Density Functional Theory Calculations on Cobalt and Platinum Transition Metal Clusters - Metallic Systems: A Quantum Chemist's Perspective - page 363

pyramidal.isomer.contradicts.the.indings.of.Bhattacharyya.and.Majumder.[89],.Huda.
et.al..[90],.Grönbeck.and.Andreoni.[106],.Xiao.and.Wang.[109],.Saenz.et.al..[86],.
and.Futschek.et.al..[87],.it.agrees.with.the.predictions.of.Majumder.et.al..[105],.Yang.
et.al..[110],.and.Seivane.and.Ferrer.[88]..Bhattacharyya.and.Majumder.[89].and.Huda.
et.al..[90].predicted.a.planar.bridge-side-capped.structure,.Grönbeck.and.Andreoni.
[106].and.Saenz.et.al..[86].predicted.a.planar.W-like.structure,.Xiao.and.Wang.[109].
and. Futschek. et. al.. [87]. predicted. a. trigonal. bipyramid. as. the. lowest. energy. con-
iguration.. Even. if. it. is. assumed. that. the. search. for. the. lowest. energy. structure. is.
performed.satisfactorily.in.all.of.these.studies,.since.the.exact.xc-functional.of.DFT.
is.not.known,.such.contradictions.in.the.results.obtained.by.different.groups.seem.to.
be.solved.only.by.the.help.of.accurate.experimental.investigations.
The.third.low-lying.isomer.is.an.out-of-plane,.W-like.structure.(see.Figure.10.7).
with.a.spin.moment.of.3.58.μ B .with.an.energy.of.173.meV.higher.than.the.global.mini-
mum..Previously,.we.identiied.a.trapezoidal.structure.as.the.ifth.lowest.lying.isomer.
[39]..However,.in.that.study.we.considered.only.its.singlet.and.triplet.states..Thus,.
the.discrepancy.can.be.attributed.to.the.limitation.of.the.previous.calculations.for.the.
irst.two.spin.multiplicities..For.the.discerning.between.the.contradictory.results,.the.
irst.thing.to.be.assessed.is.the.completeness.of.the.study..The.fourth.energetically.
favorable.structure.is.a.bipyramid.with.a.spin.moment.of.3.57.μ B ..The.planar,.bridge-
side-capped.square.structure,.which.had.been.predicted.as.the.global.minimum.of.
Pt 5 .clusters.[89,90].by.a.plane.wave.code,.was.obtained.as.the.ifth.lowest.energy.iso-
mer.in.our.calculations..Its.energies.of.0.674.(non-SO).and.0.373.eV.(SO).are.higher.
than.the.ones.for.the.lowest.energy.structure..Finally,.a.nonplanar.X-like.geometry.
was.identiied.as.a.stable.isomer.with.the.highest.total.energy..Unlike.most.of.the.
other.isomers.where.the.magnetic.moment.of.the.cluster.for.the.most.stable.magnetic.
state.in.SO.case.is.similar.to.that.of.non-SO.case,.the.most.stable.magnetic.state.of.
the.X-like.structure.in.SO.case.(3.39.μ B ).could.be.obtained.from.an.initial.nonet.state,.
which.gives.very.high.relative.energy.(2.859.eV).in.non-SO.calculations.
The.effect.of.SO.coupling.on.the.bond.lengths.of.Pt 5 .clusters.is.not.constant..For.
the.pyramidal.structure,.while.the.interatomic.distances.between.the.apex.atom.and.
the.atoms.on.the.square.plane.are.stretched,.the.distances.between.the.atoms.on.the.
square.plane.are.diminished..For.the.capped.tetrahedron,.as.SO.effects.make.the.tri-
angle.constructed.by.the.capping.atom.and.the.two.atoms.bonded.to.the.capping.atom.
a.bit.larger,.all.other.bond.lengths.are.kept.nearly.the.same..All.bond.lengths.of.W-like.
structure.and.most.of.them.in.X-like.structures.are.elongated.by.SO.coupling;.on.the.
contrary,.SO.coupling.does.not.have.a.signiicant.effect.on.the.bond.length.of.the.bipyr-
amid.and.even.causes.contractions.in.the.bond.length.of.the.capped.square.isomer.
10.3.2.4 Pt 6
The. relative. stabilities. of. 11. different. isomers. of. Pt 6 . can. be. found. in. Table. 10.6..
Their.bond.lengths.and.structures.have.been.given.in.Figure.10.8..The.most.stable.
structure.of.Pt 6 .has.been.obtained.as.a.trigonal.prism.in.the.septet.state.for.non-SO.
case. and. a. state. with. a. spin. moment. of. 5.43.μ B . for. the. SO. case.. Xiao. and. Wang.
[109].predicted.a.planar.double-capped.square,.Bhattacharyya. and.Majumder.[89].
identiied.a.planar.triangular.structure,.Futschek.et.al..[87].obtained.a.face-capped.
pyramid.as.the.lowest.energy.isomer.of.Pt 6 ..In.our.calculations,.the.triangle.is.the.