1
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Vu K, Pandian J, Zhang B, Annas C, Parker AJ, Mancini JS, Wang EB, Saldana-Greco D, Nelson ES, Springsted G, Lischka H, Plasser F, Parish CA. Multireference Averaged Quadratic Coupled Cluster (MR-AQCC) Study of the Geometries and Energies for ortho-, meta- and para-Benzyne. J Phys Chem A 2024; 128:7816-7829. [PMID: 39240216 PMCID: PMC11421082 DOI: 10.1021/acs.jpca.4c04099] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2024] [Revised: 08/21/2024] [Accepted: 08/22/2024] [Indexed: 09/07/2024]
Abstract
The diradical benzyne isomers are excellent prototypes for evaluating the ability of an electronic structure method to describe static and dynamic correlation. The benzyne isomers are also interesting molecules with which to study the fundamentals of through-space and through-bond diradical coupling that is important in so many electronic device applications. In the current study, we utilize the multireference methods MC-SCF, MR-CISD, MR-CISD+Q, and MR-AQCC with an (8,8) complete active space that includes the σ, σ*, π and π* orbitals, to characterize the electronic structure of ortho-, meta- and para-benzyne. We also determine the adiabatic and vertical singlet-triplet splittings for these isomers. MR-AQCC and MR-CISD+Q produced energy gaps in good agreement with previously obtained experimental values. Geometries, orbital energies and unpaired electron densities show significant through-space coupling in the o- and m-benzynes, while p-benzyne shows through-bond coupling, explaining the dramatically different singlet-triplet gaps between the three isomers.
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Affiliation(s)
- Khanh Vu
- Department
of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
| | - Joshua Pandian
- Department
of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
| | - Boyi Zhang
- Department
of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
| | - Christina Annas
- Department
of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
| | - Anna J. Parker
- Department
of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
| | - John S. Mancini
- Department
of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
| | - Evan B. Wang
- Department
of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
| | - Diomedes Saldana-Greco
- Department
of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
| | - Emily S. Nelson
- Department
of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
| | - Greg Springsted
- Department
of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
| | - Hans Lischka
- Department
of Chemistry and Biochemistry, Texas Tech
University, Lubbock, Texas 79409, United States
| | - Felix Plasser
- Department
of Chemistry, Loughborough University, Ashby Road, Loughborough LE11 3TU, Leicestershire, U.K.
| | - Carol A. Parish
- Department
of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
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2
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Sirianni D, Song X, Wairegi S, Wang EB, Mendoza-Gomez SA, Luxon A, Zimmerley M, Nussdorf A, Filatov M, Hoffmann R, Parish CA. Variations on the Bergman Cyclization Theme: Electrocyclizations of Ionic Penta-, Hepta-, and Octadiynes. J Am Chem Soc 2023; 145:21408-21418. [PMID: 37747784 PMCID: PMC10557144 DOI: 10.1021/jacs.3c06691] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2023] [Indexed: 09/26/2023]
Abstract
The Bergman cyclization of (Z)-hexa-3-ene-1,5-diyne to form the aromatic diradical p-benzyne has garnered attention as a potential antitumor agent due to its relatively low cyclization barrier and the stability of the resulting diradical. Here, we present a theoretical investigation of several ionic extensions of the fundamental Bergman cyclization: electrocyclizations of the penta-1,4-diyne anion, hepta-1,6-diyne cation, and octa-1,7-diyne dication, leveraging the spin-flip formulation of the equation-of-motion coupled cluster theory with single and double substitutions (EOM-SF-CCSD). Though the penta-1,4-diyne anion exhibits a large cyclization barrier of +66 kcal mol-1, cyclization of both the hepta-1,6-diyne cation and octa-1,7-diyne dication along a previously unreported triplet pathway requires relatively low energy. We also identified the presence of significant aromaticity in the triplet diradical products of these two cationic cyclizations.
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Affiliation(s)
- Dominic
A. Sirianni
- Department
of Natural Sciences, Daemen University, Amherst, New York 14226, United States
- Department
of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
| | - Xinli Song
- Department
of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
| | - Salmika Wairegi
- Department
of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
| | - Evan B. Wang
- Department
of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
| | | | - Adam Luxon
- Department
of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
| | - Maxwell Zimmerley
- Department
of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
| | - Ariana Nussdorf
- Department
of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
| | - Michael Filatov
- Department
of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
| | - Roald Hoffmann
- Department
of Chemistry, Cornell University, Ithaca, New York 14853, United States
| | - Carol A. Parish
- Department
of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
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3
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Marin K, Huang M, Evangelista FA. Signatures of diradicals in x-ray absorption spectroscopy. J Chem Phys 2023; 158:2882842. [PMID: 37094006 DOI: 10.1063/5.0140761] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2022] [Accepted: 03/09/2023] [Indexed: 04/26/2023] Open
Abstract
Theoretical simulations are critical to analyze and interpret the x-ray absorption spectrum of transient open-shell species. In this work, we propose a model of the many-body core-excited states of symmetric diradicals. We apply this model to analyze the carbon K-edge transitions of o-, m-, and p-benzyne, three organic diradicals with diverse and unusual electronic structures. The predictions of our model are compared with high-level multireference computations of the K-edge spectrum of the benzynes obtained with the driven similarity renormalization group truncated to third order. Our model shows the importance of a many-body treatment of the core-excited states of the benzynes and provides a theoretical framework to understand which properties of the ground state of these diradicals can be extracted from their x-ray spectrum.
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Affiliation(s)
- Kevin Marin
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Meng Huang
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
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4
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Saraswat M, Ravi S, Shamasundar KR, Venkataramani S. Photochemistry of 3,6-Didehydropyridazine Biradical─An Untraceable Para Benzyne Analogue. J Phys Chem A 2022; 126:557-567. [PMID: 35049300 DOI: 10.1021/acs.jpca.1c09317] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We report matrix isolation infrared spectroscopic studies to characterize 3,6-didehydropyridazine 6, a heterocyclic analogue of para benzyne, combined with computations. In this regard, we have utilized 3,6-diiodopyridazine 11 as a photolytic precursor. The experiments toward the generation of the biradical are carried out in argon and nitrogen matrices at 4 K. Instead of the elusive biradical, we have observed a ring-opening product maleonitrile (Z)-7 upon irradiation at 254 nm. In contrast, prolonged irradiation at 254 nm leads only to Z-E isomerization, forming fumaronitrile (E)-7. The mechanistic aspects of ring-opening, product selectivity, and Z-E photoisomerization steps have been investigated in detail using high-level ab initio computations. These studies have found that 3,6-didehydropyridazine 6 is an untraceable intermediate, and the ring-opening step leading to maleonitrile is barrierless. In addition, we have proposed the involvement of the S1 (π-π*) state via conical intersection in the Z-E photoisomerization of maleonitrile.
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Affiliation(s)
- Mayank Saraswat
- Department of Chemical Sciences, Indian Institute of Science Education and Research, Mohali Knowledge City, Sector 81, SAS Nagar, Manauli 140306, India
| | | | - K R Shamasundar
- Department of Chemical Sciences, Indian Institute of Science Education and Research, Mohali Knowledge City, Sector 81, SAS Nagar, Manauli 140306, India
| | - Sugumar Venkataramani
- Department of Chemical Sciences, Indian Institute of Science Education and Research, Mohali Knowledge City, Sector 81, SAS Nagar, Manauli 140306, India
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5
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Lee S, Park W, Nakata H, Filatov M, Choi CH. Recent advances in ensemble density functional theory and linear response theory for strong correlation. B KOREAN CHEM SOC 2021. [DOI: 10.1002/bkcs.12429] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Affiliation(s)
- Seunghoon Lee
- Division of Chemistry and Chemical Engineering California Institute of Technology Pasadena California USA
| | - Woojin Park
- Department of Chemistry Kyungpook National University Daegu South Korea
| | - Hiroya Nakata
- Department of Chemistry Kyungpook National University Daegu South Korea
| | - Michael Filatov
- Department of Chemistry Kyungpook National University Daegu South Korea
| | - Cheol Ho Choi
- Department of Chemistry Kyungpook National University Daegu South Korea
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6
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Accurate estimation of singlet-triplet gap of strongly correlated systems by CCSD(T) method using improved orbitals. COMPUT THEOR CHEM 2021. [DOI: 10.1016/j.comptc.2021.113326] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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7
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Horbatenko Y, Sadiq S, Lee S, Filatov M, Choi CH. Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (MRSF-TDDFT) as a Simple yet Accurate Method for Diradicals and Diradicaloids. J Chem Theory Comput 2021; 17:848-859. [PMID: 33401894 DOI: 10.1021/acs.jctc.0c01074] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
Due to their multiconfigurational nature featuring strong electron correlation, accurate description of diradicals and diradicaloids is a challenge for quantum chemical methods. The recently developed mixed-reference spin-flip (MRSF)-TDDFT method is capable of describing the multiconfigurational electronic states of these systems while avoiding the spin-contamination pitfalls of SF-TDDFT. Here, we apply MRSF-TDDFT to study the adiabatic singlet-triplet (ST) gaps in a series of well-known diradicals and diradicaloids. On average, MRSF displays a very high prediction accuracy of the adiabatic ST gaps with the mean absolute error (MAE) amounting to 0.14 eV. In addition, MRSF is capable of accurately describing the effect of the Jahn-Teller distortion occurring in the trimethylenemethane diradical, the violation of the Hund rule in a series of the didehydrotoluene diradicals, and the potential energy surfaces of the didehydrobenzene (benzyne) diradicals. A convenient criterion for distinguishing diradicals and diradicaloids is suggested on the basis of the easily obtainable quantities. In all of these cases, which are difficult for the conventional methods of density functional theory (DFT), MRSF shows results consistent with the experiment and the high-level ab initio computations. Hence, the present study documents the reliability and accuracy of MRSF and lays out the guidelines for its application to strongly correlated molecular systems.
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Affiliation(s)
- Yevhen Horbatenko
- Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea
| | - Saima Sadiq
- Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea
| | - Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Michael Filatov
- Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea
| | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea
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8
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Lischka H, Shepard R, Müller T, Szalay PG, Pitzer RM, Aquino AJA, Araújo do Nascimento MM, Barbatti M, Belcher LT, Blaudeau JP, Borges I, Brozell SR, Carter EA, Das A, Gidofalvi G, González L, Hase WL, Kedziora G, Kertesz M, Kossoski F, Machado FBC, Matsika S, do Monte SA, Nachtigallová D, Nieman R, Oppel M, Parish CA, Plasser F, Spada RFK, Stahlberg EA, Ventura E, Yarkony DR, Zhang Z. The generality of the GUGA MRCI approach in COLUMBUS for treating complex quantum chemistry. J Chem Phys 2020; 152:134110. [PMID: 32268762 DOI: 10.1063/1.5144267] [Citation(s) in RCA: 36] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview.
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Affiliation(s)
- Hans Lischka
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, USA
| | - Ron Shepard
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Thomas Müller
- Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich 52428, Germany
| | - Péter G Szalay
- ELTE Eötvös Loránd University, Institute of Chemistry, Budapest, Hungary
| | - Russell M Pitzer
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Adelia J A Aquino
- School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin 300072, People's Republic of China
| | | | | | - Lachlan T Belcher
- Laser and Optics Research Center, Department of Physics, US Air Force Academy, Colorado 80840, USA
| | | | - Itamar Borges
- Departamento de Química, Instituto Militar de Engenharia, Rio de Janeiro, RJ 22290-270, Brazil
| | - Scott R Brozell
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Emily A Carter
- Office of the Chancellor and Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, Box 951405, Los Angeles, California 90095-1405, USA
| | - Anita Das
- Indian Institute of Engineering Science and Technology, Shibpur, Howrah, India
| | - Gergely Gidofalvi
- Department of Chemistry and Biochemistry, Gonzaga University, Spokane, Washington 99258, USA
| | - Leticia González
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
| | - William L Hase
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, USA
| | - Gary Kedziora
- Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433, USA
| | - Miklos Kertesz
- Department of Chemistry, Georgetown University, 37th and O Streets, NW, Washington, DC 20057-1227, USA
| | | | - Francisco B C Machado
- Departamento de Química, Instituto Tecnológico de Aeronáutica, São José dos Campos 12228-900, São Paulo, Brazil
| | - Spiridoula Matsika
- Department of Chemistry, Temple University, 1901 N. 13th St., Philadelphia, Pennsylvania 19122, USA
| | | | - Dana Nachtigallová
- Institute of Organic Chemistry and Biochemistry v.v.i., The Czech Academy of Sciences, Flemingovo nám. 2, 160610 Prague 6, Czech Republic
| | - Reed Nieman
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, USA
| | - Markus Oppel
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
| | - Carol A Parish
- Department of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, USA
| | - Felix Plasser
- Department of Chemistry, Loughborough University, Loughborough LE11 3TU, United Kingdom
| | - Rene F K Spada
- Departamento de Física, Instituto Tecnológico de Aeronáutica, São José dos Campos 12228-900, São Paulo, Brazil
| | - Eric A Stahlberg
- Biomedical Informatics and Data Science, Frederick National Laboratory for Cancer Research, Frederick, Maryland 21702, USA
| | - Elizete Ventura
- Universidade Federal da Paraíba, 58059-900 João Pessoa, PB, Brazil
| | - David R Yarkony
- Department of Chemistry, Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218, USA
| | - Zhiyong Zhang
- Stanford Research Computing Center, Stanford University, 255 Panama Street, Stanford, California 94305, USA
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9
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Chattopadhyay S. Simplified Treatment of Electronic Structures of the Lowest Singlet and Triplet States of Didehydropyrazines. J Phys Chem A 2019; 123:5980-5994. [DOI: 10.1021/acs.jpca.9b03998] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Sudip Chattopadhyay
- Department of Chemistry, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India
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10
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Scott T, Nieman R, Luxon A, Zhang B, Lischka H, Gagliardi L, Parish CA. A Multireference Ab Initio Study of the Diradical Isomers of Pyrazine. J Phys Chem A 2019; 123:2049-2057. [DOI: 10.1021/acs.jpca.8b12440] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Thais Scott
- Department of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond Virginia 23713, United States
- Department of Chemistry, Chemical Theory Center and the Minnesota Supercomputing Institute, The University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Reed Nieman
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States
| | - Adam Luxon
- Department of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond Virginia 23713, United States
| | - Boyi Zhang
- Department of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond Virginia 23713, United States
| | - Hans Lischka
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States
- School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin, 300072 P.R. China
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center and the Minnesota Supercomputing Institute, The University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Carol A. Parish
- Department of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond Virginia 23713, United States
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11
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Hu H, Zhang B, Luxon A, Scott T, Wang B, Parish CA. An Extended Multireference Study of the Singlet and Triplet States of the 9,10-didehydroanthracene Diradical. J Phys Chem A 2018; 122:3688-3696. [DOI: 10.1021/acs.jpca.8b01233] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Hui Hu
- Department of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
| | - Boyi Zhang
- Department of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
| | - Adam Luxon
- Department of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
| | - Thais Scott
- Department of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
| | - Baoshan Wang
- College of Chemistry and Molecular Sciences, Wuhan University, Wuhan, Hubei Province 430072, P.R. China
| | - Carol A. Parish
- Department of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States
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12
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Luxon AR, Orms N, Kanters R, Krylov AI, Parish CA. An ab Initio Exploration of the Bergman Cyclization. J Phys Chem A 2017; 122:420-430. [DOI: 10.1021/acs.jpca.7b10576] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Adam R. Luxon
- Department
of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
| | - Natalie Orms
- Department
of Chemistry, University of Southern California, Los Angeles, California 90089, United States
| | - René Kanters
- Department
of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
| | - Anna I. Krylov
- Department
of Chemistry, University of Southern California, Los Angeles, California 90089, United States
| | - Carol A. Parish
- Department
of Chemistry, University of Richmond, Richmond, Virginia 23173, United States
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13
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Sand AM, Hoyer CE, Sharkas K, Kidder KM, Lindh R, Truhlar DG, Gagliardi L. Analytic Gradients for Complete Active Space Pair-Density Functional Theory. J Chem Theory Comput 2017; 14:126-138. [DOI: 10.1021/acs.jctc.7b00967] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Andrew M. Sand
- Department
of Chemistry, Chemical Theory Center, and the Minnesota Supercomputing
Institute, The University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Chad E. Hoyer
- Department
of Chemistry, Chemical Theory Center, and the Minnesota Supercomputing
Institute, The University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Kamal Sharkas
- Department
of Chemistry, Chemical Theory Center, and the Minnesota Supercomputing
Institute, The University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Katherine M. Kidder
- Department
of Chemistry, Chemical Theory Center, and the Minnesota Supercomputing
Institute, The University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Roland Lindh
- Department
of Chemistry−Ångström, The Theoretical Chemistry
Programme, Uppsala University, P.O. Box 518, SE-751 20 Uppsala, Sweden
| | - Donald G. Truhlar
- Department
of Chemistry, Chemical Theory Center, and the Minnesota Supercomputing
Institute, The University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Laura Gagliardi
- Department
of Chemistry, Chemical Theory Center, and the Minnesota Supercomputing
Institute, The University of Minnesota, Minneapolis, Minnesota 55455, United States
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14
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David G, Guihéry N, Ferré N. What Are the Physical Contents of Hubbard and Heisenberg Hamiltonian Interactions Extracted from Broken Symmetry DFT Calculations in Magnetic Compounds? J Chem Theory Comput 2017; 13:6253-6265. [DOI: 10.1021/acs.jctc.7b00976] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
| | - Nathalie Guihéry
- LCPQ,
IRSAMC, Université de Toulouse 3, Paul Sabatier, 31400 Toulouse, France
| | - Nicolas Ferré
- Aix Marseille
Univ, CNRS, ICR, 13397 Marseille, France
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15
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Hannon KP, Li C, Evangelista FA. An integral-factorized implementation of the driven similarity renormalization group second-order multireference perturbation theory. J Chem Phys 2017; 144:204111. [PMID: 27250283 DOI: 10.1063/1.4951684] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
We report an efficient implementation of a second-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT2) [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)]. Our implementation employs factorized two-electron integrals to avoid storage of large four-index intermediates. It also exploits the block structure of the reference density matrices to reduce the computational cost to that of second-order Møller-Plesset perturbation theory. Our new DSRG-MRPT2 implementation is benchmarked on ten naphthyne isomers using basis sets up to quintuple-ζ quality. We find that the singlet-triplet splittings (ΔST) of the naphthyne isomers strongly depend on the equilibrium structures. For a consistent set of geometries, the ΔST values predicted by the DSRG-MRPT2 are in good agreements with those computed by the reduced multireference coupled cluster theory with singles, doubles, and perturbative triples.
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Affiliation(s)
- Kevin P Hannon
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Chenyang Li
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
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16
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Bauer CA, Hansen A, Grimme S. The Fractional Occupation Number Weighted Density as a Versatile Analysis Tool for Molecules with a Complicated Electronic Structure. Chemistry 2017; 23:6150-6164. [DOI: 10.1002/chem.201604682] [Citation(s) in RCA: 70] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2016] [Indexed: 02/05/2023]
Affiliation(s)
- Christoph Alexander Bauer
- Mulliken Center for Theoretical Chemistry; Institut für Physikalische und Theoretische Chemie der Rheinischen Friedrich-Wilhelms-Universität Bonn; Beringstr. 4 53115 Bonn Germany
| | - Andreas Hansen
- Mulliken Center for Theoretical Chemistry; Institut für Physikalische und Theoretische Chemie der Rheinischen Friedrich-Wilhelms-Universität Bonn; Beringstr. 4 53115 Bonn Germany
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry; Institut für Physikalische und Theoretische Chemie der Rheinischen Friedrich-Wilhelms-Universität Bonn; Beringstr. 4 53115 Bonn Germany
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17
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Li C, Evangelista FA. Towards numerically robust multireference theories: The driven similarity renormalization group truncated to one- and two-body operators. J Chem Phys 2017; 144:164114. [PMID: 27131538 DOI: 10.1063/1.4947218] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The first nonperturbative version of the multireference driven similarity renormalization group (MR-DSRG) theory [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)] is introduced. The renormalization group structure of the MR-DSRG equations ensures numerical robustness and avoidance of the intruder-state problem, while the connected nature of the amplitude and energy equations guarantees size consistency and extensivity. We approximate the MR-DSRG equations by keeping only one- and two-body operators and using a linearized recursive commutator approximation of the Baker-Campbell-Hausdorff expansion [T. Yanai and G. K.-L. Chan, J. Chem. Phys. 124, 194106 (2006)]. The resulting linearized MR-DSRG scheme with one- and two-body operators [MR-LDSRG(2)] contains only 39 terms and scales as O(N(2)NP (2)NH (2)) where NH, NP, and N correspond to the number of hole, particle, and total orbitals, respectively. Benchmark MR-LDSRG(2) computations on the hydrogen fluoride and molecular nitrogen binding curves and the singlet-triplet splitting of p-benzyne yield results comparable in accuracy to those from multireference configuration interaction, Mukherjee multireference coupled cluster theory, and internally contracted multireference coupled cluster theory.
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Affiliation(s)
- Chenyang Li
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
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18
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Das A, Müller T, Plasser F, Lischka H. Polyradical Character of Triangular Non-Kekulé Structures, Zethrenes, p-Quinodimethane-Linked Bisphenalenyl, and the Clar Goblet in Comparison: An Extended Multireference Study. J Phys Chem A 2016; 120:1625-36. [PMID: 26859789 PMCID: PMC4789636 DOI: 10.1021/acs.jpca.5b12393] [Citation(s) in RCA: 76] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
In
this work, two different classes of polyaromatic hydrocarbon
(PAH) systems have been investigated in order to characterize the
amount of polyradical character and to localize the specific regions
of chemical reactivity: (a) the non-Kekulé triangular structures
phenalenyl, triangulene and a π-extended triangulene system
with high-spin ground state and (b) PAHs based on zethrenes, p-quinodimethane-linked bisphenalenyl, and the Clar goblet
containing varying polyradical character in their singlet ground state.
The first class of structures already have open-shell character because
of their high-spin ground state, which follows from the bonding pattern,
whereas for the second class the open-shell character is generated
either because of the competition between the closed-shell quinoid
Kekulé and the open-shell singlet biradical resonance structures
or the topology of the π-electron arrangement of the non-Kekulé
form. High-level ab initio calculations based on multireference theory
have been carried out to compute singlet–triplet splitting
for the above-listed compounds and to provide insight into their chemical
reactivity based on the polyradical character by means of unpaired
densities. Unrestricted density functional theory and Hartree–Fock
calculations have been performed for comparison also in order to obtain
better insight into their applicability to these types of complicated
radical systems.
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Affiliation(s)
- Anita Das
- Department of Chemistry and Biochemistry, Texas Tech University , Lubbock 79409, Texas United States
| | - Thomas Müller
- Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich , 52425 Jülich, Germany
| | - Felix Plasser
- Institute for Theoretical Chemistry, University of Vienna , A-1090 Vienna, Austria
| | - Hans Lischka
- Department of Chemistry and Biochemistry, Texas Tech University , Lubbock 79409, Texas United States.,Institute for Theoretical Chemistry, University of Vienna , A-1090 Vienna, Austria.,School of Pharmaceutical Sciences and Technology, Tianjin University , Tianjin, 300072 P.R. China
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Li C, Evangelista FA. Multireference Driven Similarity Renormalization Group: A Second-Order Perturbative Analysis. J Chem Theory Comput 2015; 11:2097-108. [DOI: 10.1021/acs.jctc.5b00134] [Citation(s) in RCA: 64] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Chenyang Li
- Department
of Chemistry and Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States
| | - Francesco A. Evangelista
- Department
of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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20
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Horn S, Lischka H. A comparison of neutral and charged species of one- and two-dimensional models of graphene nanoribbons using multireference theory. J Chem Phys 2015; 142:054302. [DOI: 10.1063/1.4906540] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Affiliation(s)
- Shawn Horn
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, USA
| | - Hans Lischka
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, USA
- Institute for Theoretical Chemistry, University of Vienna, Waehringerstrasse 17, 1090 Vienna, Austria
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21
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Perera A, Molt RW, Lotrich VF, Bartlett RJ. Singlet–triplet separations of di-radicals treated by the DEA/DIP-EOM-CCSD methods. Theor Chem Acc 2014. [DOI: 10.1007/s00214-014-1514-5] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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22
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Horn S, Plasser F, Müller T, Libisch F, Burgdörfer J, Lischka H. A comparison of singlet and triplet states for one- and two-dimensional graphene nanoribbons using multireference theory. Theor Chem Acc 2014. [DOI: 10.1007/s00214-014-1511-8] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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23
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Ramos-Cordoba E, Salvador P. Diradical character from the local spin analysis. Phys Chem Chem Phys 2014; 16:9565-71. [DOI: 10.1039/c4cp00939h] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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24
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Malrieu JP, Caballol R, Calzado CJ, de Graaf C, Guihéry N. Magnetic interactions in molecules and highly correlated materials: physical content, analytical derivation, and rigorous extraction of magnetic Hamiltonians. Chem Rev 2013; 114:429-92. [PMID: 24102410 DOI: 10.1021/cr300500z] [Citation(s) in RCA: 282] [Impact Index Per Article: 25.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Jean Paul Malrieu
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse 3 , 118 route de Narbonne, 31062 Toulouse, France
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25
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Plasser F, Pašalić H, Gerzabek MH, Libisch F, Reiter R, Burgdörfer J, Müller T, Shepard R, Lischka H. Der Multiradikalcharakter ein- und zweidimensionaler Graphen-Nanobänder. Angew Chem Int Ed Engl 2013. [DOI: 10.1002/ange.201207671] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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26
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Plasser F, Pašalić H, Gerzabek MH, Libisch F, Reiter R, Burgdörfer J, Müller T, Shepard R, Lischka H. The multiradical character of one- and two-dimensional graphene nanoribbons. Angew Chem Int Ed Engl 2013; 52:2581-4. [PMID: 23355507 PMCID: PMC3648980 DOI: 10.1002/anie.201207671] [Citation(s) in RCA: 167] [Impact Index Per Article: 15.2] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2012] [Revised: 11/14/2012] [Indexed: 11/26/2022]
Affiliation(s)
- Felix Plasser
- Institute for Theoretical Chemistry, University of Vienna, Waehringerstrasse 17, 1090 Vienna, Austria
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27
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Köhn A, Hanauer M, Mück LA, Jagau TC, Gauss J. State-specific multireference coupled-cluster theory. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2012. [DOI: 10.1002/wcms.1120] [Citation(s) in RCA: 83] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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28
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Jagau TC, Gauss J. Linear-response theory for Mukherjee's multireference coupled-cluster method: Excitation energies. J Chem Phys 2012; 137:044116. [DOI: 10.1063/1.4734309] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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29
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Jagau TC, Gauss J. Linear-response theory for Mukherjee's multireference coupled-cluster method: Static and dynamic polarizabilities. J Chem Phys 2012; 137:044115. [DOI: 10.1063/1.4734308] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Malrieu JP, Trinquier G. A Recipe for Geometry Optimization of Diradicalar Singlet States from Broken-Symmetry Calculations. J Phys Chem A 2012; 116:8226-37. [DOI: 10.1021/jp303825x] [Citation(s) in RCA: 57] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jean-Paul Malrieu
- Laboratoire de Chimie et Physique
Quantiques (CNRS-UMR5626),
IRSAMC, Université Paul-Sabatier (Toulouse III), 31062 Toulouse Cedex, France
| | - Georges Trinquier
- Laboratoire de Chimie et Physique
Quantiques (CNRS-UMR5626),
IRSAMC, Université Paul-Sabatier (Toulouse III), 31062 Toulouse Cedex, France
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31
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Ylijoki KEO, Lavy S, Fretzen A, Kündig EP, Berclaz T, Bernardinelli G, Besnard C. A Synthetic and Mechanistic Investigation of the Chromium Tricarbonyl-Mediated Masamune–Bergman Cyclization. Direct Observation of a Ground-State Triplet p-Benzyne Biradical. Organometallics 2012. [DOI: 10.1021/om300427j] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Kai E. O. Ylijoki
- Department of Organic Chemistry, University of Geneva, 30 Quai E. Ansermet, CH-1211
Geneva 4, Switzerland
| | - Séverine Lavy
- Department of Organic Chemistry, University of Geneva, 30 Quai E. Ansermet, CH-1211
Geneva 4, Switzerland
| | - Angelika Fretzen
- Department of Organic Chemistry, University of Geneva, 30 Quai E. Ansermet, CH-1211
Geneva 4, Switzerland
| | - E. Peter Kündig
- Department of Organic Chemistry, University of Geneva, 30 Quai E. Ansermet, CH-1211
Geneva 4, Switzerland
| | - Théo Berclaz
- Department
of Physical Chemistry, University of Geneva, 30 Quai E. Ansermet, CH-1211 Geneva 4, Switzerland
| | - Gérald Bernardinelli
- Laboratory
of X-ray Crystallography, University of Geneva, 24 Quai E. Ansermet, CH-1211 Geneva 4, Switzerland
| | - Céline Besnard
- Laboratory
of X-ray Crystallography, University of Geneva, 24 Quai E. Ansermet, CH-1211 Geneva 4, Switzerland
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32
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Jagau TC, Gauss J. Ground and excited state geometries via Mukherjee’s multireference coupled-cluster method. Chem Phys 2012. [DOI: 10.1016/j.chemphys.2011.10.016] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
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33
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Hanauer M, Köhn A. Perturbative treatment of triple excitations in internally contracted multireference coupled cluster theory. J Chem Phys 2012; 136:204107. [DOI: 10.1063/1.4718700] [Citation(s) in RCA: 74] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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34
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Krisiloff DB, Carter EA. Approximately size extensive local multireference singles and doubles configuration interaction. Phys Chem Chem Phys 2012; 14:7710-7. [DOI: 10.1039/c2cp23757a] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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35
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Szalay PG, Müller T, Gidofalvi G, Lischka H, Shepard R. Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications. Chem Rev 2011; 112:108-81. [DOI: 10.1021/cr200137a] [Citation(s) in RCA: 470] [Impact Index Per Article: 36.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Péter G. Szalay
- Laboratory for Theoretical Chemistry, Institute of Chemistry, Eötvös Loránd University, P. O. Box 32, H-1518 Budapest, Hungary
| | - Thomas Müller
- Jülich Supercomputer Centre, Institute of Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Gergely Gidofalvi
- Department of Chemistry and Biochemistry, Gonzaga University, 502 East Boone Avenue, Spokane, Washington 99258-0102, United States
| | - Hans Lischka
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States
- Institute for Theoretical Chemistry, University of Vienna, Waehringerstrasse 17, A-1090 Vienna, Austria
| | - Ron Shepard
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
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36
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Lischka H, Müller T, Szalay PG, Shavitt I, Pitzer RM, Shepard R. Columbus—a program system for advanced multireference theory calculations. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2011. [DOI: 10.1002/wcms.25] [Citation(s) in RCA: 134] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Hans Lischka
- Institute for Theoretical Chemistry, University of Vienna, Vienna, Austria
| | - Thomas Müller
- Institute of Advanced Simulation, Jülich Supercomputer Centre, Jülich, Germany
| | - Péter G. Szalay
- Laboratory for Theoretical Chemistry, Institute of Chemistry, Eötvös Loránd University, Budapest, Hungary
| | - Isaiah Shavitt
- Department of Chemistry, University of Illinois, Urbana, IL, USA
| | - Russell M. Pitzer
- Department of Chemistry, The Ohio State University, Columbus, OH, USA
| | - Ron Shepard
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, IL, USA
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37
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Li X, Paldus J. Multireference general-model-space state-universal and state-specific coupled-cluster approaches to excited states. J Chem Phys 2010; 133:184106. [DOI: 10.1063/1.3494538] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
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38
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Jagau TC, Prochnow E, Evangelista FA, Gauss J. Analytic gradients for Mukherjee’s multireference coupled-cluster method using two-configurational self-consistent-field orbitals. J Chem Phys 2010; 132:144110. [DOI: 10.1063/1.3370847] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Evangelista FA, Prochnow E, Gauss J, Schaefer HF. Perturbative triples corrections in state-specific multireference coupled cluster theory. J Chem Phys 2010; 132:074107. [DOI: 10.1063/1.3305335] [Citation(s) in RCA: 94] [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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40
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Prochnow E, Evangelista FA, Schaefer HF, Allen WD, Gauss J. Analytic gradients for the state-specific multireference coupled cluster singles and doubles model. J Chem Phys 2009; 131:064109. [DOI: 10.1063/1.3204017] [Citation(s) in RCA: 68] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
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41
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