Angular Velocity Autocorrelation Function Research Articles

Rotational Depolarization of Fluorescence of Prolate Molecules

Abstract The theory of rotational depolarization of fluorescence, taking into account the inertial effect, has been verified experimentally for two angular velocity autocorrelation functions obtained for both the approximate and the exact Langevin equation. To this end, the emission anisotropy was investigated as a function of viscosity for PPO, POPOP, and α-NOPON in liquid n-paraffins (from « = 5 to n = 11) at 304.5 K. For these three luminescent molecules with mean lifetimes of about 1 ns, and the viscosities ranging from 0.22 to 0.9 cP, no essential difference was found between the experiment and the theory for the angular velocity autocorrelation functions employed.

Short-time correlations in liquids: Molecular-dynamics simulation of hard spheroids.

The velocity and angular velocity autocorrelation functions obtained by molecular-dynamics simulations of liquids composed of hard spheroids indicate the existence of damped oscillations with periods as long as 40 times the mean time between molecular collisions. In addition, little correlation is found between successive collisions. This suggests that the damped oscillations are not due to semicoherent molecular librations in cells.

Theoretical study of memory kernel and velocity correlation function for condensed phase isomerization. II. Velocity correlation function, barrier crossing rates, and generalized Smoluchowski equation

The time dependent friction (TDF) introduced in paper I for barrier crossing problems is used to derive a functional form of the angular velocity autocorrelation function (AVACF) associated with the reactive coordinate. This theoretical expression is then compared with AVACFs derived directly from molecular dynamics angular velocity data. A connection between this AVACF model and Zwanzig’s waiting-time description can be made. The TDF functions from paper I can also be used to deduce barrier crossing rates using the Kramers–Grote–Hynes formalism. A special case leads to the ‘‘extended’’ Kramers equation, which was found in previous work to be congruous with experimental barrier crossing results. Using methods introduced by Okuyama and Oxtoby, a generalized Smoluchowski equation can also be derived. This Smoluchowski equation permits an examination of free diffusion and of the approach to equilibrium. Throughout papers I and II the theme is raised concerning the effects of nonlinear coupling on the methodology for analyzing barrier crossing problems. Seemingly, the appealing Langevin approach can be retained providing the parameters in this formalism are considered strictly empirical.

The non-linear itinerant oscillator model: the effect on the polarisability spectrum of including barrier-crossing by dipoles

Analysis of the itinerant oscillator model of polar fluids has hitherto been concentrated on the small-oscillation approximation. This has neglected one important contribution to the dynamic polarization, namely relaxation due to crossing ofdipoles over the hills of the cosine potential for dipole-dipole coupling. In this Letter a numerical algorithm for solution of the Fokker-Planck equation due to Reid is used to calculate the Fourier transform of the angular velocity autocorrelation function for this model when barrier-crossing is included. The results are used to calculate the frequency dependence of the polarizability. They indicate that (i) the far-infrared absorption peak is centred at a lower frequency than in the harmonic approximation, and (ii) the bandwidth of the far-infrared absorption is increased significantly over the harmonic approximation leading to additional contributions at frequencies below the far-infrared peak, in qualitative agreement with recent experimental observations.

A computer simulation study of the effect of molecular mass distribution on mass and momentum transport in molecular liquids

Molecular dynamics computer simulation has been used to determine diffusion coefficients and viscosities for four thermodynamical ly identical one component model liquids composed of rigid triatomic molecules of the type XY2 at the same temperature and density. Exactly the same intermolecular potential was used throughout. The molecules comprising these liquids all had the same total mass but the molecular mass distributions were different for each liquid. Differences in the viscosities and the diffusion coefficients clearly show that the molecular mass distribution is a factor which in itself influences transport properties, a point seldom considered in the past. The viscosities were determined by nonequilibrium molecular dynamics and a new method is described for implementing isokinetic shear flow in molecular liquid simulations which employ quaternion algorithms. To obtain satisfactory diffusion coefficients for the equilibrium liquids it was necessary to use simulations extending up to 300 ps. The results are particularly relevant to the phenomenon of rotation–translation coupling and, together with the linear and angular velocity autocorrelation functions, are discussed in this context.

A molecular dynamics study of an aqueous LiI solution between Lennard-Jones walls

An MD simulation of a 2.2 m aqueous LiI solution between 12-6 Lennard-Jones walls has been performed which extended over 19 ps at an average temperature of 283 K. The basic tetragonal cell contained 200 ST2 water molecules and eight ions of each kind described as Lennard-Jones spheres with an elementary charge at the center. The effect of the walls on the hydration shell of the ions is investigated by means of ion–water radial distribution functions. Anisotropic water pair correlation functions are reported in order to show specific structural features near the walls. Changes in translational and rotational motions of the water molecules near the walls are discussed by means of velocity and angular velocity autocorrelation functions and their spectral densities, respectively.

Molecular dynamics study of the alloy (N2)67(Ar)29

Molecular dynamics calculations are used to investigate the effect of isobaric cooling on the hexagonal alloy (N2)67(Ar)29. Particular attention is given to the behavior of the reorientational motion of the N2 molecules. No orientational or structural transition was found to accompany the cooling from 60 to 10 K at either P = 4 × 103 or P = 1 × 103 bar (1 bar = 100 kPa). However, the power spectrum of the angular-velocity autocorrelation function clearly reveals the freezing out of rotational diffusion at low temperature.

Behaviour of water at membrane surfaces - a molecular dynamics study

The molecular dynamics method was used to study the structure and dynamics of water above a layer of phosphatidylethanolamine headgroups, modelling the surface of a membrane. The simulation box contains one headgroup with sixteen ST2-water molecules. Planar periodic boundary conditions model a headgroup-water interface. The density distribution and the orientation profile along the layer normal were calculated. The water builds highly structured regions up to a ratio of ten water molecules per headgroup which compensate the dipole moments of the lipids. The velocity, angular velocity and direction autocorrelation functions show that the bound water molecules oscillate around minimum potential positions at preferred hydration sites.

Behaviour of water at membrane surfaces — a molecular dynamics study

The molecular dynamics method was used to study the structure and dynamics of water above a layer of phosphatidylethanolamine headgroups, modelling the surface of a membrane. The simulation box contains one headgroup with sixteen ST2-water molecules. Planar periodic boundary conditions model a headgroup—water interface. The density distribution and the orientation profile along the layer normal were calculated. The water builds highly structured regions up to a ratio of ten water molecules per headgroup which compensate the dipole moments of the lipids. The velocity, angular velocity and direction autocorrelation functions show that the bound water molecules oscillate around minimum potential positions at preferred hydration sites.

Reorientation of N2adsorbed on graphite in various computer simulated phases

The reorientational motion of nitrogen molecules adsorbed on graphite was investigated in simulations of four phases. In the low temperature orientationally ordered commensurate and uniaxial phases the amplitude of reorientation is small. The out-of-plane motion is nearly harmonic. The in-plane motion is somewhat more complex, but we show that it can be related to the relevant angular velocity autocorrelation function via a cumulant expansion. The complexity is due to interactions between nitrogen molecules which do not affect the out-of-plane motion. In the simulations of the orientationally disordered phases the amplitudes of reorientation are larger and the simple cumulant approximation is no longer valid. The out-of-plane motion, while still harmonic, is more strongly damped, and the in-plane motion shows features similar to those seen in liquids. There is surprisingly little qualitative difference between the reorientational motion observed in the commensurate and uniaxially compressed phases at corr...

Dynamics of chiral molecules in the liquid state: Computer simulation and field effects

The molecular dynamics of the $R$ and $S$ enantiomers of fluorochloracetonitrile (HCFC1NC), and of the racemic mixture, are investigated with computer simulation. Some novel single-molecule rotation-translation cross-correlation functions are reported in a moving frame of reference defined by that of the principal molecular moments of inertia. Two off-diagonal elements of these cross-correlation matrices have an equal and opposite time dependence for the two enantiomers and vanish for all $t$ in the racemic mixture. The application of an external electric field to the chiral liquid generates laboratory-frame cross-correlation functions between the molecular center-of-mass translational momentum and the angular momentum of the same molecule. These cross-correlation functions are, therefore, seen in standard spectroscopic investigations of the molecular liquid state. As the intensity of the external field is increased, the following transient and field-on equilibrium effects become observable in the laboratory frame of reference: (i) Orientational rise transients are opposite in sign for the two enantiomers and vanish in the racemic mixture. (ii) These transients are field dependent, the dependence being qualitatively, but not quantitatively, that given by simple diffusion equations such as the Debye equation. (iii) At field-on equilibrium, the Grigolini decoupling effect is confirmed, i.e., the envelope of the oscillatory angular-velocity autocorrelation function decays more slowly than the field-off autocorrelation function at equilibrium as the external electric field strength is increased. (iv) The orientational fall transients are accelerated considerably with respect to the time dependence of the equivalent field-off orientational autocorrelation function. These results are interpreted with reduced-model theory, with use of Kramers equations with nonlinear potential terms.

The long-time tail of the angular-velocity autocorrelation function for a rigid Brownian particle of arbitrary centrally symmetric shape

The long-time t−5/2 behaviour of the angular-velocity autocorrelation function is determined by the diffusion of fluid motion to large distances, from where the particle appears a point singularity. From an examination of this flow, the coefficient of t−5/2 can be related to some effective aspect ratios which describe how the particle rotates in a simple shear flow.

A molecular dynamics simulation study of the plastic crystalline phase of sulphur hexafluoride

A molecular dynamics simulation study of the plastic crystalline phase of SF6 is reported. Various equilibrium properties have been measured and, where possible, compared with corresponding experimental measurements. The form of the molecular orientational distribution function has been obtained and is found to be in good agreement with that determined in a recent neutron scattering study. Information concerning the single-molecule dynamics has been obtained from calculations of linear and angular velocity autocorrelation functions, and it has been shown that the SF6 molecules undergo hindered rotation. The existence of coupling between the translational and rotational motions has been demonstrated, and it is shown how the behaviour of the plastic crystal is related to the form of the intermolecular potential. In addition, a transition to a trigonal low-temperature crystal phase at 80K has been observed, and the structure of this phase has been identified and found to be in good agree with experimental results. The calculations have been performed using a large parallel-array processor, and features of the simulation algorithms that reflect the architecture of such a computer are discussed.

A molecular dynamics simulation of rotational and vibrational relaxation in liquid HCl

We have carried out a molecular dynamics simulation of liquid HCl near its normal boiling point using the C* potential of Klein and McDonald. A wide variety of equilibrium and dynamical properties have been studied, ranging from partial structure factors to velocity, angular velocity, and torque autocorrelation functions. Dipole moment and polarizability tensor correlation functions have been evaulated and compared with experimental data from dielectric relaxation and Raman line shape studies. Vibrational phase relaxation has been simulated; we show that HCl is an intermediate case between the rapid modulation and static broadening limits. The question of correlation between rotational and vibrational relaxation is discussed.

Numerical solutions for brownian motion of particles in a periodic potential

The Kramers equation for one dimensional motion of brownian particles in a multiwell cosine potential is solved by a series expansion method followed by numerical solution of the resulting set of linear differential equations to obtain angular velocity and orientational autocorrelation functions (a.c.f.s) in the Laplace domain. The former, inverted by analytic function fitting, take the correct forms at zero and large (harmonic limit) potentials and intermediate behaviours compare well with those found using other numerical techniques. Solutions evaluated using delta function initial conditions are of interest in the study of pendula or of chemical dissociation, while solutions evaluated under equilibrium initial conditions and with imaginary Laplace variable iw are important in dielectric spectroscopy. Application of the theory both to superionic conductivity and dielectric-far-I.R. absorption of rotator phases and liquids is demonstrated.

Time correlation functions for a model of liquid carbon disulphide

A three centre Lennard-Jones model of CS2 predicts time dependent properties of the liquid, along the orthobaric curve, in good agreement with experiment. The molecules diffuse more easily parallel to their original orientation. The angular velocity autocorrelation function (acf) is an excellent approximation to the first memory function of the reorientational acf. Simple models of the orientational motion fail because the torque and angular velocity acf's relax on similar time scales. Collective correlations of the orientational and centre of mass density fluctuations are calculated with increased accuracy at a number of small non-zero wavevectors.

Itinerant oscillation with a cosine potential

The equations of motion of the planar itinerant librator are extended to involve a cosine potential rather than a harmonic form for interaction, and are solved numerically to produce the angular velocity autocorrelation function and its Fourier transform (real and imaginary parts). The behaviour of the cosine potential is matched with that of the harmonic potential through these functions and in general conforms more closely to the indication of zero-THz spectroscopy and computer simulation.

Reorientational correlation functions for computer-simulated liquids of tetrahedral molecules

Molecular dynamics simulations have been carried out on fluids of tetrahedral molecules for several sets of temperatures and pressures. The results were analysed to give reorientational and angular velocity autocorrelation functions. It was found that these could be related by a cumulant expansion in powers of the angular velocity and rotation operators. This type of analysis is likely to prove simple and useful for relating orientational correlation functions to the angular velocity correlation function in dense fluids where reorientation is hindered.

Simulation of molecular orientational dynamics in a model polar fluid

A molecular dynamics simulation of a Stockmayer fluid with μ* = 1·0, ρ* = 0·7 and T* = 1·13 (±0·03) is reported. In addition to evaluations of a number of static properties, orientational time correlation functions Cl (t) = were calculated for l = 1 through 4 ; Pl is a Legendre polynomial and δθ(t) is the angle of reorientation of the dipole in time t. These time correlation functions are characteristic of nearly free rotation and agree well with curves calculated from a perturbation theory for the memory functions that utilizes the simulated value of the mean square torque. The angular velocity autocorrelation function for this fluid was also simulated and compared with perturbation theory. Agreement is not good, primarily because of the presence of a pronounced long time tail in the simulated function. The relationship between these results and those of other simulations and theories is discussed.

On the time response of the itinerant oscillator model of polar fluids

Abstract The angular velocity and orientational autocorrelation functions for the two dimensional itinerant oscillator model used in the theory of the Debye and far infrared absorption of polar fluids are obtained as explicit functions of the time. The behaviour of the orientational autocorrelation function for various limiting cases is examined and it is shown that at both long and short times the behaviour of the itinerant oscillator is the same as that of a rigid rotator.