1
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Friesecke G, Barcza G, Legeza Ö. Predicting the FCI Energy of Large Systems to Chemical Accuracy from Restricted Active Space Density Matrix Renormalization Group Calculations. J Chem Theory Comput 2024; 20:87-102. [PMID: 38109339 DOI: 10.1021/acs.jctc.3c01001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2023]
Abstract
We theoretically derive and validate with large scale simulations a remarkably accurate power law scaling of errors for the restricted active space density matrix renormalization group (DMRG-RAS) method [J. Phys. Chem. A 126, 9709] in electronic structure calculations. This yields a new extrapolation method, DMRG-RAS-X, which reaches chemical accuracy for strongly correlated systems such as the chromium dimer, dicarbon up to a large cc-pVQZ basis and even a large chemical complex such as the FeMoco with significantly lower computational demands than those of previous methods. The method is free of empirical parameters, performed robustly and reliably in all examples we tested, and has the potential to become a vital alternative method for electronic structure calculations in quantum chemistry and more generally for the computation of strong correlations in nuclear and condensed matter physics.
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Affiliation(s)
- Gero Friesecke
- Department of Mathematics, Technical University of Munich, München 85748, Germany
| | - Gergely Barcza
- Strongly Correlated Systems Lendület Research Group, Wigner Research Centre for Physics, Budapest H-1525, Hungary
| | - Örs Legeza
- Strongly Correlated Systems Lendület Research Group, Wigner Research Centre for Physics, Budapest H-1525, Hungary
- Institute for Advanced Study, Technical University of Munich, Germany, Lichtenbergstrasse 2a, Garching 85748, Germany
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2
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Barcza G, Werner MA, Zaránd G, Pershin A, Benedek Z, Legeza Ö, Szilvási T. Toward Large-Scale Restricted Active Space Calculations Inspired by the Schmidt Decomposition. J Phys Chem A 2022; 126:9709-9718. [PMID: 36520596 DOI: 10.1021/acs.jpca.2c05952] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
We present an alternative, memory-efficient, Schmidt decomposition-based description of the inherently bipartite restricted active space (RAS) scheme, which can be implemented effortlessly within the density matrix renormalization group (DMRG) method via the dynamically extended active space procedure. Benchmark calculations are compared against state-of-the-art results of C2 and Cr2, which are notorious for their multireference character. Our results for ground and excited states together with spectroscopic constants demonstrate that the proposed novel approach, dubbed as DMRG-RAS, which is variational and free of uncontrolled method errors, has the potential to outperfom conventional methods for strongly correlated molecules.
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Affiliation(s)
- Gergely Barcza
- Wigner Research Centre for Physics, H-1525Budapest, Hungary.,Department of Physics of Complex Systems, ELTE Eötvös Loránd University, H-1117, Budapest, Hungary.,Department of Chemical and Biological Engineering, The University of Alabama, Tuscaloosa, Alabama35487, United States
| | - Miklós Antal Werner
- Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1111Budapest, Hungary.,MTA-BME Quantum Dynamics and Correlations Research Group, H-1111Budapest, Hungary
| | - Gergely Zaránd
- Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1111Budapest, Hungary.,MTA-BME Quantum Dynamics and Correlations Research Group, H-1111Budapest, Hungary
| | - Anton Pershin
- Wigner Research Centre for Physics, H-1525Budapest, Hungary
| | - Zsolt Benedek
- Wigner Research Centre for Physics, H-1525Budapest, Hungary.,Department of Chemical and Biological Engineering, The University of Alabama, Tuscaloosa, Alabama35487, United States
| | - Örs Legeza
- Wigner Research Centre for Physics, H-1525Budapest, Hungary.,Fachbereich Physik, Philipps-Universität Marburg, 35032Marburg, Germany.,Institute for Advanced Study, Technical University of Munich, Lichtenbergstrasse 2a, 85748Garching, Germany
| | - Tibor Szilvási
- Department of Chemical and Biological Engineering, The University of Alabama, Tuscaloosa, Alabama35487, United States
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3
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Barcza G, Pershin A, Gali A, Legeza Ö. Excitation spectra of fully correlated donor-acceptor complexes by density matrix renormalisation group. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2130834] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/10/2022]
Affiliation(s)
- Gergely Barcza
- Wigner Research Centre for Physics, Budapest, Hungary
- Department of Chemical and Biological Engineering, The University of Alabama, Tuscaloosa, AL, USA
| | - Anton Pershin
- Wigner Research Centre for Physics, Budapest, Hungary
- Department of Atomic Physics, Institute of Physics, Budapest University of Technology and Economics, Budapest, Hungary
| | - Adam Gali
- Wigner Research Centre for Physics, Budapest, Hungary
- Department of Atomic Physics, Institute of Physics, Budapest University of Technology and Economics, Budapest, Hungary
| | - Örs Legeza
- Wigner Research Centre for Physics, Budapest, Hungary
- Fachbereich Physik, Philipps-Universität Marburg, Marburg, Germany
- Institute for Advanced Study, Technical University of Munich, Garching, Germany
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4
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Leszczyk A, Máté M, Legeza Ö, Boguslawski K. Assessing the Accuracy of Tailored Coupled Cluster Methods Corrected by Electronic Wave Functions of Polynomial Cost. J Chem Theory Comput 2021; 18:96-117. [PMID: 34965121 DOI: 10.1021/acs.jctc.1c00284] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Tailored coupled cluster theory represents a computationally inexpensive way to describe static and dynamical electron correlation effects. In this work, we scrutinize the performance of various coupled cluster methods tailored by electronic wave functions of polynomial cost. Specifically, we focus on frozen-pair coupled cluster (fpCC) methods, which are tailored by pair-coupled cluster doubles (pCCD), and coupled cluster theory tailored by matrix product state wave functions optimized by the density matrix renormalization group (DMRG) algorithm. As test system, we selected a set of various small- and medium-sized molecules containing diatomics (N2, F2, C2, CN+, CO, BN, BO+, and Cr2) and molecules (ammonia, ethylene, cyclobutadiene, benzene, hydrogen chains, rings, and cuboids) for which the conventional single-reference coupled cluster singles and doubles (CCSD) method is not able to produce accurate results for spectroscopic constants, potential energy surfaces, and barrier heights. Most importantly, DMRG-tailored and pCCD-tailored approaches yield similar errors in spectroscopic constants and potential energy surfaces compared to accurate theoretical and/or experimental reference data. Although fpCC methods provide a reliable description for the dissociation pathway of molecules featuring single and quadruple bonds, they fail in the description of triple or hextuple bond-breaking processes or avoided crossing regions.
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Affiliation(s)
- Aleksandra Leszczyk
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, ul. Grudzia̧dzka 5, 87-100 Toruń, Poland
| | - Mihály Máté
- Strongly Correlated Systems "Lendület" Research Group, Wigner Research Center for Physics, H-1525 Budapest, Hungary.,Department of Physics of Complex Systems, Eötvös Loránd University, Pf. 32, H-1518 Budapest, Hungary
| | - Örs Legeza
- Strongly Correlated Systems "Lendület" Research Group, Wigner Research Center for Physics, H-1525 Budapest, Hungary.,Institute for Advanced Study, Technical University of Munich, 80333 Munich, Germany
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, ul. Grudzia̧dzka 5, 87-100 Toruń, Poland
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5
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Nowak A, Legeza Ö, Boguslawski K. Orbital entanglement and correlation from pCCD-tailored coupled cluster wave functions. J Chem Phys 2021; 154:084111. [DOI: 10.1063/5.0038205] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Artur Nowak
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Torun, Poland
| | - Örs Legeza
- Strongly Correlated Systems “Lendület" Research Group, Wigner Research Center for Physics, H-1525 Budapest, Hungary
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Torun, Poland
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6
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Barcza G, Ivády V, Szilvási T, Vörös M, Veis L, Gali Á, Legeza Ö. DMRG on Top of Plane-Wave Kohn-Sham Orbitals: A Case Study of Defected Boron Nitride. J Chem Theory Comput 2021; 17:1143-1154. [PMID: 33435672 DOI: 10.1021/acs.jctc.0c00809] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
In this paper, we analyze the numerical aspects of the inherent multireference density matrix renormalization group (DMRG) calculations on top of the periodic Kohn-Sham density functional theory using the complete active space approach. The potential of the framework is illustrated by studying hexagonal boron nitride nanoflakes embedding a charged single boron vacancy point defect by revealing a vertical energy spectrum with a prominent multireference character. We investigate the consistency of the DMRG energy spectrum from the perspective of sample size, basis size, and active space selection protocol. Results obtained from standard quantum chemical atom-centered basis calculations and plane-wave based counterparts show excellent agreement. Furthermore, we also discuss the spectrum of the periodic sheet which is in good agreement with extrapolated data of finite clusters. These results pave the way toward applying the DMRG method in extended correlated solid-state systems, such as point defect qubit in wide band gap semiconductors.
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Affiliation(s)
- Gergely Barcza
- Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary.,J. Heyrovský Institute of Physical Chemistry, Czech Academy of Sciences, Prague CZ-18223, Czechia
| | - Viktor Ivády
- Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary.,Department of Physics, Chemistry and Biology, Linköping University, Linköping SE-581 83, Sweden
| | - Tibor Szilvási
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States.,Department of Chemical and Biological Engineering, The University of Alabama, Tuscaloosa, Alabama 35487, United States
| | - Márton Vörös
- Material Sciences Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry, Czech Academy of Sciences, Prague CZ-18223, Czechia
| | - Ádám Gali
- Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary.,Department of Atomic Physics, Budapest University of Technology and Economics, Budapest H-1111, Hungary
| | - Örs Legeza
- Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary
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7
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Brabec J, Brandejs J, Kowalski K, Xantheas S, Legeza Ö, Veis L. Massively parallel quantum chemical density matrix renormalization group method. J Comput Chem 2020; 42:534-544. [DOI: 10.1002/jcc.26476] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2020] [Revised: 11/22/2020] [Accepted: 11/26/2020] [Indexed: 01/19/2023]
Affiliation(s)
- Jiri Brabec
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic Prague Czech Republic
| | - Jan Brandejs
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic Prague Czech Republic
- Faculty of Mathematics and Physics Charles University Prague Czech Republic
| | - Karol Kowalski
- Pacific Northwest National Laboratory Richland Washington USA
| | | | - Örs Legeza
- Strongly Correlated Systems “Lendület” Research group, Wigner Research Centre for Physics Budapest Hungary
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic Prague Czech Republic
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8
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Moca CP, Izumida W, Dóra B, Legeza Ö, Asbóth JK, Zaránd G. Topologically Protected Correlated End Spin Formation in Carbon Nanotubes. Phys Rev Lett 2020; 125:056401. [PMID: 32794861 DOI: 10.1103/physrevlett.125.056401] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2019] [Accepted: 06/04/2020] [Indexed: 06/11/2023]
Abstract
For most chiralities, semiconducting nanotubes display topologically protected end states of multiple degeneracies. We demonstrate using density matrix renormalization group based quantum chemistry tools that the presence of Coulomb interactions induces the formation of robust end spins. These are the close analogs of ferromagnetic edge states emerging in graphene nanoribbons. The interaction between the two ends is sensitive to the length of the nanotube, its dielectric constant, and the size of the end spins: for S=1/2 end spins, their interaction is antiferromagnetic, while for S>1/2, it changes from antiferromagnetic to ferromagnetic as the nanotube length increases. The interaction between end spins can be controlled by changing the dielectric constant of the environment, thereby providing a possible platform for two-spin quantum manipulations.
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Affiliation(s)
- Cătălin Paşcu Moca
- MTA-BME Quantum Dynamics and Correlations Research Group, Institute of Physics, Budapest University of Technology and Economics, Budafoki út 8., H-1111 Budapest, Hungary
- Department of Physics, University of Oradea, 410087 Oradea, Romania
| | - Wataru Izumida
- Department of Physics, Tohoku University, Sendai 980-8578, Japan
| | - Balázs Dóra
- Department of Theoretical Physics and MTA-BME Lendület Topology and Correlation Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary
| | - Örs Legeza
- Strongly Correlated Systems Lendület Research Group, Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, H-1525 Budapest, Hungary
| | - János K Asbóth
- MTA-BME Quantum Dynamics and Correlations Research Group, Institute of Physics, Budapest University of Technology and Economics, Budafoki út 8., H-1111 Budapest, Hungary
- BME-MTA Exotic Quantum Phases Lendület Research Group, Institute of Physics, Budapest University of Technology and Economics, Budafoki út 8., H-1111 Budapest, Hungary
| | - Gergely Zaránd
- MTA-BME Quantum Dynamics and Correlations Research Group, Institute of Physics, Budapest University of Technology and Economics, Budafoki út 8., H-1111 Budapest, Hungary
- BME-MTA Exotic Quantum Phases Lendület Research Group, Institute of Physics, Budapest University of Technology and Economics, Budafoki út 8., H-1111 Budapest, Hungary
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9
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Lang J, Antalík A, Veis L, Brandejs J, Brabec J, Legeza Ö, Pittner J. Near-Linear Scaling in DMRG-Based Tailored Coupled Clusters: An Implementation of DLPNO-TCCSD and DLPNO-TCCSD(T). J Chem Theory Comput 2020; 16:3028-3040. [PMID: 32275424 DOI: 10.1021/acs.jctc.0c00065] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
We present a new implementation of density matrix renormalization group based tailored coupled clusters method (TCCSD), which employs the domain-based local pair natural orbital approach (DLPNO). Compared to the previous local pair natural orbital (LPNO) version of the method, the new implementation is more accurate, offers more favorable scaling, and provides more consistent behavior across the variety of systems. On top of the singles and doubles, we include the perturbative triples correction (T), which is able to retrieve even more dynamic correlation. The methods were tested on three systems: tetramethyleneethane, oxo-Mn(Salen), and iron(II)-porphyrin model. The first two were revisited to assess the performance with respect to LPNO-TCCSD. For oxo-Mn(Salen), we retrieved between 99.8 and 99.9% of the total canonical correlation energy which is an improvement of 0.2% over the LPNO version in less than 63% of the total LPNO runtime. Similar results were obtained for iron(II)-porphyrin. When the perturbative triples correction was employed, irrespective of the active space size or system, the obtained energy differences between two spin states were within the chemical accuracy of 1 kcal/mol using the default DLPNO settings.
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Affiliation(s)
- Jakub Lang
- 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 Sciences, Charles University, Albertov 6, 128 00 Prague 2, Czech Republic
| | - Andrej Antalík
- 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, Ke Karlovu 3, 12116 Prague 2, Czech Republic
| | - 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
| | - Jan Brandejs
- 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, Ke Karlovu 3, 12116 Prague 2, Czech Republic
| | - Jiří Brabec
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Örs Legeza
- Strongly Correlated Systems "Lendület" Research group, Wigner Research Centre for Physics, H-1525 Budapest, Hungary
| | - Jiří Pittner
- 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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10
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Brandejs J, Višňák J, Veis L, Maté M, Legeza Ö, Pittner J. Toward DMRG-tailored coupled cluster method in the 4c-relativistic domain. J Chem Phys 2020; 152:174107. [DOI: 10.1063/1.5144974] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jan Brandejs
- 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, Prague, Czech Republic
| | - Jakub Višňák
- 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, Prague, Czech Republic
- Czech Academic City in Erbil, Yassin Najar Street, Kurani Ankawa, Erbil, Kurdistan, Region of Iraq
| | - 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
| | - Mihály Maté
- Strongly Correlated Systems “Lendület” Research Group, Institute for Solid State Physics and Optics, MTA Wigner Research Centre for Physics, Konkoly-Thege Miklós út 29-33, H-1121 Budapest, Hungary
- Department of Physics of Complex Systems, Eötvös Loránd University, Pf. 32, H-1518 Budapest, Hungary
| | - Örs Legeza
- Strongly Correlated Systems “Lendület” Research Group, Institute for Solid State Physics and Optics, MTA Wigner Research Centre for Physics, Konkoly-Thege Miklós út 29-33, H-1121 Budapest, Hungary
| | - Jiří Pittner
- 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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11
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Nachtigallová D, Antalík A, Lo R, Sedlák R, Manna D, Tuček J, Ugolotti J, Veis L, Legeza Ö, Pittner J, Zbořil R, Hobza P. Corrigendum: An Isolated Molecule of Iron(II) Phthalocyanin Exhibits Quintet Ground‐State: A Nexus between Theory and Experiment. Chemistry 2020; 26:1691. [DOI: 10.1002/chem.201905698] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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12
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Antalík A, Nachtigallová D, Lo R, Matoušek M, Lang J, Legeza Ö, Pittner J, Hobza P, Veis L. Ground state of the Fe(ii)-porphyrin model system corresponds to quintet: a DFT and DMRG-based tailored CC study. Phys Chem Chem Phys 2020; 22:17033-17037. [DOI: 10.1039/d0cp03086d] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Fe(ii)-porphyrins play an important role in many reactions, due to their closely lying spin states. We present a thorough study of a Fe(ii)-porphyrin model system, in which we examine how the geometrical parameters influence its spin state ordering.
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Affiliation(s)
- Andrej Antalík
- J. Heyrovský Institute of Physical Chemistry
- Academy of Sciences of the Czech Republic
- 18223 Prague 8
- Czech Republic
- Faculty of Mathematics and Physics
| | - Dana Nachtigallová
- Institute of Organic Chemistry and Biochemistry
- Academy of Sciences of the Czech Republic
- 16610 Prague 6
- Czech Republic
- Regional Centre of Advanced Technologies and Materials
| | - Rabindranath Lo
- Institute of Organic Chemistry and Biochemistry
- Academy of Sciences of the Czech Republic
- 16610 Prague 6
- Czech Republic
- Regional Centre of Advanced Technologies and Materials
| | - Mikuláš Matoušek
- J. Heyrovský Institute of Physical Chemistry
- Academy of Sciences of the Czech Republic
- 18223 Prague 8
- Czech Republic
- Faculty of Mathematics and Physics
| | - Jakub Lang
- J. Heyrovský Institute of Physical Chemistry
- Academy of Sciences of the Czech Republic
- 18223 Prague 8
- Czech Republic
| | - Örs Legeza
- Strongly Correlated Systems “Lendület” Research group
- Wigner Research Centre for Physics
- Budapest
- Hungary
| | - Jiří Pittner
- J. Heyrovský Institute of Physical Chemistry
- Academy of Sciences of the Czech Republic
- 18223 Prague 8
- Czech Republic
| | - Pavel Hobza
- Institute of Organic Chemistry and Biochemistry
- Academy of Sciences of the Czech Republic
- 16610 Prague 6
- Czech Republic
- Regional Centre of Advanced Technologies and Materials
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry
- Academy of Sciences of the Czech Republic
- 18223 Prague 8
- Czech Republic
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13
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Antalík A, Veis L, Brabec J, Demel O, Legeza Ö, Pittner J. Toward the efficient local tailored coupled cluster approximation and the peculiar case of oxo-Mn(Salen). J Chem Phys 2019; 151:084112. [PMID: 31470730 DOI: 10.1063/1.5110477] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
We introduce a new implementation of the coupled cluster method with single and double excitations tailored by the matrix product state wave functions (DMRG-TCCSD), which employs the local pair natural orbital (LPNO) approach. By exploiting locality in the coupled cluster stage of the calculation, we were able to remove some of the limitations that hindered the application of the canonical version of the method to larger systems and/or with larger basis sets. We assessed the accuracy of the approximation using two systems: tetramethyleneethane (TME) and oxo-Mn(Salen). Using the default cut-off parameters, we were able to recover over 99.7% and 99.8% of the canonical correlation energy for the triplet and singlet state of TME, respectively. In the case of oxo-Mn(Salen), we found that the amount of retrieved canonical correlation energy depends on the size of the complete active space (CAS)-we retrieved over 99.6% for the larger 27 orbital CAS and over 99.8% for the smaller 22 orbital CAS. The use of LPNO-TCCSD allowed us to perform these calculations up to quadruple-ζ basis set, amounting to 1178 basis functions. Moreover, we examined dependence of the ground state of oxo-Mn(Salen) on the CAS composition. We found that the inclusion of 4dxy orbital plays an important role in stabilizing the singlet state at the DMRG-CASSCF level via double-shell effect. However, by including dynamic correlation, the ground state was found to be triplet regardless of the size of the basis set or the composition of CAS, which is in agreement with previous findings by canonical DMRG-TCCSD in smaller basis.
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Affiliation(s)
- Andrej Antalík
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - 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
| | - Jiří Brabec
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Ondřej Demel
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Örs Legeza
- Strongly Correlated Systems "Lendület" Research Group, Wigner Research Centre for Physics, H-1525 Budapest, Hungary
| | - Jiří Pittner
- 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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14
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Hagymási I, Hubig C, Legeza Ö, Schollwöck U. Dynamical Topological Quantum Phase Transitions in Nonintegrable Models. Phys Rev Lett 2019; 122:250601. [PMID: 31347875 DOI: 10.1103/physrevlett.122.250601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2019] [Revised: 05/14/2019] [Indexed: 06/10/2023]
Abstract
We consider sudden quenches across quantum phase transitions in the S=1 XXZ model starting from the Haldane phase. We demonstrate that dynamical phase transitions may occur during these quenches that are identified by nonanalyticities in the rate function for the return probability. In addition, we show that the temporal behavior of the string order parameter is intimately related to the subsequent dynamical phase transitions. We furthermore find that the dynamical quantum phase transitions can be accompanied by enhanced two-site entanglement.
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Affiliation(s)
- I Hagymási
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics (ASC), Fakultät für Physik, Ludwig-Maximilians-Universität München, D-80333 München, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
- Strongly Correlated Systems "Lendület" Research Group, Institute for Solid State Physics and Optics, MTA Wigner Research Centre for Physics, Budapest H-1525, P.O. Box 49, Hungary
| | - C Hubig
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
| | - Ö Legeza
- Strongly Correlated Systems "Lendület" Research Group, Institute for Solid State Physics and Optics, MTA Wigner Research Centre for Physics, Budapest H-1525, P.O. Box 49, Hungary
| | - U Schollwöck
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics (ASC), Fakultät für Physik, Ludwig-Maximilians-Universität München, D-80333 München, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
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15
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Shapir I, Hamo A, Pecker S, Moca CP, Legeza Ö, Zarand G, Ilani S. Imaging the electronic Wigner crystal in one dimension. Science 2019; 364:870-875. [DOI: 10.1126/science.aat0905] [Citation(s) in RCA: 54] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2018] [Revised: 08/05/2018] [Accepted: 05/01/2019] [Indexed: 11/02/2022]
Abstract
The quantum crystal of electrons, predicted more than 80 years ago by Eugene Wigner, remains one of the most elusive states of matter. In this study, we observed the one-dimensional Wigner crystal directly by imaging its charge density in real space. To image, with minimal invasiveness, the many-body electronic density of a carbon nanotube, we used another nanotube as a scanning-charge perturbation. The images we obtained of a few electrons confined in one dimension match the theoretical predictions for strongly interacting crystals. The quantum nature of the crystal emerges in the observed collective tunneling through a potential barrier. These experiments provide the direct evidence for the formation of small Wigner crystals and open the way for studying other fragile interacting states by imaging their many-body density in real space.
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16
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Abstract
Recently, the correlation theory of the chemical bond was developed, which applies concepts of quantum information theory for the characterization of chemical bonds, based on the multiorbital correlations within the molecule. Here, for the first time, we extend the use of this mathematical toolbox for the description of electron-deficient bonds. We start by verifying the theory on the textbook example of a molecule with three-center two-electron bonds, namely, diborane(6). We then show that the correlation theory of the chemical bond is able to properly describe the bonding situation in more exotic molecules which have been synthesized and characterized only recently, in particular, the diborane molecule with four hydrogen atoms [diborane(4)] and a neutral zerovalent s-block beryllium complex, whose surprising stability was attributed to a strong three-center two-electron π bond stretching across the C-Be-C core. Our approach is of high importance especially in the light of a constant chase after novel compounds with extraordinary properties where the bonding is expected to be unusual.
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Affiliation(s)
- Jan Brandejs
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - 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
| | - Szilárd Szalay
- Strongly Correlated Systems "Lendület" Research Group, Institute for Solid State Physics and Optics, MTA Wigner Research Centre for Physics, Konkoly-Thege Miklós út 29-33, H-1121 Budapest, Hungary
| | - Gergely Barcza
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Jiří Pittner
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Örs Legeza
- Strongly Correlated Systems "Lendület" Research Group, Institute for Solid State Physics and Optics, MTA Wigner Research Centre for Physics, Konkoly-Thege Miklós út 29-33, H-1121 Budapest, Hungary
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17
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Faulstich FM, Máté M, Laestadius A, Csirik MA, Veis L, Antalik A, Brabec J, Schneider R, Pittner J, Kvaal S, Legeza Ö. Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer. J Chem Theory Comput 2019; 15:2206-2220. [PMID: 30802406 PMCID: PMC7002028 DOI: 10.1021/acs.jctc.8b00960] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
![]()
In
this article, we investigate the numerical and theoretical aspects
of the coupled-cluster method tailored by matrix-product states. We
investigate formal properties of the used method, such as energy size
consistency and the equivalence of linked and unlinked formulation.
The existing mathematical analysis is here elaborated in a quantum
chemical framework. In particular, we highlight the use of what we
have defined as a complete active space-external space gap describing
the basis splitting between the complete active space and the external
part generalizing the concept of a HOMO–LUMO gap. Furthermore,
the behavior of the energy error for an optimal basis splitting, i.e.,
an active space choice minimizing the density matrix renormalization
group-tailored coupled-cluster singles doubles error, is discussed.
We show numerical investigations on the robustness with respect to
the bond dimensions of the single orbital entropy and the mutual information,
which are quantities that are used to choose a complete active space.
Moreover, the dependence of the ground-state energy error on the complete
active space has been analyzed numerically in order to find an optimal
split between the complete active space and external space by minimizing
the density matrix renormalization group-tailored coupled-cluster
error.
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Affiliation(s)
- Fabian M Faulstich
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Mihály Máté
- Strongly Correlated Systems "Lendület" Research Group , Wigner Research Center for Physics , H-1525 , P.O. Box 49, Budapest , Hungary.,Department of Physics of Complex Systems , Eötvös Loránd University , Pf. 32 , H-1518 Budapest , Hungary
| | - Andre Laestadius
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Mihály András Csirik
- Strongly Correlated Systems "Lendület" Research Group , Wigner Research Center for Physics , H-1525 , P.O. Box 49, Budapest , Hungary
| | - 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
| | - Andrej Antalik
- 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 , 11636 Prague , Czech Republic
| | - Jiří Brabec
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic , v.v.i., Dolejškova 3 , 18223 Prague 8 , Czech Republic
| | - Reinhold Schneider
- Modeling, Simulation and Optimization in Science, Department of Mathematics , Technische Universität Berlin , Sekretariat MA 5-3, Straße des 17. Juni 136 , 10623 Berlin , Germany
| | - Jiří Pittner
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic , v.v.i., Dolejškova 3 , 18223 Prague 8 , Czech Republic
| | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Örs Legeza
- Strongly Correlated Systems "Lendület" Research Group , Wigner Research Center for Physics , H-1525 , P.O. Box 49, Budapest , Hungary
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18
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Łachmańska A, Tecmer P, Legeza Ö, Boguslawski K. Elucidating cation–cation interactions in neptunyl dications using multi-reference ab initio theory. Phys Chem Chem Phys 2019; 21:744-759. [DOI: 10.1039/c8cp04267e] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
Understanding the binding mechanism in neptunyl clusters formed due to cation–cation interactions is of crucial importance in nuclear waste reprocessing and related areas of research.
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Affiliation(s)
- Aleksandra Łachmańska
- Institute of Physics
- Faculty of Physics
- Astronomy and Informatics
- Nicolaus Copernicus University in Toruń
- 87-100 Toruń
| | - Paweł Tecmer
- Institute of Physics
- Faculty of Physics
- Astronomy and Informatics
- Nicolaus Copernicus University in Toruń
- 87-100 Toruń
| | - Örs Legeza
- Strongly Correlated Systems “Lendület” Research Group
- Wigner Research Center for Physics
- H-1525 Budapest
- Hungary
| | - Katharina Boguslawski
- Institute of Physics
- Faculty of Physics
- Astronomy and Informatics
- Nicolaus Copernicus University in Toruń
- 87-100 Toruń
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19
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Nachtigallová D, Antalík A, Lo R, Sedlák R, Manna D, Tuček J, Ugolotti J, Veis L, Legeza Ö, Pittner J, Zbořil R, Hobza P. Cover Feature: An Isolated Molecule of Iron(II) Phthalocyanin Exhibits Quintet Ground-State: A Nexus between Theory and Experiment (Chem. Eur. J. 51/2018). Chemistry 2018. [DOI: 10.1002/chem.201804158] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Dana Nachtigallová
- Institute of Organic Chemistry and Biochemistry; Academy of Sciences of the Czech Republic; v.v.i., Flemingovo nám. 2 16610 Prague 6 Czech Republic
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
| | - Andrej Antalík
- 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 Prague; 11636 Prague Czech Republic Republic
| | - Rabindranath Lo
- Institute of Organic Chemistry and Biochemistry; Academy of Sciences of the Czech Republic; v.v.i., Flemingovo nám. 2 16610 Prague 6 Czech Republic
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
| | - Robert Sedlák
- Institute of Organic Chemistry and Biochemistry; Academy of Sciences of the Czech Republic; v.v.i., Flemingovo nám. 2 16610 Prague 6 Czech Republic
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
| | - Debashree Manna
- Institute of Organic Chemistry and Biochemistry; Academy of Sciences of the Czech Republic; v.v.i., Flemingovo nám. 2 16610 Prague 6 Czech Republic
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
| | - Jiří Tuček
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
| | - Juri Ugolotti
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
| | - 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
| | - Örs Legeza
- Strongly Correlated Systems “ Lendület” Research group; Wigner Research Centre for Physics; 1525 Budapest Hungary
| | - Jiří Pittner
- J. Heyrovský Institute of Physical Chemistry; Academy of Sciences of the Czech Republic; v.v.i., Dolejškova 3 18223 Prague 8 Czech Republic
| | - Radek Zbořil
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
| | - Pavel Hobza
- Institute of Organic Chemistry and Biochemistry; Academy of Sciences of the Czech Republic; v.v.i., Flemingovo nám. 2 16610 Prague 6 Czech Republic
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
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20
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Nachtigallová D, Antalík A, Lo R, Sedlák R, Manna D, Tuček J, Ugolotti J, Veis L, Legeza Ö, Pittner J, Zbořil R, Hobza P. An Isolated Molecule of Iron(II) Phthalocyanin Exhibits Quintet Ground-State: A Nexus between Theory and Experiment. Chemistry 2018; 24:13413-13417. [DOI: 10.1002/chem.201803380] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2018] [Revised: 07/31/2018] [Indexed: 01/07/2023]
Affiliation(s)
- Dana Nachtigallová
- Institute of Organic Chemistry and Biochemistry; Academy of Sciences of the Czech Republic; v.v.i., Flemingovo nám. 2 16610 Prague 6 Czech Republic
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
| | - Andrej Antalík
- 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 Prague; 11636 Prague Czech Republic Republic
| | - Rabindranath Lo
- Institute of Organic Chemistry and Biochemistry; Academy of Sciences of the Czech Republic; v.v.i., Flemingovo nám. 2 16610 Prague 6 Czech Republic
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
| | - Robert Sedlák
- Institute of Organic Chemistry and Biochemistry; Academy of Sciences of the Czech Republic; v.v.i., Flemingovo nám. 2 16610 Prague 6 Czech Republic
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
| | - Debashree Manna
- Institute of Organic Chemistry and Biochemistry; Academy of Sciences of the Czech Republic; v.v.i., Flemingovo nám. 2 16610 Prague 6 Czech Republic
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
| | - Jiří Tuček
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
| | - Juri Ugolotti
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
| | - 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
| | - Örs Legeza
- Strongly Correlated Systems “ Lendület” Research group; Wigner Research Centre for Physics; 1525 Budapest Hungary
| | - Jiří Pittner
- J. Heyrovský Institute of Physical Chemistry; Academy of Sciences of the Czech Republic; v.v.i., Dolejškova 3 18223 Prague 8 Czech Republic
| | - Radek Zbořil
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
| | - Pavel Hobza
- Institute of Organic Chemistry and Biochemistry; Academy of Sciences of the Czech Republic; v.v.i., Flemingovo nám. 2 16610 Prague 6 Czech Republic
- Regional Centre of Advanced Technologies and Materials; Department of Physical Chemistry; Faculty of Science, Palacký University in Olomouc; Šlechtitelů 27 78371 Olomouc Czech Republic
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21
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Affiliation(s)
- E. Fertitta
- Department of Physics, King's College London, London, UK
| | - D. Koch
- Department of Mechanical Engineering, National University of Singapore, Singapore
| | - B. Paulus
- Institut für Chemie und Biochemie - Physikalische und Theoretische Chemie, Freie Universität Berlin, Berlin, Germany
| | - G. Barcza
- Strongly Correlated Systems “Lendület” Research Group, Wigner Research Centre for Physics, Budapest, Hungary
| | - Ö. Legeza
- Strongly Correlated Systems “Lendület” Research Group, Wigner Research Centre for Physics, Budapest, Hungary
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22
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Veis L, Antalík A, Legeza Ö, Alavi A, Pittner J. The Intricate Case of Tetramethyleneethane: A Full Configuration Interaction Quantum Monte Carlo Benchmark and Multireference Coupled Cluster Studies. J Chem Theory Comput 2018; 14:2439-2445. [DOI: 10.1021/acs.jctc.8b00022] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- 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
| | - Andrej Antalík
- 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, 11636 Prague, Czech Republic
| | - Örs Legeza
- Strongly Correlated Systems “Lendület” Research group, Wigner Research Centre for Physics, H-1525 Budapest, Hungary
| | - Ali Alavi
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
- Max Planck Institüt für Festkörperforschung, 70569 Stuttgart, Germany
| | - Jiří Pittner
- 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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23
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Affiliation(s)
- Klaas Gunst
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, B-9000 Ghent, Belgium
| | - Frank Verstraete
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, B-9000 Ghent, Belgium
- Vienna Center for Quantum Technology, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Sebastian Wouters
- Brantsandpatents, Pauline van Pottelsberghelaan 24, 9051 Sint-Denijs Westrem (Ghent), Belgium
| | - Örs Legeza
- Strongly Correlated Systems “Lendület” Research Group, Wigner Research Centre for Physics, H-1525 Budapest, Hungary
| | - Dimitri Van Neck
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
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24
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Boguslawski K, Réal F, Tecmer P, Duperrouzel C, Gomes ASP, Legeza Ö, Ayers PW, Vallet V. On the multi-reference nature of plutonium oxides: PuO 22+, PuO 2, PuO 3 and PuO 2(OH) 2. Phys Chem Chem Phys 2018; 19:4317-4329. [PMID: 28116368 DOI: 10.1039/c6cp05429c] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
Actinide-containing complexes present formidable challenges for electronic structure methods due to the large number of degenerate or quasi-degenerate electronic states arising from partially occupied 5f and 6d shells. Conventional multi-reference methods can treat active spaces that are often at the upper limit of what is required for a proper treatment of species with complex electronic structures, leaving no room for verifying their suitability. In this work we address the issue of properly defining the active spaces in such calculations, and introduce a protocol to determine optimal active spaces based on the use of the Density Matrix Renormalization Group algorithm and concepts of quantum information theory. We apply the protocol to elucidate the electronic structure and bonding mechanism of volatile plutonium oxides (PuO3 and PuO2(OH)2), species associated with nuclear safety issues for which little is known about the electronic structure and energetics. We show how, within a scalar relativistic framework, orbital-pair correlations can be used to guide the definition of optimal active spaces which provide an accurate description of static/non-dynamic electron correlation, as well as to analyse the chemical bonding beyond a simple orbital model. From this bonding analysis we are able to show that the addition of oxo- or hydroxo-groups to the plutonium dioxide species considerably changes the π-bonding mechanism with respect to the bare triatomics, resulting in bent structures with a considerable multi-reference character.
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Affiliation(s)
- Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Grudziadzka 5, 87-100 Torun, Poland. and Faculty of Chemistry, Nicolaus Copernicus University in Torun, Gagarina 7, 87-100 Torun, Poland
| | - Florent Réal
- Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France.
| | - Paweł Tecmer
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Grudziadzka 5, 87-100 Torun, Poland.
| | - Corinne Duperrouzel
- Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France. and Department of Chemistry and Chemical Biology, McMaster University, 1280 Main Street West, Hamilton, L8S 4M1, Canada
| | | | - Örs Legeza
- Strongly Correlated Systems "Lendület" Research Group, Wigner Research Center for Physics, H-1525 Budapest, Hungary
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, 1280 Main Street West, Hamilton, L8S 4M1, Canada
| | - Valérie Vallet
- Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France.
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25
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Abstract
The quantum mechanical description of the chemical bond is generally given in terms of delocalized bonding orbitals, or, alternatively, in terms of correlations of occupations of localised orbitals. However, in the latter case, multiorbital correlations were treated only in terms of two-orbital correlations, although the structure of multiorbital correlations is far richer; and, in the case of bonds established by more than two electrons, multiorbital correlations represent a more natural point of view. Here, for the first time, we introduce the true multiorbital correlation theory, consisting of a framework for handling the structure of multiorbital correlations, a toolbox of true multiorbital correlation measures, and the formulation of the multiorbital correlation clustering, together with an algorithm for obtaining that. These make it possible to characterise quantitatively, how well a bonding picture describes the chemical system. As proof of concept, we apply the theory for the investigation of the bond structures of several molecules. We show that the non-existence of well-defined multiorbital correlation clustering provides a reason for debated bonding picture.
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Affiliation(s)
- Szilárd Szalay
- Strongly Correlated Systems "Lendület" Research Group, Institute for Solid State Physics and Optics, MTA Wigner Research Centre for Physics, H-1121, Budapest, Konkoly-Thege Miklós út 29-33, Hungary.
| | - Gergely Barcza
- Strongly Correlated Systems "Lendület" Research Group, Institute for Solid State Physics and Optics, MTA Wigner Research Centre for Physics, H-1121, Budapest, Konkoly-Thege Miklós út 29-33, Hungary
| | - Tibor Szilvási
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, 1415 Engineering Drive, Madison, Wisconsin, 53706, United States.,Department of Inorganic and Analytical Chemistry, Budapest University of Technology and Economics, H-1111, Budapest, Szent Gellért tér 4, Hungary
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, CZ-18223, Prague, Czech Republic
| | - Örs Legeza
- Strongly Correlated Systems "Lendület" Research Group, Institute for Solid State Physics and Optics, MTA Wigner Research Centre for Physics, H-1121, Budapest, Konkoly-Thege Miklós út 29-33, Hungary
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26
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Veis L, Antalík A, Brabec J, Neese F, Legeza Ö, Pittner J. Correction to Coupled Cluster Method with Single and Double Excitations Tailored by Matrix Product State Wave Functions. J Phys Chem Lett 2017; 8:291. [PMID: 28001413 DOI: 10.1021/acs.jpclett.6b02912] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
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27
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Abstract
Tensor network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin models. Recently, they have also been applied to interacting fermionic problems, specifically in the context of quantum chemistry. A new freedom arising in such nonlocal fermionic systems is the choice of orbitals, it being far from clear what choice of fermionic orbitals to make. In this Letter, we propose a way to overcome this challenge. We suggest a method intertwining the optimization over matrix product states with suitable fermionic Gaussian mode transformations. The described algorithm generalizes basis changes in the spirit of the Hartree-Fock method to matrix-product states, and provides a black box tool for basis optimization in tensor network methods.
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Affiliation(s)
- C Krumnow
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - L Veis
- Strongly Correlated Systems "Lendület" Research Group, Wigner Research Centre for Physics, Hungarian Academy of Sciences, 1525 Budapest, Hungary
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, 18223 Prague, Czech Republic
| | - Ö Legeza
- Strongly Correlated Systems "Lendület" Research Group, Wigner Research Centre for Physics, Hungarian Academy of Sciences, 1525 Budapest, Hungary
| | - J Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
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28
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Veis L, Antalík A, Brabec J, Neese F, Legeza Ö, Pittner J. Coupled Cluster Method with Single and Double Excitations Tailored by Matrix Product State Wave Functions. J Phys Chem Lett 2016; 7:4072-4078. [PMID: 27682626 DOI: 10.1021/acs.jpclett.6b01908] [Citation(s) in RCA: 57] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In the past decade, the quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as the method of choice for calculations of strongly correlated molecular systems. Despite its favorable scaling, it is in practice not suitable for computations of dynamic correlation. We present a novel method for accurate "post-DMRG" treatment of dynamic correlation based on the tailored coupled cluster (CC) theory in which the DMRG method is responsible for the proper description of nondynamic correlation, whereas dynamic correlation is incorporated through the framework of the CC theory. We illustrate the potential of this method on prominent multireference systems, in particular, N2 and Cr2 molecules and also oxo-Mn(Salen), for which we have performed the first post-DMRG computations in order to shed light on the energy ordering of the lowest spin states.
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Affiliation(s)
- 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
| | - Andrej Antalík
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic , v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Jiří Brabec
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic , v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Frank Neese
- Max Planck Institut für Chemische Energiekonversion , Stiftstrasse 34-36, D-45470 Mülheim an der Ruhr, Germany
| | - Örs Legeza
- Strongly Correlated Systems "Lendület" Research Group, Wigner Research Centre for Physics , H-1525 Budapest, Hungary
| | - Jiří Pittner
- 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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Timár M, Barcza G, Gebhard F, Veis L, Legeza Ö. Hückel-Hubbard-Ohno modeling of π-bonds in ethene and ethyne with application to trans-polyacetylene. Phys Chem Chem Phys 2016; 18:18835-45. [PMID: 27348188 DOI: 10.1039/c6cp00726k] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Quantum chemistry calculations provide the potential energy between two carbon atoms in ethane (H3C-CH3), ethene (H2C[double bond, length as m-dash]CH2), and ethyne (HC[triple bond, length as m-dash]CH) as a function of the atomic distance. Based on the energy function for the σ-bond in ethane, Vσ(r), we use the Hückel model with Hubbard-Ohno interaction for the π electrons to describe the energies Vσπ(r) and Vσππ(r) for the σπ double bond in ethene and the σππ triple bond in ethyne, respectively. The fit of the force functions shows that the electron transfer matrix element and the Peierls coupling can be estimated with some precision whereas the Hubbard-Ohno parameters are insignificant at the distances under consideration. We apply the Hückel-Hubbard-Ohno model to describe the bond lengths and the energies of elementary electronic excitations of trans-polyacetylene, (CH)n, whereby we adjust the σ-bond potential for conjugated polymers.
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Affiliation(s)
- Máté Timár
- Strongly Correlated Systems Lendület Research Group, Institute for Solid State Physics and Optics, MTA Wigner Research Centre for Physics, P. O. Box 49, H-1525 Budapest, Hungary.
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Murg V, Verstraete F, Schneider R, Nagy PR, Legeza Ö. Tree Tensor Network State with Variable Tensor Order: An Efficient Multireference Method for Strongly Correlated Systems. J Chem Theory Comput 2016; 11:1027-36. [PMID: 25844072 PMCID: PMC4357235 DOI: 10.1021/ct501187j] [Citation(s) in RCA: 50] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2014] [Indexed: 11/29/2022]
Abstract
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We
study the tree-tensor-network-state (TTNS) method with variable
tensor orders for quantum chemistry. TTNS is a variational method
to efficiently approximate complete active space (CAS) configuration
interaction (CI) wave functions in a tensor product form. TTNS can
be considered as a higher order generalization of the matrix product
state (MPS) method. The MPS wave function is formulated as products
of matrices in a multiparticle basis spanning a truncated Hilbert
space of the original CAS-CI problem. These matrices belong to active
orbitals organized in a one-dimensional array, while tensors in TTNS
are defined upon a tree-like arrangement of the same orbitals. The
tree-structure is advantageous since the distance between two arbitrary
orbitals in the tree scales only logarithmically with the number of
orbitals N, whereas the scaling is linear in the MPS array. It is
found to be beneficial from the computational costs point of view
to keep strongly correlated orbitals in close vicinity in both arrangements;
therefore, the TTNS ansatz is better suited for multireference problems
with numerous highly correlated orbitals. To exploit the advantages
of TTNS a novel algorithm is designed to optimize the tree tensor
network topology based on quantum information theory and entanglement.
The superior performance of the TTNS method is illustrated on the
ionic-neutral avoided crossing of LiF. It is also shown that the avoided
crossing of LiF can be localized using only ground state properties,
namely one-orbital entanglement.
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Fertitta E, Paulus B, Barcza G, Legeza Ö. On the calculation of complete dissociation curves of closed-shell pseudo-onedimensional systems via the complete active space method of increments. J Chem Phys 2015; 143:114108. [DOI: 10.1063/1.4930861] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- E. Fertitta
- Institut für Chemie und Biochemie, Freie Universität Berlin, Takustr. 3, 14195 Berlin, Germany
| | - B. Paulus
- Institut für Chemie und Biochemie, Freie Universität Berlin, Takustr. 3, 14195 Berlin, Germany
| | - G. Barcza
- Strongly Correlated Systems “Lendület” Research Group, Wigner Research Centre for Physics, P.O. Box 49, Budapest, Hungary
| | - Ö. Legeza
- Strongly Correlated Systems “Lendület” Research Group, Wigner Research Centre for Physics, P.O. Box 49, Budapest, Hungary
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Duperrouzel C, Tecmer P, Boguslawski K, Barcza G, Legeza Ö, Ayers PW. A quantum informational approach for dissecting chemical reactions. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.01.005] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Tecmer P, Boguslawski K, Legeza Ö, Reiher M. Unravelling the quantum-entanglement effect of noble gas coordination on the spin ground state of CUO. Phys Chem Chem Phys 2014; 16:719-27. [DOI: 10.1039/c3cp53975j] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Mottet M, Tecmer P, Boguslawski K, Legeza Ö, Reiher M. Quantum entanglement in carbon–carbon, carbon–phosphorus and silicon–silicon bonds. Phys Chem Chem Phys 2014; 16:8872-80. [DOI: 10.1039/c4cp00277f] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
We present a quantum entanglement analysis to dissect the bond orders in polyatomic molecules.
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Affiliation(s)
- Matthieu Mottet
- ETH Zürich
- Laboratory of Physical Chemistry
- CH-8093 Zürich, Switzerland
| | - Paweł Tecmer
- ETH Zürich
- Laboratory of Physical Chemistry
- CH-8093 Zürich, Switzerland
| | | | - Örs Legeza
- Strongly Correlated Systems “Lendület” Research Group
- Wigner Research Center for Physics
- H-1525 Budapest, Hungary
| | - Markus Reiher
- ETH Zürich
- Laboratory of Physical Chemistry
- CH-8093 Zürich, Switzerland
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Affiliation(s)
- Katharina Boguslawski
- ETH Zürich, Laboratory of Physical Chemistry, Wolfgang-Pauli-Str. 10, CH-8093 Zürich, Switzerland
| | - Paweł Tecmer
- ETH Zürich, Laboratory of Physical Chemistry, Wolfgang-Pauli-Str. 10, CH-8093 Zürich, Switzerland
| | - Gergely Barcza
- Strongly Correlated Systems ″Lendület″
Research Group, Wigner Research Center for Physics, H-1525 Budapest, Hungary
| | - Örs Legeza
- Strongly Correlated Systems ″Lendület″
Research Group, Wigner Research Center for Physics, H-1525 Budapest, Hungary
| | - Markus Reiher
- ETH Zürich, Laboratory of Physical Chemistry, Wolfgang-Pauli-Str. 10, CH-8093 Zürich, Switzerland
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Abstract
Electron correlation effects are essential for an accurate ab initio description of molecules. A quantitative a priori knowledge of the single- or multireference nature of electronic structures as well as of the dominant contributions to the correlation energy can facilitate the decision regarding the optimum quantum chemical method of choice. We propose concepts from quantum information theory as orbital entanglement measures that allow us to evaluate the single- and multireference character of any molecular structure in a given orbital basis set. By studying these measures we can detect possible artifacts of small active spaces.
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Affiliation(s)
- Katharina Boguslawski
- †ETH Zurich, Laboratory of Physical Chemistry, Wolfgang-Pauli-Str. 10, CH-8093 Zurich, Switzerland
| | - Pawel̷ Tecmer
- †ETH Zurich, Laboratory of Physical Chemistry, Wolfgang-Pauli-Str. 10, CH-8093 Zurich, Switzerland
| | - Örs Legeza
- ‡MTA-WRCP Strongly Correlated Systems "Lendület" Research Group, H-1525, Budapest, Hungary
| | - Markus Reiher
- †ETH Zurich, Laboratory of Physical Chemistry, Wolfgang-Pauli-Str. 10, CH-8093 Zurich, Switzerland
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Bommeli F, Degiorgi L, Wachter P, Legeza Ö, Jánossy A, Oszlanyi G, Chauvet O, Forro L. Metallic conductivity and metal-insulator transition in (AC60)n (A=K, Rb, and Cs) linear polymer fullerides. Phys Rev B Condens Matter 1995; 51:14794-14797. [PMID: 9978430 DOI: 10.1103/physrevb.51.14794] [Citation(s) in RCA: 75] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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