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I
II
III
IV
V
VI
VII
VIII
FIGURE 11.2
Geometries. of. the. silicon. cluster. (Si
9
). isomers. generated. using. a. genetic.
algorithm.technique.
TABLE 11.1
Energy of the HOMO, Binding Energy per Atom, Dipole
Polarizability, and Energy Gap for the Low-Lying Isomers of Si
9
Cluster
Symmetry
ε
H
(a.u.)
E
B
/atom (eV/atom)
α
(A/atom)
Gap (eV)
I
C
s
−0.223
−3.055
4.73
2.77
II
C
2
−0.212
−2.994
4.91
2.07
III
C
2v
−0.219
−2.988
4.80
2.77
V
C
2
−0.210
−2.945
4.79
1.99
VI
C
s
−0.207
−2.931
4.90
2.37
VII
C
2v
−0.205
−2.828
5.27
2.37
VIII
C
2v
−0.195
−2.788
5.31
1.99
vibrational.frequencies.were.calculated.and.found.to.be.positive.indicating.a.mini-
mum. geometry.. The. structures. are. given. in. Figure. 11.2. in. the. order. of. increasing.
energy..Some.of.the.properties.of.these.clusters.are.displayed.in.Table.11.1..One.can.
see.that.there.is.less.than.a.0.23.eV.difference.in.the.BE.between.the.irst.and.the.
last.isomer..BE.correlates.reasonably.well.with.the.energy.of.the.HOMO..However,.
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