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Sarkar R, Loos PF, Boggio-Pasqua M, Jacquemin D. Assessing the Performances of CASPT2 and NEVPT2 for Vertical Excitation Energies. J Chem Theory Comput 2022; 18:2418-2436. [PMID: 35333060 DOI: 10.1021/acs.jctc.1c01197] [Citation(s) in RCA: 25] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
Methods able to simultaneously account for both static and dynamic electron correlations have often been employed, not only to model photochemical events but also to provide reference values for vertical transition energies, hence allowing benchmarking of lower-order models. In this category, both the complete-active-space second-order perturbation theory (CASPT2) and the N-electron valence state second-order perturbation theory (NEVPT2) are certainly popular, the latter presenting the advantage of not requiring the application of the empirical ionization-potential-electron-affinity (IPEA) and level shifts. However, the actual accuracy of these multiconfigurational approaches is not settled yet. In this context, to assess the performances of these approaches, the present work relies on highly accurate (±0.03 eV) aug-cc-pVTZ vertical transition energies for 284 excited states of diverse character (174 singlet, 110 triplet, 206 valence, 78 Rydberg, 78 n → π*, 119 π → π*, and 9 double excitations) determined in 35 small- to medium-sized organic molecules containing from three to six non-hydrogen atoms. The CASPT2 calculations are performed with and without IPEA shift and compared to the partially contracted (PC) and strongly contracted (SC) variants of NEVPT2. We find that both CASPT2 with IPEA shift and PC-NEVPT2 provide fairly reliable vertical transition energy estimates, with slight overestimations and mean absolute errors of 0.11 and 0.13 eV, respectively. These values are found to be rather uniform for the various subgroups of transitions. The present work completes our previous benchmarks focused on single-reference wave function methods ( J. Chem. Theory Comput. 2018, 14, 4360; J. Chem. Theory Comput. 2020, 16, 1711), hence allowing for a fair comparison between various families of electronic structure methods. In particular, we show that ADC(2), CCSD, and CASPT2 deliver similar accuracies for excited states with a dominant single-excitation character.
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Affiliation(s)
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques, CNRS, UPS, Université de Toulouse, Toulouse 31062, France
| | - Martial Boggio-Pasqua
- Laboratoire de Chimie et Physique Quantiques, CNRS, UPS, Université de Toulouse, Toulouse 31062, France
| | - Denis Jacquemin
- Université de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
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Loos PF, Lipparini F, Boggio-Pasqua M, Scemama A, Jacquemin D. A Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Medium Sized Molecules. J Chem Theory Comput 2020; 16:1711-1741. [PMID: 31986042 DOI: 10.1021/acs.jctc.9b01216] [Citation(s) in RCA: 107] [Impact Index Per Article: 26.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Following our previous work focusing on compounds containing up to 3 non-hydrogen atoms [J. Chem. Theory Comput. 2018, 14, 4360-4379], we present here highly accurate vertical transition energies obtained for 27 molecules encompassing 4, 5, and 6 non-hydrogen atoms: acetone, acrolein, benzene, butadiene, cyanoacetylene, cyanoformaldehyde, cyanogen, cyclopentadiene, cyclopropenone, cyclopropenethione, diacetylene, furan, glyoxal, imidazole, isobutene, methylenecyclopropene, propynal, pyrazine, pyridazine, pyridine, pyrimidine, pyrrole, tetrazine, thioacetone, thiophene, thiopropynal, and triazine. To obtain these energies, we use equation-of-motion/linear-response coupled cluster theory up to the highest technically possible excitation order for these systems (CC3, EOM-CCSDT, and EOM-CCSDTQ) and selected configuration interaction (SCI) calculations (with tens of millions of determinants in the reference space), as well as the multiconfigurational n-electron valence state perturbation theory (NEVPT2) method. All these approaches are applied in combination with diffuse-containing atomic basis sets. For all transitions, we report at least CC3/aug-cc-pVQZ vertical excitation energies as well as CC3/aug-cc-pVTZ oscillator strengths for each dipole-allowed transition. We show that CC3 almost systematically delivers transition energies in agreement with higher-level methods with a typical deviation of ±0.04 eV, except for transitions with a dominant double excitation character where the error is much larger. The present contribution gathers a large, diverse, and accurate set of more than 200 highly accurate transition energies for states of various natures (valence, Rydberg, singlet, triplet, n → π*, π → π*, ...). We use this series of theoretical best estimates to benchmark a series of popular methods for excited state calculations: CIS(D), ADC(2), CC2, STEOM-CCSD, EOM-CCSD, CCSDR(3), CCSDT-3, CC3, and NEVPT2. The results of these benchmarks are compared to the available literature data.
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Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques, CNRS et Université Toulouse III - Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, University of Pisa, Via Moruzzi 3, 56124 Pisa, Italy
| | - Martial Boggio-Pasqua
- Laboratoire de Chimie et Physique Quantiques, CNRS et Université Toulouse III - Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques, CNRS et Université Toulouse III - Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France
| | - Denis Jacquemin
- CEISAM Lab, UMR 6230, Université de Nantes, CNRS, F-44000 Nantes, France
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Loos PF, Scemama A, Blondel A, Garniron Y, Caffarel M, Jacquemin D. A Mountaineering Strategy to Excited States: Highly Accurate Reference Energies and Benchmarks. J Chem Theory Comput 2018; 14:4360-4379. [DOI: 10.1021/acs.jctc.8b00406] [Citation(s) in RCA: 152] [Impact Index Per Article: 25.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, 31013 Toulouse Cedex 6, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, 31013 Toulouse Cedex 6, France
| | - Aymeric Blondel
- Laboratoire CEISAM - UMR CNRS 6230, Université de Nantes, 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France
| | - Yann Garniron
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, 31013 Toulouse Cedex 6, France
| | - Michel Caffarel
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, 31013 Toulouse Cedex 6, France
| | - Denis Jacquemin
- Laboratoire CEISAM - UMR CNRS 6230, Université de Nantes, 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France
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Tuna D, Lu Y, Koslowski A, Thiel W. Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Benchmarks of Electronically Excited States. J Chem Theory Comput 2016; 12:4400-22. [DOI: 10.1021/acs.jctc.6b00403] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Deniz Tuna
- Max-Planck-Institut für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany
| | - You Lu
- Max-Planck-Institut für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany
| | - Axel Koslowski
- Max-Planck-Institut für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany
| | - Walter Thiel
- Max-Planck-Institut für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany
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Śmiga S, Della Sala F, Buksztel A, Grabowski I, Fabiano E. Accurate Kohn-Sham ionization potentials from scaled-opposite-spin second-order optimized effective potential methods. J Comput Chem 2016; 37:2081-90. [DOI: 10.1002/jcc.24436] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2016] [Revised: 05/26/2016] [Accepted: 06/04/2016] [Indexed: 01/25/2023]
Affiliation(s)
- Szymon Śmiga
- Istituto Nanoscienze-CNR, Euromediterranean Center for Nanomaterial Modelling and Technology (ECMT); via Arnesano Lecce 73100
- Institute of Physics; Faculty of Physics, Astronomy and Informatics; Nicolaus Copernicus University; Grudziadzka 5 Torun 87-100 Poland
- Center for Biomolecular Nanotechnologies @UNILE; Istituto Italiano Di Tecnologia; via Barsanti Arnesano I-73010 Italy
| | - Fabio Della Sala
- Istituto Nanoscienze-CNR, Euromediterranean Center for Nanomaterial Modelling and Technology (ECMT); via Arnesano Lecce 73100
- Center for Biomolecular Nanotechnologies @UNILE; Istituto Italiano Di Tecnologia; via Barsanti Arnesano I-73010 Italy
| | - Adam Buksztel
- Institute of Physics; Faculty of Physics, Astronomy and Informatics; Nicolaus Copernicus University; Grudziadzka 5 Torun 87-100 Poland
| | - Ireneusz Grabowski
- Institute of Physics; Faculty of Physics, Astronomy and Informatics; Nicolaus Copernicus University; Grudziadzka 5 Torun 87-100 Poland
| | - Eduardo Fabiano
- Istituto Nanoscienze-CNR, Euromediterranean Center for Nanomaterial Modelling and Technology (ECMT); via Arnesano Lecce 73100
- Center for Biomolecular Nanotechnologies @UNILE; Istituto Italiano Di Tecnologia; via Barsanti Arnesano I-73010 Italy
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Jacquemin D, Duchemin I, Blase X. Benchmarking the Bethe-Salpeter Formalism on a Standard Organic Molecular Set. J Chem Theory Comput 2015; 11:3290-304. [PMID: 26207104 PMCID: PMC4504186 DOI: 10.1021/acs.jctc.5b00304] [Citation(s) in RCA: 118] [Impact Index Per Article: 13.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2015] [Indexed: 12/17/2022]
Abstract
We perform benchmark calculations of the Bethe-Salpeter vertical excitation energies for the set of 28 molecules constituting the well-known Thiel’s set, complemented by a series of small molecules representative of the dye chemistry field. We show that Bethe-Salpeter calculations based on a molecular orbital energy spectrum obtained with non-self-consistent G0W0 calculations starting from semilocal DFT functionals dramatically underestimate the transition energies. Starting from the popular PBE0 hybrid functional significantly improves the results even though this leads to an average -0.59 eV redshift compared to reference calculations for Thiel’s set. It is shown, however, that a simple self-consistent scheme at the GW level, with an update of the quasiparticle energies, not only leads to a much better agreement with reference values, but also significantly reduces the impact of the starting DFT functional. On average, the Bethe-Salpeter scheme based on self-consistent GW calculations comes close to the best time-dependent DFT calculations with the PBE0 functional with a 0.98 correlation coefficient and a 0.18 (0.25) eV mean absolute deviation compared to TD-PBE0 (theoretical best estimates) with a tendency to be red-shifted. We also observe that TD-DFT and the standard adiabatic Bethe-Salpeter implementation may differ significantly for states implying a large multiple excitation character.
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Affiliation(s)
- Denis Jacquemin
- Laboratoire
CEISAM - UMR CNR 6230, Université
de Nantes, 2 Rue de la
Houssinière, BP 92208, 44322 Nantes Cedex 3, France
- Institut
Universitaire de France, 103 bd St. Michel, 75005 Paris Cedex 5, France
| | - Ivan Duchemin
- INAC,
SP2M/L_Sim, CEA/UJF Cedex 09, Université
Grenoble Alpes, 38054 Grenoble, France
| | - Xavier Blase
- CNRS,
Inst NEEL, F-38042 Grenoble, France
- Institut
NEEL, Université Grenoble Alpes, F-38042 Grenoble, France
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Grabowski I, Teale AM, Fabiano E, Śmiga S, Buksztel A, Sala FD. A density difference based analysis of orbital-dependent exchange-correlation functionals. Mol Phys 2013. [DOI: 10.1080/00268976.2013.854424] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Domínguez A, Aradi B, Frauenheim T, Lutsker V, Niehaus TA. Extensions of the Time-Dependent Density Functional Based Tight-Binding Approach. J Chem Theory Comput 2013; 9:4901-14. [PMID: 26583409 DOI: 10.1021/ct400123t] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The time-dependent density functional based tight-binding (TD-DFTB) approach is generalized to account for fractional occupations. In addition, an on-site correction leads to marked qualitative and quantitative improvements over the original method. Especially, the known failure of TD-DFTB for the description of σ → π* and n → π* excitations is overcome. Benchmark calculations on a large set of organic molecules also indicate a better description of triplet states. The accuracy of the revised TD-DFTB method is found to be similar to first principles TD-DFT calculations at a highly reduced computational cost. As a side issue, we also discuss the generalization of the TD-DFTB method to spin-polarized systems. In contrast to an earlier study, we obtain a formalism that is fully consistent with the use of local exchange-correlation functionals in the ground state DFTB method.
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Affiliation(s)
- A Domínguez
- Bremen Center for Computational Materials Science, Universität Bremen , Am Fallturm 1, 28359 Bremen, Germany
| | - B Aradi
- Bremen Center for Computational Materials Science, Universität Bremen , Am Fallturm 1, 28359 Bremen, Germany
| | - T Frauenheim
- Bremen Center for Computational Materials Science, Universität Bremen , Am Fallturm 1, 28359 Bremen, Germany
| | - V Lutsker
- Department of Theoretical Physics, University of Regensburg , 93040 Regensburg, Germany
| | - T A Niehaus
- Department of Theoretical Physics, University of Regensburg , 93040 Regensburg, Germany
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Jacquemin D, Planchat A, Adamo C, Mennucci B. TD-DFT Assessment of Functionals for Optical 0-0 Transitions in Solvated Dyes. J Chem Theory Comput 2012; 8:2359-72. [PMID: 26588969 DOI: 10.1021/ct300326f] [Citation(s) in RCA: 326] [Impact Index Per Article: 27.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Using TD-DFT, we performed simulations of the adiabatic energies of 40 fluorescent molecules for which the experimental 0-0 energies in condensed phase are available. We used six hybrid functionals (B3LYP, PBE0, M06, M06-2X, CAM-B3LYP, and LC-PBE) that have been shown to provide accurate transition energies in previous TD-DFT assessments, selected two diffuse-containing basis sets, and applied the most recent models for estimating bulk solvation effects. In each case, the correction arising from the difference of zero-point vibrational energies between the ground and the excited states has been consistently determined. Basis set effects have also been carefully studied. It turned out that PBE0 and M06 are the most effective functionals in terms of average deviation (mean absolute error of 0.22-0.23 eV). However, both the M06-2X global hybrid that contains more exact exchange and the CAM-B3LYP range-separated hybrid significantly improve the consistency of the prediction for a relatively negligible degradation of the average error. In addition, we assessed (1) the cross-structure/spectra relationships, (2) the importance of solvent effects, and (3) the differences between adiabatic and vertical energies.
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Affiliation(s)
- Denis Jacquemin
- Laboratoire CEISAM-UMR CNR 6230, Université de Nantes , 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France
| | - Aurélien Planchat
- Laboratoire CEISAM-UMR CNR 6230, Université de Nantes , 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France
| | - Carlo Adamo
- Laboratoire LECIME, CNRS UMR-7575, Chimie-ParisTech , 11 rue Pierre et Marie Curie, F-75231 Paris Cedex 05 France.,Institut Universitaire de France , 103 bd Saint-Michel, F-75005 Paris Cedex 05, France
| | - Benedetta Mennucci
- Department of Chemistry, University of Pisa , Via Risorgimento 35, 56126 Pisa, Italy
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Frozen density embedding calculations with the orbital-dependent localized Hartree–Fock Kohn–Sham potential. Chem Phys Lett 2011. [DOI: 10.1016/j.cplett.2011.10.055] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Peach MJG, Williamson MJ, Tozer DJ. Influence of Triplet Instabilities in TDDFT. J Chem Theory Comput 2011; 7:3578-85. [PMID: 26598256 DOI: 10.1021/ct200651r] [Citation(s) in RCA: 218] [Impact Index Per Article: 16.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Singlet and triplet vertical excitation energies from time-dependent density functional theory (TDDFT) can be affected in different ways by the inclusion of exact exchange in hybrid or Coulomb-attenuated/range-separated exchange-correlation functionals; in particular, triplet excitation energies can become significantly too low. To investigate these issues, the explicit dependence of excitation energies on exact exchange is quantified for four representative molecules, paying attention to the effect of constant, short-range, and long-range contributions. A stability analysis is used to verify that the problematic TDDFT triplet excitations can be understood in terms of the ground state triplet instability problem, and it is proposed that a Hartree-Fock stability analysis should be used to identify triplet excitations for which the presence of exact exchange in the TDDFT functional is undesirable. The use of the Tamm-Dancoff approximation (TDA) significantly improves the problematic triplet excitation energies, recovering the correct state ordering in benzoquinone; it also affects the corresponding singlet states, recovering the correct state ordering in naphthalene. The impressive performance of the TDA is maintained for a wide range of molecules across representative functionals.
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Affiliation(s)
- Michael J G Peach
- Department of Chemistry, Durham University , South Road, Durham, DH1 3LE United Kingdom
| | - Matthew J Williamson
- Department of Chemistry, Durham University , South Road, Durham, DH1 3LE United Kingdom
| | - David J Tozer
- Department of Chemistry, Durham University , South Road, Durham, DH1 3LE United Kingdom
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Jacquemin D, Mennucci B, Adamo C. Excited-state calculations with TD-DFT: from benchmarks to simulations in complex environments. Phys Chem Chem Phys 2011; 13:16987-98. [PMID: 21881657 DOI: 10.1039/c1cp22144b] [Citation(s) in RCA: 251] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
In this perspective, we present an overview of recent progress on Time-Dependent Density Functional Theory (TD-DFT) with a specific focus on its accuracy and on models able to take into account environmental effects, including complex media. To this end, we first summarise recent benchmarks and define an average TD-DFT accuracy in reproducing excitation energies when a conventional approach is used. Next, coupling of TD-DFT with models able to account for different kinds of interactions between a central chromophore and nearby chemical objects (solvent, organic cage, metal as well as semi-conducting surface) is investigated. Examples of application to excitation properties are presented, allowing to briefly describe several recent computational strategies. In addition, an extension of TD-DFT to describe a phenomenon involving interacting chromophores, e.g. the electronic energy transfer (EET), is presented to illustrate that this methodology can be applied to processes beyond the vertical excitation. This perspective therefore aims to provide to non-specialists a flavour of recent trends in the field of simulations of excited states in "realistic" situations.
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Affiliation(s)
- Denis Jacquemin
- Chimie et Interdisciplinarité, Synthèse, Analyse, Modélisation (CEISAM), UMR CNRS no. 6230, BP 92208, Université de Nantes, 2, Rue de la Houssinière, 44322 Nantes Cedex 3, France.
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