where Ω represents a molecule-sized cavity. Whereas solution of Poisson's equation requires discretization of the solute's charge density and electrostatic potential throughout three-dimensional space, the PCM only requires the electrostatic potential to be evaluated on the surface of the cavity that defines Ω, the interface with the continuum. The reformulation of Poisson's equation is exact if the entirety of the solute's charge density is contained within Ω, but is highly accurate even when the tails of the charge distribution penetrate into the dielectric medium, as they do in any QM calculation with a realistic, molecule-sized cavity. Derivation of the PCM starting from Poisson's equation is predicated on the assumption that the dielectric medium is isotropic. To describe anisotropic solvation, such as an air/water interface or a water/biomolecule interface, one can always resort to solution of a general-ized Poisson equation with a permittivity function ε(r) that is defined pointwise throughout three-dimensional space. This approach is more common in plane-wave electronic structure codes, where solution of Poisson's equation is already a part of the standard computational machinery, but in localized Gaussian orbital codes it sacrifices the efficiency advantages of the PCM and the computational overhead to solve Poisson's equation is not negligible.