A novel method for analyzing energy relaxation in condensed phases using nonequilibrium molecular dynamics simulations: application to the energy relaxation of intermolecular motions in liquid water

We present a novel method to investigate energy relaxation processes in condensed phases using nonequilibrium molecular dynamics simulations. This method can reveal details of the time evolution of energy relaxation like two-color third-order IR spectroscopy. Nonetheless, the computational cost of this method is significantly lower than that of third-order response functions. We apply this method to the energy relaxation of intermolecular motions in liquid water. We show that the intermolecular energy relaxation in water is characterized by four energy transfer processes. The structural changes of the liquid associated with the energy relaxation are also analyzed by the nonequilibrium molecular dynamics technique.     

Vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to harmonic bath

The vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to a harmonic bath are examined to assess the applicability of the time correlation function (TCF), the response function, and the semiclassical frequency modulation (SFM) model to the calculation of infrared (IR) spectra. These three approaches are often used in connection with the molecular dynamics simulations but have not been compared in detail. We also analyze the vibrational energy relaxation (VER), which determines the line shape and is itself a pivotal process in energy transport. The IR spectra and VER are calculated using the generalized Langevin equation (GLE), the Gaussian wavepacket (GWP) method, and the quantum master equation (QME). By calculating the vibrational frequency TCF, a detailed analysis of the frequency fluctuation and correlation time of the model is provided. The peak amplitude and width in the IR spectra calculated by the GLE with the harmonic quantum correction are shown to agree well with those by the QME though the vibrational frequency is generally overestimated. The GWP method improves the peak position by considering the zero-point energy and the anharmonicity although the red-shift slightly overshoots the QME reference. The GWP also yields an extra peak in the higher-frequency region than the fundamental transition arising from the difference frequency of the center and width oscillations of a wavepacket. The SFM approach underestimates the peak amplitude of the IR spectra but well reproduces the peak width. Further, the dependence of the VER rate on the strength of an excitation pulse is discussed.     

Effect of the molecular mobility of epoxy amine crosslinked polymers on their relaxation and physicomechanical characteristics

The results on molecular mobility in epoxy amine crosslinked polymers at segmental (α process) and local (β process) levels are analyzed. The effect of intrachain and interchain rigidities on the above processes is considered, where the intrachain rigidity is measured with the use of flexibilizing agents and the interchain rigidity is dependent on the intermolecular-interaction intensity, which is governed by the introduction of plasticizing agents. Both modes of molecular mobility in the crosslinked polymers show a cooperative character that controls the dissipation energy of the corresponding relaxation process. The correlation between the above processes and the elastic, strength, and relaxation characteristics of the epoxy amine crosslinked polymers is studied. Molecular mobility is shown to exert an inverse effect on the relaxation and dissipative characteristics of the network polymers.     

Rotational relaxation characteristics of the monoclinic phase of CCl4

We present a study of crystalline CCl(4) spanning up to 10 orders of magnitude in time at temperatures ranging from 160 K to 190 K using molecular dynamics simulations. The relaxation process is studied using angular self correlation functions. The results show that each of the four nonequivalent molecules of the monoclinic phase have a particular relaxation time. Two of the molecules relax in an exponential way and the two other molecules have a more complex behavior, especially at the lower temperatures. In all cases, the molecular rotations correspond to quick jumps between equivalent tetrahedral equilibrium positions. Most of these rotations are about the C(3) symmetry axes, however at high temperatures, rotations about the C(2) symmetry axes are observed as well. The waiting time between rotations follows a Poisson distribution. The calculated relaxation times show an Arrhenius behavior with different activation energy for different nonequivalent molecules, in line with recently published findings of nuclear quadrupole resonance experiments.     

Local relaxation of polymers in dense media: Cooperative kinematics theory and applications

Cooperative kinematics (CK) theory and its recent applications are presented. CK theory has been developed as an efficient approach for predicting the mechanism of segmental relaxation processes in bulk polymers. The theory aims at determining the most probable changes in atomic coordinates, occurring collectively in response to a given, external or localized, structural perturbation. The basic postulate is the minimization of the energy change involved in the overall conformational motion, which naturally yields the optimal pathway of cooperative relaxation. Attention has been confined here to the collective motions accompanying the rotational transitions of backbone bonds in polyethylene (PE) and polybutadiene (PB). The strong dependence of the mechanism of motions on the geometry of the repeat unit and on chain connectivity is emphasized. The differences in the types of correlated transitions operating in different structures, the effective conformational energy changes triggered by bond rotational jumps, and the correlation lengths for particular bond isomerizations are analyzed. The reorientations of C H bond vectors in cis- and trans-PB are also examined to explain the shorter correlation time of cis units, compared to trans, detected by NMR. A good agreement between various CK predictions and results from molecular dynamics (MD) simulations is obtained. The fact that CK calculations are at least two orders of magnitude faster than MD simulations invites attention to the utility of the CK method as an efficient tool for elucidating the pathway of motion in complex systems.     

Semiclassical initial value series representation in the continuum limit: application to vibrational relaxation

A recently formulated continuum limit semiclassical initial value series representation (SCIVR) of the quantum dynamics of dissipative systems is applied to the study of vibrational relaxation of model harmonic and anharmonic oscillator systems. As is well known, the classical dynamics of dissipative systems may be described in terms of a generalized Langevin equation. The continuum limit SCIVR uses the Langevin trajectories as input, albeit with a quantum noise rather than a classical noise. Combining this development with the forward-backward form of the prefactor-free propagator leads to a tractable scheme for computing quantum thermal correlation functions. Here we present the first implementation of this continuum limit SCIVR series method to study two model problems of vibrational relaxation. Simulations of the dissipative harmonic oscillator system over a wide range of parameters demonstrate that at most only the first two terms in the SCIVR series are needed for convergence of the correlation function. The methodology is then applied to the vibrational relaxation of a dissipative Morse oscillator. Here, too, the SCIVR series converges rapidly as the first two terms are sufficient to provide the quantum mechanical relaxation with an estimated accuracy on the order of a few percent. The results in this case are compared with computations obtained using the classical Wigner approximation for the relaxation dynamics.     

Energy and capacity time correlation functions for investigation of vibrational energy relaxation

Vibrational energy relaxation of a diatomic solute in a liquid solvent is investigated by means of the generalized Langevin equation. The vibrational energy, velocity and capacity time correlation functions (TCFs) are considered. It is shown that the detailed structure of the energy TCF contains an initial fast (subpicosecond) decay segment that is followed by weak oscillations on the background of an exponential relaxation curve. The direct method for evaluating the relaxation rate constant from equilibrium molecular dynamics simulations of a flexible solute is proposed and implemented. The closed form expressions for the memory function and for the relaxation rate constant in terms of quantities accessible from the simulations are derived. The simulation results for rigid and flexible solutes are compared and analyzed.     

Molecular relaxation dynamics of self-assembled monolayers

Dielectric relaxation spectroscopy is used to quantify molecular motion in alkylsilane SAMs coated on porous glass over a broad temperature range, -30 to -150 degrees C. Systematic measurements using SAMs with variable coating densities allow us to determine the effect of monolayer disorder on molecular mobility in thin molecular films. A relaxation process with an activation energy of approximately 25 kJ/mol is found to dominate dynamics of SAM-chain segments near the substrate. By introducing polar CN groups at the ends of the chain, we show that the relaxation process in the monolayer canopy can be isolated and studied. This approach can be generalized to other substituent polar groups to probe localized relaxation dynamics in surface-grafted monolayer films.     

Dehydration-induced structural relaxation effects in poly(methyl methacrylate)

The Thermally Stimulated Depolarization (TSD) dielectric technique and Dielectric Relaxation Spectroscopy (DRS) have been used in order to investigate aging phenomena in poly(methyl methacrylate) (PMMA). Earlier TSD studies on amorphous PMMA report peculiar dielectric relaxation signals within the range of the glass transition (at ∼378 K) and the secondary relaxation (∼230 K). In the present study, an intense TSD current relaxation band maximizing around 310 K is tentatively attributed to the molecular mobility due to a residual free volume below the glass transition temperature, T_g, that allows structural recovery at the free volume released from the desorption of H₂O molecules during evacuation. Limited motions in the main backbone provoke dipole (re)orientation of the ester carbonyl pendant groups with an activation energy E=0.85±0.05 eV, being responsible for the latter dielectric relaxation effect. Alternative attributions based on the short-range jump relaxation of electric charges and boundary effects are also discussed.     

Non-markovian theory of molecular relaxation. I. Vibrational relaxation and dephasing in condensed phases

The cumulant expansion is used to derive two formally different master equations for a two-level molecular system interacting with a bath, starting wit The two master equations reduce to the same form in the markovian limit for the bath (where its correlation time is much shorter than the relaxation pr A detailed comparison is made between the predictions of the two approaches which enables us to understand their range of validity and limitations. We apply the formalism to the vibrational relaxation and dephasing of a molecular impurity in a solid matrix and obtain a closed expression for the vib In contrast to the simple stochastic approaches we predict that the line shape in the non-markovian limit contains information regarding the interactio However, the fluctuations in the mean interaction energy of the two-level system with the bath, if correlated with the frequency modulation, result in     

Simulating the relaxation dynamics of microwave-driven zeolites

We have performed equilibrium and nonequilibrium molecular dynamics simulations to study how microwave (MW)-heated zeolite systems relax to thermal equilibrium. We have simulated the relaxation of both ionic and dipolar phases in FAU-type zeolites, finding biexponential relaxation in all cases studied. Fast-decay times were uniformly below 1 ps, while slow-decay times were found to be as long as 14 ps. Fast-decay times increase with an increase in the initial temperature difference between MW-heated ions/dipoles and the equilibrium system. Slow-decay times were found to be relatively insensitive to the details of the MW-heated nonequilibrium state. Velocity, force, and orientational correlation functions, calculated at equilibrium to explore the natural dynamics of energy transfer, decay well before 1 ps and show little evidence of biexponential decay. In contrast, kinetic energy correlation functions show strong biexponential behavior with slow-decay times as long as 14 ps. We suggest a two-step mechanism involving initial, efficient energy transfer mediated by strongly anharmonic zeolite-guest forces, followed by a slower process mediated by weakly anharmonic couplings among normal modes of the zeolite framework. In addition to elucidating relaxation from MW-heated states, we expect that these studies will shed light on energy transfer in other contexts, such as adsorption and reaction in zeolites, which often involve significant heat release.     

A simple model of entropy relaxation for explaining effective activation energy behavior below the glass transition temperature

Strong changes in relaxation rates observed at the glass transition region are frequently explained in terms of a physical singularity of the molecular motions. We show that the unexpected trends and values for activation energy and preexponential factor of the relaxation time tau, obtained at the glass transition from the analysis of the thermally stimulated current signal, result from the use of the Arrhenius law for treating the experimental data obtained in nonstationary experimental conditions. We then demonstrate that a simple model of structural relaxation based on a time dependent configurational entropy and Adam-Gibbs relaxation time is sufficient to explain the experimental behavior, without invoking a kinetic singularity at the glass transition region. The pronounced variation of the effective activation energy appears as a dynamic signature of entropy relaxation that governs the change of relaxation time in nonstationary conditions. A connection is demonstrated between the peak of apparent activation energy measured in nonequilibrium dielectric techniques, with the overshoot of the dynamic specific heat that is obtained in calorimetry techniques.     

Terahertz spectrum and normal-mode relaxation in pentaerythritol tetranitrate: effect of changes in bond-stretching force-field terms

Terahertz (THz) active normal-mode relaxation in crystalline pentaerythritol tetranitrate (PETN) was studied using classical molecular dynamics simulations for energy and density conditions corresponding to room temperature and atmospheric pressure. Two modifications to the fully flexible non-reactive force field due to Borodin et al. [J. Phys. Chem. B 112, 734 (2008)] used in a previous study of THz-active normal-mode relaxation in PETN [J. Chem. Phys. 134, 014513 (2011)] were considered to assess the sensitivity of the earlier predictions to details of the covalent bond-stretching terms in the force field. In the first modification the harmonic bond-stretching potential was replaced with the Morse potential to study the effect of bond anharmonicity on the THz-region mode relaxation. In the second modification the C-H and nitro-group N-O bond lengths were constrained to constant values to mimic lower quantum occupation numbers for those high-frequency modes. The results for relaxation times of the initially excited modes were found to be insensitive to either force-field modification. Overall time scales for energy transfer to other modes in the system were essentially unaffected by the force-field modifications, whereas the detailed pathways by which the energy transfer occurs are more complicated for the Morse potential than for the harmonic-bond and fixed-bond cases. Terahertz infrared absorption spectra constructed using calculated normal-mode frequencies, transition dipoles, and relaxation times for THz-active modes were compared to the spectra obtained from the Fourier transform of the dipole-dipole time autocorrelation function (DDACF). Results from the two approaches are in near agreement with each other and with experimental results in terms of main peak positions. Both theoretical methods yield narrower peaks than observed experimentally and in addition predict a weaker peak at ω ～ 50 cm(-1) that is weak or absent experimentally. Peaks obtained using the DDACF approach are broader than those obtained from the normal-mode relaxation method.     

On the mechanism of reorientational and structural relaxation in supercooled liquids: the role of border dynamics and cooperativity

Molecular dynamics simulation and analysis based upon the many-body potential energy landscape (PEL) are employed to characterize single molecule reorientation and structural relaxation, and their interrelation, in deeply supercooled liquid CS(2). The rotational mechanism changes from small-step Debye diffusion to sudden large angle reorientation (SLAR) as the temperature falls below the mode-coupling temperature T(c). The onset of SLAR is explained in terms of the PEL; it is an essential feature of low-T rotational dynamics, along with the related phenomena of dynamic heterogeneity and the bifurcation of slow and fast relaxation processes. A long trajectory in which the system is initially trapped in a low energy local minimum, and eventually escapes, is followed in detail, both on the PEL and in real space. During the trapped period, "return" dynamics occurs, always leading back to the trap. Structural relaxation is identified with irreversible escape to a new trap. These processes lead to weak and strong SLAR, respectively; strong SLAR is a clear signal of structural relaxation. Return dynamics involves small groups of two to four molecules, while a string-like structure composed of all the active groups participates in the escape. It is proposed that, rather than simple, nearly instantaneous, one-dimensional barrier crossings, relaxation involves activation of the system to the complex, multidimensional region on the borders of the basins of attraction of the minima for an extended period.     

Re-evaluation of the model-free analysis of fast internal motion in proteins using NMR relaxation

NMR spin relaxation retains a central role in the characterization of the fast internal motion of proteins and their complexes. Knowledge of the distribution and amplitude of the motion of amino acid side chains is critical for the interpretation of the dynamical proxy for the residual conformational entropy of proteins, which can potentially significantly contribute to the entropy of protein function. A popular treatment of NMR relaxation phenomena in macromolecules dissolved in liquids is the so-called model-free approach of Lipari and Szabo. The robustness of the mode-free approach has recently been strongly criticized and the remarkable range and structural context of the internal motion of proteins, characterized by such NMR relaxation techniques, attributed to artifacts arising from the model-free treatment, particularly with respect to the symmetry of the underlying motion. We develop an objective quantification of both spatial and temporal asymmetry of motion and re-examine the foundation of the model-free treatment. Concerns regarding the robustness of the model-free approach to asymmetric motion appear to be generally unwarranted. The generalized order parameter is robustly recovered. The sensitivity of the model-free treatment to asymmetric motion is restricted to the effective correlation time, which is by definition a normalized quantity and not a true time constant and therefore of much less interest in this context. With renewed confidence in the model-free approach, we then examine the microscopic distribution of side chain motion in the complex between calcium-saturated calmodulin and the calmodulin-binding domain of the endothelial nitric oxide synthase. Deuterium relaxation is used to characterize the motion of methyl groups in the complex. A remarkable range of Lipari-Szabo model-free generalized order parameters are seen with little correlation with basic structural parameters such as the depth of burial. These results are contrasted with the homologous complex with the neuronal nitric oxide synthase calmodulin-binding domain, which has distinctly different thermodynamic origins for high affinity binding.     

Intermolecular vibrational relaxation in liquids

The influence of intermolecular vibrational relaxation on dipole moment correlation functions, as obtained from IR band shapes, is discussed. It is explicitly shown that vibrational relaxation due to intermolecular interactions depends on the reorientational behaviour of the molecules in the liquid.Therefore, an a priori separation of the dipole moment correlation function into independent reorientational and vibrational factors is not generally possible. The implications for various procedures used to “correct” Raman and IR band shapes for vibrational relaxation are discussed.The expression derived for the intermolecular vibrational relaxation is used to calculate theoretically the effect of transition dipole-transition dipole coupling on dipole moment correlation functions.Experimental data obtained from isotopic dilution measurements support the interpretation of the isotopic dilution effect in terms of the transition dipole-transition dipole coupling.     

Topological origin of stretched exponential relaxation in glass

The physical origin of stretched exponential relaxation is considered by many as one of the oldest unsolved problems in science. The functional form for stretched exponential relaxation can be deduced from the axiomatic diffusion-trap model of Phillips. The model predicts a topological origin for the dimensionless stretching exponent, with two "magic" values emerging: β = 3/5 arising from short-range molecular relaxation pathways and β = 3/7 for relaxation dominated by longer-range interactions. In this paper, we report experimental confirmation of these values using microscopically homogeneous silicate glass specimens. Our results reveal a bifurcation of the stretching exponent, with β = 3/5 for stress relaxation and β = 3/7 for structural relaxation, both on macroscopic length scales. These results point to two fundamentally different mechanisms governing stress relaxation versus structural relaxation, corresponding to different effective dimensionalities in configuration space during the relaxation process.     

Pressure dependence of the β molecular relaxation process and dielectric properties of polyvinylidene fluoride

The effects of hydrostatic pressure to 20 kbar on the β molecular relaxation process of polyvinylidene fluoride (PVDF) and on the dielectric properties in the neighborhood of this relaxation have been investigated. This relaxation has a strong influence on the electrical and mechanical properties of PVDF. Pressure causes a large shift to higher temperatures (～ 10K/kbar) of the dielectric relaxation peak and a decrease in the width of the distribution of relaxation times. This slowing down of the relaxation process is discussed in terms of the Vogel–Fulcher equation and related models, and it results from an increase in both the energy barrier to dipolar motion and the reference temperature (T₀) for the kinetic relaxation process which represents the “static” dipolar freezing temperature for the process. The general applicability of the Vogel–Fulcher equation to relaxional processes in polymers and other systems is briefly discussed. The pressure dependence of the dielectric constant both above and below the relaxation peak temperature (T_max) is found to be dominated by the change in polarizability. The effect is larger above T_max because of the relatively large decrease in the dipolar orientational polarizability with pressure.     

Anatomy of an energy transfer event in a liquid: the high-energy rotational relaxation of OH in solution

The photochemical generation of highly rotationally excited diatomics affords us an intriguing way to study energy relaxation processes in solution. Because excited products involve only a single intramolecular degree of freedom and because their relaxations can lie well outside of the linear-response regime, it may be possible to infer detailed molecular mechanisms for these processes just from transient absorption measurements. In this paper we describe a theoretical study of the rotational relaxation of a new candidate for such measurements, OH radicals. Much as we saw in our previous studies of rotationally hot CN radicals, molecular dynamics simulations of OH relaxation predict that the rotational motion should trigger a structural change in the surrounding solvent, decreasing the rotational friction and allowing the OH to rotate coherently for a dozen rotational periods. The mass distribution in OH, however, gives it a much faster rotational period and significantly different kinematics. These differences end up making it possible to identify the separate molecular events taking place at the onset of the relaxation (an unusual occurrence for a liquid-state process) and to weigh in on what collisions are really like in a liquid.