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Poirier N, Kottmann JS, Aspuru-Guzik A, Mongeau L, Najafi-Yazdi A. Range-separated density functional theory using multiresolution analysis and quantum computing. J Comput Chem 2024; 45:1987-2000. [PMID: 38709143 DOI: 10.1002/jcc.27384] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2024] [Revised: 04/03/2024] [Accepted: 04/18/2024] [Indexed: 05/07/2024]
Abstract
Quantum computers are expected to outperform classical computers for specific problems in quantum chemistry. Such calculations remain expensive, but costs can be lowered through the partition of the molecular system. In the present study, partition was achieved with range-separated density functional theory (RS-DFT). The use of RS-DFT reduces both the basis set size and the active space size dependence of the ground state energy in comparison with the use of wave function theory (WFT) alone. The utilization of pair natural orbitals (PNOs) in place of canonical molecular orbitals (MOs) results in more compact qubit Hamiltonians. To test this strategy, a basis-set independent framework, known as multiresolution analysis (MRA), was employed to generate PNOs. Tests were conducted with the variational quantum eigensolver for a number of molecules. The results show that the proposed approach reduces the number of qubits needed to reach a target energy accuracy.
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Affiliation(s)
- Nicolas Poirier
- Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada
- Anyon Systems Inc., Dorval, Quebec, Canada
| | - Jakob S Kottmann
- Institute for Computer Science, University of Augsburg, Augsburg, Germany
| | - Alán Aspuru-Guzik
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario, Canada
- Department of Computer Science, University of Toronto, Toronto, Ontario, Canada
- Vector Institute for Artificial Intelligence, Toronto, Ontario, Canada
- Canadian Institute for Advanced Research (CIFAR), Toronto, Ontario, Canada
| | - Luc Mongeau
- Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada
| | - Alireza Najafi-Yazdi
- Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada
- Anyon Systems Inc., Dorval, Quebec, Canada
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2
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Drwal D, Pernal K, Pastorczak E. Multireference Correlated Oscillator Strengths from Adiabatic Connection Approaches Based on Extended Random Phase Approximation. J Chem Theory Comput 2024; 20:3659-3668. [PMID: 38669448 PMCID: PMC11099974 DOI: 10.1021/acs.jctc.4c00103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2024] [Revised: 03/23/2024] [Accepted: 04/05/2024] [Indexed: 04/28/2024]
Abstract
We show that accurate oscillator strengths can be obtained from adiabatic connection (AC) approaches based on the extended random phase approximation (ERPA) combined with multireference (complete active space, CAS) wave functions. The oscillator strengths calculated using the perturbation-corrected ERPA transition density matrices, proposed in this work, and the excitation energies calculated with recently introduced AC correlation energy methods, AC0 and AC0D, compete with accuracy in the perturbational CASPT2 approach and require less computational effort. AC0 and AC0D methods scale more favorably with the number of active orbitals than multiconfigurational perturbation approaches like CASPT2 and NEVPT2 thanks to their dependence on reduced density matrices up to the order of 2. Importantly, the newly developed approach for computing correlated transition dipole moments does not entail any additional costs, as all intermediate quantities become available when AC0 energies are being computed. We also test the performance of the recently proposed AC method corrected for the negative-transition contributions to the correlation energy, AC0D, for triplet excitation energies. Similarly, as for the singlet excitations, the correction improves the performance of the AC0 method, particularly for the low-lying excited states.
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Affiliation(s)
- Daria Drwal
- Institute of Physics, Lodz
University of Technology, ul. Wolczanska 217/221, 93-005 Lodz, Poland
| | - Katarzyna Pernal
- Institute of Physics, Lodz
University of Technology, ul. Wolczanska 217/221, 93-005 Lodz, Poland
| | - Ewa Pastorczak
- Institute of Physics, Lodz
University of Technology, ul. Wolczanska 217/221, 93-005 Lodz, Poland
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3
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Cheng Y, Ma H. Renormalized-Residue-Based Multireference Configuration Interaction Method for Strongly Correlated Systems. J Chem Theory Comput 2024; 20:1988-2009. [PMID: 38380619 DOI: 10.1021/acs.jctc.3c01247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/22/2024]
Abstract
The implementation of multireference configuration interaction (MRCI) methods in quantum systems with large active spaces is hindered by the expansion of configuration bases or the intricate handling of reduced density matrices (RDMs). In this work, we present a spin-adapted renormalized-residue-based MRCI (RR-MRCI) approach that leverages renormalized residues to effectively capture the entanglement between active and inactive orbitals. This approach is reinforced by a novel efficient algorithm, which also facilitates an efficient deployment of spin-adapted matrix product state MRCI (MPS-MRCI). The RR-MRCI framework possesses several advantages: (1) It considers the orbital entanglement and utilizes highly compressed MPS structure, improving computational accuracy and efficiency compared with internally contracted (ic) MRCI. (2) Utilizing small-sized buffer environments of a few external orbitals as probes based on quantum information theory, it enhances computational efficiency over MPS-MRCI and offers potential application to large molecular systems. (3) The RR framework can be implemented in conjunction with ic-MRCI, eliminating the need for high-rank RDMs, by using distinct renormalized residues. We evaluated this method across nine diverse molecular systems, including Cu2O22+ with an active space of (24e,24o) and two complexes of lanthanide and actinide with active space (38e,36o), demonstrating the method's versatility and efficacy.
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Affiliation(s)
- Yifan Cheng
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210023, China
| | - Haibo Ma
- Qingdao Institute for Theoretical and Computational Sciences, School of Chemistry and Chemical Engineering, Shandong University, Qingdao, Shandong 266237, China
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4
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Teale AM, Helgaker T, Savin A, Adamo C, Aradi B, Arbuznikov AV, Ayers PW, Baerends EJ, Barone V, Calaminici P, Cancès E, Carter EA, Chattaraj PK, Chermette H, Ciofini I, Crawford TD, De Proft F, Dobson JF, Draxl C, Frauenheim T, Fromager E, Fuentealba P, Gagliardi L, Galli G, Gao J, Geerlings P, Gidopoulos N, Gill PMW, Gori-Giorgi P, Görling A, Gould T, Grimme S, Gritsenko O, Jensen HJA, Johnson ER, Jones RO, Kaupp M, Köster AM, Kronik L, Krylov AI, Kvaal S, Laestadius A, Levy M, Lewin M, Liu S, Loos PF, Maitra NT, Neese F, Perdew JP, Pernal K, Pernot P, Piecuch P, Rebolini E, Reining L, Romaniello P, Ruzsinszky A, Salahub DR, Scheffler M, Schwerdtfeger P, Staroverov VN, Sun J, Tellgren E, Tozer DJ, Trickey SB, Ullrich CA, Vela A, Vignale G, Wesolowski TA, Xu X, Yang W. DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science. Phys Chem Chem Phys 2022; 24:28700-28781. [PMID: 36269074 PMCID: PMC9728646 DOI: 10.1039/d2cp02827a] [Citation(s) in RCA: 62] [Impact Index Per Article: 31.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2022] [Accepted: 08/09/2022] [Indexed: 12/13/2022]
Abstract
In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.
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Affiliation(s)
- Andrew M. Teale
- School of Chemistry, University of Nottingham, University ParkNottinghamNG7 2RDUK
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - Andreas Savin
- Laboratoire de Chimie Théorique, CNRS and Sorbonne University, 4 Place Jussieu, CEDEX 05, 75252 Paris, France.
| | - Carlo Adamo
- PSL University, CNRS, ChimieParisTech-PSL, Institute of Chemistry for Health and Life Sciences, i-CLeHS, 11 rue P. et M. Curie, 75005 Paris, France.
| | - Bálint Aradi
- Bremen Center for Computational Materials Science, University of Bremen, P.O. Box 330440, D-28334 Bremen, Germany.
| | - Alexei V. Arbuznikov
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7Straße des 17. Juni 13510623Berlin
| | | | - Evert Jan Baerends
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
| | - Vincenzo Barone
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56125 Pisa, Italy.
| | - Patrizia Calaminici
- Departamento de Química, Centro de Investigación y de Estudios Avanzados (Cinvestav), CDMX, 07360, Mexico.
| | - Eric Cancès
- CERMICS, Ecole des Ponts and Inria Paris, 6 Avenue Blaise Pascal, 77455 Marne-la-Vallée, France.
| | - Emily A. Carter
- Department of Mechanical and Aerospace Engineering and the Andlinger Center for Energy and the Environment, Princeton UniversityPrincetonNJ 08544-5263USA
| | | | - Henry Chermette
- Institut Sciences Analytiques, Université Claude Bernard Lyon1, CNRS UMR 5280, 69622 Villeurbanne, France.
| | - Ilaria Ciofini
- PSL University, CNRS, ChimieParisTech-PSL, Institute of Chemistry for Health and Life Sciences, i-CLeHS, 11 rue P. et M. Curie, 75005 Paris, France.
| | - T. Daniel Crawford
- Department of Chemistry, Virginia TechBlacksburgVA 24061USA,Molecular Sciences Software InstituteBlacksburgVA 24060USA
| | - Frank De Proft
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium.
| | | | - Claudia Draxl
- Institut für Physik and IRIS Adlershof, Humboldt-Universität zu Berlin, 12489 Berlin, Germany. .,Fritz-Haber-Institut der Max-Planck-Gesellschaft, 14195 Berlin, Germany
| | - Thomas Frauenheim
- Bremen Center for Computational Materials Science, University of Bremen, P.O. Box 330440, D-28334 Bremen, Germany. .,Beijing Computational Science Research Center (CSRC), 100193 Beijing, China.,Shenzhen JL Computational Science and Applied Research Institute, 518110 Shenzhen, China
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 rue Blaise Pascal, 67000 Strasbourg, France.
| | - Patricio Fuentealba
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile.
| | - Laura Gagliardi
- Department of Chemistry, Pritzker School of Molecular Engineering, The James Franck Institute, and Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, USA.
| | - Giulia Galli
- Pritzker School of Molecular Engineering and Department of Chemistry, The University of Chicago, Chicago, IL, USA.
| | - Jiali Gao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China. .,Department of Chemistry, University of Minnesota, Minneapolis, MN 55455, USA
| | - Paul Geerlings
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium.
| | - Nikitas Gidopoulos
- Department of Physics, Durham University, South Road, Durham DH1 3LE, UK.
| | - Peter M. W. Gill
- School of Chemistry, University of SydneyCamperdown NSW 2006Australia
| | - Paola Gori-Giorgi
- Department of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
| | - Andreas Görling
- Chair of Theoretical Chemistry, University of Erlangen-Nuremberg, Egerlandstrasse 3, 91058 Erlangen, Germany.
| | - Tim Gould
- Qld Micro- and Nanotechnology Centre, Griffith University, Gold Coast, Qld 4222, Australia.
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, University of Bonn, Beringstrasse 4, 53115 Bonn, Germany.
| | - Oleg Gritsenko
- Department of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
| | - Hans Jørgen Aagaard Jensen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark.
| | - Erin R. Johnson
- Department of Chemistry, Dalhousie UniversityHalifaxNova ScotiaB3H 4R2Canada
| | - Robert O. Jones
- Peter Grünberg Institut PGI-1, Forschungszentrum Jülich52425 JülichGermany
| | - Martin Kaupp
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, 10623, Berlin.
| | - Andreas M. Köster
- Departamento de Química, Centro de Investigación y de Estudios Avanzados (Cinvestav)CDMX07360Mexico
| | - Leeor Kronik
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth, 76100, Israel.
| | - Anna I. Krylov
- Department of Chemistry, University of Southern CaliforniaLos AngelesCalifornia 90089USA
| | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - Andre Laestadius
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - Mel Levy
- Department of Chemistry, Tulane University, New Orleans, Louisiana, 70118, USA.
| | - Mathieu Lewin
- CNRS & CEREMADE, Université Paris-Dauphine, PSL Research University, Place de Lattre de Tassigny, 75016 Paris, France.
| | - Shubin Liu
- Research Computing Center, University of North Carolina, Chapel Hill, NC 27599-3420, USA. .,Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599-3290, USA
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, France.
| | - Neepa T. Maitra
- Department of Physics, Rutgers University at Newark101 Warren StreetNewarkNJ 07102USA
| | - Frank Neese
- Max Planck Institut für Kohlenforschung, Kaiser Wilhelm Platz 1, D-45470 Mülheim an der Ruhr, Germany.
| | - John P. Perdew
- Departments of Physics and Chemistry, Temple UniversityPhiladelphiaPA 19122USA
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland.
| | - Pascal Pernot
- Institut de Chimie Physique, UMR8000, CNRS and Université Paris-Saclay, Bât. 349, Campus d'Orsay, 91405 Orsay, France.
| | - Piotr Piecuch
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA. .,Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - Elisa Rebolini
- Institut Laue Langevin, 71 avenue des Martyrs, 38000 Grenoble, France.
| | - Lucia Reining
- Laboratoire des Solides Irradiés, CNRS, CEA/DRF/IRAMIS, École Polytechnique, Institut Polytechnique de Paris, F-91120 Palaiseau, France. .,European Theoretical Spectroscopy Facility
| | - Pina Romaniello
- Laboratoire de Physique Théorique (UMR 5152), Université de Toulouse, CNRS, UPS, France.
| | - Adrienn Ruzsinszky
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA.
| | - Dennis R. Salahub
- Department of Chemistry, Department of Physics and Astronomy, CMS – Centre for Molecular Simulation, IQST – Institute for Quantum Science and Technology, Quantum Alberta, University of Calgary2500 University Drive NWCalgaryAlbertaT2N 1N4Canada
| | - Matthias Scheffler
- The NOMAD Laboratory at the FHI of the Max-Planck-Gesellschaft and IRIS-Adlershof of the Humboldt-Universität zu Berlin, Faradayweg 4-6, D-14195, Germany.
| | - Peter Schwerdtfeger
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, 0632 Auckland, New Zealand.
| | - Viktor N. Staroverov
- Department of Chemistry, The University of Western OntarioLondonOntario N6A 5B7Canada
| | - Jianwei Sun
- Department of Physics and Engineering Physics, Tulane University, New Orleans, LA 70118, USA.
| | - Erik Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - David J. Tozer
- Department of Chemistry, Durham UniversitySouth RoadDurhamDH1 3LEUK
| | - Samuel B. Trickey
- Quantum Theory Project, Deptartment of Physics, University of FloridaGainesvilleFL 32611USA
| | - Carsten A. Ullrich
- Department of Physics and Astronomy, University of MissouriColumbiaMO 65211USA
| | - Alberto Vela
- Departamento de Química, Centro de Investigación y de Estudios Avanzados (Cinvestav), CDMX, 07360, Mexico.
| | - Giovanni Vignale
- Department of Physics, University of Missouri, Columbia, MO 65203, USA.
| | - Tomasz A. Wesolowski
- Department of Physical Chemistry, Université de Genève30 Quai Ernest-Ansermet1211 GenèveSwitzerland
| | - Xin Xu
- Shanghai Key Laboratory of Molecular Catalysis and Innovation Materials, Collaborative Innovation Centre of Chemistry for Energy Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China.
| | - Weitao Yang
- Department of Chemistry and Physics, Duke University, Durham, NC 27516, USA.
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5
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Jangrouei MR, Krzemińska A, Hapka M, Pastorczak E, Pernal K. Dispersion Interactions in Exciton-Localized States. Theory and Applications to π-π* and n-π* Excited States. J Chem Theory Comput 2022; 18:3497-3511. [PMID: 35587598 PMCID: PMC9202351 DOI: 10.1021/acs.jctc.2c00221] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
We address the problem
of intermolecular interaction energy calculations
in molecular complexes with localized excitons. Our focus is on the
correct representation of the dispersion energy. We derive an extended
Casimir-Polder formula for direct computation of this contribution
through second order in the intermolecular interaction operator V̂. An alternative formula, accurate to infinite order
in V̂, is derived within the framework of the
adiabatic connection (AC) theory. We also propose a new parametrization
of the VV10 nonlocal correlation density functional, so that it corrects
the CASSCF energy for the dispersion contribution and can be applied
to excited-state complexes. A numerical investigation is carried out
for benzene, pyridine, and peptide complexes with the local exciton
corresponding to the lowest π–π* or n– π*
states. The extended Casimir-Polder formula is implemented in the
framework of multiconfigurational symmetry-adapted perturbation theory,
SAPT(MC). A SAPT(MC) analysis shows that the creation of a localized
exciton affects mostly the electrostatic component of the interaction
energy of investigated complexes. Nevertheless, the changes in Pauli
repulsion and dispersion energies cannot be neglected. We verify the
performance of several perturbation- and AC-based methods. Best results
are obtained with a range-separated variant of an approximate AC approach
employing extended random phase approximation and CASSCF wave functions.
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Affiliation(s)
- Mohammad Reza Jangrouei
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 217/221, 93-005, Lodz, Poland
| | - Agnieszka Krzemińska
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 217/221, 93-005, Lodz, Poland
| | - Michał Hapka
- Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093, Warsaw, Poland
| | - Ewa Pastorczak
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 217/221, 93-005, Lodz, Poland
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 217/221, 93-005, Lodz, Poland
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6
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Cheng Y, Xie Z, Ma H. Post-Density Matrix Renormalization Group Methods for Describing Dynamic Electron Correlation with Large Active Spaces. J Phys Chem Lett 2022; 13:904-915. [PMID: 35049302 DOI: 10.1021/acs.jpclett.1c04078] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The ab initio density matrix renormalization group (DMRG) method has been well-established and has become one of the most accurate numerical methods for the precise electronic structure solution of large active spaces. In the past few years, to capture the missing dynamic correlation, various post-DMRG approaches have been proposed through the combination of DMRG and multireference quantum chemical methods or density functional theory. With this in mind, this work provides a brief overview of ab initio DMRG principles and the new developments within post-DMRG methods. For clarity, post-DMRG methods are classified into two main categories depending on whether high-order n-electron reduced density matrices are used, and their merits and disadvantages are properly discussed. Finally, we conclude by discussing unsolved bottlenecks and giving development perspectives of post-DMRG approaches, which are expected to yield quantitative descriptions of complex electronic structures in large strongly correlated molecules and materials.
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Affiliation(s)
- Yifan Cheng
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
| | - Zhaoxuan Xie
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
| | - Haibo Ma
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
- Chemistry and Biomedicine Innovation Center (ChemBIC), Nanjing University, Nanjing 210023, China
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7
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Zhou C, Hermes MR, Wu D, Bao JJ, Pandharkar R, King DS, Zhang D, Scott TR, Lykhin AO, Gagliardi L, Truhlar DG. Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory. Chem Sci 2022; 13:7685-7706. [PMID: 35865899 PMCID: PMC9261488 DOI: 10.1039/d2sc01022d] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Accepted: 06/01/2022] [Indexed: 12/25/2022] Open
Abstract
Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals. This feature article overviews recent work on active spaces, matrix product reference states, treatment of quasidegeneracy, hybrid theory, density-coherence functionals, machine-learned functionals, spin–orbit coupling, gradients, and dipole moments.![]()
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Affiliation(s)
- Chen Zhou
- Department of Chemistry, Chemical Theory Center, Minnesota Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, MN 55455-0431, USA
| | - Matthew R. Hermes
- Department of Chemistry, Pritzker School of Molecular Engineering, The James Franck Institute and Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, IL 60637, USA
| | - Dihua Wu
- Department of Chemistry, Chemical Theory Center, Minnesota Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, MN 55455-0431, USA
| | - Jie J. Bao
- Department of Chemistry, Chemical Theory Center, Minnesota Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, MN 55455-0431, USA
| | - Riddhish Pandharkar
- Department of Chemistry, Pritzker School of Molecular Engineering, The James Franck Institute and Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, IL 60637, USA
- Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Daniel S. King
- Department of Chemistry, Pritzker School of Molecular Engineering, The James Franck Institute and Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, IL 60637, USA
| | - Dayou Zhang
- Department of Chemistry, Chemical Theory Center, Minnesota Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, MN 55455-0431, USA
| | - Thais R. Scott
- Department of Chemistry, Pritzker School of Molecular Engineering, The James Franck Institute and Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, IL 60637, USA
| | - Aleksandr O. Lykhin
- Department of Chemistry, Pritzker School of Molecular Engineering, The James Franck Institute and Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, IL 60637, USA
| | - Laura Gagliardi
- Department of Chemistry, Pritzker School of Molecular Engineering, The James Franck Institute and Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, IL 60637, USA
- Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Donald G. Truhlar
- Department of Chemistry, Chemical Theory Center, Minnesota Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, MN 55455-0431, USA
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8
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Beran P, Matoušek M, Hapka M, Pernal K, Veis L. Density Matrix Renormalization Group with Dynamical Correlation via Adiabatic Connection. J Chem Theory Comput 2021; 17:7575-7585. [PMID: 34762423 DOI: 10.1021/acs.jctc.1c00896] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as one of the methods of choice for calculations of strongly correlated molecular systems. Despite its great ability to capture strong electronic correlation in large active spaces, it is not suitable for computations of dynamical electron correlation. In this work, we present a new approach to the electronic structure problem of strongly correlated molecules, in which DMRG is responsible for a proper description of the strong correlation, whereas dynamical correlation is computed via the recently developed adiabatic connection (AC) technique which requires only up to two-body active space reduced density matrices. We report the encouraging results of this approach on typical candidates for DMRG computations, namely, n-acenes (n = 2 → 7), Fe(II)-porphyrin, and the Fe3S4 cluster.
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Affiliation(s)
- Pavel Beran
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic.,Faculty of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic
| | - Mikuláš Matoušek
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic.,Faculty of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic
| | - Michał Hapka
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland.,Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
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9
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Hapka M, Przybytek M, Pernal K. Symmetry-Adapted Perturbation Theory Based on Multiconfigurational Wave Function Description of Monomers. J Chem Theory Comput 2021; 17:5538-5555. [PMID: 34517707 PMCID: PMC8444344 DOI: 10.1021/acs.jctc.1c00344] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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We present a formulation
of the multiconfigurational (MC) wave
function symmetry-adapted perturbation theory (SAPT). The method is
applicable to noncovalent interactions between monomers which require
a multiconfigurational description, in particular when the interacting
system is strongly correlated or in an electronically excited state.
SAPT(MC) is based on one- and two-particle reduced density matrices
of the monomers and assumes the single-exchange approximation for
the exchange energy contributions. Second-order terms are expressed
through response properties from extended random phase approximation
(ERPA). The dispersion components of SAPT(MC) have been introduced
in our previous works [HapkaM.J. Chem. Theory Comput.2019, 15, 1016−102730525591; HapkaM.J. Chem. Theory Comput.2019, 15, 6712–672331670950]. SAPT(MC) is applied either with generalized valence
bond perfect pairing (GVB) or with complete active space self-consistent
field (CASSCF) treatment of the monomers. We discuss two model multireference
systems: the H2 ··· H2 dimer
in out-of-equilibrium geometries and interaction between the argon
atom and excited state of ethylene. Using the C2H4* ··· Ar complex as an example, we examine second-order
terms arising from negative transitions in the linear response function
of an excited monomer. We demonstrate that the negative-transition
terms must be accounted for to ensure qualitative prediction of induction
and dispersion energies and develop a procedure allowing for their
computation. Factors limiting the accuracy of SAPT(MC) are discussed
in comparison with other second-order SAPT schemes on a data set of
small single-reference dimers.
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Affiliation(s)
- Michał Hapka
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland.,Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
| | - Michał Przybytek
- Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
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10
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Pernal K, Hapka M. Range‐separated multiconfigurational density functional theory methods. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2021. [DOI: 10.1002/wcms.1566] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
| | - Michał Hapka
- Lodz University of Technology Institute of Physics Lodz Poland
- Faculty of Chemistry University of Warsaw Warsaw Poland
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11
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Drwal D, Pastorczak E, Pernal K. Excited states in the adiabatic connection fluctuation-dissipation theory: Recovering missing correlation energy from the negative part of the density response spectrum. J Chem Phys 2021; 154:164102. [PMID: 33940850 DOI: 10.1063/5.0046852] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
The adiabatic connection (AC) theory offers an alternative to the perturbation theory methods for computing correlation energy in the multireference wavefunction framework. We show that the AC correlation energy formula can be expressed in terms of the density linear response function as a sum of components related to positive and negative parts of the transition energy spectrum. Consequently, generalization of the adiabatic connection fluctuation-dissipation theory to electronically excited states is obtained. The component of the linear response function related to the negative-transition energy enters the correlation energy expression with an opposite sign to that of the positive-transition part and is non-negligible in the description of excited states. To illustrate this, we analyze the approximate AC model in which the linear response function is obtained in the extended random phase approximation (ERPA). We demonstrate that AC can be successfully combined with the ERPA for excited states, provided that the negative-excitation component of the response function is rigorously accounted for. The resulting AC0D model, an extension of the AC0 scheme introduced in our earlier works, is applied to a benchmark set of singlet excitation energies of organic molecules. AC0D constitutes a significant improvement over AC0 by bringing the excitation energies of the lowest excited states to a satisfactory agreement with theoretical best estimates, which parallels or even exceeds the accuracy of the n-electron valence state perturbation theory method. For higher excitations, AC0D is less reliable due to the gradual deterioration of the underlying ERPA linear response.
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Affiliation(s)
- Daria Drwal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Ewa Pastorczak
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
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12
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Abstract
Applications of density-functional theory (DFT) in computational chemistry rely on an approximate exchange-correlation (xc) functional. However, existing approximations can fail dramatically for open-shell molecules, in particular for transition-metal complexes or radicals. Most importantly, predicting energy differences between different spin-states with approximate exchange-correlation functionals remains extremely challenging. Formally, it is known that the exact xc functional should be spin-state dependent, but none of the available approximations feature such an explicit spin-state dependence [C. R. Jacob and M. Reiher, Int. J. Quantum Chem., 2012, 112, 3661-3684]. Thus, to find novel approximations for the xc functional for open-shell systems, the development of spin-state dependent xc functionals appears to be a promising avenue. Here, we set out to shed light on the spin-state dependence of the xc functional by investigating the underlying xc holes, which we extract from configuration interaction calculations for model systems. We analyze the similarities and differences between the xc holes of the lowest-energy singlet and triplet states of the dihydrogen molecule, the helium atom, and the lithium dimer. To shed further light on the spin-state dependence of these xc holes we also discuss exact conditions that can be derived from the spin structure of the reduced two-electron density matrix. Altogether, our results suggest several possible routes towards the construction of explicitly spin-state dependent approximations for the xc functional.
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Affiliation(s)
- Julia Brüggemann
- Technische Universität Braunschweig, Institute of Physical and Theoretical Chemistry, Gaußstraße 17, 38106 Braunschweig, Germany.
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13
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Fabrizio A, Briling KR, Girardier DD, Corminboeuf C. Learning on-top: Regressing the on-top pair density for real-space visualization of electron correlation. J Chem Phys 2020; 153:204111. [DOI: 10.1063/5.0033326] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Affiliation(s)
- Alberto Fabrizio
- Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Ksenia R. Briling
- Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - David D. Girardier
- Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Clemence Corminboeuf
- Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
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14
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Hapka M, Krzemińska A, Pernal K. How Much Dispersion Energy Is Included in the Multiconfigurational Interaction Energy? J Chem Theory Comput 2020; 16:6280-6293. [PMID: 32877179 PMCID: PMC7586340 DOI: 10.1021/acs.jctc.0c00681] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Indexed: 11/30/2022]
Abstract
We demonstrate how to quantify the amount of dispersion interaction recovered by supermolecular calculations with the multiconfigurational self-consistent field (MCSCF) wave functions. For this purpose, we present a rigorous derivation which connects the portion of dispersion interaction captured by the assumed wave function model-the residual dispersion interaction-with the size of the active space. Based on the obtained expression for the residual dispersion contribution, we propose a dispersion correction for the MCSCF that avoids correlation double counting. Numerical demonstration for model four-electron dimers in both ground and excited states described with the complete active space self-consistent field (CASSCF) reference serves as a proof-of-concept for the method. Accurate results, largely independent of the size of the active space, are obtained. For many-electron systems, routine CASSCF interaction energy calculations recover a tiny fraction of the full second-order dispersion energy. We found that the residual dispersion is non-negligible only for purely dispersion-bound complexes.
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Affiliation(s)
- Michał Hapka
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
- Faculty
of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
| | - Agnieszka Krzemińska
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Katarzyna Pernal
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
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15
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Hapka M, Pernal K, Gritsenko OV. Local Enhancement of Dynamic Correlation in Excited States: Fresh Perspective on Ionicity and Development of Correlation Density Functional Approximation Based on the On-Top Pair Density. J Phys Chem Lett 2020; 11:5883-5889. [PMID: 32589027 PMCID: PMC7467739 DOI: 10.1021/acs.jpclett.0c01616] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2020] [Accepted: 06/26/2020] [Indexed: 06/11/2023]
Abstract
We discuss the interplay between the nondynamic and dynamic electron correlation in excited states from the perspective of the suppression of dynamic correlation (SDC) and enhancement of dynamic correlation (EDC) effects. We reveal that there exists a connection between the ionic character of a wave function and EDC. Following this finding we introduce a quantitative measure of ionicity based solely on local functions without referring to valence bond models. The ability to recognize both the SDC and EDC regions underlies the presented method, named CASΠDFT, combining complete active space (CAS) wave function and density functional theory (DFT) via the on-top pair density (Π) function. We extend this approach to excited states by devising an improved representation of the EDC effect in the correlation functional. The generalized CASΠDFT uses different DFT functionals for ground and excited states. Numerical demonstration for singlet π → π* excitations shows that CASΠDFT offers satisfactory accuracy at a fraction of the cost of the ab initio approaches.
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Affiliation(s)
- Michał Hapka
- Institute
of Physics, Lodz University of Technology, PL-90-924 Lodz, Poland
- Faculty
of Chemistry, University of Warsaw, 02-093 Warsaw, Poland
| | - Katarzyna Pernal
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Oleg V. Gritsenko
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
- Section
Theoretical Chemistry, VU University, NL-1081 HV Amsterdam, The Netherlands
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16
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Pernal K, Gritsenko OV. Embracing local suppression and enhancement of dynamic correlation effects in a CASΠDFT method for efficient description of excited states. Faraday Discuss 2020; 224:333-347. [DOI: 10.1039/d0fd00050g] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
In this work we show that the presence of covalent and ionic configurations in a wavefunction gives rise to spatial regions where the effects of suppression and enhancement of correlation energy, respectively, dominate.
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Affiliation(s)
- Katarzyna Pernal
- Institute of Physics
- Lodz University of Technology
- PL-90-924 Lodz
- Poland
| | - Oleg V. Gritsenko
- Institute of Physics
- Lodz University of Technology
- PL-90-924 Lodz
- Poland
- Section Theoretical Chemistry
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