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Guo Y, Zhang N, Liu W. SOiCISCF: Combining SOiCI and iCISCF for Variational Treatment of Spin-Orbit Coupling. J Chem Theory Comput 2023; 19:6668-6685. [PMID: 37728243 DOI: 10.1021/acs.jctc.3c00789] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/21/2023]
Abstract
It has recently been shown that the SOiCI approach [Zhang, N.; J. Phys.: Condens. Matter 2022, 34, 224007], in conjunction with the spin-separated exact two-component relativistic Hamiltonian, can provide very accurate fine structures of systems containing heavy elements by treating electron correlation and spin-orbit coupling (SOC) on an equal footing. Nonetheless, orbital relaxations/polarizations induced by SOC are not yet fully accounted for due to the use of scalar relativistic orbitals. This issue can be resolved by further optimizing the still real-valued orbitals self-consistently in the presence of SOC, as done in the spin-orbit coupled CASSCF approach [Ganyushin, D.; et al. J. Chem. Phys. 2013, 138, 104113] but with the iCISCF algorithm [Guo, Y.; J. Chem. Theory Comput. 2021, 17, 7545-7561] for large active spaces. The resulting SOiCISCF employs both double group and time reversal symmetries for computational efficiency and the assignment of target states. The fine structures of p-block elements are taken as showcases to reveal the efficacy of SOiCISCF.
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Affiliation(s)
- Yang Guo
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
| | - Ning Zhang
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
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2
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Liu W. Perspective: Simultaneous treatment of relativity, correlation, and
QED. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science Shandong University Qingdao Shandong China
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3
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Zhang N, Xiao Y, Liu W. SOiCI and iCISO: combining iterative configuration interaction with spin-orbit coupling in two ways. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:224007. [PMID: 35287124 DOI: 10.1088/1361-648x/ac5db4] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Accepted: 03/14/2022] [Indexed: 06/14/2023]
Abstract
The near-exact iCIPT2 approach for strongly correlated systems of electrons, which stems from the combination of iterative configuration interaction (iCI, an exact solver of full CI) with configuration selection for static correlation and second-order perturbation theory (PT2) for dynamic correlation, is extended to the relativistic domain. In the spirit of spin separation, relativistic effects are treated in two steps: scalar relativity is treated by the infinite-order, spin-free part of the exact two-component (X2C) relativistic Hamiltonian, whereas spin-orbit coupling (SOC) is treated by the first-order, Douglas-Kroll-Hess-like SOC operator derived from the same X2C Hamiltonian. Two possible combinations of iCIPT2 with SOC are considered, i.e., SOiCI and iCISO. The former treats SOC and electron correlation on an equal footing, whereas the latter treats SOC in the spirit of state interaction, by constructing and diagonalizing an effective spin-orbit Hamiltonian matrix in a small number of correlated scalar states. Both double group and time reversal symmetries are incorporated to simplify the computation. Pilot applications reveal that SOiCI is very accurate for the spin-orbit splitting (SOS) of heavy atoms, whereas the computationally very cheap iCISO can safely be applied to the SOS of light atoms and even of systems containing heavy atoms when SOC is largely quenched by ligand fields.
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Affiliation(s)
- Ning Zhang
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China
| | - Yunlong Xiao
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, People's Republic of China
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4
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Jenkins AJ, Hu H, Lu L, Frisch MJ, Li X. Two-Component Multireference Restricted Active Space Configuration Interaction for the Computation of L-Edge X-ray Absorption Spectra. J Chem Theory Comput 2021; 18:141-150. [PMID: 34908414 DOI: 10.1021/acs.jctc.1c00564] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
X-ray absorption spectroscopy is a powerful probe of local electronic and nuclear structures, providing insights into chemical processes. The theoretical prediction and interpretation of metal L-edge X-ray absorption spectra are complicated by both relativistic effects, including spin-orbit coupling and the multiconfigurational nature of the states involved. This work details an exact two-component multireference restricted active space (RAS) configuration interaction scheme that uses an exact two-component state-averaged complete active space self-consistent-field method, which includes the spin-orbit coupling in a variational manner, for the accurate description of the electronic structure before using a RAS configuration interaction method to describe the core excited states of the X-ray spectrum. Benchmark calculations are presented for a series of iron-containing complexes, with results showing key features of the spectrum being reproduced, including ligand-to-metal charge transfer and shake-up excitations.
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Affiliation(s)
- Andrew J Jenkins
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hang Hu
- Molecular Engineering and Sciences Institute, University of Washington, Seattle, Washington 98195, United States
| | - Lixin Lu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Michael J Frisch
- Gaussian Inc., 340 Quinnipiac Street, Building 40, Wallingford, Connecticut 06492, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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5
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Desmarais JK, Erba A, Flament JP, Kirtman B. Perturbation Theory Treatment of Spin-Orbit Coupling, Part I: Double Perturbation Theory Based on a Single-Reference Initial Approximation. J Chem Theory Comput 2021; 17:4697-4711. [PMID: 34288690 DOI: 10.1021/acs.jctc.1c00343] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We develop a perturbation theory for solving the many-body Dirac equation within a given relativistic effective-core potential approximation. Starting from a scalar-relativistic unrestricted Hartree-Fock (SR UHF) solution, we carry out a double perturbation expansion in terms of spin-orbit coupling (SOC) and the electron fluctuation potential. Computationally convenient energy expressions are derived through fourth order in SOC, second order in the electron fluctuation potential, and a total of third order in the coupling between the two. Illustrative calculations on the halogen series of neutral and singly positive diatomic molecules show that the perturbation expansion is well-converged by taking into account only the leading (nonvanishing) term at each order of the electron fluctuation potential. Our perturbation theory approach provides a computationally attractive alternative to a two-component self-consistent field treatment of SOC. In addition, it includes coupling with the fluctuation potential through third order and can be extended (in principle) to multireference calculations, when necessary for both closed- and open-shell cases, using quasi-degenerate perturbation theory.
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Affiliation(s)
- Jacques K Desmarais
- Dipartimento di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy.,IPREM, E2S UPPA, CNRS, Université de Pau et des Pays de l'Adour, 64053 Pau, France
| | - Alessandro Erba
- Dipartimento di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy
| | - Jean-Pierre Flament
- UMR 8523-PhLAM-Physique des Lasers, Atomes et Molécules, CNRS, Université de Lille, 59000 Lille, France
| | - Bernard Kirtman
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, Santa Barbara, California 93106, United States
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6
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Kasper JM, Jenkins AJ, Sun S, Li X. Perspective on Kramers symmetry breaking and restoration in relativistic electronic structure methods for open-shell systems. J Chem Phys 2020; 153:090903. [DOI: 10.1063/5.0015279] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joseph M. Kasper
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Andrew J. Jenkins
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Shichao Sun
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
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7
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Affiliation(s)
- Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, People’s Republic of China
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Jenkins AJ, Liu H, Kasper JM, Frisch MJ, Li X. Variational Relativistic Two-Component Complete-Active-Space Self-Consistent Field Method. J Chem Theory Comput 2019; 15:2974-2982. [DOI: 10.1021/acs.jctc.9b00011] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Andrew J. Jenkins
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hongbin Liu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Joseph M. Kasper
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Michael J. Frisch
- Gaussian Inc., 340 Quinnipiac Street, Building 40, Wallingford, Connecticut 06492, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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Reynolds RD, Yanai T, Shiozaki T. Large-scale relativistic complete active space self-consistent field with robust convergence. J Chem Phys 2018; 149:014106. [PMID: 29981535 DOI: 10.1063/1.5036594] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report an efficient algorithm using density fitting for the relativistic complete active space self-consistent field (CASSCF) method, which is significantly more stable than the algorithm previously reported by one of the authors [J. E. Bates and T. Shiozaki, J. Chem. Phys. 142, 044112 (2015)]. Our algorithm is based on the second-order orbital update scheme with an iterative augmented Hessian procedure, in which the density-fitted orbital Hessian is directly contracted to the trial vectors. Using this scheme, each microiteration is made less time consuming than one Dirac-Hartree-Fock iteration, and macroiterations converge quadratically. In addition, we show that the CASSCF calculations with the Gaunt and full Breit interactions can be efficiently performed by means of approximate orbital Hessians computed with the Dirac-Coulomb Hamiltonian. It is demonstrated that our algorithm can also be applied to systems under an external magnetic field, for which all of the molecular integrals are computed using gauge-including atomic orbitals.
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Affiliation(s)
- Ryan D Reynolds
- Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208, USA
| | - Takeshi Yanai
- Institute of Transformative Bio-Molecules (WPI-ITbM), Nagoya University, Chikusa, Nagoya 464-8602, Japan
| | - Toru Shiozaki
- Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208, USA
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10
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Battaglia S, Keller S, Knecht S. Efficient Relativistic Density-Matrix Renormalization Group Implementation in a Matrix-Product Formulation. J Chem Theory Comput 2018; 14:2353-2369. [DOI: 10.1021/acs.jctc.7b01065] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Stefano Battaglia
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Sebastian Keller
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Stefan Knecht
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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11
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Zhang B, Vandezande JE, Reynolds RD, Schaefer HF. Spin–Orbit Coupling via Four-Component Multireference Methods: Benchmarking on p-Block Elements and Tentative Recommendations. J Chem Theory Comput 2018; 14:1235-1246. [DOI: 10.1021/acs.jctc.7b00989] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Boyi Zhang
- Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States
| | - Jonathon E. Vandezande
- Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States
| | - Ryan D. Reynolds
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Henry F. Schaefer
- Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States
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12
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Sergentu DC, David G, Montavon G, Maurice R, Galland N. Scrutinizing "Invisible" astatine: A challenge for modern density functionals. J Comput Chem 2016; 37:1345-54. [PMID: 27059181 DOI: 10.1002/jcc.24326] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2015] [Revised: 01/18/2016] [Accepted: 01/19/2016] [Indexed: 12/20/2022]
Abstract
The main-group 6p elements did not receive much attention in the development of recent density functionals. In many cases it is still difficult to choose among the modern ones a relevant functional for various applications. Here, we illustrate the case of astatine species (At, Z = 85) and we report the first, and quite complete, benchmark study on several properties concerning such species. Insights on geometries, transition energies and thermodynamic properties of a set of 19 astatine species, for which reference experimental or theoretical data has been reported, are obtained with relativistic (two-component) density functional theory calculations. An extensive set of widely used functionals is employed. The hybrid meta-generalized gradient approximation (meta-GGA) PW6B95 functional is overall the best choice. It is worth noting that the range-separated HSE06 functional as well as the old and very popular B3LYP and PBE0 hybrid-GGAs appear to perform quite well too. Moreover, we found that astatine chemistry in solution can accurately be predicted using implicit solvent models, provided that specific parameters are used to build At cavities. © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- Dumitru-Claudiu Sergentu
- Laboratoire SUBATECH, UMR CNRS 6457, IN2P3/EMN Nantes/Université De Nantes, 4 Rue Alfred Kastler, BP 20722, Nantes Cedex 3, 44307, France.,Laboratoire CEISAM, UMR CNRS 6230, Université De Nantes, 2 Rue De La Houssinière, BP 92208, Nantes Cedex 3, 44322, France
| | - Grégoire David
- Laboratoire CEISAM, UMR CNRS 6230, Université De Nantes, 2 Rue De La Houssinière, BP 92208, Nantes Cedex 3, 44322, France
| | - Gilles Montavon
- Laboratoire SUBATECH, UMR CNRS 6457, IN2P3/EMN Nantes/Université De Nantes, 4 Rue Alfred Kastler, BP 20722, Nantes Cedex 3, 44307, France
| | - Rémi Maurice
- Laboratoire SUBATECH, UMR CNRS 6457, IN2P3/EMN Nantes/Université De Nantes, 4 Rue Alfred Kastler, BP 20722, Nantes Cedex 3, 44307, France
| | - Nicolas Galland
- Laboratoire CEISAM, UMR CNRS 6230, Université De Nantes, 2 Rue De La Houssinière, BP 92208, Nantes Cedex 3, 44322, France
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Maurice R, Réal F, Gomes ASP, Vallet V, Montavon G, Galland N. Effective bond orders from two-step spin–orbit coupling approaches: The I2, At2, IO+, and AtO+ case studies. J Chem Phys 2015; 142:094305. [DOI: 10.1063/1.4913738] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Affiliation(s)
- Rémi Maurice
- SUBATECH, CNRS UMR 6457, IN2P3/EMN Nantes/Université de Nantes, 4 rue Alfred Kastler, BP 20722, 44307 Nantes Cedex 3, France
| | - Florent Réal
- Laboratoire PhLAM, CNRS UMR 8523, Université de Lille, 59655 Villeneuve d’Ascq Cedex, France
| | | | - Valérie Vallet
- Laboratoire PhLAM, CNRS UMR 8523, Université de Lille, 59655 Villeneuve d’Ascq Cedex, France
| | - Gilles Montavon
- SUBATECH, CNRS UMR 6457, IN2P3/EMN Nantes/Université de Nantes, 4 rue Alfred Kastler, BP 20722, 44307 Nantes Cedex 3, France
| | - Nicolas Galland
- CEISAM, UMR CNRS 6230, Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France
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14
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Bates JE, Shiozaki T. Fully relativistic complete active space self-consistent field for large molecules: Quasi-second-order minimax optimization. J Chem Phys 2015; 142:044112. [DOI: 10.1063/1.4906344] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jefferson E. Bates
- Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208, USA
| | - Toru Shiozaki
- Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208, USA
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15
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Kim I, Lee YS. Two-component multi-configurational second-order perturbation theory with Kramers restricted complete active space self-consistent field reference function and spin-orbit relativistic effective core potential. J Chem Phys 2014; 141:164104. [DOI: 10.1063/1.4898153] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Inkoo Kim
- Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, South Korea
| | - Yoon Sup Lee
- Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, South Korea
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16
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Knecht S, Legeza Ö, Reiher M. Communication: Four-component density matrix renormalization group. J Chem Phys 2014; 140:041101. [DOI: 10.1063/1.4862495] [Citation(s) in RCA: 67] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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