Instantaneous normal mode theory of diffusion and the potential energy landscape: Application to supercooled liquid CS2

Abstract

The pure translation (TR) imaginary-frequency (or unstable) instantaneous normal modes (INM), which we have proposed as representative of barrier crossing and diffusion, are obtained for seven densities and eight temperatures of supercooled and near-melting liquid CS2 via computer simulation. The self-diffusion constant D, with a range of over two decades, has been determined previously for these 56 states [Li and Keyes, J. Chem. Phys. 111, 328 (1999)], allowing a comprehensive test of the relation of INM to diffusion. INM theory is reviewed and extended. At each density Arrhenius T-dependence is found for the fraction fu of unstable modes, for the product 〈ω〉ufu of the fraction times the averaged unstable frequency, and for D. The T-dependence of D is captured very accurately by fu at higher densities and by 〈ω〉ufu at lower densities. Since the T-dependence of 〈ω〉u is weak at high density, the formula D∝〈ω〉ufu provides a good representation at all densities; it is derived for the case of low-friction barrier crossing. Density-dependent activation energies determined by Arrhenius fits to 〈ω〉ufu are in excellent agreement with those found from D. Thus, activation energies may be obtained with INM, requiring far less computational effort than an accurate simulation of D in supercooled liquids. Im-ω densities of states, 〈ρuTR(ω,T)〉, are fit to the function a(T)ω exp[−(a2(T)ω/T)a3(T)]. The strong T-dependence of D, absent in Lennard-Jones (LJ) liquids, arises from the multiplicative factor a(T); its activation energy is determined by the inflection-point energy on barriers to diffusion. Values of the exponent a3(T) somewhat greater than 2.0 suggest that liquid CS2 is nonfragile in the extended Angell–Kivelson scheme for the available states. A striking contrast is revealed between CS2 and LJ; a3→2 at low-T in CS2 and at high-T in LJ. The INM interpretation is that barrier height fluctuations in CS2 are negligible at low-T but grow with increasing T, while the opposite is true for LJ.