Chemistry Reference
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of.Fan.et.al..[57].and.Ma.et.al..[64];.however,.it.is.in.contradiction.to.the.indings.of.
Datta.et.al..[61]..Yoshida.and.coworkers.[52].predicted.a.tetrahedral.structure.as.the.
ground.state.of.Co
4
−
.anion.by.starting.from.a.
T
d
.tetrahedron.and.a.
D
4h
.square.without.
considering.a.rhombus..We.found.a.planar.rhombus.with.a.bond.length.of.2.28.Å.in.
the.decet.state.as.the.ground.state.of.the.tetramer.anion..One.of.the.reasons.of.why.
the. various. results. disagree. with. one. another. is. the. incompleteness. of. the. global.
minimum. search.. Most. of. the. DFT. codes. perform. only. local. geometry. optimiza-
tions..When.an.author.does.not.consider.the.morphology.of.the.lowest.energy.struc-
ture. as. the. starting. coniguration. of. the. local. geometry. optimization,. that. speciic.
structure.may.be.missed..The.lowest.and.the.highest.vibrational.frequencies.of.the.
anion.are.113.and.241.cm
−1
.
10.2.2.4 Co
5
and Co
−
For. Co
5
,. seven. different. initial. geometries. were. investigated:. pyramid,. bipyramid,.
capped.tetrahedron,.X-like,.W-like,.V-like,.and.pentagon..A.planar.W-like.structure.
was. found. as. the. lowest. energy. geometry. with. a. spin. magnetic. moment. of. 11.μ
B
..
The. next. low-lying. minima. are. out-of-plane. bridge-side. capped. rhombus,. bipyra-
mid,.pentagon,.and.pyramid.(see.Figure.10.5),.respectively..Except.the.bipyramidal.
structure,. which. has. 13.μ
B
. spin. moment,. all. the. minima. have. the. same. magnetic.
moment. of. 11.μ
B
.. The. ground-state. BE. of. the. neutral. pentamer. was. calculated. as.
1.54.eV/atom..This.structure.has.the.highest.HOMO-LUMO.gap.(0.81.eV).as.well..
The. HOMO-LUMO. energy. separation. is. considered. as. a. parameter. for. chemical.
stability.since.it.is.favorable.to.add.electrons.to.a.low-lying.LUMO.and.to.receive.
electrons.from.a.high-lying.HOMO..Although.HOMO-LUMO.gaps.calculated.via.
DFT.are.not.so.reliable.in.magnitude,.they.can.provide.reasonable.estimations.for.the.
relative.size.of.the.gaps..The.energy.separations.between.the.next.low-lying.minima.
and.the.ground.state.are.0.03,.0.04,.0.05,.and.0.05.eV/atom,.respectively..Fan.et.al..
[57]. and. Ma. et. al.. [64]. identiied. the. pyramidal. structure,. and. Pereiro. et. al.. [58],.
Datta.et.al..[61],.and.Castro.et.al..[63].found.the.bipyramidal.structure.as.the.ground-
state. geometry.. Thus,. the. W-like. structure. found. in. this. study. is. reported. as. the.
ground.state.for.the.irst.time..Although.the.literature.[57,60,61].reports.ground-state.
spin.moment.as.13.μ
B
,.Ma.et.al..[64].calculated.it.as.11.μ
B,
.in.agreement.with.the.pres-
ent.result..The.bond.lengths.for.each.of.the.minima.can.be.found.in.Figure.10.5..The.
lowest.energy.structure.of.the.anionic.pentamer.has.the.same.morphology.with.the.
neutral.pentamer.(the.W-like.structure).with.the.spin.moment.of.10.μ
B
..The.addition.
of.an.electron.reduces.the.bond.lengths.from.2.25,.2.35,.and.2.35.Å.(see.the.structure.
(5-1).in.Figure.10.5).to.2.18,.2.34,.and.2.34.Å.and.stretches.those.of.2.24,.2.24,.2.29,.
and.2.28.Å.to.2.25,.2.26,.2.39,.and.2.37.Å,.respectively..The.lowest.and.the.highest.
vibrational.frequencies.of.the.anionic.pentamer.are.105.and.296.cm
−1
.
10.2.2.5 Co
6
and Co
−
At.the.end.of.several.optimizations.initially.starting.with.13.different.structural.motifs.
of.Co
6
,.we.ended.up.with.six.local.minima.structures.in.the.energetic.order.of.dis-
torted. octahedron,. planar. triangle,. face. capped. bipyramid,. planar. W-like. structure,.
trigonal. prism,. and. pentagonal. pyramid.. The. lowest. energy. structure. is. a. distorted.
octahedron.with.a.
D
3
.symmetry.and.a.spin.moment.of.14.μ
B
..Its.BE.is.1.71.eV/atom.
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