Top-down approach to liquid structure

Conventional approaches to describe the structure of simple liquid and glass are bottom-up, starting with a cluster of an atom and its nearest neighbors, and add more atoms to build the structure. But this approach fails to explain the persistence of medium-range order (MRO), the exponential decay in the pair-distribution function beyond the first neighbors, even in liquids with complex chemistry. We propose to add to the bottom-up approach the top-down approach based upon the idea of density wave instability. The interatomic potential has a strongly repulsive part, but that part is irrelevant for liquid formation because atoms never come so close to each other. We define the pseudopotential Vp(r) for which the strongly repulsive part, where V(r) >> kT, is removed and Vp(r) = Vp(r_cutoff) is assumed below r_cutoff. Surprisingly, the Fourier transform of Vp(r), Vp(Q), has a deep minimum at a wavevector Q1, close to the first peak of the structure function S(Q). The value of Q1 does not depend strongly on the cutoff energy, Vp(r_cutoff). Thus, this minimum must be the consequence of shape resonance due to atomic exclusion. This minimum stabilizes the density wave state when the pseudopotential is applied to the high-density gas state in the reciprocal space. Because liquid is isotropic, the Q1 vectors are spherically distributed forming the Bragg sphere. The coherence length of the MRO increases with decreasing temperature, and when it extrapolates to infinity such a density wave state is realized. Thus, we suggest that the pseudopotential is driving the system to such a state. But this density wave state has poor short-range order. Therefore, the two driving forces, bottom-up and top-down, are in conflict to each other, and the MRO appears as a compromise. This dual approach explains various properties of liquid and glass, including fragility and viscosity.