Size-evolutions of structural and spectral properties in two types of finit
e systems are discussed. First we focus on energetics and structures of gol
d clusters, particularly Au-N in the 40 less than or similar to N less than
or similar to 200 range exhibiting a discrete sequence of optimal clusters
with a decahedral structural motiff, and on the electronic structure of ba
re and methyl-thiol passivated Au-38 clusters. Subsequently, bonding and sp
ectra of quantum dot molecules (QDM's) are investigated, using a single-par
ticle two-center oscillator model and the local-spin-density (LSD) method,
for a broad range of interdot distances and coupling strengths. A molecular
orbital classification of the QDM states correlates between the united-dot
and separated-dots limits. LSD addition energies and spin polarization pat
terns for QDM's in the entire coupling range are analyzed, guiding the cons
truction of a constant interaction model. A generalization of the non-inter
acting-electrons Darwin-Fock model to QDM's is presented. Wigner crystalliz
ation of the electrons leading to formation of Wigner supermolecules is exp
lored in both the field-free case and with a magnetic held using a spin-and
-space unrestricted Hartree-Fock method.