global hybrid (GH) and range-separated (RS) hybrid functionals by assessment against accurate reference values obtained with coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)]. Our study was later extended to local hybrid (LH) functionals by Holzer et al. [J. Chem. Theory Comput. 2021, 17, 2928-2947]; in this work, we examine a larger selection of LH functionals, also including range-separated LH (RSLH) functionals and strong-correlation LH (scLH) functionals. Holzer et al. also studied the importance of the physically correct handling of the magnetic gauge dependence of the kinetic energy density (τ) in mGGA calculations by comparing the Maximoff-Scuseria formulation of τ used in our aforementioned study to the more physical current-density extension derived by Dobson. In this work, we also revisit this comparison with a larger selection of mGGA functionals. We find that the newly tested LH, RSLH, and scLH functionals outperform all of the functionals considered in the previous studies. The various LH functionals afford the seven lowest mean absolute errors while also showing remarkably small standard deviations and mean errors. Most strikingly, the best two functionals are scLHs that also perform remarkably well in cases with significant multiconfigurational character, such as the ozone molecule, which is traditionally excluded from statistical error evaluations due to its large errors with common density functionals.
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Affiliation(s)
- Caspar
J. Schattenberg
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Artur Wodyński
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Hugo Åström
- Department
of Chemistry, Faculty of Science, University
of Helsinki, P.O. Box 55
(A.I. Virtanens plats 1), University of Helsinki FI-00014, Finland
| | - Dage Sundholm
- Department
of Chemistry, Faculty of Science, University
of Helsinki, P.O. Box 55
(A.I. Virtanens plats 1), University of Helsinki FI-00014, Finland
| | - Martin Kaupp
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Susi Lehtola
- Department
of Chemistry, Faculty of Science, University
of Helsinki, P.O. Box 55
(A.I. Virtanens plats 1), University of Helsinki FI-00014, Finland
- Molecular
Sciences Software Institute, Blacksburg, Virginia 24061, United States
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Haasler M, Maier TM, Kaupp M. Toward a correct treatment of core properties with local hybrid functionals. J Comput Chem 2023; 44:2461-2477. [PMID: 37635647 DOI: 10.1002/jcc.27211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Revised: 08/01/2023] [Accepted: 08/03/2023] [Indexed: 08/29/2023]
Abstract
In local hybrid functionals (LHs), a local mixing function (LMF) determines the position-dependent exact-exchange admixture. We report new LHs that focus on an improvement of the LMF in the core region while retaining or partly improving upon the high accuracy in the valence region exhibited by the LH20t functional. The suggested new pt-LMFs are based on a Padé form and modify the previously used ratio between von Weizsäcker and Kohn-Sham local kinetic energies by different powers of the density to enable flexibly improved approximations to the correct high-density and iso-orbital limits relevant for the innermost core region. Using TDDFT calculations for a set of K-shell core excitations of second- and third-period systems including accurate state-of-the-art relativistic orbital corrections, the core part of the LMF is optimized, while the valence part is optimized as previously reported for test sets of atomization energies and reaction barriers (Haasler et al., J Chem Theory Comput 2020, 16, 5645). The LHs are completed by a calibration function that minimizes spurious nondynamical correlation effects caused by the gauge ambiguities of exchange-energy densities, as well as by B95c meta-GGA correlation. The resulting LH23pt functional relates to the previous LH20t functional but specifically improves upon the core region.
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Affiliation(s)
- Matthias Haasler
- Technische Universität Berlin, Institute of Chemistry Theoretical Chemistry/Quantum Chemistry, Berlin, Germany
| | - Toni M Maier
- Technische Universität Braunschweig, Institute of Physical and Theoretical Chemistry, Braunschweig, Germany
| | - Martin Kaupp
- Technische Universität Berlin, Institute of Chemistry Theoretical Chemistry/Quantum Chemistry, Berlin, Germany
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Bruder F, Franzke YJ, Holzer C, Weigend F. Zero-field splitting parameters within exact two-component theory and modern density functional theory using seminumerical integration. J Chem Phys 2023; 159:194117. [PMID: 37987521 DOI: 10.1063/5.0175758] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Accepted: 10/26/2023] [Indexed: 11/22/2023] Open
Abstract
An efficient implementation of zero-field splitting parameters based on the work of Schmitt et al. [J. Chem. Phys. 134, 194113 (2011)] is presented. Seminumerical integration techniques are used for the two-electron spin-dipole contribution and the response equations of the spin-orbit perturbation. The original formulation is further generalized. First, it is extended to meta-generalized gradient approximations and local hybrid functionals. For these functional classes, the response of the paramagnetic current density is considered in the coupled-perturbed Kohn-Sham equations for the spin-orbit perturbation term. Second, the spin-orbit perturbation is formulated within relativistic exact two-component theory and the screened nuclear spin-orbit (SNSO) approximation. The accuracy of the implementation is demonstrated for transition-metal and diatomic main-group compounds. The efficiency is assessed for Mn and Mo complexes. Here, it is found that coarse integration grids for the seminumerical schemes lead to drastic speedups while introducing clearly negligible errors. In addition, the SNSO approximation substantially reduces the computational demands and leads to very similar results as the spin-orbit mean field Ansatz.
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Affiliation(s)
- Florian Bruder
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
| | - Florian Weigend
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
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Fürst S, Kaupp M, Wodyński A. Range-Separated Local Hybrid Functionals with Small Fractional-Charge and Fractional-Spin Errors: Escaping the Zero-Sum Game of DFT Functionals. J Chem Theory Comput 2023. [PMID: 37972297 DOI: 10.1021/acs.jctc.3c00877] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2023]
Abstract
Extending recent developments on strong-correlation (sc) corrections to local hybrid functionals to the recent accurate ωLH22t range-separated local hybrid, a series of highly flexible strong-correlation-corrected range-separated local hybrids (scRSLHs) has been constructed and evaluated. This has required the position-dependent reduction of both short- and long-range exact-exchange admixtures in regions of space characterized by strong static correlations. Using damping procedures provides scRSLHs that retain largely the excellent performance of ωLH22t for weakly correlated situations and, in particular, for accurate quasiparticle energies of a wide variety of systems while reducing dramatically static-correlation errors, e.g., in stretched-bond situations. An additional correction to the local mixing function to reduce delocalization errors in abnormal open-shell situations provides further improvements in thermochemical and kinetic parameters, making scRSLH functionals such as ωLH23tdE or ωLH23tdP promising tools for complex molecular or condensed-phase systems, where low fractional-charge and fractional-spin errors are simultaneously important. The proposed rung 4 functionals thereby largely escape the usual zero-sum game between these two quantities and are expected to open new areas of accurate computations by Kohn-Sham DFT. At the same time, they require essentially no extra computational effort over the underlying ωLH22t functional, which means that their use is only moderately more demanding than that of global, local, or range-separated hybrid functionals.
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Affiliation(s)
- Susanne Fürst
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Martin Kaupp
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Artur Wodyński
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany
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7
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Grotjahn R. Learning from the 4-(dimethylamino)benzonitrile twist: Two-parameter range-separated local hybrid functional with high accuracy for triplet and charge-transfer excitations. J Chem Phys 2023; 159:174102. [PMID: 37909451 DOI: 10.1063/5.0173701] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2023] [Accepted: 10/06/2023] [Indexed: 11/03/2023] Open
Abstract
The recent ωLH22t range-separated local hybrid (RSLH) is shown to provide outstanding accuracy for the notorious benchmark problem of the two lowest excited-state potential energy curves for the amino group twist in 4-(dimethylamino)benzonitrile (DMABN). However, the design of ωLH22t as a general-purpose functional resulted in less convincing performance for triplet excitations, which is an important advantage of previous LHs. Furthermore, ωLH22t uses 8 empirical parameters to achieve broad accuracy. In this work, the RSLH ωLH23ct-sir is constructed with minimal empiricism by optimizing its local mixing function prefactor and range-separation parameter for only 8 excitation energies. ωLH23ct-sir maintains the excellent performance of ωLH22t for the DMABN twist and charge-transfer benchmarks but significantly improves the errors for triplet excitation energies (0.17 vs 0.24 eV). Additional test calculations for the AE6BH6 thermochemistry test set and large dipole moment and static polarizability test sets confirm that the focus on excitation energies in the optimization of ωLH23ct-sir has not caused any dramatic errors for ground-state properties. Although ωLH23ct-sir cannot replace ωLH22t as a general-purpose functional, it is preferable for problems requiring a universally good description of localized and charge-transfer excitations of both singlet and triplet multiplicity. Current limitations on the application of ωLH23ct-sir and other RSLHs to the study of singlet-triplet gaps of emitters for thermally activated delayed fluorescence are discussed. This work also includes the first systematic analysis of the influence of the local mixing function prefactor and the range-separation parameter in an RSLH on different types of excitations.
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Affiliation(s)
- Robin Grotjahn
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
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8
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Franzke YJ. Reducing Exact Two-Component Theory for NMR Couplings to a One-Component Approach: Efficiency and Accuracy. J Chem Theory Comput 2023; 19:2010-2028. [PMID: 36939092 DOI: 10.1021/acs.jctc.2c01248] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/21/2023]
Abstract
The self-consistent and complex spin-orbit exact two-component (X2C) formalism for NMR spin-spin coupling constants [ J. Chem. Theory Comput. 17, 2021, 3874-3994] is reduced to a scalar one-component ansatz. This way, the first-order response term can be partitioned into the Fermi-contact (FC) and spin-dipole (SD) interactions as well as the paramagnetic spin-orbit (PSO) contribution. The FC+SD terms are real and symmetric, while the PSO term is purely imaginary and antisymmetric. The relativistic one-component approach is combined with a modern density functional treatment up to local hybrid functionals including the response of the current density. Computational demands are reduced by factors of 8-24 as shown for a large tin compound consisting of 137 atoms. Limitations of the current ansatz are critically assessed for Sn, Pb, Pd, and Pt compounds, i.e. the one-component treatment is not sufficient for tin compounds featuring a few heavy halogen atoms.
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Affiliation(s)
- Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
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9
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Yamamoto Y, Baruah T, Chang PH, Romero S, Zope RR. Self-consistent implementation of locally scaled self-interaction-correction method. J Chem Phys 2023; 158:064114. [PMID: 36792502 DOI: 10.1063/5.0130436] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
Recently proposed local self-interaction correction (LSIC) method [Zope et al., J. Chem. Phys. 151, 214108 (2019)] is a one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities. The LSIC method is exact for the one-electron densities, also recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to the well-known Perdew-Zunger SIC (PZSIC) method as a special case. This article presents the self-consistent implementation of the LSIC method using the ratio of Weizsäcker and Kohn-Sham kinetic energy densities as an iso-orbital indicator. The atomic forces as well as the forces on the Fermi-Löwdin orbitals are also implemented for the LSIC energy functional. Results show that LSIC with the simplest local spin density functional predicts atomization energies of the AE6 dataset better than some of the most widely used generalized-gradient-approximation (GGA) functional [e.g., Perdew-Burke-Ernzerhof (PBE)] and barrier heights of the BH6 database better than some of the most widely used hybrid functionals (e.g., PBE0 and B3LYP). The LSIC method [a mean absolute error (MAE) of 0.008 Å] predicts bond lengths of a small set of molecules better than the PZSIC-LSDA (MAE 0.042 Å) and LSDA (0.011 Å). This work shows that accurate results can be obtained from the simplest density functional by removing the self-interaction-errors using an appropriately designed SIC method.
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Affiliation(s)
- Yoh Yamamoto
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Po-Hao Chang
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Selim Romero
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Rajendra R Zope
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
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Fürst S, Haasler M, Grotjahn R, Kaupp M. Full Implementation, Optimization, and Evaluation of a Range-Separated Local Hybrid Functional with Wide Accuracy for Ground and Excited States. J Chem Theory Comput 2023; 19:488-502. [PMID: 36625881 DOI: 10.1021/acs.jctc.2c00782] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
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.
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Affiliation(s)
- Susanne Fürst
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Matthias Haasler
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Robin Grotjahn
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Martin Kaupp
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany
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11
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Teale AM, Helgaker T, Savin A, Adamo C, Aradi B, Arbuznikov AV, Ayers PW, Baerends EJ, Barone V, Calaminici P, Cancès E, Carter EA, Chattaraj PK, Chermette H, Ciofini I, Crawford TD, De Proft F, Dobson JF, Draxl C, Frauenheim T, Fromager E, Fuentealba P, Gagliardi L, Galli G, Gao J, Geerlings P, Gidopoulos N, Gill PMW, Gori-Giorgi P, Görling A, Gould T, Grimme S, Gritsenko O, Jensen HJA, Johnson ER, Jones RO, Kaupp M, Köster AM, Kronik L, Krylov AI, Kvaal S, Laestadius A, Levy M, Lewin M, Liu S, Loos PF, Maitra NT, Neese F, Perdew JP, Pernal K, Pernot P, Piecuch P, Rebolini E, Reining L, Romaniello P, Ruzsinszky A, Salahub DR, Scheffler M, Schwerdtfeger P, Staroverov VN, Sun J, Tellgren E, Tozer DJ, Trickey SB, Ullrich CA, Vela A, Vignale G, Wesolowski TA, Xu X, Yang W. DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science. Phys Chem Chem Phys 2022; 24:28700-28781. [PMID: 36269074 PMCID: PMC9728646 DOI: 10.1039/d2cp02827a] [Citation(s) in RCA: 62] [Impact Index Per Article: 31.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2022] [Accepted: 08/09/2022] [Indexed: 12/13/2022]
Abstract
In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.
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Affiliation(s)
- Andrew M. Teale
- School of Chemistry, University of Nottingham, University ParkNottinghamNG7 2RDUK
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - Andreas Savin
- Laboratoire de Chimie Théorique, CNRS and Sorbonne University, 4 Place Jussieu, CEDEX 05, 75252 Paris, France.
| | - Carlo Adamo
- PSL University, CNRS, ChimieParisTech-PSL, Institute of Chemistry for Health and Life Sciences, i-CLeHS, 11 rue P. et M. Curie, 75005 Paris, France.
| | - Bálint Aradi
- Bremen Center for Computational Materials Science, University of Bremen, P.O. Box 330440, D-28334 Bremen, Germany.
| | - Alexei V. Arbuznikov
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7Straße des 17. Juni 13510623Berlin
| | | | - Evert Jan Baerends
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
| | - Vincenzo Barone
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56125 Pisa, Italy.
| | - Patrizia Calaminici
- Departamento de Química, Centro de Investigación y de Estudios Avanzados (Cinvestav), CDMX, 07360, Mexico.
| | - Eric Cancès
- CERMICS, Ecole des Ponts and Inria Paris, 6 Avenue Blaise Pascal, 77455 Marne-la-Vallée, France.
| | - Emily A. Carter
- Department of Mechanical and Aerospace Engineering and the Andlinger Center for Energy and the Environment, Princeton UniversityPrincetonNJ 08544-5263USA
| | | | - Henry Chermette
- Institut Sciences Analytiques, Université Claude Bernard Lyon1, CNRS UMR 5280, 69622 Villeurbanne, France.
| | - Ilaria Ciofini
- PSL University, CNRS, ChimieParisTech-PSL, Institute of Chemistry for Health and Life Sciences, i-CLeHS, 11 rue P. et M. Curie, 75005 Paris, France.
| | - T. Daniel Crawford
- Department of Chemistry, Virginia TechBlacksburgVA 24061USA,Molecular Sciences Software InstituteBlacksburgVA 24060USA
| | - Frank De Proft
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium.
| | | | - Claudia Draxl
- Institut für Physik and IRIS Adlershof, Humboldt-Universität zu Berlin, 12489 Berlin, Germany. .,Fritz-Haber-Institut der Max-Planck-Gesellschaft, 14195 Berlin, Germany
| | - Thomas Frauenheim
- Bremen Center for Computational Materials Science, University of Bremen, P.O. Box 330440, D-28334 Bremen, Germany. .,Beijing Computational Science Research Center (CSRC), 100193 Beijing, China.,Shenzhen JL Computational Science and Applied Research Institute, 518110 Shenzhen, China
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 rue Blaise Pascal, 67000 Strasbourg, France.
| | - Patricio Fuentealba
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile.
| | - Laura Gagliardi
- Department of Chemistry, Pritzker School of Molecular Engineering, The James Franck Institute, and Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, USA.
| | - Giulia Galli
- Pritzker School of Molecular Engineering and Department of Chemistry, The University of Chicago, Chicago, IL, USA.
| | - Jiali Gao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China. .,Department of Chemistry, University of Minnesota, Minneapolis, MN 55455, USA
| | - Paul Geerlings
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium.
| | - Nikitas Gidopoulos
- Department of Physics, Durham University, South Road, Durham DH1 3LE, UK.
| | - Peter M. W. Gill
- School of Chemistry, University of SydneyCamperdown NSW 2006Australia
| | - Paola Gori-Giorgi
- Department of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
| | - Andreas Görling
- Chair of Theoretical Chemistry, University of Erlangen-Nuremberg, Egerlandstrasse 3, 91058 Erlangen, Germany.
| | - Tim Gould
- Qld Micro- and Nanotechnology Centre, Griffith University, Gold Coast, Qld 4222, Australia.
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, University of Bonn, Beringstrasse 4, 53115 Bonn, Germany.
| | - Oleg Gritsenko
- Department of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
| | - Hans Jørgen Aagaard Jensen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark.
| | - Erin R. Johnson
- Department of Chemistry, Dalhousie UniversityHalifaxNova ScotiaB3H 4R2Canada
| | - Robert O. Jones
- Peter Grünberg Institut PGI-1, Forschungszentrum Jülich52425 JülichGermany
| | - Martin Kaupp
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, 10623, Berlin.
| | - Andreas M. Köster
- Departamento de Química, Centro de Investigación y de Estudios Avanzados (Cinvestav)CDMX07360Mexico
| | - Leeor Kronik
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth, 76100, Israel.
| | - Anna I. Krylov
- Department of Chemistry, University of Southern CaliforniaLos AngelesCalifornia 90089USA
| | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - Andre Laestadius
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - Mel Levy
- Department of Chemistry, Tulane University, New Orleans, Louisiana, 70118, USA.
| | - Mathieu Lewin
- CNRS & CEREMADE, Université Paris-Dauphine, PSL Research University, Place de Lattre de Tassigny, 75016 Paris, France.
| | - Shubin Liu
- Research Computing Center, University of North Carolina, Chapel Hill, NC 27599-3420, USA. .,Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599-3290, USA
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, France.
| | - Neepa T. Maitra
- Department of Physics, Rutgers University at Newark101 Warren StreetNewarkNJ 07102USA
| | - Frank Neese
- Max Planck Institut für Kohlenforschung, Kaiser Wilhelm Platz 1, D-45470 Mülheim an der Ruhr, Germany.
| | - John P. Perdew
- Departments of Physics and Chemistry, Temple UniversityPhiladelphiaPA 19122USA
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland.
| | - Pascal Pernot
- Institut de Chimie Physique, UMR8000, CNRS and Université Paris-Saclay, Bât. 349, Campus d'Orsay, 91405 Orsay, France.
| | - Piotr Piecuch
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA. .,Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - Elisa Rebolini
- Institut Laue Langevin, 71 avenue des Martyrs, 38000 Grenoble, France.
| | - Lucia Reining
- Laboratoire des Solides Irradiés, CNRS, CEA/DRF/IRAMIS, École Polytechnique, Institut Polytechnique de Paris, F-91120 Palaiseau, France. .,European Theoretical Spectroscopy Facility
| | - Pina Romaniello
- Laboratoire de Physique Théorique (UMR 5152), Université de Toulouse, CNRS, UPS, France.
| | - Adrienn Ruzsinszky
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA.
| | - Dennis R. Salahub
- Department of Chemistry, Department of Physics and Astronomy, CMS – Centre for Molecular Simulation, IQST – Institute for Quantum Science and Technology, Quantum Alberta, University of Calgary2500 University Drive NWCalgaryAlbertaT2N 1N4Canada
| | - Matthias Scheffler
- The NOMAD Laboratory at the FHI of the Max-Planck-Gesellschaft and IRIS-Adlershof of the Humboldt-Universität zu Berlin, Faradayweg 4-6, D-14195, Germany.
| | - Peter Schwerdtfeger
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, 0632 Auckland, New Zealand.
| | - Viktor N. Staroverov
- Department of Chemistry, The University of Western OntarioLondonOntario N6A 5B7Canada
| | - Jianwei Sun
- Department of Physics and Engineering Physics, Tulane University, New Orleans, LA 70118, USA.
| | - Erik Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - David J. Tozer
- Department of Chemistry, Durham UniversitySouth RoadDurhamDH1 3LEUK
| | - Samuel B. Trickey
- Quantum Theory Project, Deptartment of Physics, University of FloridaGainesvilleFL 32611USA
| | - Carsten A. Ullrich
- Department of Physics and Astronomy, University of MissouriColumbiaMO 65211USA
| | - Alberto Vela
- Departamento de Química, Centro de Investigación y de Estudios Avanzados (Cinvestav), CDMX, 07360, Mexico.
| | - Giovanni Vignale
- Department of Physics, University of Missouri, Columbia, MO 65203, USA.
| | - Tomasz A. Wesolowski
- Department of Physical Chemistry, Université de Genève30 Quai Ernest-Ansermet1211 GenèveSwitzerland
| | - Xin Xu
- Shanghai Key Laboratory of Molecular Catalysis and Innovation Materials, Collaborative Innovation Centre of Chemistry for Energy Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China.
| | - Weitao Yang
- Department of Chemistry and Physics, Duke University, Durham, NC 27516, USA.
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12
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Wodyński A, Kaupp M. Local Hybrid Functional Applicable to Weakly and Strongly Correlated Systems. J Chem Theory Comput 2022; 18:6111-6123. [PMID: 36170626 DOI: 10.1021/acs.jctc.2c00795] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The recent idea (Wodyński, A.; Arbuznikov, A. V.; Kaupp M. J. Chem. Phys. 2021, 155, 144101) to augment local hybrid functionals by a strong-correlation (sc) factor obtained from the adiabatic connection in the spirit of the KP16 model has been extended and applied to generate the accurate sc-corrected local hybrid functional scLH22t. By damping small values of the ratio between nondynamical and dynamical correlation entering the correction factor, it has become possible to avoid double counting of nondynamical correlation for weakly correlated situations and thereby preserve the excellent accuracy of the underlying LH20t local hybrid for such cases almost perfectly. On the other hand, scLH22t improves substantially over LH20t in reducing fractional-spin errors (FSEs), in providing improved spin-restricted bond dissociation curves, and in treating some typical systems with multireference character. The obtained FSEs are similar to those of the KP16/B13 model and slightly larger than for B13, but performance for weakly correlated systems is better than for these two related methods, which are also difficult to use self-consistently. The recent DM21 functional based on the training of a deep neural network still performs somewhat better than scLH22t but allows no physical insights into the origins of reduced FSEs. Examination of local mixing functions (LMFs) for the corrected scLH22t and uncorrected LH20t functionals provides further insights: in weakly correlated situations, the LMF remains essentially unchanged. Strong-correlation effects manifest in a reduction of the LMF values in certain regions of space, even to the extent of producing negative LMF values. It is suggested that this is the mechanism by which also DM21, which may be viewed as a range-separated local hybrid, is able to reduce FSEs.
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Affiliation(s)
- Artur Wodyński
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Martin Kaupp
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
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13
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Application of two-component neural network for exchange-correlation functional interpolation. Sci Rep 2022; 12:14133. [PMID: 35986067 PMCID: PMC9391383 DOI: 10.1038/s41598-022-18083-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2022] [Accepted: 08/04/2022] [Indexed: 11/09/2022] Open
Abstract
Density functional theory (DFT) is one of the primary approaches to solving the many-body Schrodinger equation. The essential part of the DFT theory is the exchange-correlation (XC) functional, which can not be obtained in analytical form. Accordingly, the accuracy improvement of the DFT is mainly based on the development of XC functional approximations. Commonly, they are built upon analytic solutions in low- and high-density limits and result from quantum Monte Carlo or post-Hartree-Fock numerical calculations. However, there is no universal functional form to incorporate these data into XC functional. Instead, various parameterizations use heuristic rules to build a specific XC functional. The neural network (NN) approach to interpolate the data from higher precision theories can give a unified path to parametrize an XC functional. Moreover, data from many existing quantum chemical databases could provide the XC functional with improved accuracy. We develop NN XC functional, which gives exchange potential and energy density without direct derivatives of exchange-correlation energy density. Proposed NN architecture consists of two parts NN-E and NN-V, which could be trained in separate ways, adding new flexibility to XC functional. We also show that the developed NN XC functional converges in the self-consistent cycle and gives reasonable energies when applied to atoms, molecules, and crystals.
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14
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Bruder F, Franzke YJ, Weigend F. Paramagnetic NMR Shielding Tensors Based on Scalar Exact Two-Component and Spin-Orbit Perturbation Theory. J Phys Chem A 2022; 126:5050-5069. [PMID: 35857421 DOI: 10.1021/acs.jpca.2c03579] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The temperature-dependent Fermi-contact and pseudocontact terms are important contributions to the paramagnetic NMR shielding tensor. Herein, we augment the scalar-relativistic (local) exact two-component (X2C) framework with spin-orbit perturbation theory including the screened nuclear spin-orbit correction for the EPR hyperfine coupling and g tensor to compute these temperature-dependent terms. The accuracy of this perturbative ansatz is assessed with the self-consistent spin-orbit two-component and four-component treatments serving as reference. This shows that the Fermi-contact and pseudocontact interaction is sufficiently described for paramagnetic NMR shifts; however, larger deviations are found for the EPR spectra and the principle components of the EPR properties of heavy elements. The impact of the perturbative treatment is further compared to that of the density functional approximation and the basis set. Large-scale calculations are routinely possible with the multipole-accelerated resolution of the identity approximation and the seminumerical exchange approximation, as shown for [CeTi6O3(OiPr)9(salicylate)6].
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Affiliation(s)
- Florian Bruder
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany
| | - Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany
| | - Florian Weigend
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany
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15
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Grotjahn R, Kaupp M. A Look at Real‐World Transition‐Metal Thermochemistry and Kinetics with Local Hybrid Functionals. Isr J Chem 2022. [DOI: 10.1002/ijch.202200021] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Robin Grotjahn
- Technische Universität Berlin Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7 Straße des 17. Juni 135 D-10623 Berlin Germany
| | - Martin Kaupp
- Technische Universität Berlin Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7 Straße des 17. Juni 135 D-10623 Berlin Germany
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16
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Holzer C, Franzke YJ. A Local Hybrid Exchange Functional Approximation from First Principles. J Chem Phys 2022; 157:034108. [DOI: 10.1063/5.0100439] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Local hybrid functionals are a more flexible class of density functional approximations allowing for a position-dependent admixture of exact exchange. This additional flexibility, however, comes with a more involved mathematical form and a more complicated design. A common denominator for previously constructed local hybrid funtionals is usage of thermochemical benchmark data to construct these functionals. Herein, we design a local hybrid functional without relying on benchmark data. Instead, we construct it in a more ab initio manner, following the principles of modern meta-generalized gradient approximations and considering theoretical constrains. To achieve this, we make use of the density matrix expansion and a local mixing function based on an approximate correlation length. The accuracy of the developed density functional approximation is assessed for thermochemistry, excitation energies, polarizabilities, magnetizabilities, NMR spin-spincoupling constants, NMR shieldings and shifts, as well as EPR g-tensors and hyperfine coupling constants. Here, the new exchange functional shows a robust performance and is especially well suited for atomization energies, barrier heights, excitation energies, NMR coupling constants, and EPR properties, whereas it looses some ground for the NMR shifts.Therefore, the designed functional is a major step forwards for functionals that have been designed from first principles.
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Affiliation(s)
- Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruher Institut für Technologie Fakultät für Physik, Germany
| | - Yannick J. Franzke
- Fachbereich Chemie, Philipps-Universität Marburg Fachbereich Chemie, Germany
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17
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Schattenberg CJ, Kaupp M. Extended Benchmark Set of Main-Group Nuclear Shielding Constants and NMR Chemical Shifts and Its Use to Evaluate Modern DFT Methods. J Chem Theory Comput 2021; 17:7602-7621. [PMID: 34797677 DOI: 10.1021/acs.jctc.1c00919] [Citation(s) in RCA: 34] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
An extended theoretical benchmark set, NS372, for light main-group nuclear shieldings and NMR shifts has been constructed based on high-level GIAO-CCSD(T)/pcSseg-3//CCSD(T)/cc-pVQZ reference data. After removal of the large static-correlation cases O3, F3-, and BH from the statistical evaluations for the 17O, 19F, and 11B subsets, the benchmark comprises overall 372 shielding values in 117 molecules with a wide range of electronic-structure situations, containing 124 1H, 14 11B, 93 13C, 43 15N, 31 17O, 47 19F, 14 31P, and 6 33S shielding constants. The CCSD(T)/pcSseg-3 data are shown to be close to the basis-set and method limit and thus provide an excellent benchmark to evaluate more approximate methods, such as density functional approaches. This dataset has been used to evaluate Hartree-Fock (HF) and MP2, and a wide range of exchange-correlation functionals from local density approximation (LDA) to generalized gradient approximations (GGAs) and meta-GGAs (focusing on their current-density functional implementations), as well as global hybrid, range-separated hybrid, local hybrid, and double-hybrid functionals. Starting with absolute shielding constants, the DSD-PBEP86 double hybrid is confirmed to provide the highest accuracy, with an aggregate relative mean absolute error (rel. MAE) of only 0.9%, followed by MP2 (1.1%). MP2 and double hybrids only show larger errors for a few systems with the largest static-correlation effects. The double-hybrid B2GP-PLYP, the two local hybrids cLH12ct-SsirPW92 and cLH12ct-SsifPW92, and the current-density functional meta-GGA cB97M-V follow closely behind (all 1.5%), as do some further functionals, cLH20t and cMN15-L (both 1.6%), as well as B2PLYP and KT3 (both 2.0%). Functionals on the lower rungs of the usual ladder offer the advantage of lower computational cost and access to larger molecules. Closer examination also reveals the best-performing methods for individual nuclei in the test set. Different ways of treating τ-dependent functionals are evaluated. When moving from absolute shielding constants to chemical shifts, some of the methods can benefit from systematic error compensation, and the overall error range somewhat narrows. Further methods now achieve the 2% threshold of relative MAEs, including functionals based on TPSS (TPSSh, cmPSTS).
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Affiliation(s)
- Caspar Jonas Schattenberg
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Martin Kaupp
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
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18
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Grotjahn R, Kaupp M. Assessment of hybrid functionals for singlet and triplet excitations: Why do some local hybrid functionals perform so well for triplet excitation energies? J Chem Phys 2021; 155:124108. [PMID: 34598568 DOI: 10.1063/5.0063751] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
The performance of various hybrid density functionals is assessed for 105 singlet and 105 corresponding triplet vertical excitation energies from the QUEST database. The overall lowest mean absolute error is obtained with the local hybrid (LH) functional LH12ct-SsirPW92 with individual errors of 0.11 eV (0.11 eV) for singlet (triplet) n → π* excitations and 0.29 eV (0.17 eV) for π → π* excitations. This is slightly better than with the overall best performing global hybrid M06-2X [n → π*: 0.13 eV (0.17 eV), π → π*: 0.30 eV (0.20 eV)], while most other global and range-separated hybrids and some LHs suffer from the "triplet problem" of time-dependent density functional theory. This is exemplified by correlating the errors for singlet and triplet excitations on a state-by-state basis. The excellent performance of LHs based on a common local mixing function, i.e., an LMF constructed from the spin-summed rather than the spin-resolved semilocal quantities, is systematically investigated by the introduction of a spin-channel interpolation scheme that allows us to continuously modulate the fraction of opposite-spin terms used in the LMF. The correlation of triplet and singlet errors is systematically improved for the n → π* excitations when larger fractions of the opposite-spin-channel are used in the LMF, whereas this effect is limited for the π → π* excitations. This strongly supports a previously made hypothesis that attributes the excellent performance of LHs based on a common LMF to cross-spin-channel nondynamical correlation terms.
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Affiliation(s)
- Robin Grotjahn
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, 10623 Berlin, Germany
| | - Martin Kaupp
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, 10623 Berlin, Germany
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19
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Grotjahn R, Kaupp M. Reliable TDDFT Protocol Based on a Local Hybrid Functional for the Prediction of Vibronic Phosphorescence Spectra Applied to Tris(2,2'-bipyridine)-Metal Complexes. J Phys Chem A 2021; 125:7099-7110. [PMID: 34370482 DOI: 10.1021/acs.jpca.1c05101] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
An efficient computational protocol for the prediction of vibrationally resolved phosphorescence spectra is developed and validated for five tris(2,2'-bipyridine)-metal complexes ([M(bpy)3]n+, where M = Zn, Ru, Rh, Os, Ir). The outstanding feature of this protocol is the use of full linear-response time-dependent density functional theory (TDDFT) for the excited-state triplet calculation, i.e., the commonly seen strategies employing the Tamm-Dancoff approximation (TDA) or unrestricted density functional theory (DFT) calculations for the T1 state are not needed. This is achieved by the use of a local hybrid functional (LH12ct-SsirPW92) that features a real-space dependent admixture of exact exchange governed by a local mixing function. The excellent performance of this LH for triplet excitation energies known from previous studies transfers to a remarkable mean absolute error of 0.06 eV for the phosphorescence 0-0 energies investigated herein, while the popular B3PW91 functional gives an error of 0.27 eV in TDDFT and 0.09 eV in unrestricted DFT calculations, respectively. The advantages of the local hybrid are particularly apparent for excited states with a mixed-valence character. The influence of spin-orbit coupling was found to be significant for [Os(bpy)3]2+ red-shifting the 0-0 energy for phosphorescence by 0.17 eV, while the effect is negligible for the other complexes (<0.03 eV). The influence of the basis-set and integration-grid sizes is evaluated, and a computationally lighter protocol is validated that leads to drastic savings in computation time with negligible loss in accuracy.
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Affiliation(s)
- Robin Grotjahn
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Martin Kaupp
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
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20
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Janesko BG. Replacing hybrid density functional theory: motivation and recent advances. Chem Soc Rev 2021; 50:8470-8495. [PMID: 34060549 DOI: 10.1039/d0cs01074j] [Citation(s) in RCA: 59] [Impact Index Per Article: 19.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Density functional theory (DFT) is the most widely-used electronic structure approximation across chemistry, physics, and materials science. Every year, thousands of papers report hybrid DFT simulations of chemical structures, mechanisms, and spectra. Unfortunately, hybrid DFT's accuracy is ultimately limited by tradeoffs between over-delocalization and under-binding. This review summarizes these tradeoffs, and introduces six modern attempts to go beyond them while maintaining hybrid DFT's relatively low computational cost: DFT+U, self-interaction corrections, localized orbital scaling corrections, local hybrid functionals, real-space nondynamical correlation, and our rung-3.5 approach. The review concludes with practical suggestions for DFT users to identify and mitigate these tradeoffs' impact on their simulations.
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Affiliation(s)
- Benjamin G Janesko
- Department of Chemistry & Biochemistry, Texas Christian University, 2800 S. University Dr, Fort Worth, TX 76129, USA.
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21
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Schattenberg CJ, Kaupp M. Implementation and Validation of Local Hybrid Functionals with Calibrated Exchange-Energy Densities for Nuclear Shielding Constants. J Phys Chem A 2021; 125:2697-2707. [PMID: 33730855 DOI: 10.1021/acs.jpca.1c01135] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A recently reported coupled-perturbed Kohn-Sham implementation to compute nuclear shielding constants with gauge-including atomic orbitals and local hybrid functionals has been extended to cover higher derivatives of the density in the local mixing function (LMF) of the local hybrid as well as the calibration function (CF) needed to deal with the ambiguity of exchange-energy densities. This allowed the first evaluation of state-of-the-art local hybrids with "calibrated" exchange-energy densities for nuclear shieldings. Compared to previously evaluated simpler local hybrids without a CF, appreciable improvements are found for proton shieldings. Furthermore, the recent LH20t functional is still competitive with the outstanding performance of the uncalibrated LH12ct-SsirSVWN and LH12ct-SsifSVWN LHs for heavier nuclei, suggesting that LH20t is possibly the most robust choice of any rung-four functional for computing the nuclear shieldings of main-group nuclei so far. Interestingly, the presence of a CF in the functional significantly reduces the number of artifacts introduced by the widely used Maximoff-Scuseria framework to treat the local kinetic energy τ. The latter occurs in so-called t-LMFs used in many of the present local hybrids. In any case, the use of Dobson's current-density functional framework is also recommended with more advanced calibrated τ-dependent local hybrid functionals.
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Affiliation(s)
- Caspar Jonas Schattenberg
- Theoretische Chemie/Quantenchemie, Institut für Chemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Martin Kaupp
- Theoretische Chemie/Quantenchemie, Institut für Chemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
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22
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Ramos C, Janesko BG. Nonlocal rung-3.5 correlation from the density matrix expansion: Flat-plane condition, thermochemistry, and kinetics. J Chem Phys 2020; 153:164116. [PMID: 33138396 DOI: 10.1063/5.0025160] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
The rung-3.5 approach to density functional theory constructs nonlocal approximate correlation from the expectation values of nonlocal one-electron operators. This offers an inexpensive solution to hybrid functionals' imbalance between exact nonlocal exchange and local approximate correlation. Our rung-3.5 correlation functionals also include a local complement to the nonlocal ingredient, analogous to the local exchange component of a hybrid functional. Here, we use the density matrix expansion (DME) to build rung-3.5 complements. We demonstrate how these provide a measure of local fractional occupancy and use them to approximate the flat-plane condition. We also use these complements in a three-parameter nonlocal correlation functional compatible with full nonlocal exchange. This functional approaches the accuracy of widely used hybrids for molecular thermochemistry and kinetics. The DME provides a foundation for practical, minimally empirical, nonlocal correlation functionals compatible with full nonlocal local exchange.
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Affiliation(s)
- Chloe Ramos
- Department of Chemistry and Biochemistry, Texas Christian University, 2800 S. University Dr., Fort Worth, Texas 76129, USA
| | - Benjamin G Janesko
- Department of Chemistry and Biochemistry, Texas Christian University, 2800 S. University Dr., Fort Worth, Texas 76129, USA
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23
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Grotjahn R, Lauter GJ, Haasler M, Kaupp M. Evaluation of Local Hybrid Functionals for Electric Properties: Dipole Moments and Static and Dynamic Polarizabilities. J Phys Chem A 2020; 124:8346-8358. [DOI: 10.1021/acs.jpca.0c06939] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Robin Grotjahn
- Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Institut für Chemie, Sekr. C7, Straße des 17. Juni 135, D-10623, Berlin, Germany
| | - Gregor J. Lauter
- Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Institut für Chemie, Sekr. C7, Straße des 17. Juni 135, D-10623, Berlin, Germany
| | - Matthias Haasler
- Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Institut für Chemie, Sekr. C7, Straße des 17. Juni 135, D-10623, Berlin, Germany
| | - Martin Kaupp
- Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Institut für Chemie, Sekr. C7, Straße des 17. Juni 135, D-10623, Berlin, Germany
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24
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Grotjahn R, Kaupp M. Validation of Local Hybrid Functionals for Excited States: Structures, Fluorescence, Phosphorescence, and Vibronic Spectra. J Chem Theory Comput 2020; 16:5821-5834. [DOI: 10.1021/acs.jctc.0c00520] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Robin Grotjahn
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Martin Kaupp
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
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25
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Haasler M, Maier TM, Grotjahn R, Gückel S, Arbuznikov AV, Kaupp M. A Local Hybrid Functional with Wide Applicability and Good Balance between (De)Localization and Left–Right Correlation. J Chem Theory Comput 2020; 16:5645-5657. [DOI: 10.1021/acs.jctc.0c00498] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Matthias Haasler
- Institute of Chemistry, Theoretical Chemistry/Quantum Chemistry, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, 10623 Berlin, Germany
| | - Toni M. Maier
- Institute of Chemistry, Theoretical Chemistry/Quantum Chemistry, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, 10623 Berlin, Germany
| | - Robin Grotjahn
- Institute of Chemistry, Theoretical Chemistry/Quantum Chemistry, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, 10623 Berlin, Germany
| | - Simon Gückel
- Institute of Chemistry, Theoretical Chemistry/Quantum Chemistry, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, 10623 Berlin, Germany
| | - Alexei V. Arbuznikov
- Institute of Chemistry, Theoretical Chemistry/Quantum Chemistry, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, 10623 Berlin, Germany
| | - Martin Kaupp
- Institute of Chemistry, Theoretical Chemistry/Quantum Chemistry, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, 10623 Berlin, Germany
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26
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Maier TM, Ikabata Y, Nakai H. Relativistic local hybrid functionals and their impact on 1s core orbital energies. J Chem Phys 2020; 152:214103. [DOI: 10.1063/5.0010400] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Toni M. Maier
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Yasuhiro Ikabata
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan
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27
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Neural network interpolation of exchange-correlation functional. Sci Rep 2020; 10:8000. [PMID: 32409657 PMCID: PMC7224278 DOI: 10.1038/s41598-020-64619-8] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2019] [Accepted: 04/17/2020] [Indexed: 11/24/2022] Open
Abstract
Density functional theory (DFT) is one of the most widely used tools to solve the many-body Schrodinger equation. The core uncertainty inside DFT theory is the exchange-correlation (XC) functional, the exact form of which is still unknown. Therefore, the essential part of DFT success is based on the progress in the development of XC approximations. Traditionally, they are built upon analytic solutions in low- and high-density limits and result from quantum Monte Carlo numerical calculations. However, there is no consistent and general scheme of XC interpolation and functional representation. Many different developed parametrizations mainly utilize a number of phenomenological rules to construct a specific XC functional. In contrast, the neural network (NN) approach can provide a general way to parametrize an XC functional without any a priori knowledge of its functional form. In this work, we develop NN XC functionals and prove their applicability to 3-dimensional physical systems. We show that both the local density approximation (LDA) and generalized gradient approximation (GGA) are well reproduced by the NN approach. It is demonstrated that the local environment can be easily considered by changing only the number of neurons in the first layer of the NN. The developed NN XC functionals show good results when applied to systems that are not presented in the training/test data. The generalizability of the formulated NN XC framework leads us to believe that it could give superior results in comparison with traditional XC schemes provided training data from high-level theories such as the quantum Monte Carlo and post-Hartree-Fock methods.
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28
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Balasubramani SG, Chen GP, Coriani S, Diedenhofen M, Frank MS, Franzke YJ, Furche F, Grotjahn R, Harding ME, Hättig C, Hellweg A, Helmich-Paris B, Holzer C, Huniar U, Kaupp M, Marefat Khah A, Karbalaei Khani S, Müller T, Mack F, Nguyen BD, Parker SM, Perlt E, Rappoport D, Reiter K, Roy S, Rückert M, Schmitz G, Sierka M, Tapavicza E, Tew DP, van Wüllen C, Voora VK, Weigend F, Wodyński A, Yu JM. TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations. J Chem Phys 2020; 152:184107. [PMID: 32414256 PMCID: PMC7228783 DOI: 10.1063/5.0004635] [Citation(s) in RCA: 533] [Impact Index Per Article: 133.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2020] [Accepted: 04/07/2020] [Indexed: 01/30/2023] Open
Abstract
TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.
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Affiliation(s)
- Sree Ganesh Balasubramani
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Guo P Chen
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Sonia Coriani
- DTU Chemistry, Technical University of Denmark, Kemitorvet Build. 207, DK-2800 Kongens Lyngby, Denmark
| | - Michael Diedenhofen
- Dassault Systèmes Deutschland GmbH, Imbacher Weg 46, 51379 Leverkusen, Germany
| | - Marius S Frank
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44801 Bochum, Germany
| | - Yannick J Franzke
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), KIT Campus South, P.O. Box 6980, 76049 Karlsruhe, Germany
| | - Filipp Furche
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Robin Grotjahn
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, 10623 Berlin, Germany
| | | | - Christof Hättig
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44801 Bochum, Germany
| | - Arnim Hellweg
- Dassault Systèmes Deutschland GmbH, Imbacher Weg 46, 51379 Leverkusen, Germany
| | - Benjamin Helmich-Paris
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Christof Holzer
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), KIT Campus South, P.O. Box 6980, 76049 Karlsruhe, Germany
| | - Uwe Huniar
- Dassault Systèmes Deutschland GmbH, Imbacher Weg 46, 51379 Leverkusen, Germany
| | - Martin Kaupp
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, 10623 Berlin, Germany
| | - Alireza Marefat Khah
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44801 Bochum, Germany
| | | | - Thomas Müller
- Forschungszentrum Jülich, Jülich Supercomputer Centre, Wilhelm-Jonen Straße, 52425 Jülich, Germany
| | - Fabian Mack
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), KIT Campus South, P.O. Box 6980, 76049 Karlsruhe, Germany
| | - Brian D Nguyen
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Shane M Parker
- Department of Chemistry, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106, USA
| | - Eva Perlt
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Dmitrij Rappoport
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
| | - Kevin Reiter
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), KIT Campus North, P.O. Box 3640, 76021 Karlsruhe, Germany
| | - Saswata Roy
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Matthias Rückert
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44801 Bochum, Germany
| | - Gunnar Schmitz
- Department of Chemistry, Aarhus Universitet, Langelandsgade 140, DK-8000 Aarhus, Denmark
| | - Marek Sierka
- TURBOMOLE GmbH, Litzenhardtstraße 19, 76135 Karlsruhe, Germany
| | - Enrico Tapavicza
- Department of Chemistry and Biochemistry, California State University, Long Beach, 1250 Bellflower Boulevard, Long Beach, California 90840, USA
| | - David P Tew
- Max Planck Institute for Solid State Research, Heisenbergstaße 1, 70569 Stuttgart, Germany
| | - Christoph van Wüllen
- Fachbereich Chemie and Forschungszentrum OPTIMAS, Technische Universität Kaiserslautern, Erwin-Schrödinger-Staße 52, 67663 Kaiserslautern, Germany
| | - Vamsee K Voora
- Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Florian Weigend
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), KIT Campus North, P.O. Box 3640, 76021 Karlsruhe, Germany
| | - Artur Wodyński
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, 10623 Berlin, Germany
| | - Jason M Yu
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
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29
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Kraisler E. Asymptotic Behavior of the Exchange‐Correlation Energy Density and the Kohn‐Sham Potential in Density Functional Theory: Exact Results and Strategy for Approximations. Isr J Chem 2020. [DOI: 10.1002/ijch.201900103] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Eli Kraisler
- Fritz Haber Center for Molecular Dynamics and Institute of Chemistry The Hebrew University of Jerusalem 9091401 Jerusalem Israel
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30
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Schattenberg CJ, Reiter K, Weigend F, Kaupp M. An Efficient Coupled-Perturbed Kohn–Sham Implementation of NMR Chemical Shift Computations with Local Hybrid Functionals and Gauge-Including Atomic Orbitals. J Chem Theory Comput 2020; 16:931-943. [DOI: 10.1021/acs.jctc.9b00944] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Caspar Jonas Schattenberg
- Technische Universität Berlin, Institut für Chemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Kevin Reiter
- Karlsruher Institut für Technologie (KIT), Institut für Nanotechnologie, Postfach 3640, D-76021 Karlsruhe, Germany
| | - Florian Weigend
- Karlsruher Institut für Technologie (KIT), Institut für Nanotechnologie, Postfach 3640, D-76021 Karlsruhe, Germany
| | - Martin Kaupp
- Technische Universität Berlin, Institut für Chemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
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31
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Detailed investigation of N-(4-n-pentyl-oxybenzylidene)-4′-n-hexylaniline liquid crystal molecule. J Mol Struct 2019. [DOI: 10.1016/j.molstruc.2019.06.068] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
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32
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Janesko BG, Scalmani G, Frisch MJ. Density functionals for nondynamical correlation constructed from an upper bound to the exact exchange energy density. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1535673] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Benjamin G. Janesko
- Department of Chemistry and Biochemistry, Texas Christian University, Fort Worth, TX, USA
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33
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Schattenberg CJ, Maier TM, Kaupp M. Lessons from the Spin-Polarization/Spin-Contamination Dilemma of Transition-Metal Hyperfine Couplings for the Construction of Exchange-Correlation Functionals. J Chem Theory Comput 2018; 14:5653-5672. [DOI: 10.1021/acs.jctc.8b00597] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Caspar J. Schattenberg
- Institut für Chemie, Technische Universität Berlin, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Toni M. Maier
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Martin Kaupp
- Institut für Chemie, Technische Universität Berlin, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
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34
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Ghosh S, Verma P, Cramer CJ, Gagliardi L, Truhlar DG. Combining Wave Function Methods with Density Functional Theory for Excited States. Chem Rev 2018; 118:7249-7292. [PMID: 30044618 DOI: 10.1021/acs.chemrev.8b00193] [Citation(s) in RCA: 128] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.
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Affiliation(s)
- Soumen Ghosh
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Pragya Verma
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Christopher J Cramer
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
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35
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Maier TM, Arbuznikov AV, Kaupp M. Local hybrid functionals: Theory, implementation, and performance of an emerging new tool in quantum chemistry and beyond. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2018. [DOI: 10.1002/wcms.1378] [Citation(s) in RCA: 65] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Toni M. Maier
- Institut für Chemie Theoretische Chemie/Quantenchemie Technische Universität Berlin Berlin Germany
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering Waseda University Tokyo Japan
| | - Alexei V. Arbuznikov
- Institut für Chemie Theoretische Chemie/Quantenchemie Technische Universität Berlin Berlin Germany
| | - Martin Kaupp
- Institut für Chemie Theoretische Chemie/Quantenchemie Technische Universität Berlin Berlin Germany
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36
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Vuckovic S, Gori-Giorgi P, Della Sala F, Fabiano E. Restoring Size Consistency of Approximate Functionals Constructed from the Adiabatic Connection. J Phys Chem Lett 2018; 9:3137-3142. [PMID: 29787273 PMCID: PMC5994725 DOI: 10.1021/acs.jpclett.8b01054] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2018] [Accepted: 05/22/2018] [Indexed: 05/24/2023]
Abstract
Approximate exchange-correlation functionals built by modeling in a nonlinear way the adiabatic connection (AC) integrand of density functional theory have many attractive features, being virtually parameter-free and satisfying different exact properties, but they also have a fundamental flaw: they violate the size-consistency condition, crucial to evaluate interaction energies of molecular systems. We show that size consistency in the AC-based functionals can be restored in a very simple way at no extra computational cost. Results on a large set of benchmark molecular interaction energies show that functionals based on the interaction strength interpolation approximations are significantly more accurate than second-order perturbation theory.
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Affiliation(s)
- Stefan Vuckovic
- Department
of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling,
FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Paola Gori-Giorgi
- Department
of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling,
FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Fabio Della Sala
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center
for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
| | - Eduardo Fabiano
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center
for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
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37
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Borlido P, Marques MAL, Botti S. Local Hybrid Density Functional for Interfaces. J Chem Theory Comput 2018; 14:939-947. [DOI: 10.1021/acs.jctc.7b00853] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Pedro Borlido
- Institut
für Festkörpertheorie und-optik, Friedrich-Schiller-Universität Jena and European Theoretical Spectroscopy Facility, Max-Wien-Platz 1, 07743 Jena, Germany
| | - Miguel A. L. Marques
- Institut
für Physik, Martin-Luther-Universität Halle-Wittenberg and European Theoretical Spectroscopy Facility, D-06099 Halle, Germany
| | - Silvana Botti
- Institut
für Festkörpertheorie und-optik, Friedrich-Schiller-Universität Jena and European Theoretical Spectroscopy Facility, Max-Wien-Platz 1, 07743 Jena, Germany
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38
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Klawohn S, Bahmann H, Kaupp M. Implementation of Molecular Gradients for Local Hybrid Density Functionals Using Seminumerical Integration Techniques. J Chem Theory Comput 2016; 12:4254-62. [DOI: 10.1021/acs.jctc.6b00486] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Sascha Klawohn
- Institut für Chemie,
Theoretische Chemie/Quantenchemie Sekretariat C7, Technische Universität Berlin, Straße des 17, Juni 135, 10623 Berlin, Germany
| | - Hilke Bahmann
- Institut für Chemie,
Theoretische Chemie/Quantenchemie Sekretariat C7, Technische Universität Berlin, Straße des 17, Juni 135, 10623 Berlin, Germany
| | - Martin Kaupp
- Institut für Chemie,
Theoretische Chemie/Quantenchemie Sekretariat C7, Technische Universität Berlin, Straße des 17, Juni 135, 10623 Berlin, Germany
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39
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Kaupp M, Karton A, Bischoff FA. [Al2O4](-), a Benchmark Gas-Phase Class II Mixed-Valence Radical Anion for the Evaluation of Quantum-Chemical Methods. J Chem Theory Comput 2016; 12:3796-806. [PMID: 27434425 DOI: 10.1021/acs.jctc.6b00594] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The radical anion [Al2O4](-) has been identified as a rare example of a small gas-phase mixed-valence system with partially localized, weakly coupled class II character in the Robin/Day classification. It exhibits a low-lying C2v minimum with one terminal oxyl radical ligand and a high-lying D2h minimum at about 70 kJ/mol relative energy with predominantly bridge-localized-hole character. Two identical C2v minima and the D2h minimum are connected by two C2v-symmetrical transition states, which are only ca. 6-10 kJ/mol above the D2h local minimum. The small size of the system and the absence of environmental effects has for the first time enabled the computation of accurate ab initio benchmark energies, at the CCSDT(Q)/CBS level using W3-F12 theory, for a class-II mixed-valence system. These energies have been used to evaluate wave function-based methods [CCSD(T), CCSD, SCS-MP2, MP2, UHF] and density functionals ranging from semilocal (e.g., BLYP, PBE, M06L, M11L, N12) via global hybrids (B3LYP, PBE0, BLYP35, BMK, M06, M062X, M06HF, PW6B95) and range-separated hybrids (CAM-B3LYP, ωB97, ωB97X-D, LC-BLYP, LC-ωPBE, M11, N12SX), the B2PLYP double hybrid, and some local hybrid functionals. Global hybrids with about 35-43% exact-exchange (EXX) admixture (e.g., BLYP35, BMK), several range hybrids (CAM-B3LYP, ωB97X-D, ω-B97), and a local hybrid provide good to excellent agreement with benchmark energetics. In contrast, too low EXX admixture leads to an incorrect delocalized class III picture, while too large EXX overlocalizes and gives too large energy differences. These results provide support for previous method choices for mixed-valence systems in solution and for the treatment of oxyl defect sites in alumosilicates and SiO2. Vibrational gas-phase spectra at various computational levels have been compared directly to experiment and to CCSD(T)/aug-cc-pV(T+d)Z data.
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Affiliation(s)
- Martin Kaupp
- Institut für Chemie, Theoretische Chemie/Quantenchemie Technische, Sekr. C7, Universität Berlin , Straße des 17. Juni 135, D-10623, Berlin, Germany
| | - Amir Karton
- School of Chemistry and Biochemistry, The University of Western Australia , 35 Stirling Highway, Crawley, Perth 6009, Australia
| | - Florian A Bischoff
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Humboldt-Universität zu Berlin , Brook-Taylor-Strasse 2, 12489 Berlin, Germany
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