Exponential multiplicity of inherent structures

The mechanically stable spatial arrangements of interacting molecules (potential energy minima, ``inherent structures'') provide a discrete fiducial basis for understanding condensed phase properties. Simple plausibility arguments have been advanced previously suggesting that at fixed positive density the number of distinguishable inherent structures rises exponentially with system size. A more systematic analysis is presented here, using lower and upper bounds, that leads to the same conclusion. Further examination reveals that the characteristic exponential rise rate for inherent structure enumeration diverges as the density approaches zero, when attractive interparticle forces are present.