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The Journal of Chemical Physics

Simulation of vibrational dephasing of I2 in solid Kr using the semiclassical Liouville method

Jeanne M. Riga, Erick Fredj, Craig C. Martens

Published Feb 9, 2006• 23 citations
Publisher

Abstract

In this paper, we present simulations of the decay of quantum coherence between vibrational states of I(2) in its ground (X) electronic state embedded in a cryogenic Kr matrix. We employ a numerical method based on the semiclassical limit of the quantum Liouville equation, which allows the simulation of the evolution and decay of quantum vibrational coherence using classical trajectories and ensemble averaging. The vibrational level-dependent interaction of the I(2)(X) oscillator with the rare-gas environment is modeled using a recently developed method for constructing state-dependent many-body potentials for quantum vibrations in a many-body classical environment [J. M. Riga, E. Fredj, and C. C. Martens, J. Chem. Phys. 122, 174107 (2005)]. The vibrational dephasing rates gamma(0n) for coherences prepared between the ground vibrational state mid R:0 and excited vibrational state mid R:n are calculated as a function of n and lattice temperature T. Excellent agreement with recent experiments performed by Karavitis et al. [Phys. Chem. Chem. Phys. 7, 791 (2005)] is obtained.

DOI
10.1063/1.2162878

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In this paper, we present simulations of the decay of quantum coherence between vibrational states of I(2) in its ground (X) electronic state embedded in a cryogenic Kr matrix. We employ a numerical method based on the semiclassical limit of the quantum Liouville equation, which allows the simulation of the evolution and decay of quantum vibrational coherence using classical trajectories and ensemble averaging. The vibrational level-dependent interaction of the I(2)(X) oscillator with the rare-gas environment is modeled using a recently developed method for constructing state-dependent many-body potentials for quantum vibrations in a many-body classical environment [J. M. Riga, E. Fredj, and C. C. Martens, J. Chem. Phys. 122, 174107 (2005)]. The vibrational dephasing rates gamma(0n) for coherences prepared between the ground vibrational state mid R:0 and excited vibrational state mid R:n are calculated as a function of n and lattice temperature T. Excellent agreement with recent experiments performed by Karavitis et al. [Phys. Chem. Chem. Phys. 7, 791 (2005)] is obtained.
In this paper, we describe recent work on modelling the loss of quantum coherence in condensed phase systems. We review numerical methodology based on a semiclassical limit of the quantum Liouville equation for simulating quantum coherent processes using classical-like molecular dynamics simulation and ensemble averaging, and apply the approach to simulating vibrational dephasing of I 2 in cryogenic rare gas matrices and the quantum vibrations of OH stretches of HOD in D 2 O. We then describe a simple analytic and numerical model that highlights novel behaviour that can be exhibited by quantum coherent processes in the presence of a nonequilibrium environment.
Abstract In this article, we describe recent work on investigating the role of the environment in influencing coherent quantum dynamics. We review numerical methodology based on a semiclassical limit of the quantum Liouville equation for simulating quantum coherent processes using classical‐like molecular dynamics simulation and ensemble averaging and apply the approach to simulate vibrational dephasing of I2 in cryogenic rare gas matrices and the quantum vibrations of OH stretches of HOD in D2O. We then describe a simple analytic and numerical model that highlights novel behavior that can be exhibited by quantum coherent processes in the presence of an environment that is not at thermal equilibrium. © 2012 Wiley Periodicals, Inc.
In this paper we describe an application of the trajectory-based semiclassical Liouville method for modeling coherent molecular dynamics on multiple electronic surfaces to the treatment of the evolution and decay of quantum electronic coherence in many-body systems. We consider a model representing the coherent evolution of quantum wave packets on two excited electronic surfaces of a diatomic molecule in the gas phase and in rare gas solvent environments, ranging from small clusters to a cryogenic solid. For the gas phase system, the semiclassical trajectory method is shown to reproduce the evolution of the electronic-nuclear coherence nearly quantitatively. The dynamics of decoherence are then investigated for the solvated systems using the semiclassical approach. It is found that, although solvation in general leads to more rapid and extensive loss of quantum coherence, the details of the coupled system-bath dynamics are important, and in some cases the environment can preserve or even enhance quantum coherence beyond that seen in the isolated system.
Time-resolved coherent anti-Stokes Raman scattering, with a resolution of 20 fs, is used to prepare a broadband vibrational superposition on the ground electronic state of I2 isolated in solid Kr. The coherent evolution of a packet consisting of nu=1-6 is monitored for as many as 1000 periods, allowing a precise analysis of the material response and radiation coherence. The molecular vibrations are characterized by omega(e)=211.330(2) cm(-1), omega(e)x(e)=0.6523(6) cm(-1), omega(e)y(e)=2.9(1) x 10(-3) cm(-1); the dephasing rates at 32 K range from 110 ps for nu=1 to 34 ps for nu=6, with nu dependence: gamma(nu)=8.5 x 10(-3)+4.9 x 10(-4)nu2+2.1 x 10(-6)nu4 ps(-1). The signal amplitude is also modulated at omega(q)=41.56(3) cm(-1); which can be interpreted as coupling between the molecule and a local mode. The surprising implication is that this resonant local mode is decoupled from the lattice phonons, a finding that cannot be rationalized based on a normal-mode analysis.
The process of decoherence of vibrational states of I2 in a dense helium environment is studied theoretically using the mixed quantum/classical method based on the Bohmian formulation of quantum mechanics [E. Gindensperger, C. Meier, and J. A. Beswick, J. Chem. Phys. 113, 9369 (2000)]. Specifically, the revival of vibrational wave packets is a quantum phenomena which depends sensitively on the coherence between the vibrational states excited by an ultrafast laser pulse. Its detection by a pump-probe setup as a function of rare gas pressure forms a very accurate way of detecting vibrational dephasing. Vibrational revivals of I2 in high pressure rare gas environments have been observed experimentally, and the very good agreement with the simulated spectra confirms that the method can accurately describe decoherence processes of quantum systems in interaction with an environment.
We study the vibrational decoherence dynamics of an iodine molecule in a finite krypton cluster comprising the first solvation shell. A normal mode analysis allows us to successively increase the complexity of the description. For the ground state dynamics, comparison with experimental matrix results shows that already four degrees of freedom are sufficient to capture the main decoherence mechanism. For electronically excited iodine, we model the vibrational dynamics of initial Schrödinger cat-like states by the semiclassical hybrid dynamics [Grossmann, F. J. Chem. Phys. 2006, 125, 014111] and full quantum calculations, where available. Good agreement of the results is found for a reduced model with three degrees of freedom. We find non-Gaussian distortions of the bath density matrix, which is a necessary condition, if Schrödinger catlike states in the bath are to be identified. However, in contrast to the experiment [Segale, D.; et al. J. Chem. Phys. 2005, 122, 111104], we observe only incoherent superpositions of bath vibrational states.