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Dupuy L, Rikus A, Maitra NT. Exact-Factorization-Based Surface Hopping without Velocity Adjustment. J Phys Chem Lett 2024:2643-2649. [PMID: 38422391 DOI: 10.1021/acs.jpclett.4c00115] [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: 03/02/2024]
Abstract
While surface hopping has emerged as a powerful method for simulating non-adiabatic dynamics in large molecules, the ad hoc nature of the necessary velocity adjustments and decoherence corrections in the algorithm somewhat reduces its reliability. Here we propose a new scheme that eliminates these aspects by combining the nuclear equation from the quantum-trajectory surface-hopping approach with the electronic equation derived from the exact-factorization approach. The resulting method, denoted QTSH-XF, yields a surface-hopping method on firmer ground than previous and is shown to successfully capture dynamics in Tully models and in a linear vibronic coupling model of the photoexcited uracil cation.
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Affiliation(s)
- Lucien Dupuy
- Department of Physics, Rutgers University, Newark, New Jersey 07102, United States
| | - Anton Rikus
- Department of Physics, Rutgers University, Newark, New Jersey 07102, United States
- University of Münster, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, 48149 Münster, Germany
| | - Neepa T Maitra
- Department of Physics, Rutgers University, Newark, New Jersey 07102, United States
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2
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Villaseco Arribas E, Maitra NT, Agostini F. Nonadiabatic dynamics with classical trajectories: The problem of an initial coherent superposition of electronic states. J Chem Phys 2024; 160:054102. [PMID: 38310471 DOI: 10.1063/5.0186984] [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] [Received: 11/10/2023] [Accepted: 01/11/2024] [Indexed: 02/05/2024] Open
Abstract
Advances in coherent light sources and development of pump-probe techniques in recent decades have opened the way to study electronic motion in its natural time scale. When an ultrashort laser pulse interacts with a molecular target, a coherent superposition of electronic states is created and the triggered electron dynamics is coupled to the nuclear motion. A natural and computationally efficient choice to simulate this correlated dynamics is a trajectory-based method where the quantum-mechanical electronic evolution is coupled to a classical-like nuclear dynamics. These methods must approximate the initial correlated electron-nuclear state by associating an initial electronic wavefunction to each classical trajectory in the ensemble. Different possibilities exist that reproduce the initial populations of the exact molecular wavefunction when represented in a basis. We show that different choices yield different dynamics and explore the effect of this choice in Ehrenfest, surface hopping, and exact-factorization-based coupled-trajectory schemes in a one-dimensional two-electronic-state model system that can be solved numerically exactly. This work aims to clarify the problems that standard trajectory-based techniques might have when a coherent superposition of electronic states is created to initialize the dynamics, to discuss what properties and observables are affected by different choices of electronic initial conditions and to point out the importance of quantum-momentum-induced electronic transitions in coupled-trajectory schemes.
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Affiliation(s)
- Evaristo Villaseco Arribas
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
| | - Neepa T Maitra
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
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3
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Dar DB, Maitra NT. Oscillator strengths and excited-state couplings for double excitations in time-dependent density functional theory. J Chem Phys 2023; 159:211104. [PMID: 38038212 DOI: 10.1063/5.0176705] [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] [Received: 09/15/2023] [Accepted: 11/08/2023] [Indexed: 12/02/2023] Open
Abstract
Although useful to extract excitation energies of states of double-excitation character in time-dependent density functional theory that are missing in the adiabatic approximation, the frequency-dependent kernel derived earlier [Maitra et al., J. Chem. Phys. 120, 5932 (2004)] was not designed to yield oscillator strengths. These are required to fully determine linear absorption spectra, and they also impact excited-to-excited-state couplings that appear in dynamics simulations and other quadratic response properties. Here, we derive a modified non-adiabatic kernel that yields both accurate excitation energies and oscillator strengths for these states. We demonstrate its performance on a model two-electron system, the Be atom, and on excited-state transition dipoles in the LiH molecule at stretched bond-lengths, in all cases producing significant improvements over the traditional approximations.
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Affiliation(s)
- Davood B Dar
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
| | - Neepa T Maitra
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
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4
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Arribas EV, Ibele LM, Lauvergnat D, Maitra NT, Agostini F. Significance of Energy Conservation in Coupled-Trajectory Approaches to Nonadiabatic Dynamics. J Chem Theory Comput 2023; 19:7787-7800. [PMID: 37853509 DOI: 10.1021/acs.jctc.3c00845] [Citation(s) in RCA: 1] [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: 10/20/2023]
Abstract
Through approximating electron-nuclear correlation terms in the exact factorization approach, trajectory-based methods have been derived and successfully applied to the dynamics of a variety of light-induced molecular processes, capturing quantum (de)coherence effects rigorously. These terms account for the coupling among the trajectories, recovering the nonlocal nature of quantum nuclear dynamics that is completely overlooked in traditional independent-trajectory algorithms. Nevertheless, some of the approximations introduced in the derivation of some of these methods do not conserve the total energy. We analyze energy conservation in the coupled-trajectory mixed quantum-classical (CTMQC) algorithm and explore the performance of a modified algorithm, CTMQC-E, where some of the terms are redefined to restore energy conservation. A set of molecular models is used as a test, namely, 2-cis-penta-2,4-dienimium cation, bis(methylene) adamantyl radical cation, butatriene cation, uracil radical cation, and neutral pyrazine.
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Affiliation(s)
| | - Lea M Ibele
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
| | - David Lauvergnat
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
| | - Neepa T Maitra
- Department of Physics, Rutgers University, Newark, New Jersey 07102, United States
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
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5
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Villaseco Arribas E, Vindel-Zandbergen P, Roy S, Maitra NT. Different flavors of exact-factorization-based mixed quantum-classical methods for multistate dynamics. Phys Chem Chem Phys 2023; 25:26380-26395. [PMID: 37750820 DOI: 10.1039/d3cp03464j] [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: 09/27/2023]
Abstract
The exact factorization approach has led to the development of new mixed quantum-classical methods for simulating coupled electron-ion dynamics. We compare their performance for dynamics when more than two electronic states are occupied at a given time, and analyze: (1) the use of coupled versus auxiliary trajectories in evaluating the electron-nuclear correlation terms, (2) the approximation of using these terms within surface-hopping and Ehrenfest frameworks, and (3) the relevance of the exact conditions of zero population transfer away from nonadiabatic coupling regions and total energy conservation. Dynamics through the three-state conical intersection in the uracil radical cation as well as polaritonic models in one dimension are studied.
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Affiliation(s)
| | - Patricia Vindel-Zandbergen
- Department of Physics, Rutgers University, Newark 07102, New Jersey, USA.
- Department of Chemistry, New York University, New York, New York 10003, USA
| | - Saswata Roy
- Department of Physics, Rutgers University, Newark 07102, New Jersey, USA.
| | - Neepa T Maitra
- Department of Physics, Rutgers University, Newark 07102, New Jersey, USA.
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6
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Villaseco Arribas E, Maitra NT. Energy-conserving coupled trajectory mixed quantum-classical dynamics. J Chem Phys 2023; 158:2885328. [PMID: 37096853 DOI: 10.1063/5.0149116] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2023] [Accepted: 04/13/2023] [Indexed: 04/26/2023] Open
Abstract
The coupled-trajectory mixed quantum-classical method (CTMQC), derived from the exact factorization approach, has successfully predicted photo-chemical dynamics in a number of interesting molecules, capturing population transfer and decoherence from first principles. However, due to the approximations made, CTMQC does not guarantee energy conservation. We propose a modified algorithm, CTMQC-E, which redefines the integrated force in the coupled-trajectory term so to restore energy conservation, and demonstrate its accuracy on scattering in Tully's extended coupling region model and photoisomerization in a retinal chromophore model.
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Affiliation(s)
| | - Neepa T Maitra
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
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7
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Dar D, Roy S, Maitra NT. Curing the Divergence in Time-Dependent Density Functional Quadratic Response Theory. J Phys Chem Lett 2023; 14:3186-3192. [PMID: 36971411 DOI: 10.1021/acs.jpclett.3c00122] [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: 06/18/2023]
Abstract
The adiabatic approximation in time-dependent density functional theory is known to give an incorrect pole structure in the quadratic response function, leading to unphysical divergences in excited state-to-state transition probabilities and hyperpolarizabilties. We find the form of the exact quadratic response kernel and derive a practical and accurate approximation that cures the divergence. We demonstrate our results on excited state-to-state transition probabilities of a model system and of the LiH molecule.
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Affiliation(s)
- Davood Dar
- Department of Physics, Rutgers University, Newark, New Jersey 07102, United States
| | - Saswata Roy
- Department of Physics, Rutgers University, Newark, New Jersey 07102, United States
| | - Neepa T Maitra
- Department of Physics, Rutgers University, Newark, New Jersey 07102, United States
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8
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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: 54] [Impact Index Per Article: 27.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [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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9
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Villaseco Arribas E, Agostini F, Maitra NT. Exact Factorization Adventures: A Promising Approach for Non-Bound States. Molecules 2022; 27:molecules27134002. [PMID: 35807246 PMCID: PMC9267945 DOI: 10.3390/molecules27134002] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2022] [Revised: 06/07/2022] [Accepted: 06/09/2022] [Indexed: 11/29/2022] Open
Abstract
Modeling the dynamics of non-bound states in molecules requires an accurate description of how electronic motion affects nuclear motion and vice-versa. The exact factorization (XF) approach offers a unique perspective, in that it provides potentials that act on the nuclear subsystem or electronic subsystem, which contain the effects of the coupling to the other subsystem in an exact way. We briefly review the various applications of the XF idea in different realms, and how features of these potentials aid in the interpretation of two different laser-driven dissociation mechanisms. We present a detailed study of the different ways the coupling terms in recently-developed XF-based mixed quantum-classical approximations are evaluated, where either truly coupled trajectories, or auxiliary trajectories that mimic the coupling are used, and discuss their effect in both a surface-hopping framework as well as the rigorously-derived coupled-trajectory mixed quantum-classical approach.
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Affiliation(s)
| | - Federica Agostini
- Institut de Chimie Physique UMR8000, Université Paris-Saclay, CNRS, 91405 Orsay, France;
| | - Neepa T. Maitra
- Department of Physics, Rutgers University, Newark, NJ 07102, USA;
- Correspondence:
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10
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Abstract
A surface-hopping algorithm recently derived from the exact factorization approach, SHXF [Ha et al. J. Phys. Chem. Lett. 2018, 9, 1097], introduces an additional term in the electronic equation of surface hopping that couples electronic states through the quantum momentum. This term not only provides a first-principles description of decoherence, but here we show it is crucial to accurately capture nonadiabatic dynamics when more than two states are occupied at any given time. Using a vibronic coupling model of the uracil cation, we show that the lack of this term in traditional surface-hopping methods, including those with decoherence corrections, leads to failure to predict the dynamics through a three-state intersection, while SHXF performs similarly to the multiconfiguration time-dependent Hartree quantum dynamics benchmark.
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Affiliation(s)
| | - Spiridoula Matsika
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States
| | - Neepa T Maitra
- Department of Physics, Rutgers University, Newark, New Jersey 07102, United States
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11
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Rosenzweig B, Hoffmann NM, Lacombe L, Maitra NT. Analysis of the classical trajectory treatment of photon dynamics for polaritonic phenomena. J Chem Phys 2022; 156:054101. [DOI: 10.1063/5.0079379] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [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)
- Bart Rosenzweig
- Department of Mathematics and Statistics, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Norah M. Hoffmann
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Lionel Lacombe
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
| | - Neepa T. Maitra
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
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12
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Abstract
Time-dependent density functional theory has emerged as a method of choice for calculations of spectra and response properties in physics, chemistry, and biology, with its system-size scaling enabling computations on systems much larger than otherwise possible. While increasingly complex and interesting systems have been successfully tackled with relatively simple functional approximations, there has also been increasing awareness that these functionals tend to fail for certain classes of approximations. Here I review the fundamental challenges the approximate functionals have in describing double excitations and charge-transfer excitations, which are two of the most common impediments for the theory to be applied in a black-box way. At the same time, I describe the progress made in recent decades in developing functional approximations that give useful predictions for these excitations. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Neepa T Maitra
- Department of Physics, Rutgers University at Newark, Newark, New Jersey, USA;
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13
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Abstract
Simulating electron-ion dynamics using time-dependent density functional theory within an Ehrenfest dynamics scheme can be done in two ways that are in principle exact and identical: propagating time-dependent electronic Kohn-Sham equations or propagating electronic coefficients on surfaces obtained from linear-response. We show here that using an approximate functional leads to qualitatively different dynamics in the two approaches. We argue that the latter is more accurate because the functionals are evaluated on domains close to the ground state where currently used approximations perform better. We demonstrate this on an exactly solvable model of charge transfer and discuss implications for time-resolved spectroscopy.
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Affiliation(s)
- Lionel Lacombe
- Department of Physics, Rutgers University, Newark 07102, New Jersey United States
| | - Neepa T Maitra
- Department of Physics, Rutgers University, Newark 07102, New Jersey United States
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14
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Vindel-Zandbergen P, Ibele LM, Ha JK, Min SK, Curchod BFE, Maitra NT. Study of the Decoherence Correction Derived from the Exact Factorization Approach for Nonadiabatic Dynamics. J Chem Theory Comput 2021; 17:3852-3862. [PMID: 34138553 PMCID: PMC8280698 DOI: 10.1021/acs.jctc.1c00346] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [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: 02/03/2023]
Abstract
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We present a detailed
study of the decoherence correction to surface
hopping that was recently derived from the exact factorization approach.
Ab initio multiple spawning calculations that use the same initial
conditions and the same electronic structure method are used as a
reference for three molecules: ethylene, the methaniminium cation,
and fulvene, for which nonadiabatic dynamics follows a photoexcitation.
A comparison with the Granucci–Persico energy-based decoherence
correction and the augmented fewest-switches surface-hopping scheme
shows that the three decoherence-corrected methods operate on individual
trajectories in a qualitatively different way, but the results averaged
over trajectories are similar for these systems.
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Affiliation(s)
| | - Lea M Ibele
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, U.K
| | - Jong-Kwon Ha
- Department of Chemistry, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulsan 44919, Republic of Korea
| | - Seung Kyu Min
- Department of Chemistry, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulsan 44919, Republic of Korea
| | - Basile F E Curchod
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, U.K
| | - Neepa T Maitra
- Department of Physics, Rutgers University, Newark, New Jersey 07102, United States
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15
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Martinez P, Rosenzweig B, Hoffmann NM, Lacombe L, Maitra NT. Case studies of the time-dependent potential energy surface for dynamics in cavities. J Chem Phys 2021; 154:014102. [PMID: 33412864 PMCID: PMC7968936 DOI: 10.1063/5.0033386] [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] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2020] [Accepted: 12/10/2020] [Indexed: 11/14/2022] Open
Abstract
The exact time-dependent potential energy surface driving the nuclear dynamics was recently shown to be a useful tool to understand and interpret the coupling of nuclei, electrons, and photons in cavity settings. Here, we provide a detailed analysis of its structure for exactly solvable systems that model two phenomena: cavity-induced suppression of proton-coupled electron-transfer and its dependence on the initial state, and cavity-induced electronic excitation. We demonstrate the inadequacy of simply using a weighted average of polaritonic surfaces to determine the dynamics. Such a weighted average misses a crucial term that redistributes energy between the nuclear and the polaritonic systems, and this term can in fact become a predominant term in determining the nuclear dynamics when several polaritonic surfaces are involved. Evolving an ensemble of classical trajectories on the exact potential energy surface reproduces the nuclear wavepacket quite accurately, while evolving on the weighted polaritonic surface fails after a short period of time. The implications and prospects for application of mixed quantum-classical methods based on this surface are discussed.
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Affiliation(s)
- Phillip Martinez
- Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | | | - Norah M. Hoffmann
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
| | - Lionel Lacombe
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
| | - Neepa T. Maitra
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
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16
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Brandenburg JG, Burke K, Fromager E, Gatti M, Giarrusso S, Gidopoulos NI, Gori-Giorgi P, Gowland D, Helgaker T, Hodgson MJP, Lacombe L, Levi G, Loos PF, Maitra NT, Maurina Morais E, Mehta N, Monti F, Mulay MR, Pernal K, Reining L, Romaniello P, Ryder MR, Savin A, Sirbu D, Teale AM, Thom AJW, Truhlar DG, Wetherell J, Yang W. New approaches to study excited states in density functional theory: general discussion. Faraday Discuss 2020; 224:483-508. [PMID: 33245076 DOI: 10.1039/d0fd90026e] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [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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17
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Hoffmann NM, Lacombe L, Rubio A, Maitra NT. Effect of many modes on self-polarization and photochemical suppression in cavities. J Chem Phys 2020; 153:104103. [PMID: 32933282 DOI: 10.1063/5.0012723] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The standard description of cavity-modified molecular reactions typically involves a single (resonant) mode, while in reality, the quantum cavity supports a range of photon modes. Here, we demonstrate that as more photon modes are accounted for, physicochemical phenomena can dramatically change, as illustrated by the cavity-induced suppression of the important and ubiquitous process of proton-coupled electron-transfer. Using a multi-trajectory Ehrenfest treatment for the photon-modes, we find that self-polarization effects become essential, and we introduce the concept of self-polarization-modified Born-Oppenheimer surfaces as a new construct to analyze dynamics. As the number of cavity photon modes increases, the increasing deviation of these surfaces from the cavity-free Born-Oppenheimer surfaces, together with the interplay between photon emission and absorption inside the widening bands of these surfaces, leads to enhanced suppression. The present findings are general and will have implications for the description and control of cavity-driven physical processes of molecules, nanostructures, and solids embedded in cavities.
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Affiliation(s)
- Norah M Hoffmann
- Department of Physics, Rutgers University at Newark, Newark, New Jersey 07102, USA
| | - Lionel Lacombe
- Department of Physics, Rutgers University at Newark, Newark, New Jersey 07102, USA
| | - Angel Rubio
- Department of Physics, Center for Free-Electron Laser Science, Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Neepa T Maitra
- Department of Physics, Rutgers University at Newark, Newark, New Jersey 07102, USA
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18
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Abstract
We present a quantum electronic embedding method derived from the exact factorization approach to calculate static properties of a many-electron system. The method is exact in principle but the practical power lies in utilizing input from a low-level calculation on the entire system in a high-level method computed on a small fragment, as in other embedding methods. Here, the exact factorization approach defines an embedding Hamiltonian on the fragment. Various Hubbard models demonstrate that remarkably accurate ground-state energies are obtained over the full range of weak to strongly correlated systems.
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Affiliation(s)
- Lionel Lacombe
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
| | - Neepa T Maitra
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
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19
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Abstract
When a system has evolved far from a ground-state, the adiabatic approximations commonly used in time-dependent density functional theory calculations completely fail in some applications, while giving qualitatively good predictions in others, and sometimes even quantitative predictions. It is not clearly understood why this is so, and developing practical approximations going beyond the adiabatic approximation remains a challenge. This paper explores three different lines of investigation. First, an expression for the exact time-dependent exchange-correlation potential suggests that the accuracy of an adiabatic approximation is intimately related to the deviation between the natural orbital occupation numbers of the physical system and those of the Kohn-Sham system, and we explore this on some exactly-solvable model systems. The exact expression further suggests a path to go beyond the adiabatic approximations, and in the second part we discuss a newly proposed class of memory-dependent approximations developed in this way. Finally, we derive a new expression for the exact exchange-correlation potential from a coupling-constant path integration.
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Affiliation(s)
- Lionel Lacombe
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA.
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20
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Abstract
We find and analyze the exact time-dependent potential energy surface driving the proton motion for a model of cavity-induced suppression of proton-coupled electron transfer. We show how, in contrast to the polaritonic surfaces, its features directly correlate to the proton dynamics and we discuss cavity modifications of its structure responsible for the suppression. The results highlight the interplay between nonadiabatic effects from coupling to photons and coupling to electrons and suggest caution is needed when applying traditional dynamics methods based on polaritonic surfaces.
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Affiliation(s)
- Lionel Lacombe
- Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Norah M Hoffmann
- Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science and Department of Physics, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Neepa T Maitra
- Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
- Physics Program and Chemistry Program, Graduate Center of the City University of New York, New York 10016, USA
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21
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Abstract
The exact factorization (EF) approach to coupled electron-ion dynamics recasts the time-dependent molecular Schrödinger equation as two coupled equations, one for the nuclear wavefunction and one for the conditional electronic wavefunction. The potentials appearing in these equations have provided insight into non-adiabatic processes, and new practical non-adiabatic dynamics methods have been formulated starting from these equations. Here, we provide a first demonstration of a self-consistent solution of the exact equations, with a preliminary analysis of their stability and convergence properties. The equations have an unprecedented mathematical form, involving a Hamiltonian outside the class of Hermitian Hamiltonians usually encountered in time-propagation, and so the usual numerical methods for time-dependent Schrödinger fail when applied in a straightforward way to the EF equations. We find an approach that enables stable propagation long enough to witness non-adiabatic behavior in a model system before non-trivial instabilities take over. Implications for the development and analysis of EF-based methods are discussed.
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Affiliation(s)
- Graeme H Gossel
- Department of Physics and Astronomy, Hunter College and the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Lionel Lacombe
- Department of Physics and Astronomy, Hunter College and the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Neepa T Maitra
- Department of Physics and Astronomy, Hunter College and the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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22
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Affiliation(s)
- Lionel Lacombe
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, United States
| | - Neepa T. Maitra
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, United States
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23
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Affiliation(s)
- Graeme H. Gossel
- Department of Physics and Astronomy, Hunter College and the City University of New York, 695 Park Avenue, New York, New York 10065, United States
| | - Federica Agostini
- Laboratoire de Chimie Physique, UMR 8000 CNRS/University Paris-Sud, 91405 Orsay, France
| | - Neepa T. Maitra
- Department of Physics and Astronomy, Hunter College and the City University of New York, 695 Park Avenue, New York, New York 10065, United States
- The Physics Program and the Chemistry Program of the Graduate Center, City University of New York, 365 Fifth Avenue, New York, United States
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24
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Fuks JI, Lacombe L, Nielsen SEB, Maitra NT. Exploring non-adiabatic approximations to the exchange–correlation functional of TDDFT. Phys Chem Chem Phys 2018; 20:26145-26160. [DOI: 10.1039/c8cp03957g] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Decomposition of the exact time-dependent exchange–correlation potential offers a new starting point to build approximations with memory.
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Affiliation(s)
- Johanna I. Fuks
- Departamento de Física and IFIBA
- FCEN
- Universidad de Buenos Aires
- Ciudad Universitaria
- C1428EHA Ciudad de Buenos Aires
| | - Lionel Lacombe
- Department of Physics and Astronomy
- Hunter College and the Graduate Center of the City University of New York
- New York
- USA
| | - Søren E. B. Nielsen
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science
- 22761 Hamburg
- Germany
| | - Neepa T. Maitra
- Department of Physics and Astronomy
- Hunter College and the Graduate Center of the City University of New York
- New York
- USA
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25
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Suzuki Y, Lacombe L, Watanabe K, Maitra NT. Exact Time-Dependent Exchange-Correlation Potential in Electron Scattering Processes. Phys Rev Lett 2017; 119:263401. [PMID: 29328727 DOI: 10.1103/physrevlett.119.263401] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2017] [Indexed: 06/07/2023]
Abstract
We identify peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory that are crucial for time-resolved electron scattering in a model one-dimensional system. These structures are completely missed by adiabatic approximations that, consequently, significantly underestimate the scattering probability. A recently proposed nonadiabatic approximation is shown to correctly capture the approach of the electron to the target when the initial Kohn-Sham state is chosen judiciously, and it is more accurate than standard adiabatic functionals but ultimately fails to accurately capture reflection. These results may explain the underestimation of scattering probabilities in some recent studies on molecules and surfaces.
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Affiliation(s)
- Yasumitsu Suzuki
- Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
| | - Lionel Lacombe
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Kazuyuki Watanabe
- Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
| | - Neepa T Maitra
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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26
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Abstract
Charge transfer plays a crucial role in many processes of interest in physics, chemistry, and bio-chemistry. In many applications the size of the systems involved calls for time-dependent density functional theory (TDDFT) to be used in their computational modeling, due to its unprecedented balance between accuracy and efficiency. However, although exact in principle, in practise approximations must be made for the exchange-correlation functional in this theory, and the standard functional approximations perform poorly for excitations which have a long-range charge-transfer component. Intense progress has been made in developing more sophisticated functionals for this problem, which we review. We point out an essential difference between the properties of the exchange-correlation kernel needed for an accurate description of charge-transfer between open-shell fragments and between closed-shell fragments. We then turn to charge-transfer dynamics, which, in contrast to the excitation problem, is a highly non-equilibrium, non-perturbative, process involving a transfer of one full electron in space. This turns out to be a much more challenging problem for TDDFT functionals. We describe dynamical step and peak features in the exact functional evolving over time, that are missing in the functionals currently used. The latter underestimate the amount of charge transferred and manifest a spurious shift in the charge transfer resonance position. We discuss some explicit examples.
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Affiliation(s)
- Neepa T Maitra
- Department of Physics and Astronomy, Hunter College and the Physics Program at the Graduate Center of the City University of New York, 695 Park Avenue, NY 10065, United States of America
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27
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Khosravi E, Abedi A, Rubio A, Maitra NT. Electronic non-adiabatic dynamics in enhanced ionization of isotopologues of hydrogen molecular ions from the exact factorization perspective. Phys Chem Chem Phys 2017; 19:8269-8281. [DOI: 10.1039/c6cp08539c] [Citation(s) in RCA: 16] [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: 11/21/2022]
Abstract
An exact-factorization perspective of enhanced ionization in isotopologues of H2+ demonstrates the concept of the exact potential driving the electrons in non-adiabatic motion of molecules in strong fields, and sets a new platform for introducing various approximations.
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Affiliation(s)
- Elham Khosravi
- Nano-Bio Spectroscopy Group and ETSF
- Universidad del País Vasco
- CFM CSIC-UPV/EHU
- 20018 San Sebastián
- Spain
| | - Ali Abedi
- Nano-Bio Spectroscopy Group and ETSF
- Universidad del País Vasco
- CFM CSIC-UPV/EHU
- 20018 San Sebastián
- Spain
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter
- 22761 Hamburg
- Germany
- Nano-Bio Spectroscopy Group and ETSF
- Universidad del País Vasco
| | - Neepa T. Maitra
- Department of Physics and Astronomy
- Hunter College and the Graduate Center of the City University of New York
- New York
- USA
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28
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Affiliation(s)
- Kai Luo
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
- Department of Chemistry and Chemical Biology, Cornell University, 259 East Ave., Ithaca, New York 14850, USA
| | - Johanna I. Fuks
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Neepa T. Maitra
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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29
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Affiliation(s)
- Neepa T. Maitra
- Department of Physics and Astronomy, Hunter College and the Physics Program at the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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30
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Fuks JI, Nielsen SEB, Ruggenthaler M, Maitra NT. Time-dependent density functional theory beyond Kohn–Sham Slater determinants. Phys Chem Chem Phys 2016; 18:20976-85. [DOI: 10.1039/c6cp00722h] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [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
Different choices of initial Kohn Sham wavefunction shape the time-dependent exchange–correlation potential.
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Affiliation(s)
- Johanna I. Fuks
- Department of Physics and Astronomy
- Hunter College and the Graduate Center of the City University of New York
- New York
- USA
| | - Søren E. B. Nielsen
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics
- 22761 Hamburg
- Germany
- Institut für Theoretische Physik
- Universität Innsbruck
| | - Michael Ruggenthaler
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics
- 22761 Hamburg
- Germany
- Institut für Theoretische Physik
- Universität Innsbruck
| | - Neepa T. Maitra
- Department of Physics and Astronomy
- Hunter College and the Graduate Center of the City University of New York
- New York
- USA
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31
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Khosravi E, Abedi A, Maitra NT. Exact Potential Driving the Electron Dynamics in Enhanced Ionization of H(2)(+). Phys Rev Lett 2015; 115:263002. [PMID: 26764989 DOI: 10.1103/physrevlett.115.263002] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2015] [Indexed: 06/05/2023]
Abstract
It was recently shown that the exact factorization of the electron-nuclear wave function allows the construction of a Schrödinger equation for the electronic system, in which the potential contains exactly the effect of coupling to the nuclear degrees of freedom and any external fields. Here we study the exact potential acting on the electron in charge-resonance enhanced ionization in a model one-dimensional H(2)(+) molecule. We show there can be significant differences between the exact potential and that used in the traditional quasistatic analyses, arising from nonadiabatic coupling to the nuclear system, and that these are crucial to include for accurate simulations of time-resolved ionization dynamics and predictions of the ionization yield.
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Affiliation(s)
- Elham Khosravi
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco CFM CSIC-UPV/EHU-MPC and DIPC, Av. Tolosa 72, 20018 San Sebastián, Spain
| | - Ali Abedi
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco CFM CSIC-UPV/EHU-MPC and DIPC, Av. Tolosa 72, 20018 San Sebastián, Spain
| | - Neepa T Maitra
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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32
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Agostini F, Abedi A, Suzuki Y, Min SK, Maitra NT, Gross EKU. The exact forces on classical nuclei in non-adiabatic charge transfer. J Chem Phys 2015; 142:084303. [PMID: 25725727 DOI: 10.1063/1.4908133] [Citation(s) in RCA: 78] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect.
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Affiliation(s)
- Federica Agostini
- Max-Planck-Institut of Microstructure Physics, Weinberg 2, D-06120 Halle, Germany
| | - Ali Abedi
- Max-Planck-Institut of Microstructure Physics, Weinberg 2, D-06120 Halle, Germany
| | - Yasumitsu Suzuki
- Max-Planck-Institut of Microstructure Physics, Weinberg 2, D-06120 Halle, Germany
| | - Seung Kyu Min
- Max-Planck-Institut of Microstructure Physics, Weinberg 2, D-06120 Halle, Germany
| | - Neepa T Maitra
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - E K U Gross
- Max-Planck-Institut of Microstructure Physics, Weinberg 2, D-06120 Halle, Germany
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33
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Fuks JI, Luo K, Sandoval ED, Maitra NT. Time-resolved spectroscopy in time-dependent density functional theory: an exact condition. Phys Rev Lett 2015; 114:183002. [PMID: 26000998 PMCID: PMC6135656 DOI: 10.1103/physrevlett.114.183002] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2014] [Indexed: 05/17/2023]
Abstract
A fundamental property of a quantum system driven by an external field is that when the field is turned off the positions of its response frequencies are independent of the time at which the field is turned off. We show that this leads to an exact condition for the exchange-correlation potential of time-dependent density functional theory. The Kohn-Sham potential typically continues to evolve after the field is turned off, which leads to time dependence in the response frequencies of the Kohn-Sham response function. The exchange-correlation kernel must cancel out this time dependence. The condition is typically violated by approximations currently in use, as we demonstrate by several examples, which has severe consequences for their predictions of time-resolved spectroscopy.
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Affiliation(s)
- Johanna I Fuks
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Kai Luo
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Ernesto D Sandoval
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Neepa T Maitra
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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34
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Luo K, Fuks JI, Sandoval ED, Elliott P, Maitra NT. Kinetic and interaction components of the exact time-dependent correlation potential. J Chem Phys 2015; 140:18A515. [PMID: 24832323 DOI: 10.1063/1.4867002] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
The exact exchange-correlation (xc) potential of time-dependent density functional theory has been shown to have striking features. For example, step and peak features are generically found when the system is far from its ground-state, and these depend nonlocally on the density in space and time. We analyze the xc potential by decomposing it into kinetic and interaction components and comparing each with their exact-adiabatic counterparts, for a range of dynamical situations in model one-dimensional two-electron systems. We find that often, but not always, the kinetic contribution is largely responsible for these features that are missed by the adiabatic approximation. The adiabatic approximation often makes a smaller error for the interaction component, which we write in two parts, one being the Coulomb potential due to the time-dependent xc hole. Non-adiabatic features of the kinetic component were also larger than those of the interaction component in cases that we studied when there is negligible step structure. In ground-state situations, step and peak structures arise in cases of static correlation, when more than one determinant is essential to describe the interacting state. We investigate the time-dependent natural orbital occupation numbers and find the corresponding relation between these and the dynamical step is more complex than for the ground-state case.
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Affiliation(s)
- Kai Luo
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Johanna I Fuks
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Ernesto D Sandoval
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Peter Elliott
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, 06120 Halle (Saale), Germany
| | - Neepa T Maitra
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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Suzuki Y, Abedi A, Maitra NT, Gross EKU. Laser-induced electron localization in H2+: mixed quantum-classical dynamics based on the exact time-dependent potential energy surface. Phys Chem Chem Phys 2015; 17:29271-80. [DOI: 10.1039/c5cp03418c] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
The exact nuclear time-dependent potential energy surface for laser-induced electron localization is studied with a view to developing a mixed quantum-classical dynamics method for strong-field processes.
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Affiliation(s)
| | - Ali Abedi
- Max-Planck Institut für Mikrostrukturphysik
- D-06120 Halle
- Germany
- Department of Physics and Astronomy
- Hunter College and the City University of New York
| | - Neepa T. Maitra
- Department of Physics and Astronomy
- Hunter College and the City University of New York
- New York
- USA
| | - E. K. U. Gross
- Max-Planck Institut für Mikrostrukturphysik
- D-06120 Halle
- Germany
- European Theoretical Spectroscopy Facility (ETSF)
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Fuks JI, Maitra NT. Challenging adiabatic time-dependent density functional theory with a Hubbard dimer: the case of time-resolved long-range charge transfer. Phys Chem Chem Phys 2014; 16:14504-13. [DOI: 10.1039/c4cp00118d] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Adiabatic TDDFT fails for time-resolved charge-transfer in a simple model, even when linear response spectra is accurate.
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Affiliation(s)
- Johanna I Fuks
- Department of Physics and Astronomy, Hunter College and the City University of New York, 695 Park Avenue, New York, New York 10065, USA.
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Abedi A, Maitra NT, Gross EKU. Response to “Comment on ‘Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction”' [J. Chem. Phys. 139, 087101 (2013)]. J Chem Phys 2013; 139:087102. [DOI: 10.1063/1.4818523] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Abstract
We show that whenever an electron transfers between closed-shell molecular fragments, the exact correlation potential of time-dependent density functional theory develops a step and peak structure in the bonding region. This structure has a density dependence that is nonlocal both in space and in time that even the exact adiabatic ground-state exchange-correlation functional fails to capture it. For charge-transfer between open-shell fragments, an initial step and peak vanish as the charge-transfer state is reached. The inability of usual approximations to develop these structures leads to inaccurate charge-transfer dynamics. This is illustrated by the complete lack of Rabi oscillations in the dipole moment under conditions of resonant charge transfer for an exactly solvable model system. The results transcend the model and are applicable to more realistic molecular complexes.
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Affiliation(s)
- J I Fuks
- †Nano-Bio Spectroscopy Group, Departamento Fı́sica de Materiales, Universidad del Paı́s Vasco, Centro de Fı́sica de Materiales CSIC-UPV/EHU-MPC and DIPC, Av. Tolosa 72, E-20018 San Sebastián, Spain
| | - P Elliott
- ‡Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, 06120 Halle (Saale), Germany
| | - A Rubio
- †Nano-Bio Spectroscopy Group, Departamento Fı́sica de Materiales, Universidad del Paı́s Vasco, Centro de Fı́sica de Materiales CSIC-UPV/EHU-MPC and DIPC, Av. Tolosa 72, E-20018 San Sebastián, Spain
- §Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
| | - N T Maitra
- ⊥Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, United States
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Abstract
It was recently shown [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] that the complete wavefunction for a system of electrons and nuclei evolving in a time-dependent external potential can be exactly factorized into an electronic wavefunction and a nuclear wavefunction. The concepts of an exact time-dependent potential energy surface (TDPES) and exact time-dependent vector potential emerge naturally from the formalism. Here, we present a detailed description of the formalism, including a full derivation of the equations that the electronic and nuclear wavefunctions satisfy. We demonstrate the relationship of this exact factorization to the traditional Born-Oppenheimer expansion. A one-dimensional model of the H(2)(+) molecule in a laser field shows the usefulness of the exact TDPES in interpreting coupled electron-nuclear dynamics: we show how features of its structure indicate the mechanism of dissociation. We compare the exact TDPES with potential energy surfaces from the time-dependent Hartree-approach, and also compare traditional Ehrenfest dynamics with Ehrenfest dynamics on the exact TDPES.
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Affiliation(s)
- Ali Abedi
- Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
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Elliott P, Fuks JI, Rubio A, Maitra NT. Universal dynamical steps in the exact time-dependent exchange-correlation potential. Phys Rev Lett 2012; 109:266404. [PMID: 23368591 DOI: 10.1103/physrevlett.109.266404] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2012] [Indexed: 06/01/2023]
Abstract
We show that the exact exchange-correlation potential of time-dependent density-functional theory displays dynamical step structures that have a spatially nonlocal and time nonlocal dependence on the density. Using one-dimensional two-electron model systems, we illustrate these steps for a range of nonequilibrium dynamical situations relevant for modeling of photochemical or physical processes: field-free evolution of a nonstationary state, resonant local excitation, resonant complete charge transfer, and evolution under an arbitrary field. A lack of these steps in the usual approximations yields inaccurate dynamics, for example, predicting faster dynamics and incomplete charge transfer.
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Affiliation(s)
- P Elliott
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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Roy D, Marianski M, Maitra NT, Dannenberg JJ. Comparison of some dispersion-corrected and traditional functionals with CCSD(T) and MP2 ab initio methods: dispersion, induction, and basis set superposition error. J Chem Phys 2012; 137:134109. [PMID: 23039587 PMCID: PMC3477180 DOI: 10.1063/1.4755990] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2012] [Accepted: 09/17/2012] [Indexed: 11/14/2022] Open
Abstract
We compare dispersion and induction interactions for noble gas dimers and for Ne, methane, and 2-butyne with HF and LiF using a variety of functionals (including some specifically parameterized to evaluate dispersion interactions) with ab initio methods including CCSD(T) and MP2. We see that inductive interactions tend to enhance dispersion and may be accompanied by charge-transfer. We show that the functionals do not generally follow the expected trends in interaction energies, basis set superposition errors (BSSE), and interaction distances as a function of basis set size. The functionals parameterized to treat dispersion interactions often overestimate these interactions, sometimes by quite a lot, when compared to higher level calculations. Which functionals work best depends upon the examples chosen. The B3LYP and X3LYP functionals, which do not describe pure dispersion interactions, appear to describe dispersion mixed with induction about as accurately as those parametrized to treat dispersion. We observed significant differences in high-level wavefunction calculations in a basis set larger than those used to generate the structures in many of the databases. We discuss the implications for highly parameterized functionals based on these databases, as well as the use of simple potential energy for fitting the parameters rather than experimentally determinable thermodynamic state functions that involve consideration of vibrational states.
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Affiliation(s)
- Dipankar Roy
- Departments of Chemistry, City University of New York-Hunter College and the Graduate School, 695 Park Avenue, New York, New York 10065, USA
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Abstract
Within nonrelativistic quantum mechanics, spatial cusps in initial wave functions can lead to nonanalytic behavior in time. We suggest a method for calculating the short-time behavior in such situations. For these cases, the density does not match its Taylor expansion in time, but the Runge-Gross proof of time-dependent density functional theory still holds, as it requires only the potential to be time analytic.
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Affiliation(s)
- Zeng-hui Yang
- Department of Chemistry, University of California-Irvine, Irvine, California 92697, USA
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Abstract
We investigate the accuracy and efficiency of the semiclassical frozen Gaussian method in describing electron dynamics in real time. Model systems of two soft-Coulomb-interacting electrons are used to study correlated dynamics under non-perturbative electric fields, as well as the excitation spectrum. The results show that a recently proposed method that combines exact-exchange with semiclassical correlation to propagate the one-body density-matrix holds promise for electron dynamics in many situations that either wavefunction or density-functional methods have difficulty describing. The results also however point out challenges in such a method that need to be addressed before it can become widely applicable.
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Affiliation(s)
- Peter Elliott
- Department of Physics and Astronomy, Hunter College and the City University of New York, 695 Park Avenue, New York, New York 10065, USA.
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Abstract
We present an exact decomposition of the complete wave function for a system of nuclei and electrons evolving in a time-dependent external potential. We derive formally exact equations for the nuclear and electronic wave functions that lead to rigorous definitions of a time-dependent potential energy surface (TDPES) and a time-dependent geometric phase. For the H(2)(+) molecular ion exposed to a laser field, the TDPES proves to be a useful interpretive tool to identify different mechanisms of dissociation.
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Affiliation(s)
- Ali Abedi
- Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
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Rajam AK, Raczkowska I, Maitra NT. Semiclassical electron correlation in density-matrix time propagation. Phys Rev Lett 2010; 105:113002. [PMID: 20867568 DOI: 10.1103/physrevlett.105.113002] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2010] [Indexed: 05/29/2023]
Abstract
Lack of memory (locality in time) is a major limitation of almost all present time-dependent density-functional approximations. By using semiclassical dynamics to compute correlation effects in the time propagation of the density matrix, we incorporate memory, including initial-state dependence, as well as changing occupation numbers, and predict more observables in strong-field applications.
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Affiliation(s)
- A K Rajam
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Ave, New York, New York 10065, USA
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Affiliation(s)
- David G. Tempel
- Department of Physics and Astronomy, Hunter College and City University of New York, 695 Park Avenue, New York, New York 10065, and Department of Chemistry and The Beckman Institute, University of Illinois, Urbana, Illinois 61801
| | - Todd J. Martínez
- Department of Physics and Astronomy, Hunter College and City University of New York, 695 Park Avenue, New York, New York 10065, and Department of Chemistry and The Beckman Institute, University of Illinois, Urbana, Illinois 61801
| | - Neepa T. Maitra
- Department of Physics and Astronomy, Hunter College and City University of New York, 695 Park Avenue, New York, New York 10065, and Department of Chemistry and The Beckman Institute, University of Illinois, Urbana, Illinois 61801
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Maitra NT, Burke K. Comment on “Analysis of Floquet formulation of time-dependent density-functional theory”[Chem. Phys. Lett. 433 (2006) 204]. Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2007.04.091] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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