1
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Gelin MF, Borrelli R. Thermo-Field Dynamics Approach to Photo-induced Electronic Transitions Driven by Incoherent Thermal Radiation. J Chem Theory Comput 2023; 19:6402-6413. [PMID: 37656914 DOI: 10.1021/acs.jctc.3c00590] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/03/2023]
Abstract
The effects of thermal light-matter interaction on the dynamics of photo-induced electronic transitions in molecules are investigated using a novel first principles approach based on the thermo-field dynamics description of both the molecular vibrational modes and of the radiation field. The developed approach permits numerically accurate simulations of quantum dynamics of electronic/excitonic systems coupled to nuclear and photonic baths kept at different temperatures. The baths can be described by arbitrary spectral densities and can have any system-bath coupling strengths. In agreement with the results obtained previously by less rigorous methods, we show that the excitation process obtained by the continuous interaction with the suddenly turned-on thermal radiation field creates a mixed ensemble having a nonnegligible component consisting of a superposition of vibronic eigenstates which can sustain coherent oscillations for relatively long times. The results become especially relevant for the dynamics of electronic transitions upon sunlight excitation. Analytical results based on time-dependent perturbation theory support the numerical simulations and provide a simple interpretation of the time evolution of quantum observables.
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Affiliation(s)
- Maxim F Gelin
- School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Raffaele Borrelli
- DISAFA, University of Torino, Largo Paolo Braccini 2, Grugliasco I-10095, Italy
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2
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Toutounji M. Mixed Quantum-Classical Liouville Equation Treatment of Electronic Spectroscopy of Condensed Systems: Harmonic and Anharmonic Electron-Phonon Coupling. J Chem Theory Comput 2023. [PMID: 37365487 DOI: 10.1021/acs.jctc.2c01225] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/28/2023]
Abstract
This Review integrates the use of electronic optical response function theory and the mixed quantum-classical (MQC) Liouville equation (MQCLE), thereby leading to electronic spectroscopy in MQC media. It further sheds light on the applicability, utility, and efficiency of the mixed quantum-classical dynamics (MQCD) formalism, which starts off with the MQCLE, in probing spectroscopy and dynamics of condensed systems, whereby quantum mechanics and classical mechanics are combined systematically. The author has been exploring and implementing MQCD to investigate electron-phonon coupling effects on electronic dephasing in harmonic and anharmonic systems by calculating linear and nonlinear optical transition analytically and numerically dipole moment time correlation functions in an MQC environment, thereby presenting an in depth spectral profile analysis and their shape and symmetry. The distinctive capability of the MQC time correlation functions is that ergodicity and stationarity properties are inherently satisfied as part of the mixed quantum-classical dynamics (MQCD) framework, unlike classical correlation functions. While some research groups have applied MQCLE to calculate vibrational spectra to study hydrogen-bonded complexes in a MQC environment and other groups calculated Optical response function to probe electron transfer dynamics using the basis mapping technique, the approach, purpose, rigor, applications, and path to the end results reported herein are different. Finally, the same framework is employed to study dissipative systems in the MQC limit, whereby the zero-phonon line adopts the correct width and eliminates its asymmetry. While the full quantum mechanical model, like the multimode Brownian oscillator (MBO) model, yields the correct width and inaccurate shape in the low-temperature limit, the MQCD formalism seems to produce an accurate zero-phonon profile. Nonlinear optical signals are also reviewed in MQC media to show the applicability and utility of this approach. The vibronic optical response functions developed here will account for geometry change, frequency change, and anharmonicity upon electronic excitation to accurately probe electronic dephasing, electron-phonon coupling, shape, and symmetry of profiles and present differences and similarities to the MBO model on pure electronic dephasing. Frequency change and anharmonicity are vitally crucial for accurately assessing electron-phonon coupling upon electronic excitation. This is an additional unique result obtained by the author to further demonstrate the applicability and utility of this approach over other approximation schemes in probing electronic dephasing including that of the MBO model.
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Affiliation(s)
- Mohamad Toutounji
- College of Science, Department of Chemistry, P.O. Box 15551, UAE University, Al-Ain, 33000, UAE
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3
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Toutounji M. Electronic dephasing of polyatomic molecules interacting with mixed quantum-classical media. Phys Chem Chem Phys 2021; 23:21981-21994. [PMID: 34569571 DOI: 10.1039/d1cp00783a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
This paper offers an expedient, efficient, and unique treatment of multimode quantum subsystems (polyatomic molecules) interacting with a classical environment in which the time evolution of the coupling term is governed by the algebraic rules of statistical mechanics in mixed quantum-classical systems developed by Kapral and Nielsen [S. Nielsen, R. Kapral, and G. Ciccotti, J. Chem. Phys., 2001, 115, 5805]. This unique time evolution of the coupling term is neither quantal nor classical but rather something different that relies heavily on Wigner transform, thereby leading to non-Newtonian mechanics. As such, an argument is presented that the approach provided herein for treating polyatomic molecular systems in a mixed quantum-classical environment is new and different as opposed to the many other schemes of semiclassical dynamics that are normally employed to study such systems. The merits of expediency and efficiency of the herein mixed quantum-classical dynamics calculations emanate from avoiding using integrals for time evolutions, and, instead, employing matrix mechanics whereby LU decomposition and singular value decomposition (SVD) numerical techniques are utilized for diagonalization. An electronic 2-level subsystem interacting with a classical bath through the spin-boson model to render accurate pure electronic dephasing in multimode molecular systems by eliminating the unphysical asymmetry in the line shape of the zero-phonon line (ZPL) exhibited by other models is exploited. This work has a superior advantage over the single-mode spin-boson model, published previously, whereby a multitude of types of vibrational modes (slow, fast, or both) of the quantum subsystem may readily be handled using different spectral densities. The spin-boson model used here is a composite system made up of a quantum subsystem, i.e., a subsystem bilinearly coupled to a multidimensional harmonic oscillator (representing the intermediate quantum vibrational modes between the electronic subsystem and the bath), interacting with a classical bath, where the coupling term is governed by the mixed quantum-classical Liouville equation. A multidimensional coherent-state approach is employed to deal with the time evolution of the quantum subsystem. A closed-form expression of linear and nonlinear optical electronic transition dipole moment time correlation functions in mixed quantum-classical dissipative media is derived. Pure electronic dephasing is probed using the aforementioned approach. Linear absorption spectra and 4-wave mixing signals (e.g., photon echo and pump-probe) are calculated showing a reasonable thermal broadening, temporal decay, and accurate pure dephasing.
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Affiliation(s)
- Mohamad Toutounji
- College of Science, Department of Chemistry, P. O. Box 15551, UAE University, Al-Ain, United Arab Emirates.
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4
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Toutounji M. Excited state distribution function for probing Herzberg-Teller vibronic coupling using linear optical response theory: Application to glassy pheophytin a. J Comput Chem 2021; 42:1905-1913. [PMID: 34309873 DOI: 10.1002/jcc.26724] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2021] [Revised: 05/31/2021] [Accepted: 06/17/2021] [Indexed: 11/05/2022]
Abstract
The goal of the present work is to develop an excited-state distribution function that can be used to calculate electronic transition dipole moment time correlation functions at a considerably low computational cost. An additional merit of the distribution function is its capability to probe the Hertzberg-Teller vibronic coupling effect in terms of the previously reported Condon correlation functions in the literature without having to start from the equilibrium density operator to probe spectral non-Condon effects, thereby exploring Hertzberg-Teller vibronic coupling by building on the Condon regime. It is easily extendable to anharmonic systems. Model calculations are reported to show the high degree of accuracy and computational efficiency of the presented approach. Application to a photosynthetic system such as pheophytin a in triethylamine is provided.
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5
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Rognoni A, Conte R, Ceotto M. Caldeira-Leggett model vs ab initio potential: A vibrational spectroscopy test of water solvation. J Chem Phys 2021; 154:094106. [PMID: 33685187 DOI: 10.1063/5.0040494] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a semiclassically approximate quantum treatment of solvation with the purpose of investigating the accuracy of the Caldeira-Leggett model. We do that by simulating the vibrational features of water solvation by means of two different approaches. One is entirely based on the adoption of an accurate ab initio potential to describe water clusters of increasing dimensionality. The other one consists of a model made of a central water molecule coupled to a high-dimensional Caldeira-Leggett harmonic bath. We demonstrate the role of quantum effects in the detection of water solvation and show that the computationally cheap approach based on the Caldeira-Leggett bath is only partially effective. The main conclusion of the study is that quantum methods associated with high-level potential energy surfaces are necessary to correctly study solvation features, while simplified models, even if attractive owing to their reduced computational cost, can provide some useful insights but are not able to come up with a comprehensive description of the solvation phenomenon.
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Affiliation(s)
- Alessandro Rognoni
- Dipartimento di Chimica, Universitá degli Studi di Milano, via Golgi 19, 20133 Milano, Italy
| | - Riccardo Conte
- Dipartimento di Chimica, Universitá degli Studi di Milano, via Golgi 19, 20133 Milano, Italy
| | - Michele Ceotto
- Dipartimento di Chimica, Universitá degli Studi di Milano, via Golgi 19, 20133 Milano, Italy
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6
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Talotta F, Agostini F, Ciccotti G. Quantum Trajectories for the Dynamics in the Exact Factorization Framework: A Proof-of-Principle Test. J Phys Chem A 2020; 124:6764-6777. [PMID: 32786992 DOI: 10.1021/acs.jpca.0c03969] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In the framework of the exact factorization of the time-dependent electron-nuclear wave function, we investigate the possibility of solving the nuclear time-dependent Schrödinger equation based on trajectories. The nuclear equation is separated in a Hamilton-Jacobi equation for the phase of the wave function, and a continuity equation for its (squared) modulus. For illustrative adiabatic and nonadiabatic one-dimensional models, we implement a procedure to follow the evolution of the nuclear density along the characteristics of the Hamilton-Jacobi equation. Those characteristics are referred to as quantum trajectories, since they are generated via ordinary differential equations similar to Hamilton's equations, but including the so-called quantum potential, and they can be used to reconstruct exactly the quantum-mechanical nuclear wave function, provided infinite initial conditions are propagated in time.
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Affiliation(s)
- Francesco Talotta
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405, Orsay, France.,Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay, 91405, Orsay, France
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405, Orsay, France.,Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay, 91405, Orsay, France
| | - Giovanni Ciccotti
- CNR, Institute for Applied Computing "Mauro Picone" (IAC), Via dei Taurini 19, 00185 Rome, Italy.,School of Physics, University College of Dublin UCD - Belfield, Dublin 4, Ireland.,Dipartimento di Fisica, Università di Roma La Sapienza, P. le A. Moro 5, 00185 Roma, Italy
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7
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Tao G. Topology of quantum coherence in singlet fission: Mapping out spin micro-states in quasi-classical nonadiabatic simulations. J Chem Phys 2020; 152:074305. [DOI: 10.1063/1.5139538] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Affiliation(s)
- Guohua Tao
- School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen 518055, China and Shenzhen Key Laboratory of New Energy Materials by Design, Peking University, Shenzhen 518055, China
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8
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On the Husimi Version of the Classical Limit of Quantum Correlation Functions. CONDENSED MATTER 2020. [DOI: 10.3390/condmat5010003] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
We extend the Husimi (coherent state) based version of linearized semiclassical theories for the calculation of correlation functions to the case of survival probabilities. This is a case that could be dealt with before only by use of the Wigner version of linearized semiclassical theory. Numerical comparisons of the Husimi and the Wigner case with full quantum results as well as with full semiclassical ones will be given for the revival dynamics in a Morse oscillator with and without coupling to an additional harmonic degree of freedom.
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9
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Church MS, Ananth N. Semiclassical dynamics in the mixed quantum-classical limit. J Chem Phys 2019; 151:134109. [PMID: 31594341 DOI: 10.1063/1.5117160] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The semiclassical double Herman-Kluk initial value representation is an accurate approach to computing quantum real time correlation functions, but its applications are limited by the need to evaluate an oscillatory integral. In previous work, we have shown that this "sign problem" can be mitigated using the modified Filinov filtration technique to control the extent to which individual modes of the system contribute to the overall phase of the integrand. Here, we follow this idea to a logical conclusion: we analytically derive a general expression for the mixed quantum-classical limit of the semiclassical correlation function-analytical mixed quantum-classical-initial value representation (AMQC-IVR), where the phase contributions from the "classical" modes of the system are filtered while the "quantum" modes are treated in the full semiclassical limit. We numerically demonstrate the accuracy and efficiency of the AMQC-IVR formulation in calculations of quantum correlation functions and reaction rates using three model systems with varied coupling strengths between the classical and quantum subsystems. We also introduce a separable prefactor approximation that further reduces computational cost but is only accurate in the limit of weak coupling between the quantum and classical subsystems.
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Affiliation(s)
- Matthew S Church
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Nandini Ananth
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
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10
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Tao G. Nonadiabatic simulation of singlet fission dynamics in tetracene clusters: The topology of quantum coherence in a global view. J Chem Phys 2019. [DOI: 10.1063/1.5100196] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Guohua Tao
- School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen 518055, China and Shenzhen Key Laboratory of New Energy Materials by Design, Peking University, Shenzhen 518055, China
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11
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Garashchuk S, Rassolov V. Quantum Trajectory Dynamics Based on Local Approximations to the Quantum Potential and Force. J Chem Theory Comput 2019; 15:3906-3916. [DOI: 10.1021/acs.jctc.9b00027] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Sophya Garashchuk
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Vitaly Rassolov
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
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12
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Sala M, Egorova D. Quantum dynamics of multi-dimensional rhodopsin photoisomerization models: Approximate versus accurate treatment of the secondary modes. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2018.07.052] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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13
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Buchholz M, Grossmann F, Ceotto M. Simplified approach to the mixed time-averaging semiclassical initial value representation for the calculation of dense vibrational spectra. J Chem Phys 2018; 148:114107. [DOI: 10.1063/1.5020144] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Max Buchholz
- Dipartimento di Chimica, Università degli Studi di Milano, Via C. Golgi 19, 20133 Milano, Italy
| | - Frank Grossmann
- Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
| | - Michele Ceotto
- Dipartimento di Chimica, Università degli Studi di Milano, Via C. Golgi 19, 20133 Milano, Italy
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14
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Buchholz M, Grossmann F, Ceotto M. Application of the mixed time-averaging semiclassical initial value representation method to complex molecular spectra. J Chem Phys 2017; 147:164110. [DOI: 10.1063/1.4998510] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Max Buchholz
- Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
- Dipartimento di Chimica, Università degli Studi di Milano, Via C. Golgi 19, 20133 Milano, Italy
| | - Frank Grossmann
- Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
| | - Michele Ceotto
- Dipartimento di Chimica, Università degli Studi di Milano, Via C. Golgi 19, 20133 Milano, Italy
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15
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Church MS, Antipov SV, Ananth N. Validating and implementing modified Filinov phase filtration in semiclassical dynamics. J Chem Phys 2017. [DOI: 10.1063/1.4986645] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Aieta C, Ceotto M. A quantum method for thermal rate constant calculations from stationary phase approximation of the thermal flux-flux correlation function integral. J Chem Phys 2017; 146:214115. [DOI: 10.1063/1.4984099] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Chiara Aieta
- Dipartimento di Chimica, Università degli Studi di Milano, Via C. Golgi 19, 20133 Milano, Italy
| | - Michele Ceotto
- Dipartimento di Chimica, Università degli Studi di Milano, Via C. Golgi 19, 20133 Milano, Italy
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17
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Tao G, Shen N. Mapping State Space to Quasiclassical Trajectory Dynamics in Coherence-Controlled Nonadiabatic Simulations for Condensed Phase Problems. J Phys Chem A 2017; 121:1734-1747. [DOI: 10.1021/acs.jpca.6b10936] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Guohua Tao
- School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen, China 518055
- Shenzhen Key Laboratory of
New Energy Materials by Design, Peking University, Shenzhen, China 518055
| | - Na Shen
- School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen, China 518055
- Shenzhen Key Laboratory of
New Energy Materials by Design, Peking University, Shenzhen, China 518055
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18
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Di Liberto G, Ceotto M. The importance of the pre-exponential factor in semiclassical molecular dynamics. J Chem Phys 2017; 145:144107. [PMID: 27782528 DOI: 10.1063/1.4964308] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This paper deals with the critical issue of approximating the pre-exponential factor in semiclassical molecular dynamics. The pre-exponential factor is important because it accounts for the quantum contribution to the semiclassical propagator of the classical Feynman path fluctuations. Pre-exponential factor approximations are necessary when chaotic or complex systems are simulated. We introduced pre-exponential factor approximations based either on analytical considerations or numerical regularization. The approximations are tested for power spectrum calculations of more and more chaotic model systems and on several molecules, for which exact quantum mechanical values are available. The results show that the pre-exponential factor approximations introduced are accurate enough to be safely employed for semiclassical simulations of complex systems.
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Affiliation(s)
- Giovanni Di Liberto
- Dipartimento di Chimica, Università degli Studi di Milano, via Golgi 19, 20133 Milano, Italy
| | - Michele Ceotto
- Dipartimento di Chimica, Università degli Studi di Milano, via Golgi 19, 20133 Milano, Italy
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19
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Lee MK, Huo P, Coker DF. Semiclassical Path Integral Dynamics: Photosynthetic Energy Transfer with Realistic Environment Interactions. Annu Rev Phys Chem 2016; 67:639-68. [DOI: 10.1146/annurev-physchem-040215-112252] [Citation(s) in RCA: 96] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Mi Kyung Lee
- Department of Chemistry, Boston University, Boston, Massachusetts 02215;
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, Rochester, New York 14627;
| | - David F. Coker
- Department of Chemistry, Boston University, Boston, Massachusetts 02215;
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20
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Tao G. A multi-state trajectory method for non-adiabatic dynamics simulations. J Chem Phys 2016; 144:094108. [DOI: 10.1063/1.4943006] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Guohua Tao
- Shenzhen Key Laboratory of New Energy Materials by Design, Peking University, Shenzhen 518055, China and School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen 518055, China
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21
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Tao G. Understanding Electronically Non-Adiabatic Relaxation Dynamics in Singlet Fission. J Chem Theory Comput 2014; 11:28-36. [DOI: 10.1021/ct500953r] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Affiliation(s)
- Guohua Tao
- Shenzhen
Key Laboratory of
New Energy Materials by Design, Peking University, Shenzhen 518055, China
- School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen 518055, China
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22
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Grossmann F. Quantum effects in intermediate-temperature dipole-dipole correlation-functions in the presence of an environment. J Chem Phys 2014; 141:144305. [DOI: 10.1063/1.4896835] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- F. Grossmann
- Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
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23
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Makri N. Blip decomposition of the path integral: Exponential acceleration of real-time calculations on quantum dissipative systems. J Chem Phys 2014; 141:134117. [DOI: 10.1063/1.4896736] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nancy Makri
- Departments of Chemistry and Physics, University of Illinois, Urbana, Illinois 61801, USA
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24
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Keller J, Lasser C. Quasi-classical description of molecular dynamics based on Egorov's theorem. J Chem Phys 2014; 141:054104. [DOI: 10.1063/1.4891517] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Affiliation(s)
- Johannes Keller
- Zentrum Mathematik, Technische Universität München, 80290 München, Germany
| | - Caroline Lasser
- Zentrum Mathematik, Technische Universität München, 80290 München, Germany
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25
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Herman MF. Improving the efficiency of Monte Carlo surface hopping calculations. J Phys Chem B 2014; 118:8026-33. [PMID: 24650188 DOI: 10.1021/jp501139s] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
A surface hopping method with a Monte Carlo procedure for deciding whether to hop at each step along the classical trajectories used in the semiclassical calculation is discussed. It is shown for a simple one-dimensional model problem that the numerical efficiency of the method can be improved by averaging over several copies of the sections of each trajectory that span the interaction regions. The use of Sobol sequences in the selection of the initial momentum for the trajectories is also explored. It is found that accurate results can be obtained with relatively small trajectory samples.
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Affiliation(s)
- Michael F Herman
- Department of Chemistry, Tulane University , New Orleans, Louisiana 70118, United States
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26
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Abstract
Effective descriptions accounting for the evolution of quantum systems that are acted on by a bath are desirable. As the number of bath degrees of freedom increases and full quantum simulations turn out computationally prohibitive, simpler models become essential to understand and gain an insight into the main physical mechanisms involved in the system dynamics. In this regard, vibrational decoherence of an I2 diatomics is tackled here within the framework of Markovian quantum state diffusion. The I2 dynamics are analyzed in terms of an effective decoherence rate, Λ, and the specific choice of the initial state, in particular, Gaussian wave packets and two-state superpositions. It is found that, for Markovian baths, the relevant quantity regarding decoherence is the product of friction (η) and temperature (T); there is no distinction between varying one or the other. It is also observed that decoherence becomes faster as the energy levels involved in the system state correspond to higher eigenvalues. This effect is due to a population redistribution during the dynamical process and an eventual irreversible loss of the initial coherence. These results have been compared with those available in the literature from more detailed semiclassical IVR simulations, finding a good agreement.
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Affiliation(s)
- A.S. Sanz
- Instituto de Física Fundamental (IFF–CSIC), Serrano 123, 28006 Madrid, Spain
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27
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Exploiting classical decoherence in dissipative quantum dynamics: Memory, phonon emission, and the blip sum. Chem Phys Lett 2014. [DOI: 10.1016/j.cplett.2013.11.064] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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28
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Efficient importance sampling in semiclassical initial value representation calculations for time correlation functions. Theor Chem Acc 2014. [DOI: 10.1007/s00214-014-1448-y] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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29
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The Interplay of Nuclear and Electron Wavepacket Motion in the Control of Molecular Processes: A Theoretical Perspective. ACTA ACUST UNITED AC 2013. [DOI: 10.1007/978-3-642-45290-1_8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/21/2023]
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30
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Non-adiabatic Photochemistry: Ultrafast Electronic State Transitions and Nuclear Wavepacket Coherence. ACTA ACUST UNITED AC 2013. [DOI: 10.1007/978-3-642-45290-1_7] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/21/2023]
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31
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Barak H, Kay KG. Semiclassical initial-value representation of the transfer operator. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062926. [PMID: 24483550 DOI: 10.1103/physreve.88.062926] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2013] [Indexed: 06/03/2023]
Abstract
The ability of semiclassical initial-value representation (IVR) methods to determine approximate energy levels for bound systems is limited due to problems associated with long classical trajectories. These difficulties become especially severe for large or classically chaotic systems. This work attempts to overcome such problems by developing an IVR expression that is classically equivalent to Bogomolny's formula for the transfer matrix [E. B. Bogomolny, Nonlinearity 5, 805 (1992); Chaos 2, 5 (1992)] and can be used to determine semiclassical energy levels. The method is adapted to levels associated with states of desired symmetries and applied to two two-dimensional quartic oscillator systems, one integrable and one mostly chaotic. For both cases, the technique is found to resolve all energy levels in the ranges investigated. The IVR method does not require a search for special trajectories obeying boundary conditions on the Poincaré surface of section and leads to more rapid convergence of Monte Carlo phase space integrations than a previously developed IVR technique. It is found that semiclassical energies can be extracted from the eigenvalues of transfer matrices of dimension close to the theoretical minimum determined by Bogomolny's theory. The results support the assertion that the present IVR theory provides a different semiclassical approximation to the transfer matrix than that of Bogomolny for ℏ≠0. For the chaotic system investigated the IVR energies are found to be generally more accurate than those predicted by Bogomolny's theory.
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Affiliation(s)
- Haim Barak
- Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Kenneth G Kay
- Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
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Kocia L, Heller EJ. Generalized dephasing relation for fidelity and application as an efficient propagator. J Chem Phys 2013; 139:124110. [DOI: 10.1063/1.4820880] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Tao G. Electronically nonadiabatic dynamics in complex molecular systems: an efficient and accurate semiclassical solution. J Phys Chem A 2013; 117:5821-5. [PMID: 23799272 DOI: 10.1021/jp404856p] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Chemical reaction dynamics is always a central theme in chemistry research. In many important chemical processes, reaction dynamics is electronically nonadiabatic, i.e., dynamics involves coupled multiple electronic states. We demonstrate in this paper that a semiclassical (SC) treatment based on an initial value representation methodology and a classical mapping formalism for the electronic degrees of freedom is now able to provide a rigorous and practical solution to electronically nonadiabatic dynamics in complex molecular systems. The key component of this treatment is to incorporate a correlated importance sampling protocol in nonadiabatic SC calculations, which results in a speedup factor of 100 or more in comparison with that using the standard sampling approach. This is illustrated by application to a two-state model coupled with up to 10 nuclear bath modes for a benchmark nonadiabatic excitation energy transfer problem. This work provides great opportunities for the effectively theoretical investigations on reaction mechanisms in complex molecular systems, in which electronically nonadiabatic dynamics plays an importance role.
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Affiliation(s)
- Guohua Tao
- School of Advanced Materials, Peking University , Shenzhen Graduate School, Shenzhen, China 518055
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Habershon S, Manolopoulos DE, Markland TE, Miller TF. Ring-Polymer Molecular Dynamics: Quantum Effects in Chemical Dynamics from Classical Trajectories in an Extended Phase Space. Annu Rev Phys Chem 2013; 64:387-413. [DOI: 10.1146/annurev-physchem-040412-110122] [Citation(s) in RCA: 448] [Impact Index Per Article: 40.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Scott Habershon
- Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom;
| | - David E. Manolopoulos
- Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom;
| | - Thomas E. Markland
- Department of Chemistry, Stanford University, Stanford, California 94305;
| | - Thomas F. Miller
- Department of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125;
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Pan F, Tao G. Communication: importance sampling including path correlation in semiclassical initial value representation calculations for time correlation functions. J Chem Phys 2013; 138:091101. [PMID: 23485270 DOI: 10.1063/1.4794191] [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
Full semiclassical (SC) initial value representation (IVR) for time correlation functions involves a double phase space average over a set of two phase points, each of which evolves along a classical path. Conventionally, the two initial phase points are sampled independently for all degrees of freedom (DOF) in the Monte Carlo procedure. Here, we present an efficient importance sampling scheme by including the path correlation between the two initial phase points for the bath DOF, which greatly improves the performance of the SC-IVR calculations for large molecular systems. Satisfactory convergence in the study of quantum coherence in vibrational relaxation has been achieved for a benchmark system-bath model with up to 21 DOF.
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Affiliation(s)
- Feng Pan
- School of Advanced Materials, Peking University, Shenzhen Graduate School, Shenzhen 518055, China
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36
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Ceotto M, Zhuang Y, Hase WL. Accelerated direct semiclassical molecular dynamics using a compact finite difference Hessian scheme. J Chem Phys 2013; 138:054116. [DOI: 10.1063/1.4789759] [Citation(s) in RCA: 46] [Impact Index Per Article: 4.2] [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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Huo P, Coker DF. Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation. J Chem Phys 2012; 137:22A535. [DOI: 10.1063/1.4748316] [Citation(s) in RCA: 82] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
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38
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Tao G, Miller WH. Time-dependent importance sampling in semiclassical initial value representation calculations for time correlation functions. II. A simplified implementation. J Chem Phys 2012; 137:124105. [DOI: 10.1063/1.4752206] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Buchholz M, Goletz CM, Grossmann F, Schmidt B, Heyda J, Jungwirth P. Semiclassical Hybrid Approach to Condensed Phase Molecular Dynamics: Application to the I2Kr17 Cluster. J Phys Chem A 2012; 116:11199-210. [DOI: 10.1021/jp305084f] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Max Buchholz
- Institut für Theoretische
Physik, Technische Universität Dresden, 01062 Dresden, Germany
| | | | - Frank Grossmann
- Institut für Theoretische
Physik, Technische Universität Dresden, 01062 Dresden, Germany
| | - Burkhard Schmidt
- Institut für Mathematik, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Jan Heyda
- Institute for Soft Matter and Functional
Materials, Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Hahn-Meitner-Platz 1, 14109 Berlin,
Germany
| | - Pavel Jungwirth
- Institute of Organic
Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo nam. 2, 16610 Prague 6, Czech
Republic
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Affiliation(s)
- William H. Miller
- Department of Chemistry and K. S. Pitzer Center for Theoretical Chemistry, University of California and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720-1460, USA
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Igumenshchev K, Ovchinnikov M, Prezhdo OV. Herman–Kluk allows analysis of quantum discrete breathers in higher dimensional systems. Mol Phys 2012. [DOI: 10.1080/00268976.2012.680513] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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42
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Huo P, Coker DF. Semi-classical path integral non-adiabatic dynamics: a partial linearized classical mapping Hamiltonian approach. Mol Phys 2012. [DOI: 10.1080/00268976.2012.684896] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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43
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Head-Gordon M. Publications. Mol Phys 2012. [DOI: 10.1080/00268976.2012.693252] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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44
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Liu J, Miller WH, Fanourgakis GS, Xantheas SS, Imoto S, Saito S. Insights in quantum dynamical effects in the infrared spectroscopy of liquid water from a semiclassical study with an ab initio-based flexible and polarizable force field. J Chem Phys 2012; 135:244503. [PMID: 22225165 DOI: 10.1063/1.3670960] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The dynamical properties of liquid water play an important role in many processes in nature. In this paper, we focus on the infrared (IR) absorption spectrum of liquid water based on the linearized semiclassical initial value representation (LSC-IVR) with the local Gaussian approximation (LGA) [J. Liu and W. H. Miller, J. Chem. Phys. 131, 074113 (2009)] and an ab initio based, flexible, polarizable Thole-type model (TTM3-F) [G. S. Fanourgakis and S. S. Xantheas, J. Chem. Phys. 128, 074506 (2008)]. Although the LSC-IVR (LGA) gives the exact result for the isolated three-dimensional shifted harmonic stretching model, it yields a blueshifted peak position for the more realistic anharmonic stretching potential. By using the short-time information of the LSC-IVR correlation function; however, it is shown how one can obtain more accurate results for the position of the stretching peak. Due to the physical decay in the condensed phase system, the LSC-IVR (LGA) is a good and practical approximate quantum approach for the IR spectrum of liquid water. The present results offer valuable insight into future attempts to improve the accuracy of the TTM3-F potential or other ab initio-based models in reproducing the IR spectrum of liquid water.
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Affiliation(s)
- Jian Liu
- Department of Chemistry, University of California, Berkeley, California 94720-1460, USA
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MAKRI NANCY, NAKAYAMA AKIRA, WRIGHT NICHOLASJ. FORWARD-BACKWARD SEMICLASSICAL SIMULATION OF DYNAMICAL PROCESSES IN LIQUIDS. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1142/s0219633604001112] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Forward-backward semiclassical dynamics (FBSD) provides a practical methodology for including quantum mechanical effects in classical trajectory simulations of polyatomic systems. FBSD expressions for time-dependent expectation values or correlation functions take the form of phase space integrals with respect to trajectory initial conditions, weighted by the coherent state transform of a corrected density operator. Quantization through a discretized path integral representation of the Boltzmann operator ensures a proper treatment of zero point energy effects and of imaginary components in finite-temperature correlation functions, and extension to systems obeying Bose statistics is possible. Accelerated convergence is achieved via Monte Carlo or molecular dynamics sampling techniques and through the construction of improved imaginary time propagators. The accuracy of the methodology is demonstrated on several model systems, including models of Bose and Fermi particles. Applications to liquid argon, neon and para-hydrogen are presented.
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Affiliation(s)
- NANCY MAKRI
- Department of Chemistry, University of Illinois, 601 S. Goodwin Avenue, Urbana, Illinois 61801, USA
| | - AKIRA NAKAYAMA
- Department of Chemistry, University of Illinois, 601 S. Goodwin Avenue, Urbana, Illinois 61801, USA
| | - NICHOLAS J. WRIGHT
- Department of Chemistry, University of Illinois, 601 S. Goodwin Avenue, Urbana, Illinois 61801, USA
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46
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SCHWARTZ STEVEND. A NEW SEMICLASSICAL DYNAMICS FROM THE INTERACTION REPRESENTATION. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1142/s0219633605001908] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This paper develops a new semiclassical mechanics from an exact quantum prescription. In this formulation, a zeroth order propagation, rather than Hamiltonian, is specified. The exact, full evolution operator is then given from a specific interaction representation of the evolved "perturbation" Hamiltonian. We then investigate a variety of approximate, semiclassical, and mixed Quantum/Classical methods, along with exact methodologies to evaluate this time dependent interaction Hamiltonian. The approximate full evolution operator can be described in a variety of ways including an iterated Lippman-Schwinger like equation, and an expansion of the perturbation propagator generated from the time evolved Hamiltonian.
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Affiliation(s)
- STEVEN D. SCHWARTZ
- Departments of Biophysics and Biochemistry, Seaver Center for Bioinformatics, Albert Einstein College of Medicine, Bronx, NY 10461, USA
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47
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Tao G, Miller WH. Time-dependent importance sampling in semiclassical initial value representation calculations for time correlation functions. J Chem Phys 2011; 135:024104. [DOI: 10.1063/1.3600656] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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48
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Makri N. Forward–backward semiclassical and quantum trajectory methods for time correlation functions. Phys Chem Chem Phys 2011; 13:14442-52. [DOI: 10.1039/c0cp02374d] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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49
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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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50
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