Chemistry Reference
In-Depth Information
[143],.which.in.turn.depends.on.the.relative.stability.of.the.atomic.
d
.orbitals..The.
well-known. trend. in. DFT. calculations. to. overestimate. the. stability. of. the. atomic.
d
.functions.in.TM.elements.results.in.V
3
.in.an.extra.(artiicial).stabilization.of.the.
�
a
1
.orbital..As.a.result,.a.Jahn-Teller.distortion.of.the.V
3
.ground.state.may.occur.if.
the.ordering.of.the.
�
a
1
.and.e′.orbitals.has.exchanged..Whether.this.distortion.is.real.
or.artiicial.cannot.be.concluded.from.the.calculations.alone..Therefore,.the.vana-
dium.trimer.ground-state.structure.cannot.be.assigned.based.on.these.calculations..
Fortunately,.Hackett.and.coworkers.recorded.a.well-resolved.PFI-ZEKE.spectrum.of.
V
3
.[112]..The.simulation.of.this.spectrum.from.our.DFT.results.allowed.us.to.assign.
the.V
3
.ground-state.structure..For.this.purpose,.we.have.calculated.the.harmonic.fre-
quencies.of.the.optimized.neutral.and.cationic.vanadium.trimers.[143]..From.these.
frequencies. and. the. corresponding. normal. mode. vectors,. we. calculated. harmonic.
Franck-Condon.factors.and.simulated.the.PFI-ZEKE.spectrum.of.V
3
..The.simulated.
spectrum.will.be.shown.and.discussed.in.Section.9.4.
Another. goal. in. our. studies. of. TM. clusters. is. to. explain. the. experimentally.
observed.pattern.in.stability.and.other.molecular.properties.on.the.basis.of.electronic.
structure. of. these. systems.. Here. we. present. an. example. for. small. copper. clusters.
with.up.to.10.atoms.[144,145]..Structure.optimizations.were.performed.in.the.LDA.
with. the. VWN. exchange-correlation. functional,. and. all-electron. basis. sets. were.
employed..The.same.functional.was.used.for.the.frequency.analysis.in.order.to.dis-
tinguish.between.stable.structures.and.transition.structures..LDA.studies.on.small.
copper.clusters.with.up.to.ive.atoms.[105].have.already.shown.that.the.DZVP.basis.
together.with.the.A2.auxiliary.function.set.[46].supplies.very.reliable.geometries.for.
structure.optimizations..Since.such.calculations.are.insuficient.for.energetic.consid-
erations,.single.point.energies.were.inally.calculated.using.the.same.basis.and.aux-
iliary. function. set. with. the. exchange-correlation. functional. PW86-P86. [146-148]..
This.approach.has.already.proven.reliable.for.small.copper.clusters.with.up.to.ive.
atoms.[105]..The.corresponding.cluster.structures.are.depicted.in.Figure.9.9.showing.
all.bonds.with.bond.lengths.up.to.2.6.Å.
The. neutral. hexamer. is. the. largest. copper. cluster. ground. state. with. a. two-.
dimensional.structure..At.the.GGA.level,.the.Cu
6
.C
5v
.isomer.is.only.slightly.higher.
in.energy..In.contrast.to.the.hexamer,.the.most.stable.neutral.heptamers.have.three-
dimensional. structures.. We. ind. in. our. calculations. a. pentagonal. bipyramid. of.
D
5h
. symmetry. as. the. global. minimum. for. Cu
7
. both. at. the. LDA. and. GGA. levels..
Compared. with. the. C
5v
. structure. of. Cu
6
,. the. ring. distances. of. the. Cu
7
. cluster. are.
slightly. shortened. from. 2.41. to. 2.39. Å. and. the. cap-ring. distance. is. substantially.
lengthened.from.2.32.to.2.39.Å..Still,.the.cap-cap.distance.is.only.2.50.Å,.indicat-
ing.a.bond.between.the.capping.atoms..Another.relatively.stable.Cu
7
.isomer.is.the.
depicted.C
3v
.structure.in.Figure.9.9..This.structure.was.obtained.from.the.relaxation.
of. a. crystal. fragment.. During. this. relaxation,. the. average. bond. length. decreased.
from. 2.56. to. 2.39. Å.. Planar. structures. of. the. heptamer. were. found. considerably.
higher.in.energy.and.were.excluded.as.possible.ground.states.from.the.study.
To.arrive.at.new.cluster.structures,.the.capping.of.stable.structures.seems.to.be.a.
reasonable.procedure..Starting.from.the.Cu
7
.bipyramid,.a.capping.of.one.of.the.tri-
angles.has.been.proposed.and.calculated.on.the.LDA.level.[151,152]..In.our.study,.we.
found.that.such.a.structure.is.not.stable.and.relaxes..The.global.minimum.of.Cu
8
.has.
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