Time Correlation Function Of Force Research Articles

Coupling between Translational Diffusion of a Solute and Dynamics of the Heterogeneous Structure: Higher Alcohols and Ionic Liquids.

Translational diffusion of nonpolar monoatomic solutes in a room-temperature ionic liquid and 1-octanol was studied by molecular dynamics simulation. The diffusion coefficient was evaluated in two different ways: (1) from the mean-square displacement of a freely diffusing solute and (2) from the time correlation function of force acting on a fixed solute. The diffusion of the free solute is much greater than the prediction of the Stokes-Einstein (SE) relation when the size of the solute is small, as has been reported by many experimental works. In contrast, the friction on fixed small solutes follows the SE relation. The mechanism of the solute diffusion in both solvents was then analyzed based on the coupling between the translational motion of the solute and the collective dynamics of the heterogeneous intermediate-range structure characteristic to these solvents. Analysis revealed that the coupling is present in all systems, but the relaxation is fast in the cases of free and small solutes. This suggests that the coupling can relax through the motion of the solute when the solute is free and small, while the relaxation of the heterogeneous structure itself is required for large or fixed solutes. The difference in the relaxation dynamics of the friction on the solute and the shear viscosity is explained as the coupling with different dynamic modes of the solvent. Therefore, the validity of the SE relation may not be a good criterion to judge whether the mechanisms of the diffusion and the viscosity are the same or not.

Molecular dynamics study on the vibrational energy relaxation of O–D stretch of HOD in liquid H2O

Vibrational energy relaxation of O–D stretch of HOD in liquid H2O at 300K is studied with molecular dynamics simulation based on the Fermi’s golden rule. The Fourier transform of the force force time correlation function along the O–D stretch obtained from the simulation is used to calculate the relaxation time. Both rigid and flexible solvents are applied to reveal the relaxation mechanism. We find that the relaxation time of O–D stretch fundamental is 19.05ps for the rigid solvent and 5.04ps for the flexible solvent which is comparable to the experimental value 1.45ps. The main pathway of O–D stretch fundamental is transition to the bend fundamental for the rigid solvent and direct relaxation to the ground state when solvent vibrations are included.

Role of many-body correlations in dynamics of liquids

A time correlation function is written exactly in terms of infinite series with each term containing contributions separately due to two, three, and higher body static correlations. For a time correlation function of force acting on a tagged particle, it is found that contributions due to two and three body static correlation functions are sufficient to understand dynamics of dense gases whereas at the triple point and in the glassy phase it is necessary to include contributions due to a four body correlation function.

Calculating Vibrational Energy Relaxation Rates from Classical Molecular Dynamics Simulations: Quantum Correction Factors for Processes Involving Vibration−Vibration Energy Transfer

A convenient starting point for calculating vibrational energy relaxation rate constants is Fermi's golden rule, which relates the rate constant to the Fourier transform of a certain quantum-mechanical force−force time-correlation function. Often, researchers replace this Fourier transform by the Fourier transform of the analogous classical time-correlation function multiplied by a quantum correction factor. This approach has the great advantage that the classical time-correlation function and its Fourier transform can be calculated easily from a classical molecular dynamics simulation. The disadvantage is that it is often unclear what form one should take for the quantum correction factor. In this paper we suggest several possible forms for this factor for vibrational energy relaxation processes involving intermolecular vibration−vibration energy transfer. We apply our results to vibrational energy relaxation in the B state of carbonmonoxy-myoglobin.

Microscopic description of vibrational energy relaxation in supercritical fluids: On the dominance of binary solute–solvent contributions

The representation of the frequency dependent friction coefficient ia a four-particle two-time correlation function is used to analyze the applicability of collisional and hydrodynamical models of vibrational energy relaxation (VER). The solute–solvent binary dynamics is separated from collective equilibrium correlations by means of Green's functions. The collective contributions manifest themselves mainly ia the solute–solvent radial distribution function (RDF), which reflects peculiarities of the particular solvent thermodynamical (e.g., supercritical) state. The binary dynamics is also closely related to many-body equilibrium correlations, as initial conditions sample microscopic system states in the vicinity of the solute which are the most important for VER. VER rates along a close to critical isotherm are calculated on the basis of the breathing sphere model and the Douglas approximation for force–time correlation functions, while Monte Carlo simulations are used for calculating RDFs. The results are compared with molecular dynamics simulations at low, intermediate and high densities. It is shown that at near-critical conditions as well as far from the critical point the key contribution to VER comes from the short and intermediate time behavior of the force–time correlation function. In configuration space only short range binary solute–solvent correlations are important. Analytical estimations, Monte Carlo and molecular dynamics simulations clearly show that the dynamics of VER can only be understood on the basis of a detailed description of local solute–solvent interactions and correlations.

Quantum Dynamics and Vibrational Relaxation

The accurate numerical calculation of general quantum time correlation functions for many-body systems is not possible at present. We discuss several schemes for obtaining approximate quantum time correlation functions using as input only the corresponding classical results, and assess the merits of each scheme by considering three exactly solvable model problems. We then turn to the problem of the vibrational energy relaxation of a high-frequency oscillator in a liquid, where the relaxation rate constant can be related to a certain quantum force−force time correlation function. Focusing specifically on the case of liquid oxygen, we calculate the classical force−force time correlation function using a molecular dynamics simulation and then determine various approximations to the relaxation rate constant by applying the schemes considered earlier. The Egelstaff scheme is found to lead to reasonable agreement with experiment.

Computer simulation study of the subquadratic quantum number dependence of vibrational overtone dephasing: Comparison with the mode-coupling theory predictions

Experimental studies have demonstrated that the vibrational dephasing of overtones do not always follow the quadratic quantum number (n) dependence predicted by the Kubo–Oxtoby theory of vibrational line shapes. While the reason for this failure of the theory is not quite clear yet, a recent theory suggested that the pronounced Gaussian time dependence of the frequency-modulation time-correlation function (tcf) could be a possible reason [Gayathri et al., J. Chem. Phys., 107, 10381 (1997)]. The theoretical study was based on a mode coupling theory calculation of the force–force time-correlation function that is required in the calculation of the frequency-modulation tcf. In order to test this and other predictions of the above study, detailed computer simulations of two neat liquids have been carried out. The systems studied are N–N stretch in liquid N2 and the C–I stretch in CH3I. It is found that although the frequency-modulation time-correlation function is largely Gaussian in both the cases, the overtone dephasing remains largely quadratic in n for N2. For methyl iodide, on the other hand, a pronounced sub-quadratic n dependence has been observed. Both the theory and the computer simulations suggest that this nonquadratic dependence can be expected when not only the decay of the frequency time-correlation function is Gaussian but the time scale of decay of the frequency-modulation tcf is comparable to that of the normal coordinate. The latter can happen when the following conditions are satisfied. First, the frequency of the normal mode should not be too large. Second, the mean-square fluctuation of the frequency-modulation and the anharmonicity coefficient of vibration should be large. It is found that both for N2 and CH3I, the resonant energy transfer between different molecules is significant. The effect of rotational–vibrational coupling, on the other hand, is found to be negligible for the systems studied.

Dynamical Conductivity of the Dilute Lorentz Gas with Spherically Symmetric Scatterers

The dynamical conductivity of the Lorentz gas with spherically symmetric potentials is studied to lowest order in the density of scatterers. The frequency-dependent friction coefficient is calculated from the Fourier transform of the force–force time-correlation function determined by the dynamics of a single scattering process. The corresponding dynamical conductivity varies with frequency on the scale of the inverse collision time. As an example, the conductivity is calculated for a scattering potential of the Maxwell type.

Computing vibrational energy relaxation for high-frequency modes in condensed environments

In this paper we consider vibrational relaxation of high-frequency impurity modes in condensed environments as a computational problem. Linear response theory provides convenient routes for this computation: The vibrational relaxation rate is obtained as a Fourier transform of a force–force time correlation function. However, numerical difficulties arise for processes characterized by a direct relaxation of high-frequency modes into an environment characterized by a relatively low cutoff frequency. It is shown that modern signal processing procedures can significantly enhance the efficiency and accuracy of the needed computation. Since the relevant “signal” can be very small, the computation can be very sensitive to boundary conditions, and care must be taken to avoid artifacts. The computation may be facilitated by using the expected functional form, exponential dependence on the impurity frequency for high frequency, and fitting the parameters of this form from the simulation. It is emphasized that this exponential dependence seems to be the correct functional form, in spite of theoretical arguments in favor of a Gaussian dependence. The main difficulty in the numerical evaluation of the relaxation rate of high-frequency modes results from the fact that at low temperature the dynamical behavior of such modes is essentially quantum mechanical. We demonstrate this issue by considering vibrational relaxation of an impurity CO molecule in a low-temperature Ar matrix. The results obtained for this system by estimating the quantum correction to the classical force–force correlation function are consistent with experimental results, which indicate that under these conditions the relaxation of the vibrationally excited CO is dominated by radiative decay.

A theory of vibrational energy relaxation in liquids

A microscopic statistical mechanical theory of the vibrational energy relaxation of a diatomic solute in an atomic solvent is presented. The diatomic is treated as a breathing Lennard-Jones sphere. The relaxation rate is obtained from the Fourier transform of the force–force time-correlation function. The latter is expanded in powers of time (up to t4), and expressions for the expansion coefficients are derived using equilibrium statistical mechanics. These coefficients are used to determine the parameters of an analytic ansatz for this correlation function, which can be evaluated at all times (and thus can be Fourier transformed). The resulting theory for the time-correlation function is compared to numerical results from a molecular dynamics simulation. Theoretical results for the vibrational relaxation rate are compared to experiments on I2 in Xe over a wide range of densities and temperatures.

Solvation structure and dynamics of the Fe2+–Fe3+ ion pair in water

Computer simulations are performed to study the structure of the coordination shells of Fe+2 and Fe+3 ions fixed at a very close reactive separation. The simulations show that it is possible for the two octahedral aquo complexes, i.e., Fe(H2O)62+ and Fe(H2O)63+, to come as close as 5 Å without disrupting their coordination shells. The reorientational dynamics within the hydration shells of these ions at this separation is examined by studying the time correlation functions (TCFs) of the unit vectors on the water molecules and along the iron–oxygen vector. The quantities related to the solvent polarization relaxation during a change in the charge, the dipole moment, and the quadrupole moment located at the solute ions are examined by studying the corresponding TCFs in the system. The TCFs exhibited a bimodal response, with a very fast initial relaxation due to inertial motions of the solvent, followed by a long tail corresponding to a diffusive component. The polarization fluctuations are also estimated via the cavity field time correlation function (CFTCF), which is useful in the theory of electron transfer processes. The memory kernel or the time dependent friction (TDF) of the solvent is also estimated from the force–force time correlation function. The cross correlations between the Coulombic and the non-Coulombic components of the forces at the ions contribute significantly to the TDF.

Microscopic theory of the dynamics of polymeric liquids: General formulation of a mode–mode-coupling approach

A formally exact, nonlinear generalized Langevin equation (GLE) for a flexible probe polymer in a dense melt has been derived using molecular phase space kinetic theory and Mori–Zwanzig projection operator techniques. An approximate, linearized dynamic memory function is developed, and the resulting GLE is specialized to the problem of an overdamped liquid of uncrossable Rouse polymers. An analytically tractable, perturbative/short time evaluation of the projected force time correlation function matrix is proposed which accounts for uncorrelated intermolecular pair interaction effects in the polymer melt. The detailed predictions for transport coefficients and various time correlation functions are determined for linear chains, and compared with recent lattice Monte Carlo simulations. Significant slowing down of all dynamical processes relative to the Rouse behavior is found, but the molecular weight scaling is not correctly described. A nonperturbative approach based on a polymeric generalization of molecular-scale mode–mode coupling theory is formulated which does properly capture the strong caging and viscoelastic effects in dense melts. The phenomenological concepts of topological entanglements, a static tube, and primitive path are not employed, and simplified assumptions about liquid structure and mode of motion are not introduced a priori. The microscopic theory is based on an explicit nonlinear coupling of the collective fluid density fluctuations with the segmental density fields of a probe polymer. Equilibrium structural information is naturally incorporated, and the associated renormalized intermolecular potential, or vertex, is found to be spatially long range due to chain connectivity and correlation hole effects. The projected dynamics describing the time evolution of the mode-coupling part of the memory function matrix is evaluated using the short time/pair interaction theory. The polymeric mode-coupling theory can be employed as a rigorous and unified framework for qualitatively and quantitatively studying transport coefficients, material response functions, crossover phenomena, collective density fluctuation dynamical effects, nonlinear molecular architectures (e.g., ring polymers), tracer diffusion, semidilute solutions and blends.