Density Functional Theory Calculations on Cobalt and Platinum Transition Metal Clusters - Metallic Systems: A Quantum Chemist's Perspective - page 349

A 2 u : σ * ((sd z 2 ) 1 -(sd z 2 ) 1 ) : non-occupied

X

A 2 u : σ * ((sd z 2 ) 2 -(sd z 2 ) 2 ) : doubly occupied

X

Z

Y

B 2 u : δ * (d x 2 - y 2 -d x 2 - y 2 ) : doubly occupied

Y

X

Y

E g : π * (d xz -d xz and d yz -d yz ) : both singly occupied

Z

A 1 g : σ ((sd z 2 ) 2 -(sd z 2 ) 2 ) : doubly occupied

X

Y

Z

B 1 g : δ (d x 2 - y 2 -d x 2 - y 2 ) : doubly occupied

X

B 1 u : δ * (d xy -d xy ) : singly occupied

Y

Z

X

B 2 g : δ (d xy -d xy ) : singly occupied

Z

Y

X
X E u : π (d xz -d xz and d yz -d yz ) : both doubly occupied

Z

Y

A 1 g : σ ((sd z 2 ) 1 -(sd z 2 ) 1 ) : doubly occupied

X

FIGURE 10.4 Co 2 .dimer.molecular.orbitals..(Reprinted.from. Chem. Phys .,.354,.Sebetci,.A.,.
Cobalt.clusters.(Co n ,. n .<=.6).and.their.anions,.196-201,.Copyright.(2008)..With.permission.
from.Elsevier.)

bonding. B 2 u . and. antibonding. B 1 u . δ-bonds. are. formed. by. the. d xy . orbital. and. the.
.bonding.B 1 g .and.antibonding.B 2 u .δ-bonds.are.formed.by. d x 2 − .atomic..orbitals..Since.
the.B 2 g :.δ.(d xy .−.d xy ),.B 1 u :.δ*.(d xy .−.d xy ),.E g :.π*.(d xz .−.d xz ),.and.E g:. π*.(d yz .−.d yz ),.molecular.
orbitals.have.higher.energy.than.orbitals.in.the.minority.spin.channel.(the.high.lying.
A 2 u .is.not.occupied.in.majority.spin.state).they.are.singly.occupied..Thus,.the.ground.
state. was. found. with. the. following. electronic. assignment. in. terms. of. the. ininite.
symmetry.group:.1σ g 2 1π u 4 1δ g 1 1δ u 1 2δ g 2 2σ g 2 1π g 2 2δ u 2 1σ u 2 .

10.2.2.2 Co 3 and Co −
We.found.that.the.linear.structure.of.Co 3. trimer.is.more.stable.than.the.triangular.ones.
(see.Figure.10.5).in.contrast.to.the.indings.of.Jamorski.et.al..[62],.Castro.et.al..[63],.
Fan.et.al..[57],.Pereiro.et.al..[58],.and.Datta.et.al..[61]..To.the.best.of.our.knowledge,.
only.a.single.study.performed.by.Ma.et.al..in.the.literature.is.in.agreement.with.our.
results.[64]..Fan.et.al..[57].and.Pereiro.et.al..[58].found.the.lowest.energy.geometry.
of.Co 3 .to.be.an.equilateral.triangle,.while.Jamorski.et.al..[62],.Castro.et.al..[63],.and.
Datta.et.al..[61].suggested.an.isosceles.triangle..Previous.calculations.for.the.trimer.
are.summarized.in.Table.10.2..In.Ref..[81].it.is.reported.that.the.spin.resonance.spec-
tra.of.Co 3 .in.an.Ar/Kr.matrix.indicates.a.triangular.structure.with.a.total.magnetic.
moment.of.5.or.7.μ B ..We.estimate.that.the.lowest.energy.structure.of.the.trimer.is.the.