Instantaneous Normal Mode Spectrum Research Articles

A combined instantaneous normal mode and time correlation function description of the optical Kerr effect and Raman spectroscopy of liquid CS2

The depolarized reduced Raman and corresponding optical Kerr effect (OKE) spectral density of ambient CS2 have been calculated by way of time correlation function (TCF) and instantaneous normal mode (INM) methods and compared with experimental OKE data. When compared in the reduced Raman spectrum form, where the INM spectrum is proportional to the squared polarizability derivative weighted density of states (DOS), the INM results agree nearly quantitatively (at all but the lowest frequencies) with the TCF results. Both are in excellent agreement with experimental measurements. The INM signal has a significant contribution from the imaginary INMs. Within our INM theory of spectroscopy the imaginary INMs contribute like the real modes, at the magnitude of their imaginary frequency. When only the real modes are allowed to contribute, and the spectrum is rescaled to account for the missing degrees of freedom, the results are much poorer, as has been observed previously. When the spectra are compared in their OKE form, the INM spectrum is found to lack the low-frequency spike which is associated with long time scale rotational diffusion, and it is not surprising that an INM theory would not capture such a feature. The results demonstrate that while the OKE and spontaneous depolarized Raman spectrum contain the same information, they clearly highlight different dynamical time scales. At higher frequencies (ω>25 cm−1) the INM OKE results are in excellent agreement with TCF and experimental results. The TCF results capture the low-frequency spike and are in agreement with experiment everywhere within the precision of the present calculations. The molecular contributions to the OKE signal are analyzed using INM methods.

Instantaneous Normal Mode Analysis of the Levitation Effect in Zeolites

An instantaneous normal mode (INM) analysis of the levitation effect in zeolites is presented in this paper. Lennard-Jones sorbates of variable size and polarizability diffusing in Na−Y zeolite are studied using microcanonical molecular dynamics (MD) simulations. A comparison of the dynamical information from the MD simulations with predictions based on INM analysis shows that the INM spectrum carries several striking signatures of the levitation effect. The fraction of imaginary modes mirrors the trend in the diffusion coefficient as a function of sorbate size and shows an anomalous levitation peak. The Einstein frequency, as a function of sorbate size, shows a minimum at the position of the anomalous peak. The qualitative shape of the INM spectrum changes in the anomalous regime, reflecting the availability of 12-ring window sites for adsorption, in addition to the α-cage sites. The velocity autocorrelation functions of the sorbate are well-reproduced from INM data for short time scales of one picosecon...

The instantaneous normal mode spectrum of a liquid undergoing shear flow

The instantaneous normal mode spectrum of a Lennard-Jones liquid undergoing shear flow is determined as a function of shear rate. Shear flow is shown to deplete the density of states at low frequencies and augment the density of states at high frequencies, for both the real and imaginary modes. Shear flow also leads to an increase in the fraction of modes with imaginary frequencies. The implications of these changes are discussed in regard to other system properties.

Analytic Computation of the Instantaneous Normal Modes Spectrum in Low-Density Liquids

We analytically compute the spectrum of the Hessian of the Hamiltonian for a system of N particles interacting via a purely repulsive potential in one dimension. Our approach is valid in the low density regime, where we compute the exact spectrum also in the localized sector. We finally perform a numerical analysis of the localization properties of the eigenfunctions.

Dynamics of Rare Gases in Zeolites: Instantaneous Normal Mode Analysis

The instantaneous normal mode (INM) spectra of rare gases in zeolites is analyzed with a view to understanding the short-time dynamical behavior of fluids adsorbed in confining media. Xenon adsorption in all-silica polymorphs of four zeolites (silicalite, mordenite, zeolite-A, and zeolite-Y) is studied using molecular dynamics and Monte Carlo simulations. The participation ratio distribution is shown to be a particularly good indicator of the extent of ballistic behavior in the short-time dynamics. The fraction of imaginary modes in the INM spectrum is shown to be correlated with the self-diffusion coefficient; however, a significant number of imaginary modes would appear to be due to the negative curvature of the confining potential rather than to the existence of barrier crossing motions. The Einstein frequency shows interesting temperature-dependent behavior which is sensitive to the structure and framework density of the zeolite. The gradual emergence of liquidlike behavior with increasing concentration is reflected in both the participation ratio distribution and the harmonicity ratio; these features of the INM spectrum are therefore expected to be useful for indexing the modification of dynamical behavior of a fluid on confinement.

Anharmonic potentials in supercooled liquids: The soft-potential model

Instantaneous normal modes (INM) are the harmonic approximation to liquid dynamics. This is an extension of the phonon description of lattice dynamics, in which case Bloch's theorem shows that all modes are extended. Long-range order is destroyed in liquids and glasses, and the INM spectrum has contributions from both extended and localized modes. We use the soft-potential mode to describe localized modes. This model is a high-temperature extension of the standard two-level-system model for glasses. The equilibrium position of any atom in the liquid has only temporary character, and relaxation processes in the liquid are associated with particles hopping over potential energy barriers. Barrier tops have negative curvature so that an INM spectrum has an imaginary frequency (unstable) lobe in addition to the conventional stable mode contributions; conversely the unstable modes carry information about diffusion. We derive analytic expressions for the frequency and temperature dependence of the unstable lobe that are in agreement with results from computer simulations. Self-diffusion of particles in the liquid is governed by the fraction of unstable modes originating from double-well potentials. For the diffusion constant, we find a crossover behavior from Arrhenius temperature dependence to Zwanzig-B\"assler dependence. We find an explicit expression for the distribution of barrier heights. In agreement with Stillinger's inherent structure approach to glass-forming liquids, this distribution is uniform, or Gaussian, for high and low temperatures, respectively.

Instantaneous normal mode spectra of quantum clusters

The spectrum of instantaneous normal mode (INM) frequencies of finite Lennard-Jones clusters is studied as a function of the extent of quantum delocalization. Configurations are sampled from the equilibrium distribution by a Fourier path integral Monte Carlo procedure. The INM spectra, average force constants and Einstein frequencies are shown to be interesting dynamical markers for the quantum delocalization-induced cluster solid–liquid transition. Comparisons are made with INM spectra of quantum and classical Lennard-Jones liquids. The methodology used here suggests a general strategy to obtain quantal analogs of various classical dynamical quantities.

Contributions of rotation and translation to polarizability anisotropy and solvation dynamics in acetonitrile

In liquids, a substantial portion of the polarizability anisotropy is interaction induced and its time correlation function (TCF), observable in depolarized light scattering, optical Kerr effect (OKE) and other experiments, decays through translational as well as rotational mechanisms. In this work we develop methods, based on instantaneous normal mode (INM) analysis and on a theory due to W. A. Steele [Mol. Phys. 61, 1031 (1987)], to identify the contributions of rotation, translation, and their cross correlations to polarizability anisotropy dynamics. The Steele theory is also used to extend the analysis of the dynamical origin of solvation response beyond the short-time regime. We use this methodology to investigate the contributions of rotation and translation to the OKE response of acetonitrile at room temperature and to compare it to electrostatic solvation dynamics in this liquid. We find that rotation is the largest contributor to polarizability anisotropy dynamics, but that the translational and translation–rotation cross correlation components are important at all times relevant to the rise and decay of the OKE signal. The polarizability anisotropy INM spectrum of acetonitrile is quite similar to the corresponding electrostatic solvation spectrum determined earlier [B. M. Ladanyi and R. M. Stratt, J. Phys. Chem. 99, 2502 (1995)]. This similarity extends to the polarizability anisotropy and solvation energy velocity TCFs and their decomposition into rotational, translational, and their cross-correlation components. The implication of these results to the use of the OKE spectral density to predict the solvation response in acetonitrile and in other liquids is discussed.

Lyapunov spectra, instantaneous normal mode spectra, and relaxation in the Lennard-Jones liquid.

Lyapunov spectra are obtained numerically for the Lennard-Jones liquid for a range of temperatures. An approximation scheme for calculating the Lyapunov spectrum is described, assuming knowledge of (i) the instantaneous normal mode spectrum which characterizes the local potential energy landscape, and (ii) a decorrelation time. The adaptation, for this purpose, of an analytical relation by Newman is described. The temperature dependence of the maximum Lyapunov exponent, calculated with an ansatz for the decorrelation time, is shown to be in excellent agreement with simulation results.