The short-time dynamics of molecular reorientation in liquids. I. The instantaneous generalized Langevin equation

Orientational relaxation of a quantum linear rotor in a dissipative environment: Simulations with the hierarchical equations-of-motion method

We study the effect of a dissipative environment on the orientational relaxation of a three-dimensional quantum linear rotor. We provide a derivation of the Hamiltonian of a linear rotor coupled to a harmonic bath from first principles, confirming earlier conjectures. The dynamics generated by this Hamiltonian is investigated by the hierarchical equations-of-motion method assuming a Drude spectral density of the bath. We perform numerically accurate simulations and analyze the behavior of orientational correlation functions and the rotational structures of infrared absorption and Raman scattering spectra. We explore the features of orientational correlation functions and their spectra for a wide range of system-bath couplings, bath memory times, and temperatures. We discuss the signatures of the orientational relaxation in the underdamped regime, the strongly damped regime, and the librational regime. We show that the behavior of orientational correlation functions and their spectra can conveniently be analyzed in terms of three characteristic times, which are explicitly expressed in terms of the parameters of the Hamiltonian.

Local structural effects on orientational relaxation of OH-bond in liquid water over short to intermediate timescales

By simulating the rigid simple point charge extended model at temperature T = 300 K, the orientational relaxation of the OH-bond in water was investigated over short to intermediate timescales, within which molecules undergo inertial rotation and libration and then enter the rotational diffusion regime. According to the second-cumulant approximation, the orientational time correlation function (TCF) of each axis that is parallel or perpendicular to an OH-bond is related to an effective rotational density of states (DOS), which is determined using the power spectra of angular velocity autocorrelation functions (AVAFs) of the other two axes. In addition, the AVAF power spectrum of an axis was approximated as the rotational stable instantaneous normal mode (INM) spectrum of the axis. As described in a previous study [S. L. Chang, T. M. Wu, and C. Y. Mou, J. Chem. Phys. 121, 3605 (2004)], simulated molecules were classified into subensembles, according to either the local structures or the H-bond configurations of the molecules. For global molecules and the classified subensembles, the simulation results for the first- and second-rank orientational TCFs were compared with the second-cumulant predictions obtained using the effective rotational DOSs and the rotational stable-INM spectra. On short timescales, the OH-bond in water behaves similar to an inertial rotor and its anisotropy is lower than that of a water molecule. For molecules with three or more H-bonds, the OH-bond orientational TCFs are characterized by a recurrence, which is an indication for libration of the OH-bond. The recurrence can generally be described by the second-cumulant prediction obtained using the rotational stable-INM spectra; however, the orientational TCFs after the recurrence switch to a behavior similar to that predicted using the AVAF power spectra. By contrast, the OH-bond orientational TCFs of molecules initially connected with one or two H-bonds decay monotonically or exhibit a weak recurrence, indicating rapid relaxation into the rotational diffusion regime after the initial Gaussian decay. In addition to accurately describing the Gaussian decay, the second-cumulant predictions formulated using the rotational stable-INM spectra and the AVAF power spectra serve as the upper and lower limits, respectively, for the OH-bond orientational TCFs of these molecules after the Gaussian decay.

Angular momentum dependent friction slows down rotational relaxation under nonequilibrium conditions

It has recently been shown that relaxation of the rotational energy of hot nonequilibrium photofragments (i) slows down significantly with the increase of their initial rotational temperature and (ii) differs dramatically from the relaxation of the equilibrium rotational energy correlation function, manifesting thereby the breakdown of the linear response description [A. C. Moskun et al., Science 311, 1907 (2006)]. We demonstrate that this phenomenon may be caused by the angular momentum dependence of rotational friction. We have developed the generalized Fokker-Planck equation whose rotational friction depends upon angular momentum algebraically. The calculated rotational correlation functions correspond well to their counterparts obtained via molecular dynamics simulations in a broad range of initial nonequilibrium conditions. It is suggested that the angular momentum dependence of friction should be taken into account while describing rotational relaxation far from equilibrium.

The molecular origins of nonlinear response in solute energy relaxation: The example of high-energy rotational relaxation

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.

Molecular reorientation in hydrogen-bonding liquids: Through algebraic ∼t−3∕2 relaxation toward exponential decay

We present a model for the description of orientational relaxation in hydrogen-bonding liquids. The model contains two relaxation parameters which regulate the intensity and efficiency of dissipation, as well as the memory function which is responsible for the short-time relaxation effects. It is shown that the librational portion of the orientational relaxation is described by an algebraic approximately t(-32) contribution, on top of which more rapid and nonmonotonous decays caused by the memory effects are superimposed. The long-time behavior of the orientational relaxation is exponential, although nondiffusional. It is governed by the rotational energy relaxation. We apply the model to interpret recent molecular dynamic simulations and polarization pump-probe experiments on HOD in liquid D(2)O [C. J. Fecko et al., J. Chem. Phys. 122, 054506 (2005)].