  The atomic volume and surface are important geometric quantities for
calculating various macroscopic physical quantities from atomic models. This
paper proposes a new analytical method to calculate the atomic volumes and
surfaces of a metal cluster. This method adopts metallic radii to describe atom
sizes and constructs the overall volume/surface by the molecular surface (MS)
model. It divides cluster atoms into two types: interior atoms and boundary
atoms. For an interior atom, the method defines a variational Voronoi cell as
its volume. For a boundary atom, the method defines the intersection of the
overall cluster volume and its variational Voronoi cell as its volume. The
atomic surfaces are calculated along with the volume calculations. This new
method considers the effect of atom sizes and can calculate not only the
overall volume of a cluster but also the individual volume for each atom. This
method provides computational support for multiscale coupled calculations from
the microscale to macroscale.
