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Reddy CS, Prasad MD. A Gaussian Wave Packet Propagation Approach to Vibrationally Resolved Optical Spectra at Non-Zero Temperatures. J Phys Chem A 2016; 120:2583-90. [PMID: 27035861 DOI: 10.1021/acs.jpca.6b00308] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
An effective time dependent approach based on a method that is similar to the Gaussian wave packet propagation (GWP) technique of Heller is developed for the computation of vibrationally resolved electronic spectra at finite temperatures in the harmonic, Franck-Condon/Hertzberg-Teller approximations. Since the vibrational thermal density matrix of the ground electronic surface and the time evolution operator on that surface commute, it is possible to write the spectrum generating correlation function as a trace of the time evolved doorway state. In the stated approximations, the doorway state is a superposition of the harmonic oscillator zero and one quantum eigenfunctions and thus can be propagated by the GWP. The algorithm has an O(N(3)) dependence on the number of vibrational modes. An application to pyrene absorption spectrum at two temperatures is presented as a proof of the concept.
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Affiliation(s)
- Ch Sridhar Reddy
- School of Chemistry, University of Hyderabad , Hyderabad 500 046, India
| | - M Durga Prasad
- School of Chemistry, University of Hyderabad , Hyderabad 500 046, India
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2
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Toutounji M. Electronic energy gap correlation function and spectral density of anharmonic molecules at low temperatures I: Theory. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2014.10.053] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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3
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A new methodology for dealing with time-dependent quantities in anharmonic molecules I: theory. Theor Chem Acc 2014. [DOI: 10.1007/s00214-014-1461-1] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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4
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Akimov AV, Neukirch AJ, Prezhdo OV. Theoretical Insights into Photoinduced Charge Transfer and Catalysis at Oxide Interfaces. Chem Rev 2013; 113:4496-565. [DOI: 10.1021/cr3004899] [Citation(s) in RCA: 402] [Impact Index Per Article: 36.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Alexey V. Akimov
- Department of Chemistry, University of Rochester, Rochester, New York 14627,
United States
- Chemistry
Department, Brookhaven National Laboratory, Upton, New York 11973-5000,
United States
| | - Amanda J. Neukirch
- Department
of Physics and Astronomy, University of Rochester, Rochester, New York 14627,
United States
| | - Oleg V. Prezhdo
- Department of Chemistry, University of Rochester, Rochester, New York 14627,
United States
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Akimov AV, Prezhdo OV. Formulation of quantized Hamiltonian dynamics in terms of natural variables. J Chem Phys 2012; 137:224115. [DOI: 10.1063/1.4770224] [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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6
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Toutounji M. Anharmonic nuclear dynamics in the mixed quantum-classical limit. Phys Chem Chem Phys 2012; 14:626-36. [PMID: 22086187 DOI: 10.1039/c1cp22776a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
This study employs mixed quantum-classical dynamics (MQCD) formalism to evaluate the linear electronic dipole moment time correlation function (DMTCF) in which a Morse oscillator serves to model the associated vibrations in a mixed quantum-classical (MQC) environment. While the main purpose of this work is to study the applicability of MQCD formalism to anharmonic systems in condensed phase, approximate schemes to physically evaluate the mathematically divergent integrals have been developed in order to deal with the essential singularities that arise while evaluating the Morse oscillator canonical partition function and the DMTCF in MQC systems in the classical limit. The motivation for numerically and analytically evaluating these divergent integrals is that a partition function of any system should lead to a finite value at any temperature and therefore this divergence is unphysical. Additionally, since a partition function is to signify the number of accessible states to the system at hand, divergent results are not physically acceptable. As such, straightforward approximate analytic expressions, at different levels of rigor, for both the classical Morse oscillator partition function and the DMTCF in MQC systems are derived, for the first time. Calculations of Morse oscillator partition function values using different approaches at various temperatures for CO, HCl, and I(2) molecules, showing good results, are presented to test the expressions derived herein. It is found that this divergence, due to singularity, diminishes upon lowering the temperature and only arises at high temperatures. The gradual diminishing of the singularity upon lowering the temperature is sensible since the Morse potential fits the parabolic potential at low temperatures. Model calculations and discussion of the DMTCF and linear absorption spectra in MQC systems using the molecular constants of CO molecule are provided. The linear absorption lineshape is derived by two methods, one of which is asymptotic expansion.
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Affiliation(s)
- Mohamad Toutounji
- College of Science, Department of Chemistry, United Arab Emirates University, Al-Ain, UAE.
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Toutounji M. Anharmonic electron-phonon coupling in condensed media: 1. Formalism. J Phys Chem B 2011; 115:5121-32. [PMID: 20722358 DOI: 10.1021/jp104731s] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Three different schemes for calculating anharmonic line shape functions are reported and discussed for the first time in this article using eigenstate representation. First, the linear dipole-moment time correlation function (DMTCF), homogeneous (single-site) absorption line shape function, and the respective Franck-Condon factors (FCF) are derived and explored as a molecule makes a transition from a harmonic to an anharmonic (Morse potential) electronic state. Second, the linear DMTCF, homogeneous absorption line shape function, and FCFs are also derived as a molecule makes a transition from one anharmonic to another linearly displaced anharmonic state; FCFs in this case are reported in an exact closed-form expressed in terms of Appell's hypergeometric function. Third, same as the latter set of results are reported but with both linearly displaced and distorted shape of the upper Morse potential. FCFs of the zero-phonon line in all three cases are reported. The first case is rather mathematically complex as a result of taking the overlap integral of the Morse oscillator eigenfunctions, whose spatial decay is a simple exponential, with those of harmonic oscillator, whose decay is a Gaussian. This form of a functional disparity gives rise to some challenges. Model calculations are presented and discussed.
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Affiliation(s)
- Mohamad Toutounji
- College of Science, Department of Chemistry, United Arab Emirates University, Al-Ain, UAE.
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Toutounji M. Exploring Anharmonic Nuclear Dynamics and Spectroscopy Using the Kratzer Oscillator. J Chem Theory Comput 2011; 7:1804-13. [DOI: 10.1021/ct1007185] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Mohamad Toutounji
- Department of Chemistry, College of Science, United Arab Emirates University, Al-Ain, United Arab Emirates
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Pereverzev A, Pereverzev YV, Prezhdo OV. Dissipation of classical energy in nonlinear quantum systems. J Chem Phys 2008; 128:134107. [DOI: 10.1063/1.2844597] [Citation(s) in RCA: 11] [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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Mukamel S. Solvation Effects in Four-Wave Mixing and Spontaneous Raman and Fluorescence Lineshapes of Polyatomic Molecules. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141199.ch6] [Citation(s) in RCA: 58] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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11
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Heatwole EM, Prezhdo OV. Second-order quantized Hamilton dynamics coupled to classical heat bath. J Chem Phys 2005; 122:234109. [PMID: 16008432 DOI: 10.1063/1.1931666] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
Starting with a quantum Langevin equation describing in the Heisenberg representation a quantum system coupled to a quantum bath, the Markov approximation and, further, the closure approximation are applied to derive a semiclassical Langevin equation for the second-order quantized Hamilton dynamics (QHD) coupled to a classical bath. The expectation values of the system operators are decomposed into products of the first and second moments of the position and momentum operators that incorporate zero-point energy and moderate tunneling effects. The random force and friction as well as the system-bath coupling are decomposed to the lowest classical level. The resulting Langevin equation describing QHD-2 coupled to classical bath is analyzed and applied to free particle, harmonic oscillator, and the Morse potential representing the OH stretch of the SPC-flexible water model.
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Affiliation(s)
- Eric M Heatwole
- Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, USA
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Heatwole E, Prezhdo OV. A canonical averaging in the second-order quantized Hamilton dynamics. J Chem Phys 2004; 121:10967-75. [PMID: 15634046 DOI: 10.1063/1.1812749] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Quantized Hamilton dynamics (QHD) is a simple and elegant extension of classical Hamilton dynamics that accurately includes zero-point energy, tunneling, dephasing, and other quantum effects. Formulated as a hierarchy of approximations to exact quantum dynamics in the Heisenberg formulation, QHD has been used to study evolution of observables subject to a single initial condition. In present, we develop a practical solution for generating canonical ensembles in the second-order QHD for position and momentum operators, which can be mapped onto classical phase space in doubled dimensionality and which in certain limits is equivalent to thawed Gaussian. We define a thermal distribution in the space of the QHD-2 variables and show that the standard beta=1/kT relationship becomes beta'=2/kT in the high temperature limit due to an overcounting of states in the extended phase space, and a more complicated function at low temperatures. The QHD thermal distribution is used to compute total energy, kinetic energy, heat capacity, and other canonical averages for a series of quartic potentials, showing good agreement with the quantum results.
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Affiliation(s)
- Eric Heatwole
- Department of Chemistry, University of Washington, Seattle, WA 98195-1700, USA
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13
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Quantum interference by non-interacting classical trajectories evolving on a quasi-classical potential. Chem Phys Lett 2003. [DOI: 10.1016/s0009-2614(03)01342-3] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Burghardt I, Møller KB. Quantum dynamics for dissipative systems: A hydrodynamic perspective. J Chem Phys 2002. [DOI: 10.1063/1.1509061] [Citation(s) in RCA: 47] [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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Burghardt I, Cederbaum LS. Hydrodynamic equations for mixed quantum states. I. General formulation. J Chem Phys 2001. [DOI: 10.1063/1.1416493] [Citation(s) in RCA: 64] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Broeckhove J, Lathouwers L, Leuven PV. Time-dependent variational principles and conservation laws in wavepacket dynamics. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/22/20/016] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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22
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Batista VS, Miller WH. Semiclassical molecular dynamics simulations of ultrafast photodissociation dynamics associated with the Chappuis band of ozone. J Chem Phys 1998. [DOI: 10.1063/1.475413] [Citation(s) in RCA: 64] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Martínez TJ, Ben-Nun M, Levine RD. Molecular Collision Dynamics on Several Electronic States. J Phys Chem A 1997. [DOI: 10.1021/jp970842t] [Citation(s) in RCA: 107] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- T. J. Martínez
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801
| | - M. Ben-Nun
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093-0339
| | - R. D. Levine
- The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University, Jerusalem 91904, Israel
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Ma J, Hsu D, Straub JE. Approximate solution of the classical Liouville equation using Gaussian phase packet dynamics: Application to enhanced equilibrium averaging and global optimization. J Chem Phys 1993. [DOI: 10.1063/1.466098] [Citation(s) in RCA: 54] [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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Walkup RE. A local‐Gaussian approximation for the propagation of a classical distribution function. J Chem Phys 1991. [DOI: 10.1063/1.461564] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Knoester J, Mukamel S. Nonlinear optics using the multipolar Hamiltonian: The Bloch-Maxwell equations and local fields. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 39:1899-1914. [PMID: 9901445 DOI: 10.1103/physreva.39.1899] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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28
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Yan YJ, Mukamel S. Electronic dephasing, vibrational relaxation, and solvent friction in molecular nonlinear optical line shapes. J Chem Phys 1988. [DOI: 10.1063/1.455634] [Citation(s) in RCA: 161] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kress JD, DePristo AE. Semiclassical Gaussian wave packet dynamics for collinear reactive scattering. J Chem Phys 1988. [DOI: 10.1063/1.454993] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Rose TS, Rosker MJ, Zewail AH. Femtosecond real‐time observation of wave packet oscillations (resonance) in dissociation reactions. J Chem Phys 1988. [DOI: 10.1063/1.454408] [Citation(s) in RCA: 350] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Yan YJ, Mukamel S. Semiclassical dynamics in Liouville space: Application to molecular electronic spectroscopy. J Chem Phys 1988. [DOI: 10.1063/1.454533] [Citation(s) in RCA: 61] [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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