  In this work the induced van der Waals interaction between a pair of neutral
atoms or molecules is considered by use of a statistical mechanical method.
Commonly this interaction is obtained by standard quantum mechanical
perturbation theory to second order. However, the latter is restricted to
electrostatic interactions between charges and dipole moments. So with
radiating dipole-dipole interaction where retardation effects are important for
large separations of the particles, other methods are needed, and the resulting
induced interaction is the Casimir-Polder interaction usually obtained by field
theory. It can also be evaluated, however, by a statistical mechanical method
that utilizes the path integral representation. We here show explicitly by use
of the statistical mechanical method the equivalence of the Casimir-Polder and
van der Waals interactions to leading order for short separations where
retardation effects can be neglected. Physically this is well known, but in our
opinion the mathematics of this transition process is not so obvious. The
evaluations needed mean a transform of the statistical mechanical free energy
expression to a form that can be identified with second order perturbation
theory. In recent works [H{\o}ye 2010] the Casimir-Polder or Casimir energy has
been added as a correction to calculations of systems like the electron clouds
of molecules.
  The equivalence to van der Waals interactions to leading order indicates that
the added Casimir energy will improve the accuracy of calculated molecular
energies. We here also give numerical estimates of this energy including
analysis and estimates for the uniform electron gas.
