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Shafir U, Kosloff R. Wave Function Realization of a Thermal Collision Model. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1808. [PMID: 36554213 PMCID: PMC9777790 DOI: 10.3390/e24121808] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Revised: 12/05/2022] [Accepted: 12/07/2022] [Indexed: 06/17/2023]
Abstract
An efficient algorithm to simulate dynamics of open quantum system is presented. The method describes the dynamics by unraveling stochastic wave functions converging to a density operator description. The stochastic techniques are based on the quantum collision model. Modeling systems dynamics with wave functions and modeling the interaction with the environment with a collision sequence reduces the scale of the complexity significantly. The algorithm developed can be implemented on quantum computers. We introduce stochastic methods that exploit statistical characteristics of the model such as Markovianity, Brownian motion, and binary distribution. The central limit theorem is employed to study the convergence of distributions of stochastic dynamics of pure quantum states represented by wave vectors. By averaging a sample of functions in the distribution we prove and demonstrate the convergence of the dynamics to the mixed quantum state described by a density operator.
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2
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Habecker F, Röhse R, Klüner T. Dissipative quantum dynamics using the stochastic surrogate Hamiltonian approach. J Chem Phys 2019; 151:134113. [PMID: 31594331 DOI: 10.1063/1.5119195] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Based on the original Stochastic Surrogate Hamiltonian approach for the simulation of open quantum system dynamics, we present a modified algorithm for the swap procedure. The implementation is tested with nuclear relaxation dynamics of model systems known from literature, i.e., the harmonic oscillator and the Morse oscillator. Finally, the stochastic surrogate Hamiltonian is applied to simulate the dynamical electronic excitation and relaxation of a photodesorption process. This is the first application of the stochastic surrogate Hamiltonian in an ab initio context. A comparison to a surrogate Hamiltonian benchmark allows us to evaluate the results obtained. For this purpose, the well-studied laser-induced desorption of NO from NiO(100) is chosen.
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Affiliation(s)
- F Habecker
- Theoretical Chemistry, Department of Chemistry, Carl von Ossietzky University of Oldenburg, Ammerländer Heerstr. 114-118, Oldenburg D-26129, Germany
| | - R Röhse
- Theoretical Chemistry, Department of Chemistry, Carl von Ossietzky University of Oldenburg, Ammerländer Heerstr. 114-118, Oldenburg D-26129, Germany
| | - T Klüner
- Theoretical Chemistry, Department of Chemistry, Carl von Ossietzky University of Oldenburg, Ammerländer Heerstr. 114-118, Oldenburg D-26129, Germany
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3
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Petersen T, Mitschker J, Klüner T. High-dimensional wave packet dynamics from first principles: Photodissociation of water on TiO2-rutile (110). J Photochem Photobiol A Chem 2018. [DOI: 10.1016/j.jphotochem.2018.01.037] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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4
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Lee MH, Troisi A. Vibronic enhancement of excitation energy transport: Interplay between local and non-local exciton-phonon interactions. J Chem Phys 2017; 146:075101. [DOI: 10.1063/1.4976558] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Affiliation(s)
- Myeong H. Lee
- Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Alessandro Troisi
- Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom
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5
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Lee MH, Troisi A. Quantum dynamics of a vibronically coupled linear chain using a surrogate Hamiltonian approach. J Chem Phys 2016; 144:214106. [DOI: 10.1063/1.4953043] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Myeong H. Lee
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Alessandro Troisi
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
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6
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Joubert-Doriol L, Ryabinkin IG, Izmaylov AF. Non-stochastic matrix Schrödinger equation for open systems. J Chem Phys 2014; 141:234112. [PMID: 25527924 DOI: 10.1063/1.4903829] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
We propose an extension of the Schrödinger equation for a quantum system interacting with environment. This extension describes dynamics of a collection of auxiliary wavefunctions organized as a matrix m, from which the system density matrix can be reconstructed as ρ̂=mm(†). We formulate a compatibility condition, which ensures that the reconstructed density satisfies a given quantum master equation for the system density. The resulting non-stochastic evolution equation preserves positive-definiteness of the system density and is applicable to both Markovian and non-Markovian system-bath treatments. Our formalism also resolves a long-standing problem of energy loss in the time-dependent variational principle applied to mixed states of closed systems.
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Affiliation(s)
- Loïc Joubert-Doriol
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
| | - Ilya G Ryabinkin
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
| | - Artur F Izmaylov
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
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Asplund E, Klüner T. Quantum dynamical study of femtosecond photodesorption of CO from TiO2(110). J Chem Phys 2014; 141:084715. [PMID: 25173038 DOI: 10.1063/1.4893528] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Abstract
The photodesorption of CO from TiO2(110) by femtosecond pulses is investigated with the Surrogate Hamiltonian approach. The aim of the study is to resolve the relaxation mechanism and forecast the lifetime of the exited state based on a microscopic description of the excitation and relaxation processes. The parameters characterizing the system are obtained from ab initio and Density Functional Theory-calculations with one parameter estimated from physical considerations and convergence studies. Two electronic states are considered and the relaxation is assumed to be due to the interaction of the excited adsorbate with electron hole pairs in the surface. Desorption probabilities and velocity distributions of the desorbing molecules are calculated and an exited state lifetime is predicted. Throughout this paper atomic units, i.e., ℏ = me = e = a0 = 1, have been used unless otherwise stated.
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Affiliation(s)
- Erik Asplund
- Theoretische Chemie, Institut für Chemie, Carl von Ossietzky Universität Oldenburg, Ammerländer Heerstr. 114-118, D-26129 Oldenburg, Germany
| | - Thorsten Klüner
- Theoretische Chemie, Institut für Chemie, Carl von Ossietzky Universität Oldenburg, Ammerländer Heerstr. 114-118, D-26129 Oldenburg, Germany
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8
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Asplund E, Klüner T. A Surrogate Hamiltonian study of femtosecond photodesorption of CO from NiO(100). Mol Phys 2013. [DOI: 10.1080/00268976.2013.813589] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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9
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Sousa C, Tosoni S, Illas F. Theoretical Approaches to Excited-State-Related Phenomena in Oxide Surfaces. Chem Rev 2012. [DOI: 10.1021/cr300228z] [Citation(s) in RCA: 71] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Affiliation(s)
- Carmen Sousa
- Departament de Química
Física and Institut de Química Teòrica i Computacional
(IQTCUB), Universitat de Barcelona, C/Martí
i Franquès 1, 08028 Barcelona, Spain
| | - Sergio Tosoni
- Departament de Química
Física and Institut de Química Teòrica i Computacional
(IQTCUB), Universitat de Barcelona, C/Martí
i Franquès 1, 08028 Barcelona, Spain
- Departamento de Química, Universidad de Las Palmas de Gran Canaria, Campus Universitario
de Tafira, 35017 Las Palmas de Gran Canaria, Spain
| | - Francesc Illas
- Departament de Química
Física and Institut de Química Teòrica i Computacional
(IQTCUB), Universitat de Barcelona, C/Martí
i Franquès 1, 08028 Barcelona, Spain
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10
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Affiliation(s)
- Jan Mitschker
- Institute of Pure and Applied
Chemistry, Theoretical
Chemistry, Carl von Ossietzky Universität Oldenburg, Carl-von-Ossietzky Straße 9-11, 26129 Oldenburg, Germany
| | - Thorsten Klüner
- Institute of Pure and Applied
Chemistry, Theoretical
Chemistry, Carl von Ossietzky Universität Oldenburg, Carl-von-Ossietzky Straße 9-11, 26129 Oldenburg, Germany
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11
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Asplund E, Klüner T. Optimal control of open quantum systems: A combined surrogate Hamiltonian optimal control theory approach applied to photochemistry on surfaces. J Chem Phys 2012; 136:124118. [DOI: 10.1063/1.3698289] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
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12
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Katz G, Ratner MA, Kosloff R. Hot Injection Dynamics: Design Mechanisms and Ideas. J Phys Chem A 2010; 115:5833-7. [DOI: 10.1021/jp109706h] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Affiliation(s)
- Gil Katz
- Fritz Haber Research Center for Molecular Dynamics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel
| | - Mark A. Ratner
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208-3113, United States
| | - Ronnie Kosloff
- Institute of Chemistry and the Fritz Haber Research Center for Molecular Dynamics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel
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Chulkov EV, Borisov AG, Gauyacq JP, Sanchez-Portal D, Silkin VM, Zhukov VP, Echenique PM. Electronic Excitations in Metals and at Metal Surfaces. Chem Rev 2006; 106:4160-206. [PMID: 17031983 DOI: 10.1021/cr050166o] [Citation(s) in RCA: 208] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- E V Chulkov
- Departamento de Física de Materiales and Centro Mixto CSIC-UPV/EHU, Facultad de Ciencias Químicas, Universidad del País Vasco UPV/EHU, Apdo. 1072, 20080 San Sebastian/Donostia, Basque Country, Spain.
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14
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Dittrich S, Klüner T. The role of laser pulse duration in the photodesorption of NO/NiO(100). Chem Phys Lett 2006. [DOI: 10.1016/j.cplett.2006.09.017] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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15
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Saalfrank P. Quantum Dynamical Approach to Ultrafast Molecular Desorption from Surfaces. Chem Rev 2006; 106:4116-59. [PMID: 17031982 DOI: 10.1021/cr0501691] [Citation(s) in RCA: 130] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Peter Saalfrank
- Theoretische Chemie, Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm, Germany
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16
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Nakamura H, Yamashita K. Theoretical study of the photodesorption mechanism of nitric oxide on a Ag(111) surface: A nonequilibrium Green’s function approach to hot-electron tunneling. J Chem Phys 2006; 125:084708. [PMID: 16965040 DOI: 10.1063/1.2338027] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The photoinduced desorption of NO molecules on a Ag surface was studied theoretically using a recently developed method based on the nonequilibrium Green's function approach combined with the density functional theory. Geometry optimizations for the stable NO dimer phase were carried out, and two structures of adsorbed dimers were identified. We calculated the reaction probabilities as a function of incident photon energy for each of the dimers and compared them with experimental action spectra. The two main features of the action spectra, (i) a long tail to the long wavelength (approximately 600 nm) and (ii) a rapid increase at approximately 350 nm, were well reproduced. By theoretical analysis, we found the importance of quantum interference for the interfacial charge transfer between the metal substrate and the adsorbate, as well as the contribution of secondary electrons. Our calculations suggest that the photoactive species is dimeric and that the resonant level is single for the photodesorption of NO.
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Affiliation(s)
- Hisao Nakamura
- Department of Chemical System Engineering, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan.
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Velocity distribution of CO desorbing from NiO(100)/Ni(100) after picosecond UV laser irradiation. Chem Phys Lett 2006. [DOI: 10.1016/j.cplett.2005.12.057] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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18
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Dittrich S, Freund HJ, Koch CP, Kosloff R, Klüner T. Two-dimensional surrogate Hamiltonian investigation of laser-induced desorption of NO∕NiO(100). J Chem Phys 2006; 124:024702. [PMID: 16422621 DOI: 10.1063/1.2140697] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
The photodesorption of NO from NiO(100) is studied from first principles, with electronic relaxation treated by the use of the surrogate Hamiltonian approach. Two nuclear degrees of freedom of the adsorbate-substrate system are taken into account. To perform the quantum dynamical wave-packet calculations, a massively parallel implementation with a one-dimensional data decomposition had to be introduced. The calculated desorption probabilities and velocity distributions are in qualitative agreement with experimental data. The results are compared to those of stochastic wave-packet calculations where a sufficiently large number of quantum trajectories is propagated within a jumping wave-packet scenario.
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Affiliation(s)
- Sören Dittrich
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
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Bach C, Carbogno C, Gross A. Mixed quantum-classical treatment of reactions at surfaces with electronic transitions. Isr J Chem 2005. [DOI: 10.1560/t4cn-fwag-yyxe-l7g7] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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20
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Katz G, Zeiri Y, Kosloff R. Nonadiabatic charge transfer processes of oxygen on metal surfaces. Isr J Chem 2005. [DOI: 10.1560/tff4-y5jm-3lpq-d2fj] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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21
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Gelman D, Koch CP, Kosloff R. Dissipative quantum dynamics with the surrogate Hamiltonian approach. A comparison between spin and harmonic baths. J Chem Phys 2004; 121:661-71. [PMID: 15260592 DOI: 10.1063/1.1759312] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The dissipative quantum dynamics of an anharmonic oscillator coupled to a bath is studied with the purpose of elucidating the differences between the relaxation to a spin bath and to a harmonic bath. Converged results are obtained for the spin bath by the surrogate Hamiltonian approach. This method is based on constructing a system-bath Hamiltonian, with a finite but large number of spin bath modes, that mimics exactly a bath with an infinite number of modes for a finite time interval. Convergence with respect to the number of simultaneous excitations of bath modes can be checked. The results are compared to calculations that include a finite number of harmonic modes carried out by using the multiconfiguration time-dependent Hartree method of Nest and Meyer [J. Chem. Phys. 119, 24 (2003)]. In the weak coupling regime, at zero temperature and for small excitations of the primary system, both methods converge to the Markovian limit. When initially the primary system is significantly excited, the spin bath can saturate restricting the energy acceptance. An interaction term between bath modes that spreads the excitation eliminates the saturation. The loss of phase between two cat states has been analyzed and the results for the spin and harmonic baths are almost identical. For stronger couplings, the dynamics induced by the two types of baths deviate. The accumulation and degree of entanglement between the bath modes have been characterized. Only in the spin bath the dynamics generate entanglement between the bath modes.
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Affiliation(s)
- David Gelman
- Fritz Haber Research Center for Molecular Dynamics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel
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