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

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 f(u) of unstable modes, for the product <omega >(u)f(u) of the fraction times the averaged unstable frequency, and for D. The T-dependence of D is captured very accurately by f(u) at higher densities and by <omega >(u)f(u) at lower densities. Since the T-dependence of <omega >(u) is weak at high density, the formula D proportional to <omega >(u)f(u) 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 <omega >(u)f(u) 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-omega densities of states, <rho(u)(TR)(omega,T)>, are fit to the function a(T)omega exp[-(a(2)(T)omega/root 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 a(3)(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; a(3)--> 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. (C) 1999 American Institute of Physics. [S0021-9606(99)50636-3].