51
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Tao G, Miller WH. Gaussian approximation for the structure function in semiclassical forward-backward initial value representations of time correlation functions. J Chem Phys 2009; 131:224107. [PMID: 20001024 DOI: 10.1063/1.3271241] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Initial value representations (IVRs) of semiclassical (SC) theory provide a general approach for adding quantum mechanical effects to classical molecular dynamics simulations of large molecular systems. Of the various versions of SC-IVR methodology for evaluating time correlation functions, the Fourier transform forward-backward (FB) approach is the simplest one that is able to describe true quantum coherence effects, so it is of considerable importance to find efficient and systematic ways for implementing it. It is shown in this paper that a Gaussian approximation for the "structure function"-the dependence of the correlation function on the (typically) momentum jump parameter-provides an efficient and accurate way for doing so. The approach is illustrated by an application to the time-dependent radial distribution function of I(2) (after photoexcitation) in a cluster of (up to 16) argon atoms.
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Affiliation(s)
- Guohua Tao
- Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720-1460, USA
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52
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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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53
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Kryvohuz M, Cao J. The influence of dissipation on the quantum-classical correspondence: Stability of stochastic trajectories. J Chem Phys 2009; 130:234107. [PMID: 19548711 DOI: 10.1063/1.3154142] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Maksym Kryvohuz
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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54
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Bukhman E, Makri N. Mixed Quantum and Forward−Backward Semiclassical Dynamics. J Phys Chem A 2009; 113:7183-8. [DOI: 10.1021/jp809741x] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Ed Bukhman
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801
| | - Nancy Makri
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801
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55
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Wu LA, Kurizki G, Brumer P. Master equation and control of an open quantum system with leakage. PHYSICAL REVIEW LETTERS 2009; 102:080405. [PMID: 19257726 DOI: 10.1103/physrevlett.102.080405] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2008] [Indexed: 05/27/2023]
Abstract
Given a multilevel system coupled to a bath, we use a Feshbach P, Q partitioning technique to derive an exact trace-nonpreserving master equation for a subspace S_{i} of the system. The resultant equation properly treats the leakage effect from S_{i} into the remainder of the system space. Focusing on a second-order approximation, we show that a one-dimensional master equation is sufficient to study problems of quantum state storage and is a good approximation, or exact, for several analytical models. It allows a natural definition of a leakage function and its control and provides a general approach to study and control decoherence and leakage. Numerical calculations on an harmonic oscillator coupled to a room temperature harmonic bath show that the leakage can be suppressed by the pulse control technique without requiring ideal pulses.
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Affiliation(s)
- Lian-Ao Wu
- Center for Quantum Information and Quantum Control and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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56
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Tao G, Miller WH. Semiclassical description of vibrational quantum coherence in a three dimensional I[sub 2]Ar[sub n] (n≤6) cluster: A forward-backward initial value representation implementation. J Chem Phys 2009; 130:184108. [DOI: 10.1063/1.3132224] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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57
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Herman MF. Semiclassical nonadiabatic surface-hopping wave function expansion at low energies: hops in the forbidden region. J Phys Chem B 2008; 112:15966-72. [PMID: 19367994 DOI: 10.1021/jp804937q] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
The accuracy of a semiclassical surface-hopping expansion of the time-independent wave function for problems in which the nonadiabatic coupling is peaked in the classically forbidden regions is studied numerically for a one-dimensional curve-crossing problem. This surface-hopping expansion has recently been shown to satisfy the Schrodinger equation to all orders in h and all orders in the nonadiabatic coupling. It has also been found to provide very accurate transition probabilities for problems in which the crossing points of the diabatic energy surfaces are classically allowed. In the numerical study reported here, transition probabilities are evaluated for energies well below the crossing point energy. It is found that the expansion provides accurate results for transition probabilities as small as 10(-11).
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Affiliation(s)
- Michael F Herman
- Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, USA
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58
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Vendrell O, Gelabert R, Moreno M, Lluch JM. Exploring the Effects of Intramolecular Vibrational Energy Redistribution on the Operation of the Proton Wire in Green Fluorescent Protein. J Phys Chem B 2008; 112:13443-52. [DOI: 10.1021/jp805049c] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Oriol Vendrell
- Departament de Química, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain, Institut de Biotecnologia i de Biomedicina, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain, and Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany
| | - Ricard Gelabert
- Departament de Química, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain, Institut de Biotecnologia i de Biomedicina, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain, and Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany
| | - Miquel Moreno
- Departament de Química, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain, Institut de Biotecnologia i de Biomedicina, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain, and Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany
| | - José M. Lluch
- Departament de Química, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain, Institut de Biotecnologia i de Biomedicina, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain, and Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany
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59
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Wang H, Thoss M. Nonperturbative quantum simulation of time-resolved nonlinear spectra: Methodology and application to electron transfer reactions in the condensed phase. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2007.12.004] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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60
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Toutounji M. Algebraic approach to electronic spectroscopy and dynamics. J Chem Phys 2008; 128:164103. [DOI: 10.1063/1.2903748] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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61
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Chen J, Makri N. Forward–backward semiclassical dynamics with single-bead coherent state density. Mol Phys 2008. [DOI: 10.1080/00268970701854797] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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62
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Ananth N, Venkataraman C, Miller WH. Semiclassical description of electronically nonadiabatic dynamics via the initial value representation. J Chem Phys 2007; 127:084114. [PMID: 17764236 DOI: 10.1063/1.2759932] [Citation(s) in RCA: 88] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The initial value representation (IVR) of semiclassical (SC) theory is used in conjunction with the Meyer-Miller/Stock-Thoss description of electronic degrees of freedom in order to treat electronically nonadiabatic processes. It is emphasized that the classical equations of motion for the nuclear and electronic degrees of freedom that emerge in this description are precisely the Ehrenfest equations of motion (the force on the nuclei is the force averaged over the electronic wave function) but that the trajectories given by these equations of motion do not have the usual shortcomings of the traditional Ehrenfest model when they are used within the SC-IVR framework. For example, in the traditional Ehrenfest model (a mixed quantum-classical approach) the nuclear motion emerges from a nonadiabatic encounter on an average potential energy surface (a weighted average according to the population in the various electronic states), while the SC-IVR describes the correct correlation between electronic and nuclear dynamics, i.e., the nuclear motion is on one potential energy surface or the other depending on the electronic state. Calculations using forward-backward versions of SC-IVR theory are presented to illustrate this behavior. An even more approximate version of the SC-IVR, the linearized approximation (LSC-IVR), is slightly better than the traditional Ehrenfest model, but since it cannot describe quantum coherence effects, the LSC-IVR is also not able to describe the correct correlation between nuclear and electronic dynamics.
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Affiliation(s)
- Nandini Ananth
- Department of Chemistry, University of California, Berkeley, California 94720-1460, USA
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63
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Bukhman E, Makri N. Forward−Backward Semiclassical Dynamics with Information-Guided Noise Reduction for a Molecule in Solution. J Phys Chem A 2007; 111:11320-7. [PMID: 17658736 DOI: 10.1021/jp0721907] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The forward--backward semiclassical dynamics (FBSD) methodology is used to obtain expressions for time correlation functions of a system (atom or molecule) in solution. We use information-guided noise reduction (IGNoR) [Makri, N. Chem. Phys. Lett. 2004, 400, 446] to minimize the statistical error associated with the Monte Carlo integration of oscillatory functions. This is possible by reformulating the correlation function in terms of an oscillatory solvent-dependent contribution whose integral can be obtained analytically and a slowly varying function obtained via a grid-based iterative evaluation of solute properties. Knowledge of the exact integral of the oscillatory function, combined with correlated statistics, leads to partial cancellation of the Monte Carlo error. Application on a one-dimensional solute-solvent model shows a substantial improvement of convergence in the IGNoR-enhanced FBSD correlation function for a fixed number of Monte Carlo samples. The reduction of statistical error achieved by using the IGNoR methodology becomes more significant as the number of solvent particles increases.
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Affiliation(s)
- Edward Bukhman
- Department of Chemistry, University of Illinois, 601 South Goodwin Avenue, Urbana, Illinois 61801, USA
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64
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Kegerreis J, Makri N. Optimized Monte Carlo sampling in forward–backward semiclassical dynamics. J Comput Chem 2007; 28:818-24. [PMID: 17226835 DOI: 10.1002/jcc.20608] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Forward-backward semiclassical dynamics (FBSD) provides a rigorous and powerful methodology for calculating time correlation functions in condensed phase systems characterized by substantial quantum mechanical effects associated with zero-point motion, quantum dispersion, or identical particle exchange symmetries. The efficiency of these simulations arises from the use of classical trajectories to capture all dynamical information. However, full quantization of the density operator makes these calculations rather expensive compared to fully classical molecular dynamics simulations. This article discusses the convergence properties of various correlation functions and introduces an optimal Monte Carlo sampling scheme that leads to a significant reduction of statistical error. A simple and efficient procedure for normalizing the FBSD results is also discussed. Illustrative examples on model systems are presented.
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Affiliation(s)
- Jeb Kegerreis
- Department of Chemistry, University of Illinois, 601 S. Goodwin Avenue, Urbana, Illinois 61801, USA
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65
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Liu J, Miller WH. Using the thermal Gaussian approximation for the Boltzmann operator in semiclassical initial value time correlation functions. J Chem Phys 2006; 125:224104. [PMID: 17176131 DOI: 10.1063/1.2395941] [Citation(s) in RCA: 80] [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 thermal Gaussian approximation (TGA) recently developed by Frantsuzov et al. [Chem. Phys. Lett. 381, 117 (2003)] has been demonstrated to be a practical way for approximating the Boltzmann operator exp(-betaH) for multidimensional systems. In this paper the TGA is combined with semiclassical (SC) initial value representations (IVRs) for thermal time correlation functions. Specifically, it is used with the linearized SC-IVR (LSC-IVR, equivalent to the classical Wigner model), and the "forward-backward semiclassical dynamics" approximation developed by Shao and Makri [J. Phys. Chem. A 103, 7753 (1999); 103, 9749 (1999)]. Use of the TGA with both of these approximate SC-IVRs allows the oscillatory part of the IVR to be integrated out explicitly, providing an extremely simple result that is readily applicable to large molecular systems. Calculation of the force-force autocorrelation for a strongly anharmonic oscillator demonstrates its accuracy, and calculation of the velocity autocorrelation function (and thus the diffusion coefficient) of liquid neon demonstrates its applicability.
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Affiliation(s)
- Jian Liu
- Department of Chemistry and K. S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720-1460, USA
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66
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Toutounji M. Mixed quantum-classical description of spectroscopy of dissipative systems. J Chem Phys 2006; 125:194520. [PMID: 17129136 DOI: 10.1063/1.2382916] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Mixed quantum-classical statistical mechanics is employed to calculate dipole moment correlation function and linear absorption spectra. A quantum two-level subsystem interacting with quantum vibrations (primary oscillators) which in turn are coupled to a classical bath composed of infinite set of harmonic oscillators is used as a dissipative system. Starting with mixed quantum-classical Liouville equation for the evaluation of the mixed quantum-classical dipole moment correlation function and using coherent states and the inverse of Baker-Campbell-Hausdorf formula to evaluate the trace over the primary oscillators, whereby, a closed analytical expression for the electronic dipole moment correlation function is obtained. Illustrations of several absorption spectra at different temperatures are provided. An approximate optical four-point correlation is obtained in the high temperature limit. A strategy for deriving an exact optical four-point correlation is suggested.
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Affiliation(s)
- Mohamad Toutounji
- College of Science, Department of Chemistry, P.O. Box 17551, United Arab Emirates University, Al-Ain, United Arab Emirates.
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67
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Wang H, Skinner DE, Thoss M. Calculation of reactive flux correlation functions for systems in a condensed phase environment: A multilayer multiconfiguration time-dependent Hartree approach. J Chem Phys 2006; 125:174502. [PMID: 17100449 DOI: 10.1063/1.2363195] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
A numerically exact quantum mechanical approach is proposed to evaluate thermal rate constants for systems in a model condensed phase environment. Employing the reactive flux correlation function formalism, the approach efficiently combines the multilayer multiconfiguration time-dependent Hartree theory with an importance sampling scheme for thermal distribution of the initial states. The performance of the method is illustrated by applications to two models of condensed phase dynamics: the donor-acceptor electron transfer model also known as the spin-boson model and a model for proton transfer reactions in the condensed phase.
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Affiliation(s)
- Haobin Wang
- Department of Chemistry and Biochemistry, New Mexico State University, Las Cruces, NM 88003, USA.
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68
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Miller WH. Including quantum effects in the dynamics of complex (i.e., large) molecular systems. J Chem Phys 2006; 125:132305. [PMID: 17029424 DOI: 10.1063/1.2211608] [Citation(s) in RCA: 75] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The development in the 1950s and 1960s of crossed molecular beam methods for studying chemical reactions at the single-collision molecular level stimulated the need and desire for theoretical methods to describe these and other dynamical processes in molecular systems. Chemical dynamics theory has made great strides in the ensuing decades, so that methods are now available for treating the quantum dynamics of small molecular systems essentially completely. For the large molecular systems that are of so much interest nowadays (e.g., chemical reactions in solution, in clusters, in nanostructures, in biological systems, etc.), however, the only generally available theoretical approach is classical molecular dynamics (MD) simulations. Much effort is currently being devoted to the development of approaches for describing the quantum dynamics of these complex systems. This paper reviews some of these approaches, especially the use of semiclassical approximations for adding quantum effects to classical MD simulations, also showing some new versions that should make these semiclassical approaches even more practical and accurate.
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Affiliation(s)
- William H Miller
- Department of Chemistry and K. S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720-1460, USA.
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69
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Uranga-Piña L, Martínez-Mesa A, Rubayo-Soneira J, Rojas-Lorenzo G. An effective temperature approach for molecular dynamics simulations of quantum solids. Chem Phys Lett 2006. [DOI: 10.1016/j.cplett.2006.06.013] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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70
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Mancal T, Pisliakov AV, Fleming GR. Two-dimensional optical three-pulse photon echo spectroscopy. I. Nonperturbative approach to the calculation of spectra. J Chem Phys 2006; 124:234504. [PMID: 16821926 DOI: 10.1063/1.2200704] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
The nonperturbative approach to the calculation of nonlinear optical spectra of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)] is extended to describe four-wave mixing experiments. The system-field interaction is treated nonperturbatively in the semiclassical dipole approximation, enabling a calculation of third order nonlinear spectroscopic signals directly from molecular dynamics and an efficient modeling of multilevel systems exhibiting relaxation and transfer phenomena. The method, coupled with the treatment of dynamics within the Bloch model, is illustrated by calculations of the two-dimensional three-pulse photon echo spectra of a simple model system-a two-electronic-level molecule. The nonperturbative calculations reproduce well-known results obtained by perturbative methods. Technical limitations of the nonperturbative approach in dealing with a dynamic inhomogeneity are discussed, and possible solutions are suggested. An application of the approach to an excitonically coupled dimer system with emphasis on the manifestation of complex exciton dynamics in two-dimensional optical spectra is presented in paper II Pisliakov et al. [J. Chem. Phys. 124, 234505 (2006), following paper].
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Affiliation(s)
- Tomás Mancal
- Department of Chemistry, University of California-Berkeley, Berkeley, CA 94720, USA
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71
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Wang H, Thoss M. Quantum-mechanical evaluation of the Boltzmann operator in correlation functions for large molecular systems: A multilayer multiconfiguration time-dependent Hartree approach. J Chem Phys 2006; 124:034114. [PMID: 16438574 DOI: 10.1063/1.2161178] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It is shown that the Boltzmann operator in time correlation functions for complex molecular systems can be evaluated in a numerically exact way employing the multilayer formulation of the multiconfiguration time-dependent Hartree theory in combination with Monte Carlo importance sampling techniques. The performance of the method is illustrated by selected applications to photoinduced intervalence electron transfer reactions in the condensed phase. Furthermore, the validity of approximate schemes to evaluate the Boltzmann is discussed.
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Affiliation(s)
- Haobin Wang
- Department of Chemistry and Biochemistry, MSC 3C, New Mexico State University, Las Cruces, New Mexico 88003, USA.
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72
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Mil'nikov GV, Zou S, Nakamura H. Incorporation of nonadiabatic transition into wave-packet dynamics. J Chem Phys 2005; 123:141101. [PMID: 16238365 DOI: 10.1063/1.2074457] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Nonadiabatic wave-packet dynamics is factorized into purely adiabatic propagation and instantaneous localized nonadiabatic transition. A general formula is derived for the quantum-mechanical local nonadiabatic operator which is implemented within the framework of the R-matrix method. The operator can be used for incorporating the nonadiabatic transition in semiclassical wave-packet dynamics.
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Affiliation(s)
- Gennady V Mil'nikov
- Department of Theoretical Studies, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan.
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73
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Abstract
This review describes some developments in the theory and application of the semiclassical initial representation for the treatment of the dynamical and static properties of atoms and molecules. The theoretical basis of initial value treatments for the propagator is discussed. A variety of useful alternative initial value expressions for the propagator and other quantities are presented as generalizations of the well-known Herman-Kluk approximation. Special emphasis is given to treatments that involve integration over only half the phase space variables. The recent development of semiclassical initial value expressions that are exact for specific, desired systems is reviewed and some of the implications are described.
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Affiliation(s)
- Kenneth G Kay
- Department of Chemistry, Bar-Ilan University, Ramat-Gan, Israel.
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74
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Abstract
This Perspective presents a broad overview of the present status of theoretical capabilities for describing quantum dynamics in molecular systems with many degrees of freedom, e.g., chemical reactions in solution, clusters, solids, or biomolecular environments.
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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, CA 94720-1460, USA.
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75
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Shi Q, Geva E. A comparison between different semiclassical approximations for optical response functions in nonpolar liquid solutions. J Chem Phys 2005; 122:064506. [PMID: 15740387 DOI: 10.1063/1.1843813] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
The temporal behavior of optical response functions (ORFs) reflects the quantum dynamics of an electronic superposition state, and as such lacks a well-defined classical limit. In this paper, we consider the importance of accounting for the quantum nature of the dynamics when calculating ORFs of different types. To this end, we calculated the ORFs associated with the linear absorption spectrum and the nonlinear two-pulse photon-echo experiment, via the following approaches: (1) the semiclassical forward-backward approach; (2) an approach based on linearizing the path-integral forward-backward action in terms of the difference between the forward and backward paths; (3) an approach based on ground state nuclear dynamics. The calculations were performed on a model that consists of a two-state chromophore solvated in a nonpolar liquid. The different methods were found to yield very similar results for the absorption spectrum and "diagonal" two-pulse photon echo (i.e., the homodyne-detected signal at time t=t(0) after the second pulse, where t(0) is the time interval between the two pulses). The different approximations yielded somewhat different results in the case of the time-integrated photon-echo signal. The reasons for the similarity between the predictions of different approximations are also discussed.
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Affiliation(s)
- Qiang Shi
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
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76
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Nakayama A, Makri N. Forward–backward semiclassical dynamics for systems of indistinguishable particles. Chem Phys 2004. [DOI: 10.1016/j.chemphys.2004.06.029] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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77
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Wang H, Thoss M. Semiclassical simulation of absorption spectra for a chromophore coupled to an anharmonic bath. Chem Phys 2004. [DOI: 10.1016/j.chemphys.2004.06.007] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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78
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Yonetani Y, Kinugawa K. Centroid molecular dynamics approach to the transport properties of liquid para-hydrogen over the wide temperature range. J Chem Phys 2004; 120:10624-33. [PMID: 15268088 DOI: 10.1063/1.1735613] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Fundamental transport properties of liquid para-hydrogen (p-H(2)), i.e., diffusion coefficients, thermal conductivity, shear viscosity, and bulk viscosity, have been evaluated by means of the path integral centroid molecular dynamics (CMD) calculations. These transport properties have been obtained over the wide temperature range, 14-32 K. Calculated values of the diffusion coefficients and the shear viscosity are in good agreement with the experimental values at all the investigated temperatures. Although a relatively large deviation is found for the thermal conductivity, the calculated values are less than three times the amount of the experimental values at any temperature. On the other hand, the classical molecular dynamics has led all the transport properties to much larger deviation. For the bulk viscosity of liquid p-H(2), which was never known from experiments, the present CMD has given a clear temperature dependence. In addition, from the comparison based on the principle of corresponding states, it has been shown that the marked deviation of the transport properties of liquid p-H(2) from the feature which is expected from the molecular parameters is due to the quantum effect.
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Affiliation(s)
- Yoshiteru Yonetani
- Japan Science and Technology Corporation, Department of Chemistry, Faculty of Science, Nara Women's University, Nara 630-8506, Japan
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79
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Thoss M, Wang H. SEMICLASSICAL DESCRIPTION OF MOLECULAR DYNAMICS BASED ON INITIAL-VALUE REPRESENTATION METHODS. Annu Rev Phys Chem 2004; 55:299-332. [PMID: 15117255 DOI: 10.1146/annurev.physchem.55.091602.094429] [Citation(s) in RCA: 137] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Recent progress in the development of semiclassical methods to describe quantum effects in molecular dynamics is reviewed. Focusing on rigorous semiclassical methods that are based on the initial-value representation of the semiclassical propagator, we discuss several promising schemes that have been developed in the past few years to extend the applicability of semiclassical approaches to complex molecular systems. In particular, integral-filtering techniques and forward-backward methods are surveyed. Furthermore, recently proposed approaches that allow the semiclassical description of nonadiabatic molecular dynamics are discussed. The potential and efficiency of these methods is illustrated by selected applications.
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Affiliation(s)
- Michael Thoss
- Theoretische Chemie, Technische Universitat Munchen, D-85747 Garching, Germany.
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80
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Bihary Z, Karavitis M, Apkarian VA. Onset of decoherence: Six-wave mixing measurements of vibrational decoherence on the excited electronic state of I2 in solid argon. J Chem Phys 2004; 120:8144-56. [PMID: 15267734 DOI: 10.1063/1.1691407] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
Pump-probe, four-wave, and six-wave mixing measurements of I2 isolated in solid argon are used to provide a clear experimental measure for the onset of vibrational quantum decoherence on the excited electronic state. The electronically resonant, six-wave mixing measurements bypass the rapid electronic dephasing, and measure the quantum cross-correlation between two packets launched on the B-state. The vibrational quantum coherence survives one period of motion, 400 fs, during which approximately 2000 cm(-1) of energy is transferred to the lattice. The decoherence occurs during the second cycle of motion, while classically coherent motion measured via pump-probe spectroscopy using the same electronic resonances continues for approximately 15 periods. This is contrasted with vibrational dephasing on the ground electronic surface, which lasts for 10(2) periods, as measured through time-resolved coherent anti-Stokes Raman scattering. The measurements and observables are discussed through time-circuit diagrams, and a mechanistic description of decoherence is derived through semiclassical analysis and simulations that reproduce the experiments.
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Affiliation(s)
- Z Bihary
- Department of Chemistry, University of California, Irvine, California 92697, USA
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81
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Rassolov VA, Garashchuk S. Bohmian dynamics on subspaces using linearized quantum force. J Chem Phys 2004; 120:6815-25. [PMID: 15267580 DOI: 10.1063/1.1669385] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In the de Broglie-Bohm formulation of quantum mechanics the time-dependent Schrodinger equation is solved in terms of quantum trajectories evolving under the influence of quantum and classical potentials. For a practical implementation that scales favorably with system size and is accurate for semiclassical systems, we use approximate quantum potentials. Recently, we have shown that optimization of the nonclassical component of the momentum operator in terms of fitting functions leads to the energy-conserving approximate quantum potential. In particular, linear fitting functions give the exact time evolution of a Gaussian wave packet in a locally quadratic potential and can describe the dominant quantum-mechanical effects in the semiclassical scattering problems of nuclear dynamics. In this paper we formulate the Bohmian dynamics on subspaces and define the energy-conserving approximate quantum potential in terms of optimized nonclassical momentum, extended to include the domain boundary functions. This generalization allows a better description of the non-Gaussian wave packets and general potentials in terms of simple fitting functions. The optimization is performed independently for each domain and each dimension. For linear fitting functions optimal parameters are expressed in terms of the first and second moments of the trajectory distribution. Examples are given for one-dimensional anharmonic systems and for the collinear hydrogen exchange reaction.
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Affiliation(s)
- Vitaly A Rassolov
- Department of Chemistry & Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
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82
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Wright NJ, Makri N. Phase Space Features and Statistical Aspects of Forward−Backward Semiclassical Dynamics. J Phys Chem B 2004. [DOI: 10.1021/jp037600f] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Nicholas J. Wright
- Department of Chemistry, University of Illinois, 601 South Goodwin Avenue, Urbana, Illinois 61801
| | - Nancy Makri
- Department of Chemistry, University of Illinois, 601 South Goodwin Avenue, Urbana, Illinois 61801
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83
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Affiliation(s)
- Nancy Makri
- Departments of Chemistry and Physics, University of Illinois, 601 South Goodwin Avenue, Urbana, Illinois 61801
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84
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Elran Y, Brumer P. Decoherence in an anharmonic oscillator coupled to a thermal environment: A semiclassical forward-backward approach. J Chem Phys 2004; 121:2673-84. [PMID: 15281868 DOI: 10.1063/1.1766009] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The decoherence of an anharmonic oscillator in a thermal harmonic bath is examined via a semiclassical approach. A computational strategy is presented and exploited to calculate the time dependence of the purity and the decay of individual matrix elements in the energy representation for a variety of initial states. The time dependence of the decoherence is found to depend on the temperature of the bath, the coupling strength, the initial state of the oscillator, and the choice of quantity measuring the decoherence. Recurrences in the purity and in the off-diagonal matrix elements are observed, as well as the collapse of these matrix elements to the diagonal, providing evidence for the retention of quantum coherence for time scales longer than that indicated by the purity. The results are used to analyze the utility of the Caldeira-Leggett and Redfield models of decoherence and to assess the dependence of dephasing rates on the degree of structure in phase space. In several cases we find that the dephasing dynamics can be described as an initial Zeno-effect regime, followed by a Caldeira-Leggett region, followed by recurrences.
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Affiliation(s)
- Yossi Elran
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto M5S 3H6, Canada
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85
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Thoss M, Domcke W, Wang H. Theoretical study of vibrational wave-packet dynamics in electron-transfer systems. Chem Phys 2004. [DOI: 10.1016/j.chemphys.2003.08.029] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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86
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Nakayama A, Makri N. Forward–backward semiclassical dynamics for quantum fluids using pair propagators: Application to liquidpara-hydrogen. J Chem Phys 2003. [DOI: 10.1063/1.1611473] [Citation(s) in RCA: 86] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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87
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Wright NJ, Makri N. Forward–backward semiclassical dynamics for condensed phase time correlation functions. J Chem Phys 2003. [DOI: 10.1063/1.1580472] [Citation(s) in RCA: 65] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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88
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Shi Q, Geva E. A relationship between semiclassical and centroid correlation functions. J Chem Phys 2003. [DOI: 10.1063/1.1564814] [Citation(s) in RCA: 122] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
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89
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Gong J, Brumer P. When is quantum decoherence dynamics classical? PHYSICAL REVIEW LETTERS 2003; 90:050402. [PMID: 12633342 DOI: 10.1103/physrevlett.90.050402] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2002] [Indexed: 05/24/2023]
Abstract
A direct classical analog of quantum decoherence is introduced. Similarities and differences between decoherence dynamics examined quantum mechanically and classically are exposed via a second-order perturbative treatment and via a strong decoherence theory, showing a strong dependence on the nature of the system-environment coupling. For example, for the traditionally assumed linear coupling, the classical and quantum results are shown to be in exact agreement.
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Affiliation(s)
- Jiangbin Gong
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Canada M5S 3H6
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90
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Kaledin AL, Miller WH. Time averaging the semiclassical initial value representation for the calculation of vibrational energy levels. J Chem Phys 2003. [DOI: 10.1063/1.1562158] [Citation(s) in RCA: 84] [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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91
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Wang H, Thoss M. Self-consistent hybrid approach for simulating electron transfer reactions in condensed phases. Isr J Chem 2002. [DOI: 10.1560/kj0g-kb9c-g0jb-area] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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92
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Zhao Y, Miller WH. Semiclassical initial value representation for the Boltzmann operator in thermal rate constants. J Chem Phys 2002. [DOI: 10.1063/1.1517044] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
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93
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Babikov D, Walker RB, T Pack R. A quantum symmetry preserving semiclassical method. J Chem Phys 2002. [DOI: 10.1063/1.1513457] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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94
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Torres L, Gelabert R, Giménez X, Moreno M, Lluch JM. Semiclassical initial value representation description of molecular structure problems: An elongated dihydrogen ruthenium complex. J Chem Phys 2002. [DOI: 10.1063/1.1502649] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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95
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Sun SX, Miller WH. Statistical sampling of semiclassical distributions: Calculating quantum mechanical effects using Metropolis Monte Carlo. J Chem Phys 2002. [DOI: 10.1063/1.1501130] [Citation(s) in RCA: 11] [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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96
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Makri N. Monte Carlo Evaluation of Forward−Backward Semiclassical Correlation Functions with a Quantized Coherent State Density. J Phys Chem B 2002. [DOI: 10.1021/jp020907e] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Nancy Makri
- Departments of Chemistry and Physics, University of Illinois, 601 S. Goodwin Avenue, Urbana, Illinois 61801
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97
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Makri N, Miller WH. Coherent state semiclassical initial value representation for the Boltzmann operator in thermal correlation functions. J Chem Phys 2002. [DOI: 10.1063/1.1472518] [Citation(s) in RCA: 52] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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98
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99
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Yamamoto T, Wang H, Miller WH. Combining semiclassical time evolution and quantum Boltzmann operator to evaluate reactive flux correlation function for thermal rate constants of complex systems. J Chem Phys 2002. [DOI: 10.1063/1.1464539] [Citation(s) in RCA: 75] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
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100
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Wang H, Manolopoulos DE, Miller WH. Generalized Filinov transformation of the semiclassical initial value representation. J Chem Phys 2001. [DOI: 10.1063/1.1402992] [Citation(s) in RCA: 88] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
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