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Fischer EW, Werther M, Bouakline F, Grossmann F, Saalfrank P. Non-Markovian Vibrational Relaxation Dynamics at Surfaces. J Chem Phys 2022; 156:214702. [DOI: 10.1063/5.0092836] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Vibrational dynamics of adsorbates near surfaces plays both an important role for applied surface science and as model lab for studying fundamental problems of open quantum systems. We employ a previously developed model for the relaxation of a D-Si-Si bending mode at a D:Si(100)-(2$\times$1) surface, induced by a ``bath' of more than $2000$ phonon modes [U. Lorenz, P. Saalfrank, Chem. Phys. {\bf 482}, 69 (2017)], to extend previous work along various directions. First, we use a Hierarchical Effective Mode (HEM) model [E.W. Fischer, F. Bouakline, M. Werther, P. Saalfrank, J. Chem. Phys. {\bf 153}, 064704 (2020)] to study relaxation of higher excited vibrational states than hitherto done, by solving a high-dimensional system-bath time-dependent Schr\"odinger equation (TDSE). In the HEM approach, (many) real bath modes are replaced by (much less) effective bath modes. Accordingly, we are able to examine scaling laws for vibrational relaxation lifetimes for a realistic surface science problem. Second, we compare the performance of the multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) approach with the recently developed coherent-state based multi-Davydov D2 {\it ansatz} [N. Zhou, Z. Huang, J. Zhu, V. Chernyak, Y. Zhao, {J. Chem. Phys.} {\bf 143}, 014113 (2015)]. Both approaches work well, with some computational advantages for the latter in the presented context. Third, we apply open-system density matrix theory in comparison with basically ``exact' solutions of the multi-mode TDSEs. Specifically, we use an open-system Liouville-von Neumann (LvN) equation treating vibration-phonon coupling as Markovian dissipation in Lindblad form to quantify effects beyond the Born-Markov approximation.
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Affiliation(s)
| | | | - Foudhil Bouakline
- Institute of Chemistry, Universität Potsdam Institut für Chemie, Germany
| | - Frank Grossmann
- Institute for Theoretical Physics, Technische Universität Dresden Fachrichtung Physik, Germany
| | - Peter Saalfrank
- Institut für Chemie, Universität Potsdam Institut für Chemie, Germany
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2
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Ollitrault PJ, Mazzola G, Tavernelli I. Nonadiabatic Molecular Quantum Dynamics with Quantum Computers. PHYSICAL REVIEW LETTERS 2020; 125:260511. [PMID: 33449795 DOI: 10.1103/physrevlett.125.260511] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2020] [Accepted: 12/10/2020] [Indexed: 05/11/2023]
Abstract
The theoretical investigation of nonadiabatic processes is hampered by the complexity of the coupled electron-nuclear dynamics beyond the Born-Oppenheimer approximation. Classically, the simulation of such reactions is limited by the unfavorable scaling of the computational resources as a function of the system size. While quantum computing exhibits proven quantum advantage for the simulation of real-time dynamics, the study of quantum algorithms for the description of nonadiabatic phenomena is still unexplored. In this Letter, we propose a quantum algorithm for the simulation of fast nonadiabatic chemical processes together with an initialization scheme for quantum hardware calculations. In particular, we introduce a first-quantization method for the time evolution of a wave packet on two coupled harmonic potential energy surfaces (Marcus model). In our approach, the computational resources scale polynomially in the system dimensions, opening up new avenues for the study of photophysical processes that are classically intractable.
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Affiliation(s)
- Pauline J Ollitrault
- IBM Quantum, IBM Research-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Guglielmo Mazzola
- IBM Quantum, IBM Research-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Ivano Tavernelli
- IBM Quantum, IBM Research-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
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Werther M, Choudhury SL, Großmann F. Coherent state based solutions of the time-dependent Schrödinger equation: hierarchy of approximations to the variational principle. INT REV PHYS CHEM 2020. [DOI: 10.1080/0144235x.2020.1823168] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Michael Werther
- Max-Planck-Institut für Physik Komplexer Systeme, Dresden, Germany
- Institut für Theoretische Physik, Technische Universität Dresden, Dresden, Germany
| | | | - Frank Großmann
- Institut für Theoretische Physik, Technische Universität Dresden, Dresden, Germany
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Titov E, Humeniuk A, Mitrić R. Comparison of moving and fixed basis sets for nonadiabatic quantum dynamics at conical intersections. Chem Phys 2020. [DOI: 10.1016/j.chemphys.2019.110526] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
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6
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Bouakline F, Fischer EW, Saalfrank P. A quantum-mechanical tier model for phonon-driven vibrational relaxation dynamics of adsorbates at surfaces. J Chem Phys 2019; 150:244105. [DOI: 10.1063/1.5099902] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- F. Bouakline
- Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm, Germany
| | - E. W. Fischer
- Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm, Germany
| | - P. Saalfrank
- Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm, Germany
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7
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Picconi D, Cina JA, Burghardt I. Quantum dynamics and spectroscopy of dihalogens in solid matrices. I. Efficient simulation of the photodynamics of the embedded I 2Kr 18 cluster using the G-MCTDH method. J Chem Phys 2019; 150:064111. [PMID: 30770011 DOI: 10.1063/1.5082650] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
The molecular dynamics following the electronic BΠu30+⟵XΣg+1 photoexcitation of the iodine molecule embedded in solid krypton are studied quantum mechanically using the Gaussian variant of the multiconfigurational time-dependent Hartree method (G-MCTDH). The accuracy of the Gaussian wave packet approximation is validated against numerically exact MCTDH simulations for a fully anharmonic seven-dimensional model of the I2Kr18 cluster in a crystal Kr cage. The linear absorption spectrum, time-evolving vibrational probability densities, and I2 energy expectation value are accurately reproduced by the numerically efficient G-MCTDH approach. The reduced density matrix of the chromophore is analyzed in the coordinate, Wigner and energy representations, so as to obtain a multifaceted dynamical view of the guest-host interactions. Vibrational coherences extending over the bond distance range 2.7 Å < RI-I < 4.0 Å are found to survive for several vibrational periods, despite extensive dissipation. The present results prepare the ground for the simulation of time-resolved coherent Raman spectroscopy of the I2-krypton system addressed in Paper II.
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Affiliation(s)
- David Picconi
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Straße 7, D-60438 Frankfurt am Main, Germany
| | - Jeffrey A Cina
- Department of Chemistry and Biochemistry, and Oregon Center for Optical, Molecular, and Quantum Science, University of Oregon, Eugene, Oregon 97403, USA
| | - Irene Burghardt
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Straße 7, D-60438 Frankfurt am Main, Germany
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Eisenbrandt P, Ruckenbauer M, Römer S, Burghardt I. Gaussian-based multiconfiguration time-dependent Hartree: A two-layer approach. II. Application to vibrational energy transport in a molecular chain. J Chem Phys 2018; 149:174101. [DOI: 10.1063/1.5053414] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- P. Eisenbrandt
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt, Germany
| | - M. Ruckenbauer
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt, Germany
| | - S. Römer
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt, Germany
| | - I. Burghardt
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt, Germany
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Bonfanti M, Petersen J, Eisenbrandt P, Burghardt I, Pollak E. Computation of the S 1 ← S 0 Vibronic Absorption Spectrum of Formaldehyde by Variational Gaussian Wavepacket and Semiclassical IVR Methods. J Chem Theory Comput 2018; 14:5310-5323. [PMID: 30141930 DOI: 10.1021/acs.jctc.8b00355] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The vibronic absorption spectrum of the electric dipole forbidden and vibronically allowed S1(1 A2) ← S0(1 A1) transition of formaldehyde is calculated by Gaussian wavepacket and semiclassical methods, along with numerically exact reference calculations, using the potential energy surface of Fu, Shepler, and Bowman ( J. Am. Chem. Soc. 2011, 133, 7957). Specifically, the variational multiconfigurational Gaussian (vMCG) approach and the Herman-Kluk semiclassical initial value representation (HK-SCIVR) are compared to assess the accuracy and convergence of these methods, benchmarked against numerically exact time-dependent wavepacket propagation (TDWP) on the reference potential energy surface. The vMCG calculation is shown to converge quite well with about 100 variationally evolving Gaussian functions and using a local cubic expansion instead of the conventional local harmonic approximation. By contrast, the HK-SCIVR approach with ∼105 trajectories reproduces the vibrationally structured spectral envelope correctly but yields a strongly broadened spectrum. The comparison of the computed absorption spectrum with experiment shows that the relevant vibronic progressions are reasonably reproduced by all computations, but deviations of the order of 10-100 cm-1 occur, underscoring that both electronic structure calculations and dynamical approaches remain challenging in the calculation of typical small-molecule excited-state spectra by trajectory-based methods.
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Affiliation(s)
- Matteo Bonfanti
- Institute of Physical and Theoretical Chemistry , Goethe University Frankfurt , Max-von-Laue-Str. 7 , D-60438 Frankfurt/Main , Germany
| | - Jakob Petersen
- Chemical and Biological Physics Department , Weizmann Institute of Science , 76000 Rehovot , Israel
| | - Pierre Eisenbrandt
- Institute of Physical and Theoretical Chemistry , Goethe University Frankfurt , Max-von-Laue-Str. 7 , D-60438 Frankfurt/Main , Germany
| | - Irene Burghardt
- Institute of Physical and Theoretical Chemistry , Goethe University Frankfurt , Max-von-Laue-Str. 7 , D-60438 Frankfurt/Main , Germany
| | - Eli Pollak
- Chemical and Biological Physics Department , Weizmann Institute of Science , 76000 Rehovot , Israel
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Comparison of the results of a mean-field mixed quantum/classical method with full quantum predictions for nonadiabatic dynamics: application to the $$\pi \pi ^*/n\pi ^*$$ π π ∗ / n π ∗ decay of thymine. Theor Chem Acc 2018. [DOI: 10.1007/s00214-018-2218-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
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11
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Chen L, Borrelli R, Zhao Y. Dynamics of Coupled Electron–Boson Systems with the Multiple Davydov D1 Ansatz and the Generalized Coherent State. J Phys Chem A 2017; 121:8757-8770. [DOI: 10.1021/acs.jpca.7b07069] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Lipeng Chen
- Division
of Materials Science, Nanyang Technological University, 639798, Singapore
| | - Raffaele Borrelli
- Department
of Agricultural, Forestry and Food Science, Universitá di Torino, I-10095 Grugliasco, Turin, Italy
| | - Yang Zhao
- Division
of Materials Science, Nanyang Technological University, 639798, Singapore
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12
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Bouakline F, Lorenz U, Melani G, Paramonov GK, Saalfrank P. Isotopic effects in vibrational relaxation dynamics of H on a Si(100) surface. J Chem Phys 2017; 147:144703. [PMID: 29031276 DOI: 10.1063/1.4994635] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In a recent paper [U. Lorenz and P. Saalfrank, Chem. Phys. 482, 69 (2017)], we proposed a robust scheme to set up a system-bath model Hamiltonian, describing the coupling of adsorbate vibrations (system) to surface phonons (bath), from first principles. The method is based on an embedded cluster approach, using orthogonal coordinates for system and bath modes, and an anharmonic phononic expansion of the system-bath interaction up to second order. In this contribution, we use this model Hamiltonian to calculate vibrational relaxation rates of H-Si and D-Si bending modes, coupled to a fully H(D)-covered Si(100)-(2×1) surface, at zero temperature. The D-Si bending mode has an anharmonic frequency lying inside the bath frequency spectrum, whereas the H-Si bending mode frequency is outside the bath Debye band. Therefore, in the present calculations, we only take into account one-phonon system-bath couplings for the D-Si system and both one- and two-phonon interaction terms in the case of H-Si. The computation of vibrational lifetimes is performed with two different approaches, namely, Fermi's golden rule, and a generalized Bixon-Jortner model built in a restricted vibrational space of the adsorbate-surface zeroth-order Hamiltonian. For D-Si, the Bixon-Jortner Hamiltonian can be solved by exact diagonalization, serving as a benchmark, whereas for H-Si, an iterative scheme based on the recursive residue generation method is applied, with excellent convergence properties. We found that the lifetimes obtained with perturbation theory, albeit having almost the same order of magnitude-a few hundred fs for D-Si and a couple of ps for H-Si-, are strongly dependent on the discretized numerical representation of the bath spectral density. On the other hand, the Bixon-Jortner model is free of such numerical deficiencies, therefore providing better estimates of vibrational relaxation rates, at a very low computational cost. The results obtained with this model clearly show a net exponential decay of the time-dependent survival probability for the H-Si initial vibrational state, allowing an easy extraction of the bending mode "lifetime." This is in contrast with the D-Si system, whose survival probability exhibits a non-monotonic decay, making it difficult to define such a lifetime. This different behavior of the vibrational decay is rationalized in terms of the power spectrum of the adsorbate-surface system. In the case of D-Si, it consists of several, non-uniformly distributed peaks around the bending mode frequency, whereas the H-Si spectrum exhibits a single Lorentzian lineshape, whose width corresponds to the calculated lifetime. The present work gives some insight into mechanisms of vibration-phonon coupling at surfaces. It also serves as a benchmark for multidimensional system-bath quantum dynamics, for comparison with approximate schemes such as reduced, open-system density matrix theory (where the bath is traced out and a Liouville-von Neumann equation is solved) or approximate wavefunction methods to solve the combined system-bath Schrödinger equation.
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Affiliation(s)
- F Bouakline
- Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm, Germany
| | - U Lorenz
- Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm, Germany
| | - G Melani
- Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm, Germany
| | - G K Paramonov
- Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm, Germany
| | - P Saalfrank
- Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm, Germany
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13
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Borrelli R, Gelin MF. The Generalized Coherent State ansatz: Application to quantum electron-vibrational dynamics. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.05.013] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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14
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Borrelli R, Peluso A. Quantum dynamics of electronic transitions with Gauss-Hermite wave packets. J Chem Phys 2016; 144:114102. [DOI: 10.1063/1.4943538] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Raffaele Borrelli
- Department of Agricultural, Forestry and Food Science, Università di Torino, I-10095 Grugliasco, TO, Italy
| | - Andrea Peluso
- Department of Chemistry and Biology, Università di Salerno, I-84081 Fisciano, SA, Italy
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15
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Kong X, Markmann A, Batista VS. Time-Sliced Thawed Gaussian Propagation Method for Simulations of Quantum Dynamics. J Phys Chem A 2016; 120:3260-9. [DOI: 10.1021/acs.jpca.5b12192] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Xiangmeng Kong
- Department of Chemistry, Yale University, 225 Prospect
Street, New Haven, Connecticut 06520-8107, United States
| | - Andreas Markmann
- Department of Chemistry, Yale University, 225 Prospect
Street, New Haven, Connecticut 06520-8107, United States
| | - Victor S. Batista
- Department of Chemistry, Yale University, 225 Prospect
Street, New Haven, Connecticut 06520-8107, United States
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16
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Richings G, Polyak I, Spinlove K, Worth G, Burghardt I, Lasorne B. Quantum dynamics simulations using Gaussian wavepackets: the vMCG method. INT REV PHYS CHEM 2015. [DOI: 10.1080/0144235x.2015.1051354] [Citation(s) in RCA: 174] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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17
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Römer S, Burghardt I. Towards a variational formulation of mixed quantum-classical molecular dynamics. Mol Phys 2013. [DOI: 10.1080/00268976.2013.844371] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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18
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Wu N, Duan L, Li X, Zhao Y. Dynamics of the sub-Ohmic spin-boson model: A time-dependent variational study. J Chem Phys 2013; 138:084111. [DOI: 10.1063/1.4792502] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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19
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Römer S, Ruckenbauer M, Burghardt I. Gaussian-based multiconfiguration time-dependent Hartree: A two-layer approach. I. Theory. J Chem Phys 2013; 138:064106. [DOI: 10.1063/1.4788830] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
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20
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Mendive-Tapia D, Lasorne B, Worth GA, Robb MA, Bearpark MJ. Towards converging non-adiabatic direct dynamics calculations using frozen-width variational Gaussian product basis functions. J Chem Phys 2012; 137:22A548. [DOI: 10.1063/1.4765087] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Bonfanti M, Tantardini GF, Hughes KH, Martinazzo R, Burghardt I. Compact MCTDH Wave Functions for High-Dimensional System-Bath Quantum Dynamics. J Phys Chem A 2012; 116:11406-13. [DOI: 10.1021/jp3064504] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- M. Bonfanti
- Dipartimento di
Chimica, Università degli Studi di Milano, v. Golgi 19, 20133 Milano, Italy
| | - G. F. Tantardini
- Dipartimento di
Chimica, Università degli Studi di Milano, v. Golgi 19, 20133 Milano, Italy
| | - K. H. Hughes
- School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW, United
Kingdom
| | - R. Martinazzo
- Dipartimento di
Chimica, Università degli Studi di Milano, v. Golgi 19, 20133 Milano, Italy
| | - I. Burghardt
- Institute of Physical and Theoretical
Chemistry, Goethe University Frankfurt,
Max-von-Laue-Strasse 7, 60438, Frankfurt, Germany
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Bouakline F, Lüder F, Martinazzo R, Saalfrank P. Reduced and Exact Quantum Dynamics of the Vibrational Relaxation of a Molecular System Interacting with a Finite-Dimensional Bath. J Phys Chem A 2012; 116:11118-27. [DOI: 10.1021/jp304466u] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Foudhil Bouakline
- Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm, Germany
| | - Franziska Lüder
- Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm, Germany
| | - Rocco Martinazzo
- Department of Physical Chemistry and Electrochemistry, University of Milan, V. Golgi 19, 20133 Milan, Italy
| | - Peter Saalfrank
- Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm, Germany
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Chapman CT, Cheng X, Cina JA. Numerical Tests of a Fixed Vibrational Basis/Gaussian Bath Theory for Small Molecule Dynamics in Low-Temperature Media. J Phys Chem A 2011; 115:3980-9. [DOI: 10.1021/jp108921x] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Craig T. Chapman
- Departments of †Chemistry and ‡Physics and Oregon Center for Optics, University of Oregon, Eugene, Oregon 97403, United States
| | - Xiaolu Cheng
- Departments of †Chemistry and ‡Physics and Oregon Center for Optics, University of Oregon, Eugene, Oregon 97403, United States
| | - Jeffrey A. Cina
- Departments of †Chemistry and ‡Physics and Oregon Center for Optics, University of Oregon, Eugene, Oregon 97403, United States
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López-López S, Martinazzo R, Nest M. Benchmark calculations for dissipative dynamics of a system coupled to an anharmonic bath with the multiconfiguration time-dependent Hartree method. J Chem Phys 2011; 134:094102. [DOI: 10.1063/1.3556940] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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López-López S, Nest M, Martinazzo R. Generalized CC-TDSCF and LCSA: The system-energy representation. J Chem Phys 2011; 134:014102. [PMID: 21218992 DOI: 10.1063/1.3518418] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Typical (sub)system-bath quantum dynamical problems are often investigated by means of (approximate) reduced equations of motion. Wavepacket approaches to the dynamics of the whole system have gained momentum in recent years and there is hope that properly designed approximations to the wavefunction will allow one to correctly describe the subsystem evolution. The continuous-configuration time-dependent self-consistent field (CC-TDSCF) and local coherent-state approximation (LCSA) methods, for instance, use a simple Hartree product of bath single-particle-functions for each discrete variable representation (DVR) state introduced in the Hilbert space of the subsystem. Here we focus on the above two methods and replace the DVR states with the eigenstates of the subsystem Hamiltonian, i.e., we adopt an energy-local representation for the subsystem. We find that stable and semiquantitative results are obtained for a number of dissipative problems, at the same (small) computational cost of the original methods. Furthermore, we find that both methods give very similar results, thus suggesting that coherent-states are well suited to describe (local) bath states. As a whole, present results highlight the importance of the system basis-set in the selected-multiconfiguration expansion of the wavefunction. They suggest that accurate and yet computationally cheap methods may be simply obtained from CC-TDSCF/LCSA by letting the subsystem states be variationally optimized.
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Affiliation(s)
- Sergio López-López
- Department of Theoretical Chemistry, Technische Universität München, Lichtenbergstraße 4, 85747 Garching, Germany
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26
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Goletz CM, Koch W, Grossmann F. Semiclassical dynamics of open quantum systems: Comparing the finite with the infinite perspective. Chem Phys 2010. [DOI: 10.1016/j.chemphys.2010.06.019] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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27
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Gelman D, Schwartz SD. Dissipative dynamics with the corrected propagator method. Numerical comparison between fully quantum and mixed quantum/classical simulations. Chem Phys 2010. [DOI: 10.1016/j.chemphys.2010.01.021] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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29
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López-López S, Nest M. Analysis of the continuous-configuration time-dependent self-consistent field method applied to system-bath dynamics. J Chem Phys 2010; 132:104103. [DOI: 10.1063/1.3351903] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Temperature effects for vibrational relaxation of hydrogen adsorbed on Si(100): a stochastic multiconfigurational time-dependent Hartree (MCTDH) study. Theor Chem Acc 2010. [DOI: 10.1007/s00214-009-0721-y] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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31
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Hughes KH, Christ CD, Burghardt I. Effective-mode representation of non-Markovian dynamics: a hierarchical approximation of the spectral density. I. Application to single surface dynamics. J Chem Phys 2009; 131:024109. [PMID: 19603972 DOI: 10.1063/1.3159671] [Citation(s) in RCA: 65] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
An approach to non-Markovian system-environment dynamics is described which is based on the construction of a hierarchy of coupled effective environmental modes that is terminated by coupling the final member of the hierarchy to a Markovian bath. For an arbitrary environment, which is linearly coupled to the subsystem, the discretized spectral density is replaced by a series of approximate spectral densities involving an increasing number of effective modes. This series of approximants, which are constructed analytically in this paper, guarantees the accurate representation of the overall system-plus-bath dynamics up to increasing times. The hierarchical structure is manifested in the approximate spectral densities in the form of the imaginary part of a continued fraction similar to Mori theory. The results are described for cases where the hierarchy is truncated at the first-, second-, and third-order level. It is demonstrated that the results generated from a reduced density matrix equation of motion and large dimensional system-plus-bath wavepacket calculations are in excellent agreement. For the reduced density matrix calculations, the system and hierarchy of effective modes are treated explicitly and the effects of the bath on the final member of the hierarchy are described by the Caldeira-Leggett equation and its generalization to zero temperature.
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Affiliation(s)
- Keith H Hughes
- School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW, United Kingdom.
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32
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Gelman D, Schwartz SD. Modeling vibrational resonance in linear hydrocarbon chain with a mixed quantum-classical method. J Chem Phys 2009; 130:134110. [PMID: 19355720 DOI: 10.1063/1.3110063] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The quantum dynamics of a vibrational excitation in a linear hydrocarbon model system is studied with a new mixed quantum-classical method. The method is suited to treat many-body systems consisting of a low dimensional quantum primary part coupled to a classical bath. The dynamics of the primary part is governed by the quantum corrected propagator, with the corrections defined in terms of matrix elements of zeroth order propagators. The corrections are taken to the classical limit by introducing the frozen Gaussian approximation for the bath degrees of freedom. The ability of the method to describe dynamics of multidimensional systems has been tested. The results obtained by the method have been compared to previous quantum simulations performed with the quasiadiabatic path integral method.
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Affiliation(s)
- David Gelman
- Department of Biophysics, Albert Einstein College of Medicine, 1300 Morris Park Ave., Bronx, New York 10461, USA
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33
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Goletz CM, Grossmann F. Decoherence and dissipation in a molecular system coupled to an environment: An application of semiclassical hybrid dynamics. J Chem Phys 2009; 130:244107. [DOI: 10.1063/1.3157162] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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34
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Shalashilin DV. Quantum mechanics with the basis set guided by Ehrenfest trajectories: Theory and application to spin-boson model. J Chem Phys 2009; 130:244101. [DOI: 10.1063/1.3153302] [Citation(s) in RCA: 117] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Casolo S, Martinazzo R, Bonfanti M, Tantardini GF. Quantum Dynamics of the Eley−Rideal Hydrogen Formation Reaction on Graphite at Typical Interstellar Cloud Conditions. J Phys Chem A 2009; 113:14545-53. [DOI: 10.1021/jp9040265] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Simone Casolo
- Dipartimento di Chimica Fisica ed Elettrochimica, Università degli Studi di Milano, V. Golgi 19, 20133 Milan, Italy; CIMAINA, Interdisciplinary Center of Nanostructured Materials and Interfaces, University of Milan; and CNR Institute of Molecular Sciences and Technology, V. Golgi 19, 20133 Milan, Italy
| | - Rocco Martinazzo
- Dipartimento di Chimica Fisica ed Elettrochimica, Università degli Studi di Milano, V. Golgi 19, 20133 Milan, Italy; CIMAINA, Interdisciplinary Center of Nanostructured Materials and Interfaces, University of Milan; and CNR Institute of Molecular Sciences and Technology, V. Golgi 19, 20133 Milan, Italy
| | - Matteo Bonfanti
- Dipartimento di Chimica Fisica ed Elettrochimica, Università degli Studi di Milano, V. Golgi 19, 20133 Milan, Italy; CIMAINA, Interdisciplinary Center of Nanostructured Materials and Interfaces, University of Milan; and CNR Institute of Molecular Sciences and Technology, V. Golgi 19, 20133 Milan, Italy
| | - Gian Franco Tantardini
- Dipartimento di Chimica Fisica ed Elettrochimica, Università degli Studi di Milano, V. Golgi 19, 20133 Milan, Italy; CIMAINA, Interdisciplinary Center of Nanostructured Materials and Interfaces, University of Milan; and CNR Institute of Molecular Sciences and Technology, V. Golgi 19, 20133 Milan, Italy
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36
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Burghardt I, Giri K, Worth GA. Multimode quantum dynamics using Gaussian wavepackets: The Gaussian-based multiconfiguration time-dependent Hartree (G-MCTDH) method applied to the absorption spectrum of pyrazine. J Chem Phys 2008; 129:174104. [DOI: 10.1063/1.2996349] [Citation(s) in RCA: 145] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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37
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Shalashilin DV, Burghardt I. Gaussian-based techniques for quantum propagation from the time-dependent variational principle: Formulation in terms of trajectories of coupled classical and quantum variables. J Chem Phys 2008; 129:084104. [DOI: 10.1063/1.2969101] [Citation(s) in RCA: 67] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
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38
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Gelman D, Schwartz SD. Tunneling dynamics with a mixed quantum-classical method: Quantum corrected propagator combined with frozen Gaussian wave packets. J Chem Phys 2008; 129:024504. [DOI: 10.1063/1.2949818] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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39
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Shalashilin DV, Child MS. Basis set sampling in the method of coupled coherent states: Coherent state swarms, trains, and pancakes. J Chem Phys 2008; 128:054102. [DOI: 10.1063/1.2828509] [Citation(s) in RCA: 64] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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40
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Nest M, Kosloff R. Quantum dynamical treatment of inelastic scattering of atoms at a surface at finite temperature: the random phase thermal wave function approach. J Chem Phys 2007; 127:134711. [PMID: 17919047 DOI: 10.1063/1.2786088] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
We present quantum dynamical calculations for the inelastic scattering of atoms at a nonrigid surface at finite temperature. The surface degrees of freedom are discretized and treated in a multiconfigurational wave function picture. The thermal averaging is carried out with the random phase thermal wave function approach. We show that it is sufficient to restrict the random phases to the intermediate basis of single particle functions, discuss the convergence of the method with the number of configurations and realizations, and analyze the flow of energy between different parts of the system for a range of temperatures between 4 and 500 K.
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Affiliation(s)
- M Nest
- Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Str. 25, 14476 Potsdam, Germany.
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41
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Tamura H, Bittner ER, Burghardt I. Nonadiabatic quantum dynamics based on a hierarchical electron-phonon model: Exciton dissociation in semiconducting polymers. J Chem Phys 2007; 127:034706. [PMID: 17655454 DOI: 10.1063/1.2748050] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A hierarchical electron-phonon coupling model is applied to describe the ultrafast decay of a photogenerated exciton at a donor-acceptor polymer heterojunction, via a vibronic coupling mechanism by which a charge-localized interfacial state is created. Expanding upon an earlier Communication [H. Tamura et al., J. Chem. Phys. 126, 021103 (2007)], we present a quantum dynamical analysis based on a two-state linear vibronic coupling model, which accounts for a two-band phonon bath including high-frequency C[Double Bond]C stretch modes and low-frequency ring torsional modes. Building upon this model, an analysis in terms of a hierarchical chain of effective modes is carried out, whose construction is detailed in the present paper. Truncation of this chain at the order n (i.e., 3n+3 modes) conserves the Hamiltonian moments (cumulants) up to the (2n+3)rd order. The effective-mode analysis highlights (i) the dominance of the high-frequency modes in the coupling to the electronic subsystem and (ii) the key role of the low-frequency modes in the intramolecular vibrational redistribution process that is essential in mediating the decay to the charge-localized state. Due to this dynamical interplay, the effective-mode hierarchy has to be carried beyond the first order in order to obtain a qualitatively correct picture of the nonadiabatic process. A reduced model of the dynamics, including a Markovian closure of the hierarchy, is presented. Dynamical calculations were carried out using the multiconfiguration time-dependent Hartree method.
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Affiliation(s)
- Hiroyuki Tamura
- Département de Chimie, Ecole Normale Supérieure, 24 Rue Lhomond, F-75231 Paris Cedex 05, France.
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42
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Lanzani G, Martinazzo R, Materzanini G, Pino I, Tantardini GF. Chemistry at surfaces: from ab initio structures to quantum dynamics. Theor Chem Acc 2007. [DOI: 10.1007/s00214-006-0201-6] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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43
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Andrianov I, Saalfrank P. Free vibrational relaxation of H adsorbed on a Si(1 0 0) surface investigated with the multi-configurational time-dependent Hartree method. Chem Phys Lett 2006. [DOI: 10.1016/j.cplett.2006.11.067] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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