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The Journal of Physical Chemistry A

Semiclassical Hybrid Approach to Condensed Phase Molecular Dynamics: Application to the I2Kr17 Cluster

Max Buchholz, Christoph-Marian Goletz, Frank Großmann, Burkhard Schmidt, Jan Heyda, Pavel Jungwirth

Published Jul 23, 2012• 20 citations
Publisher

Abstract

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.

DOI
10.1021/jp305084f

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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.
Applying the recently developed semiclassical hybrid dynamics [Grossmann, J. Chem. Phys. 125, 014111 (2006)], we study the decay of interference patterns in the reduced density as well as of the purity in a Morse oscillator test system due to the interaction with a finite harmonic bath at zero temperature. In the case that the bath mimics a continuous Ohmic spectral density, in addition to the quantum classical transition induced by the interaction with the environment, we corroborate the existence of a blueshift due to the bath coupling, predicted by Pollak [Phys. Rev. A 33, 4244 (1986)]. Furthermore, the decoherence dynamics of cat states is confirmed to be faster than that of single coherent states and we show that for a resonant bath the dissipation leads to an increase in the decoherence rate as compared to the low frequency bath.
A quantum/semiclassical theory for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium is developed, tested and applied to simulate and interpret ultrafast optical signals. Linear wave-packet interferometry and time-resolved coherent anti-Stokes Raman scattering signals for a model of molecular iodine in a 2D krypton lattice are calculated and used to study the vibrational decoherence and energy dissipation of iodine molecules in condensed media. The total wave function of the whole model is approximately obtained instead of a reduced system density matrix, and therefore the theory enables us to analyze the behavior and the role of the host matrix in quantum dynamics. \n \nThis dissertation includes previously published co-authored material.
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.
The Wigner phase space formulation of quantum mechanics is a complete framework for quantum dynamic calculations that elegantly highlights connections with classical dynamics. In this series of two articles, building upon previous efforts, we derive the full hierarchy of approximate semiclassical (SC) dynamic methods for adiabatic and non-adiabatic problems in Wigner phase space. In Paper I, focusing on adiabatic single surface processes, we derive the well-known double Herman-Kluk (DHK) approximation for real-time correlation functions in Wigner phase space and connect it to the linearized SC (LSC) approximation through a stationary phase approximation. We exploit this relationship to introduce a new hybrid SC method, termed Adiabatic Hybrid Wigner Dynamics (AHWD) that allows for a few important "system" degrees of freedom (dofs) to be treated at the DHK level, while treating the rest of the dofs (the "bath") at the LSC level. AHWD is shown to accurately capture quantum interference effects in models of coupled oscillators and the decoherence of vibrational probability density of a model I2 Morse oscillator coupled to an Ohmic thermal bath. We show that AHWD significantly mitigates the sign problem and employs reduced dimensional prefactors bringing calculations of complex system-bath problems within the reach of SC methods. Paper II focuses on extending this hybrid SC dynamics to nonadiabatic processes.
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.
Electronic decoherence processes in molecules and materials are usually thought and modeled via schemes for the system-bath evolution in which the bath is treated either implicitly or approximately. Here we present computations of the electronic decoherence dynamics of a model many-body molecular system described by the Su-Schrieffer-Heeger Hamiltonian with Hubbard electron-electron interactions using an exact method in which both electronic and nuclear degrees of freedom are taken into account explicitly and fully quantum mechanically. To represent the electron-nuclear Hamiltonian in matrix form and propagate the dynamics, the computations employ the Jordan-Wigner transformation for the fermionic creation/annihilation operators and the discrete variable representation for the nuclear operators. The simulations offer a standard for electronic decoherence that can be used to test approximations. They also provide a useful platform to answer fundamental questions about electronic decoherence that cannot be addressed through approximate or implicit schemes. Specifically, through simulations, we isolate basic mechanisms for electronic coherence loss and demonstrate that electronic decoherence is possible even for one-dimensional nuclear bath. Furthermore, we show that (i) decreasing the mass of the bath generally leads to faster electronic decoherence; (ii) electron-electron interactions strongly affect the electronic decoherence when the electron-nuclear dynamics is not pure-dephasing; (iii) classical bath models with initial conditions sampled from the Wigner distribution accurately capture the short-time electronic decoherence dynamics; (iv) model separable initial superpositions often used to understand decoherence after photoexcitation are only relevant in experiments that employ delta-like laser pulses to initiate the dynamics. These insights can be employed to interpret and properly model coherence phenomena in molecules.