Dynamics of Rare Gases in Zeolites: Instantaneous Normal Mode Analysis Vishal Mehra, † Ritu Basra, Monika Khanna, and Charusita Chakravarty* Department of Chemistry, Indian Institute of TechnologysDelhi, Hauz Khas, New Delhi 110016, India ReceiVed: August 27, 1998; In Final Form: January 28, 1999 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. 1. Introduction Dynamics of sorbate molecules in microporous and meso- porous media is of interest from the point of view of catalysis and separation. Porous media can range from highly ordered crystalline structures such as zeolites to random media such as carbon blacks and Vycor. While the chemistry and physics of complex and/or reactive sorbates such as saturated and unsatur- ated long-chain hydrocarbons are of greatest interest industrially, even the study of rare gas adsorption in zeolites and other microporous media reveals a surprisingly diverse range of effects due to confinement on structural and dynamical properties. 1,2 Computer simulations have played an important role in develop- ing an understanding of the microscopic behavior of such complex sorbate-sorbent systems. 3-6 In particular, the dynamics of rare gases, Ne, Ar, Kr, and Xe, in various zeolites have been extensively studied by both computational tools such as micro- canonical molecular dynamics, as well as experimental, for example, using Xe 129 NMR studies. 7-11 Despite the relative simplicity of these systems, interesting dynamical phenomena have been uncovered such as the levitation effect in which sorbates of a specific size range diffuse unusually rapidly through zeolites. In this paper we correlate dynamics of rare gases in zeolites with an equilibrium property of the systemsthe instantaneous normal mode spectrum. The instantaneous normal mode (INM) spectrum is obtained as the set of normal mode frequencies associated with configurations sampled from some suitable ensemble. Since at finite temperatures the configurations will not correspond exactly to local minima on the potential energy surface (PES), the INM spectrum will have real and imaginary branches indicating the extent to which positive and negative curvature regions respectively are sampled by the system. The INM frequencies will be related to the short-time dynamics since, for sufficiently small displacements and therefore for sufficiently small times, a quadratic expansion of the potential about any reference configuration will be adequate. This has motivated the development of INM analysis as a tool to understand liquid-state dynamics and solvation. 12,13 Translational and rotational velocity autocorrelation functions for molecular liquids can be reproduced for time scales of less than a picosecond from INM data. 14 The degree of delocalization of the imaginary branch modes can be correlated with the onset of glassy behavior. 15 Based on Zwanzig’s model of self-diffusion in which a liquid hops between local minima on the PES with a lifetime in each minima described by some survival time distribution, Keyes and co-workers have derived long-time dynamical properties, such as the diffusion coefficient, from the INM spectrum. 16-19 The Lyapunov spectra of Lennard- Jones liquids can also be derived from the INM spectrum with the aid of a reasonable estimate of the decorrelation time. 20 However, connecting the INM data to such long-time averaged dynamical quantities as the diffusion constants or Lyapunov spectra requires additional assumptions about the nature of liquid-state dynamics and is therefore more controversial. 21 Despite this caveat, simulations on a wide range of systems, including atomic clusters, molecular liquids, liquid metals, and ionic melts, have indicated that the INM spectrum is a useful indicator of dynamical behavior. 22-27 This is particularly convenient for systems or phenomena for which a reliable dynamical simulation method does not exist. For example, for quantum many-body systems, path integral methods provide a way to simulate static but not dynamic properties. Since the INM spectrum is an equilibrium quantity it can be computed for a quantum system and is relevant since there is no reliable simulation method for many-body quantum dynamics. 28,29 In the case of classical systems, for many problems such as adsorption or phase transitions, ensembles other than the microcanonical are convenient. 30,31 While molecular dynamics schemes can be set up in other ensembles, such as the canonical or the isothermal-isobaric, the interpretation of the simulation * Author to whom correspondence should be addressed. † Present Address: Departamento de Fisica, Universidad Federal de Sao Carlos, Via Washington Luiz km 235, 13565-905, Caixa Postal 676, Sao Carlos, SP, Brazil. 2740 J. Phys. Chem. B 1999, 103, 2740-2748 10.1021/jp983544k CCC: $18.00 © 1999 American Chemical Society Published on Web 03/23/1999