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It is possible in principle to probe the many--atom potential surface usingdensity functional theory (DFT). This will allow us to apply DFT to theHamiltonian formulation of atomic motion in monatomic liquids [\textit{Phys.Rev. E} {\bf 56}, 4179 (1997)]. For a monatomic system, analysis of thepotential surface is facilitated by the random and symmetric classification ofpotential energy valleys. Since the random valleys are numerically dominant anduniform in their macroscopic potential properties, only a few quenches arenecessary to establish these properties. Here we describe an efficienttechnique for doing this. Quenches are done from easily generated "stochastic"configurations, in which the nuclei are distributed uniformly within aconstraint limiting the closeness of approach. For metallic Na with atomic pairpotential interactions, it is shown that quenches from stochasticconfigurations and quenches from equilibrium liquid Molecular Dynamics (MD)configurations produce statistically identical distributions of the structuralpotential energy. Again for metallic Na, it is shown that DFT quenches fromstochastic configurations provide the parameters which calibrate theHamiltonian. A statistical mechanical analysis shows how the underlyingpotential properties can be extracted from the distributions found in quenchesfrom stochastic configurations.

An \emph{ab initio} method for locating characteristic potential energy minima of liquids