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ABSTRACT: An efficient time-dependent (TD) Monte Carlo (MC) importance sampling method has recently been developed [G. Tao and W. H. Miller, J. Chem. Phys. 135, 024104 (2011)] for the evaluation of time correlation functions using the semiclassical (SC) initial value representation (IVR) methodology. In this TD-SC-IVR method, the MC sampling uses information from both time-evolved phase points as well as their initial values, and only the "important" trajectories are sampled frequently. Even though the TD-SC-IVR was shown in some benchmark examples to be much more efficient than the traditional time-independent sampling method (which uses only initial conditions), the calculation of the SC prefactor-which is computationally expensive, especially for large systems-is still required for accepted trajectories. In the present work, we present an approximate implementation of the TD-SC-IVR method that is completely prefactor-free; it gives the time correlation function as a classical-like magnitude function multiplied by a phase function. Application of this approach to flux-flux correlation functions (which yield reaction rate constants) for the benchmark H + H(2) system shows very good agreement with exact quantum results. Limitations of the approximate approach are also discussed.
The Journal of chemical physics 09/2012; 137(12):124105. · 3.09 Impact Factor
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ABSTRACT: The frozen Gaussian approximation to the quantum propagator may be a viable method for obtaining "on the fly" quantum dynamical information on systems with many degrees of freedom. However, it has two severe limitations, it rapidly loses normalization and one needs to know the Gaussian averaged potential, hence it is not a purely local theory in the force field. These limitations are in principle remedied by using the Herman-Kluk (HK) form for the semiclassical propagator. The HK propagator approximately conserves unitarity for relatively long times and depends only locally on the bare potential and its second derivatives. However, the HK propagator involves a much more expensive computation due to the need for evaluating the monodromy matrix elements. In this paper, we (a) derive a new formula for the normalization integral based on a prefactor free HK propagator which is amenable to "on the fly" computations; (b) show that a frozen Gaussian version of the normalization integral is not readily computable "on the fly"; (c) provide a new insight into how the HK prefactor leads to approximate unitarity; and (d) how one may construct a prefactor free approximation which combines the advantages of the frozen Gaussian and the HK propagators. The theoretical developments are backed by numerical examples on a Morse oscillator and a quartic double well potential.
The Journal of chemical physics 04/2011; 134(13):134104. · 3.09 Impact Factor
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ABSTRACT: Recently, Fleming’s group observed direct evidence that the electronic excitation energy (and population) transfers coherently rather than through incoherent hopping motions in the Fenna−Mathews−Olson pigment−protein complex. Ishizaki and Fleming further developed a hierarchy equation approach to describe this excitation population transfer dynamics in a model photosynthetic system. Here, we treat this same model system via the linearized approximation to the semiclassical (SC) initial value representation (IVR) for time correlation functions, in combination with the Meyer−Miller−Stock−Thoss model for the electronic degrees of freedom. Our approach is able to describe the long-lived quantum coherent dynamics, in excellent agreement with Ishizaki−Fleming’s results. Moreover, the advantage of the linearlized SC-IVR approach is that it can be applied to any molecular model for which classical MD simulations are feasible, all the way up to a full all-atom MD simulation, while at the same time treating the electronic and nuclear dynamics in a consistent fashion.Keywords (keywords): photosynthesis; quantum coherence; initial value problems; molecular dynamics method; electronic coupling; system−bath interactions
02/2010;
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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.
The Journal of chemical physics 12/2009; 131(22):224107. · 3.09 Impact Factor
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ABSTRACT: The semiclassical (SC) initial value representation (IVR) has been applied to describe true quantum coherence effects in a complex molecular system in full three dimensional space. The specific quantity considered is the time-dependent probability distribution of the I(2) vibrational coordinate following photoexcitation of I(2) in a rare gas cluster. The "forward-backward" version of the IVR method is shown to be capable of capturing detailed quantum coherence in this quantity, coherence that cannot be described by a classical Wigner model (which is equivalent to a linearized approximation to the more general SC-IVR). Solvent effects on this vibrational quantum coherence have also been investigated for a I(2)Ar(n) (n=1,6) cluster. A solvent cage consisting of six argon atoms reduces the fraction of iodine molecules that dissociate (an example of the "cage effect") and also diminishes, but does not entirely eliminate, quantum coherence in the vibrational motion of the molecules that remain undissociated.
The Journal of chemical physics 06/2009; 130(18):184108. · 3.09 Impact Factor
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ABSTRACT: Experimental and theoretical work on the relaxation of rapidly rotating solutes in liquids have pointed out a number of striking features. Even in rapidly relaxing solvents, the relaxation proceeds quite slowly, exhibiting a manifestly nonlinear response that depends explicitly on the initial rotational energy. In this paper, we show how the long-time behavior, in particular, stems from a strong coupling of solute orientation to local solvent geometry. This coupling creates a rotational friction that decreases sharply with rotational energy, allowing for the protracted survival of not only high-angular-momentum rotational states but the cavity-like low-friction solvent geometries. We show, further, that the slow dynamics is dynamically heterogeneous. The distribution of excited rotors is marked by a distinct population of slowly relaxing hot rotational states. This population can be traced directly to the small subset of liquid configurations that happen to have low rotational friction values at the instant at which the rapid rotation started, indicating an unusual failure of the normally chaotic environment of a liquid to randomize initial conditions.
The Journal of Physical Chemistry B 02/2008; 112(2):369-77. · 3.70 Impact Factor
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ABSTRACT: A key step in solution-phase chemical reactions is often the removal of excess internal energy from the product. Yet, the way one typically studies this process is to follow the relaxation of a solute that has been excited into some distribution of excited states quite different from that produced by any reaction of interest. That the effects of these different excitations can frequently be ignored is a consequence of the near universality of linear-response behavior, the idea that relaxation dynamics is determined by the solvent fluctuations (which may not be all that different for different kinds of solute excitation). Nonetheless, there are some clear examples of linear-response breakdowns seen in solute relaxation, including a recent theoretical and experimental study of rapidly rotating diatomics in liquids. In this paper we use this rotational relaxation example to carry out a theoretical exploration of the conditions that lead to linear-response failure. Some features common to all of the linear-response breakdowns studied to date, including our example, are that the initial solute preparation is far from equilibrium, that the subsequent relaxation promotes a significant rearrangement of the liquid structure, and that the nonequilibrium response is nonstationary. However, we show that none of these phenomena is enough to guarantee a nonlinear response. One also needs a sufficient separation between the solute time scale and that of the solvent geometry evolution. We illustrate these points by demonstrating precisely how our relaxation rate is tied to our liquid-structural evolution, how we can quantitatively account for the initial nonstationarity of our effective rotational friction, and how one can tune our rotational relaxation into and out of linear response.
The Journal of Chemical Physics 10/2006; 125(11):114501. · 3.33 Impact Factor
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ABSTRACT: Highly energized molecules normally are rapidly equilibrated by a solvent; this finding is central to the conventional (linear-response) view of how chemical reactions occur in solution. However, when a reaction initiated by 33-femtosecond deep ultraviolet laser pulses is used to eject highly rotationally excited diatomic molecules into alcohols and water, rotational coherence persists for many rotational periods despite the solvent. Molecular dynamics simulations trace this slow development of molecular-scale friction to a clearly identifiable molecular event: an abrupt liquid-structure change triggered by the rapid rotation. This example shows that molecular relaxation can sometimes switch from linear to nonlinear response.
Science 04/2006; 311(5769):1907-11. · 31.20 Impact Factor
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ABSTRACT: The combination of optical-Kerr-effect (OKE) spectroscopy and molecular dynamics simulations has provided us with a newfound ability to delve into the librational dynamics of liquids, revealing, in the process, some surprising commonalities among aromatic liquids. Benzene and biphenyl, for example, have remarkably similar OKE spectra despite marked differences in their shapes, sizes, and moments of inertia--and even more chemically distinct aromatics tend to have noticeable similarities in their spectra. We explore this universality by using a molecular dynamics simulation to investigate the librational dynamics of molten biphenyl and to predict its OKE spectrum, comparing the results with our previous calculations for liquid benzene. We suggest that the impressive level of quantitative agreement between these two liquids is largely a reflection of the fact that librations in these and other aromatic liquids act as torsional oscillations with oscillator frequencies selected from the liquid's librational bands. Since these bands are centered about the librational Einstein frequencies, the quantitative similarities between the liquids are essentially reflections of the near identities of their Einstein frequencies. Why then are the Einstein frequencies themselves so insensitive to molecular details? We show that, for nearly planar molecules, mean-square torques and moments of inertia tend to scale with molecular dimensions in much the same way. We demonstrate that this near cancellation provides both a quantitative explanation of the close relationship between benzene and biphenyl and a more general perspective on the similarities seen in the ultrafast dynamics of aromatic liquids.
The Journal of Physical Chemistry B 02/2006; 110(2):976-87. · 3.70 Impact Factor
