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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