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Damour Y, Scemama A, Jacquemin D, Kossoski F, Loos PF. State-Specific Coupled-Cluster Methods for Excited States. J Chem Theory Comput 2024; 20:4129-4145. [PMID: 38749498 PMCID: PMC11137840 DOI: 10.1021/acs.jctc.4c00034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2024] [Revised: 03/06/2024] [Accepted: 03/06/2024] [Indexed: 05/29/2024]
Abstract
We reexamine ΔCCSD, a state-specific coupled-cluster (CC) with single and double excitations (CCSD) approach that targets excited states through the utilization of non-Aufbau determinants. This methodology is particularly efficient when dealing with doubly excited states, a domain in which the standard equation-of-motion CCSD (EOM-CCSD) formalism falls short. Our goal here to evaluate the effectiveness of ΔCCSD when applied to other types of excited states, comparing its consistency and accuracy with EOM-CCSD. To this end, we report a benchmark on excitation energies computed with the ΔCCSD and EOM-CCSD methods for a set of molecular excited-state energies that encompasses not only doubly excited states but also doublet-doublet transitions and (singlet and triplet) singly excited states of closed-shell systems. In the latter case, we rely on a minimalist version of multireference CC known as the two-determinant CCSD method to compute the excited states. Our data set, consisting of 276 excited states stemming from the quest database [Véril et al., WIREs Comput. Mol. Sci. 2021, 11, e1517], provides a significant base to draw general conclusions concerning the accuracy of ΔCCSD. Except for the doubly excited states, we found that ΔCCSD underperforms EOM-CCSD. For doublet-doublet transitions, the difference between the mean absolute errors (MAEs) of the two methodologies (of 0.10 and 0.07 eV) is less pronounced than that obtained for singly excited states of closed-shell systems (MAEs of 0.15 and 0.08 eV). This discrepancy is largely attributed to a greater number of excited states in the latter set exhibiting multiconfigurational characters, which are more challenging for ΔCCSD. We also found typically small improvements by employing state-specific optimized orbitals.
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Affiliation(s)
- Yann Damour
- Laboratoire
de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31000 Toulouse, France
| | - Anthony Scemama
- Laboratoire
de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31000 Toulouse, France
| | - Denis Jacquemin
- Nantes
Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
- Institut
Universitaire de France (IUF), F-75005 Paris, France
| | - Fábris Kossoski
- Laboratoire
de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31000 Toulouse, France
| | - Pierre-François Loos
- Laboratoire
de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31000 Toulouse, France
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2
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Schraivogel T, Kats D. Two determinant distinguishable cluster. J Chem Phys 2024; 160:124109. [PMID: 38526108 DOI: 10.1063/5.0199274] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2024] [Accepted: 03/06/2024] [Indexed: 03/26/2024] Open
Abstract
A two reference determinant version of the distinguishable cluster with singles and doubles (DCSD) has been developed. We have implemented the two determinant distinguishable cluster (2D-DCSD) and the corresponding traditional 2D-CCSD method in a new open-source package written in Julia called ElemCo.jl. The methods were benchmarked on singlet and triplet excited states of valence and Rydberg character, as well as for singlet-triplet gaps of diradicals. It is demonstrated that the distinguishable cluster approximation improves the accuracy of 2D-CCSD.
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Affiliation(s)
- Thomas Schraivogel
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Daniel Kats
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
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3
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Ferté A, Giner E, Taïeb R, Carniato S. Unraveling the variational breakdown of core valence separation calculations: Diagnostic and cure to the over relaxation error of double core hole states. J Chem Phys 2023; 159:144104. [PMID: 37811825 DOI: 10.1063/5.0159493] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2023] [Accepted: 09/21/2023] [Indexed: 10/10/2023] Open
Abstract
The core valence separation (CVS) approximation is the most employed strategy to prevent the variational collapse of standard wave function optimization when attempting to compute electronic states bearing one or more electronic vacancies in core orbitals. Here, we explore the spurious consequences of this approximation on the properties of the computed core hole states. We especially focus on the less studied case of double core hole (DCH) states, whose spectroscopic interest has recently been rapidly growing. We show that the CVS error leads to a systematic underestimation of DCH energies, a property in stark contrast with the case of single core hole states. We highlight that the CVS error can then be interpreted as an over relaxation effect and design a new correction strategy adapted to these specificities.
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Affiliation(s)
- Anthony Ferté
- Laboratoire de Chimie Physique-Matière et Rayonnement, Sorbonne Université and CNRS, F-75005 Paris, France
- Laboratoire de Chimie et Interdisciplinarité, Synthèse, Analyse, Modélisation, Nantes Université and CNRS, F-44000 Nantes, France
| | - Emmanuel Giner
- Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France
| | - Richard Taïeb
- Laboratoire de Chimie Physique-Matière et Rayonnement, Sorbonne Université and CNRS, F-75005 Paris, France
| | - Stéphane Carniato
- Laboratoire de Chimie Physique-Matière et Rayonnement, Sorbonne Université and CNRS, F-75005 Paris, France
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4
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Fouda AEA, Koulentianos D, Young L, Doumy G, Ho PJ. Resonant double-core excitations with ultrafast, intense X-ray pulses. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2133749] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Affiliation(s)
- Adam E. A. Fouda
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, IL, USA
| | - Dimitris Koulentianos
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, IL, USA
| | - Linda Young
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, IL, USA
- Department of Physics and James Franck Institute, The University of Chicago, Chicago, IL, USA
| | - Gilles Doumy
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, IL, USA
| | - Phay J. Ho
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, IL, USA
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5
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Arias-Martinez JE, Cunha LA, Oosterbaan KJ, Lee J, Head-Gordon M. Accurate core excitation and ionization energies from a state-specific coupled-cluster singles and doubles approach. Phys Chem Chem Phys 2022; 24:20728-20741. [PMID: 36004629 DOI: 10.1039/d2cp01998a] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We investigate the use of orbital-optimized references in conjunction with single-reference coupled-cluster theory with single and double substitutions (CCSD) for the study of core excitations and ionizations of 18 small organic molecules, without the use of response theory or equation-of-motion (EOM) formalisms. Three schemes are employed to successfully address the convergence difficulties associated with the coupled-cluster equations, and the spin contamination resulting from the use of a spin symmetry-broken reference, in the case of excitations. In order to gauge the inherent potential of the methods studied, an effort is made to provide reasonable basis set limit estimates for the transition energies. Overall, we find that the two best-performing schemes studied here for ΔCCSD are capable of predicting excitation and ionization energies with errors comparable to experimental accuracies. The proposed ΔCCSD schemes reduces statistical errors against experimental excitation energies by more than a factor of two when compared to the frozen-core core-valence separated (FC-CVS) EOM-CCSD approach - a successful variant of EOM-CCSD tailored towards core excitations.
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Affiliation(s)
- Juan E Arias-Martinez
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA. .,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Leonardo A Cunha
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA. .,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Katherine J Oosterbaan
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA.
| | - Joonho Lee
- Department of Chemistry, Columbia University, New York 10027, USA
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA. .,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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6
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Zheng X, Zhang C, Jin Z, Southworth SH, Cheng L. Benchmark relativistic delta-coupled-cluster calculations of K-edge core-ionization energies of third-row elements. Phys Chem Chem Phys 2022; 24:13587-13596. [PMID: 35616685 DOI: 10.1039/d2cp00993e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
A benchmark computational study of K-edge core-ionization energies of third-row elements using relativistic delta-coupled-cluster (ΔCC) methods and a revised core-valence separation (CVS) scheme is reported. High-level relativistic (HLR) corrections beyond the spin-free exact two-component theory in its one-electron variant (SFX2C-1e), including the contributions from two-electron picture-change effects, spin-orbit coupling, the Breit term, and quantum electrodynamics effects, have been taken into account and demonstrated to play an important role. Relativistic ΔCC calculations are shown to provide accurate results for core-ionization energies of third-row elements. The SFX2C-1e-CVS-ΔCC results augmented with HLR corrections show a maximum deviation of less than 0.5 eV with respect to experimental values.
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Affiliation(s)
- Xuechen Zheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Chaoqun Zhang
- Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Zheqi Jin
- Department of Chemistry, University College London, London, WC1E 6BT, UK
| | - Stephen H Southworth
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA.
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Cunha LA, Hait D, Kang R, Mao Y, Head-Gordon M. Relativistic Orbital-Optimized Density Functional Theory for Accurate Core-Level Spectroscopy. J Phys Chem Lett 2022; 13:3438-3449. [PMID: 35412838 DOI: 10.1021/acs.jpclett.2c00578] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Core-level spectra of 1s electrons of elements heavier than Ne show significant relativistic effects. We combine advances in orbital-optimized density functional theory (OO-DFT) with the spin-free exact two-component (X2C) model for scalar relativistic effects to study K-edge spectra of third period elements. OO-DFT/X2C is found to be quite accurate at predicting energies, yielding a ∼0.5 eV root-mean-square error versus experiment with the modern SCAN (and related) functionals. This marks a significant improvement over the >50 eV deviations that are typical for the popular time-dependent DFT (TDDFT) approach. Consequently, experimental spectra are quite well reproduced by OO-DFT/X2C, sans empirical shifts for alignment. OO-DFT/X2C combines high accuracy with ground state DFT cost and is thus a promising route for computing core-level spectra of third period elements. We also explored K and L edges of 3d transition metals to identify limitations of the OO-DFT/X2C approach in modeling the spectra of heavier atoms.
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Affiliation(s)
- Leonardo A Cunha
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Diptarka Hait
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Richard Kang
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Yuezhi Mao
- Department of Chemistry, Stanford University, Stanford, California 94305, United States
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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Tenorio BNC, Decleva P, Coriani S. Multi-reference approach to the computation of double core-hole spectra. J Chem Phys 2021; 155:131101. [PMID: 34624974 DOI: 10.1063/5.0062130] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Double Core-Hole (DCH) states of small molecules are assessed with the restricted active space self-consistent field and multi-state restricted active space perturbation theory of second order approximations. To ensure an unbiased description of the relaxation and correlation effects on the DCH states, the neutral ground-state and DCH wave functions are optimized separately, whereas the spectral intensities are computed with a biorthonormalized set of molecular orbitals within the state-interaction approximation. Accurate shake-up satellite binding energies and intensities of double-core-ionized states (K-2) are obtained for H2O, N2, CO, and C2H2n (n = 1-3). The results are analyzed in detail and show excellent agreement with recent theoretical and experimental data. The K-2 shake-up spectra of H2O and C2H2n molecules are here completely characterized for the first time.
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Affiliation(s)
- Bruno Nunes Cabral Tenorio
- DTU Chemistry - Department of Chemistry, Technical University of Denmark, Kemitorvet Bldg. 207, 2800 Kongens Lyngby, Denmark
| | - Piero Decleva
- Istituto Officina dei Materiali IOM-CNR and Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, I-34121 Trieste, Italy
| | - Sonia Coriani
- DTU Chemistry - Department of Chemistry, Technical University of Denmark, Kemitorvet Bldg. 207, 2800 Kongens Lyngby, Denmark
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9
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Besley NA. Modeling of the spectroscopy of core electrons with density functional theory. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2021. [DOI: 10.1002/wcms.1527] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Nicholas A. Besley
- School of Chemistry, University of Nottingham University Park Nottingham UK
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