[citation needed] Also referred to as a van der Waals envelope, the van der Waals surface is named for Johannes Diderik van der Waals, a Dutch theoretical physicist and thermodynamicist who developed theory to provide a liquid-gas equation of state that accounted for the non-zero volume of atoms and molecules, and on their exhibiting an attractive force when they interacted (theoretical constructions that also bear his name).
van der Waals surfaces are therefore a tool used in the abstract representations of molecules, whether accessed, as they were originally, via hand calculation, or via physical wood/plastic models, or now digitally, via computational chemistry software.
As above, in simplest case, for a spherical monatomic gas, Vw is simply the computed volume of a sphere of radius equal to the van der Waals radius of the gaseous atom: For a molecule, Vw is the volume enclosed by the van der Waals surface; hence, computation of Vw presumes ability to describe and compute a van der Waals surface.
In this sense, a van der Waals surface of a homonuclear diatomic molecule can be viewed as an pictorial overlap of the two spherical van der Waals surfaces of the individual atoms, likewise for larger molecules like methane, ammonia, etc.
van der Waals radii and volumes may be determined from the mechanical properties of gases (the original method, determining the van der Waals constant), from the critical point (e.g., of a fluid), from crystallographic measurements of the spacing between pairs of unbonded atoms in crystals, or from measurements of electrical or optical properties (i.e., polarizability or molar refractivity).