Normal mode theory of two step relaxation in liquids: Polarizability dynamics in CS2

Molecular Dynamics Study of Polarizability Anisotropy Relaxation in Aromatic Liquids and Its Connection with Local Structure

The collective polarizability anisotropy dynamics in a set of three aromatic liquids, benzene (Bz), hexafluorobenzene (HFB), and 1,3,5-trifluorobenzene (TFB), has been studied by molecular dynamics simulation. These liquids have very similar shapes, but different electrostatic interactions due to opposite polarities of C-H and C-F bonds, giving rise to different local intermolecular structures in the liquid phase. We have investigated how these structural arrangements affect polarizability anisotropy dynamics observed in optical Kerr-effect (OKE) spectroscopy. We have modeled the interaction-induced polarizability with the first-order dipole-induced dipole approximation, with the molecular polarizability distributed over the carbon sites. Local contributions to the librational OKE spectrum were computed separately for molecules participating in parallel or perpendicular relative orientations within the first coordination shell. We found that the relative locations of parallel and perpendicular librational bands of the OKE spectra are closely related to the corresponding pair energy distributions of the closest four neighbors of a given molecule, corresponding to a model of a harmonic oscillator in a cage of nearest neighbors. This model predicts higher librational frequencies for more attractive intermolecular interactions, which in all three liquids correspond to parallel local arrangements. On the diffusive orientational time scale, all three liquids exhibit slower relaxation of molecules in parallel arrangements, although the difference in relaxation rates is substantial only in TFB, which has the strongest tendency toward parallel stacking. The analysis of the collective polarizability relaxation was performed using two different approaches, the projection scheme (J. Chem. Phys. 1980, 72, 2801) and the theory developed by Steele (Mol. Phys. 1987, 61, 1031) for the second time derivatives applied to collective time correlations. Both approaches allow the decomposition of the OKE response into contributions from orientational relaxation and other dynamical processes. We find that they lead to different predictions on how the response depends on collective reorientation and processes arising from fluctuations in the interaction-induced polarizability. We discuss the reasons for these differences and the advantages and disadvantages of the two analysis schemes.

Induction model for molecular electrostatics: Application to the infrared spectroscopy of CO liquid

Far-infrared intermolecular and midinfrared vibrational spectra of CO liquid have been calculated by Fourier transforming the quantum-corrected classical dipole correlation. The time dependence of the coordinates is determined from a standard nonpolarizable force field, and the dipole is determined from the coordinates with a "spectroscopic model" proposed herein. The model includes intramolecular induction and atomic charges, polarizabilities, and permanent dipoles. A good agreement with available experimental spectra is achieved. Our results demonstrate that the use of an anharmonic potential is necessary to reproduce the experimentally observed shift upon going from gas to liquid. The behavior of the simulated dipole time correlation functions suggests that CO liquid at 80 K exhibits aspects of both free rotation and solidlike caging. The proposition of some free rotation present in CO liquid supports Ewing's experimental hypothesis.

Polarizability response in polar solvents: Molecular-dynamics simulations of acetonitrile and chloroform

The relaxation of the many-body polarizability in liquid acetonitrile and chloroform at room temperature was studied by molecular-dynamics simulations. The collective polarizability induced by intermolecular interactions was included using first- and all-orders dipole-induced-dipole models and calculated considering both molecule-centered and distributed site polarizabilities. The anisotropic response was analyzed using a separation scheme that allows a decomposition of the total response in terms of orientational and collision-induced effects. We found the method effective in approximately separating the contributions of these relaxation mechanisms, although the orientational-collision-induced interference makes a non-negligible contribution to the total response. In both liquids the main contribution to the anisotropic response is due to orientational dynamics, but intermolecular collision-induced (or translational) effects are important, especially at short times. We found that higher-order interaction-induced effects were essentially negligible for both liquids. Larger differences were found between the center-center and site-site models, with the latter showing faster polarizability relaxation and better agreement with experiment. Isotropic and anisotropic spectra were computed from the corresponding time correlation functions. The lowest-frequency contributions are largely suppressed in the isotropic spectra and their overall shape is similar to the purely collision-induced contribution to the anisotropic spectra, but with an amplitude which is smaller by a factor of approximately 5 in acetonitrile and approximately 3 in chloroform.

Relative pair dynamics in simple supercooled liquids: longitudinal contributions

The pair dynamics of simulated argon samples is investigated at the melting (85 K), supercooled (55 K), and quenched (20 K) liquid states, and in the crystal (20 K) state. Tagged pairs, initially lying in a given shell, were divided into incoming and outgoing groups and followed along simulated trajectories. Over them, specific correlation functions deltaB(r(0);t), involving the pair separation vector projected along its initial value r(0) (longitudinal dynamics), have been evaluated. More or less pronounced oscillations are detected according to the temperature of the thermodynamic states (and, obviously, their solid or liquid nature); for each state, they depend on the initial pair distance r(0), too. The oscillations vanish after few picoseconds (fast dynamics) in the case of crystal, whereas in the supercooled liquid they decay towards a plateau, whose height increases with the temperature. It is shown that the power spectrum of deltaB(r(0);t) practically yields the same density of states (DOS) produced by the pair velocity correlation function. The deltaB(r(0);t) functions obtained from the argon crystal at 20 K produce DOS curves dominated by two main frequency contributions, at about 40 and 60 cm(-1) (Einstein and Debye frequency, respectively). Their shape is quite well reproduced by damped harmonic oscillator-like (DHO) functions vibrating at that frequencies. In liquid states, the deltaB(r(0);t) plateau, that forms after the fast DHO dynamics, accounts for the system diffusivity. The relaxation towards the plateau is modeled by an exponential function whose decay time is comparable with the average vibration period. Evidence that the liquid states conserve a certain memory of the vibrational modes of the crystal is obtained. In these states, the DHO functions at the Einstein and Debye frequencies plus an exponential function cannot reproduce the deltaB(r(0);t) shape. A pronounced shoulder, that forms around 0.5 ps, requires the contribution of a third DHO. In the DOS, it yields a band centered below 20 cm(-1) that produces low frequency DOS excess in comparison with the DOS of the crystal. This contribution is present in liquid and supercooled high temperature states and survives near the temperature of the glass transition whereas the diffusion practically vanishes.

Generalized Langevin equation approach to higher-order classical response: second-order-response time-resolved Raman experiment in CS2

A simple, systematic generalized Langevin equation approach for calculating classical nonlinear response functions is formulated and discussed. The two-time Poisson brackets appearing at second and higher order are rendered tractable by a physically motivated approximation. The method is used to calculate the fifth order (second order response) Raman response of liquid CS2. Agreement with simulation is good, but the simplicity of the theoretical expression suggests that the path to obtaining qualitatively new information about liquids with the fifth order experiment is uncertain. Further applications of the basic approach are suggested.