We present a new theory for studying and exploring the potential energy surface of compressed molecular systems as described within the extreme pressure polarizable continuum model framework. The effective potential energy surface is defined as the sum of the electronic energy of the compressed system and the pressure-volume work that is necessary in order to create the compression cavity at the given condition of pressure. We show that the resulting total energy Gt is related to the electronic energy by a Legendre transform in which the pressure and volume of the compression cavity are the conjugate variables. We present an analytical expression for the evaluation of the gradient of the total energy ∇Gt to be used for the geometry optimization of equilibrium geometries and transition states of compressed molecular systems. We also show that, as a result of the Legendre transform property, the potential energy surface can be studied explicitly as a function of the pressure, leading to an explicit connection with the well-known Hammond postulate. As a proof of concept, we present the application of the theory to studying and determining the optimized geometry of compressed methane and the transition states of the electrocyclic ring-closure of hexatriene and of H-transfer between two methyl radicals.