  In this work we have applied the recently formulated self-compressed
inhomogeneous stabilized jellium model [M. Payami and T. Mahmoodi, Can. J.
Phys. {\bf 89}, 967 (2011)] to describe the equilibrium electronic and
geometric properties of atomic-closed-shell simple metal clusters of Al$_N$
($N$=13, 19, 43, 55, 79, 87, 135, 141), Na$_N$, and Cs$_N$ ($N$=9, 15, 27, 51,
59, 65, 89, 113). To validate the results, we have also performed
first-principles pseudo-potential calculations and used them as our reference.
In the model, we have considered two regions consisting of "surface" and
"inner" ones, the border separating them is sharp. This generalization makes
possible to decouple the relaxations of different parts of the system. The
results show that the present model correctly predicts the size reductions seen
in most of the clusters. It also predicts increase in size of some clusters, as
observed from first-principles results. The other property is the change of
inter-layer distances, which in most cases were realized as contractions and in
a few cases as expansions, are reproduced in good agreement with the atomic
simulation results. For a better description of the properties, it is possible
to improve the method of choosing the thicknesses or generalize the model to
include more regions than just two.
