Chemistry Reference
In-Depth Information
TABLE 10.2
Comparisons of the Obtained Results for Co
3
Along with
Results from the Literature (Those of the Previous Works)
Spin
Moment (μ
B
)
Binding
Energy (eV)
Bond
Length (Å)
Reference
Symmetry
[66]
D
∞
h
7
3.60
2.21
[57]
D
3h
7
2.55
2.28
[58]
C
3v
7
1.68
2.04
[61]
C
2v
5
5.34
2.10,.2.19,.2.19
[62,63]
C
2v
5
4.60
2.12,.2.12,.2.24
[64]
D
∞
h
7
8.68
2.27
Source:
. Reprinted. from.
Chem. Phys
.,. 354,. Sebetci,. A.,. Cobalt. clusters. (Co
n
,.
n
.<=.6).and.their.anions,.196-201,.Copyright.(2008)..With.permission.
from.Elsevier.
linear.(
D
∞
h
).coniguration.with.a.bond.length.of.2.21.Å.in.the.octet.state..The.vibra-
tional.frequencies.were.calculated.as.80,.190,.and.237.cm
−1
..Another.linear.structure.
with.
C
s
.symmetry.in.the.quartet.state.was.found.as.the.second.lowest.energy.structure.
where.the.bond.lengths.are.2.13.and.2.32.Å..The.energy.separation.between.these.two.
structures. is. 0.16.eV.. The. two. isosceles. triangles. (
C
2v
). have. similar. energies,. which.
is.0.68.eV.higher.than.the.ground-state.energy..The.bond.lengths.are.2.22,.2.29,.and.
2.29.Å,.and.2.22,.2.22,.and.2.21.Å,.which.resemble.an.equilateral.triangle.
Structural.assignments,.point.group.symmetries,.total.spin.moments,.BEs,.high-
est. occupied. and. lowest. unoccupied. molecular. orbital. (HOMO-LUMO). gaps,. and.
the.lowest.and.the.highest.vibrational.frequencies.of.Co
3
.and.all.other.minima.of.Co
n
.
clusters.(
n
.≤.6).are.depicted.in.Table.10.3..The.charge.distribution.of.a.single.Co.atom.
in.the.lowest.energy.structure.of.the.trimer.(3d
8.07
4s
0.92
).is.slightly.different.from.that.
of.the.dimer..The.HOMO-LUMO.gap.of.the.ground-state.geometry.is.particularly.
high,.1.04.eV..This.is.not.unusual.for.a.DFT.code.since.many.common.xc-functionals.
can.mismatch.HOMO-LUMO.gaps.of.the.order.of.electron.volt..Yoshida.et.al..[52].
reported.that.Co
3
−
.has.a.linear.structure.with.a.bond.length.between.2.25.and.2.50.Å.
based. on. photoelectron. spectroscopy. measurements.. We. found. a. linear. structure.
with.a.bond.distance.of.2.29.Å.as.the.lowest.energy.structure.of.the.anionic.trimer,.
which.is.consistent.with.the.experimental.measurements.[52]..The.ground-state.lin-
ear.structure.of.the.anionic.trimer.is.a.septet.state..The.isosceles.triangular.conigu-
ration.of.Co
−
.is.found.to.be.in.the.nonet.state,.which.has.an.energy.of.0.46.eV.higher.
than.the.linear.coniguration.where.the.bond.lengths.are.2.14,.2.33,.and.2.33.Å.
10.2.2.3 Co
4
and Co
−
Five. different. initial. geometries. were. considered. for. the. tetramer:. tetrahedron,.
square,.rhombus,.planar.Y-like,.and.linear..The.lowest.energy.structure.is.found.to.be.
an.out-of-plane.rhombus.(C
s
).with.a.spin.moment.of.10.μ
B
..It.has.a.BE.of.1.37.eV/atom.
and.HOMO-LUMO.gap.of.0.94.eV..One.pair.of.the.bond.lengths.in.this.structure.is.
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