Density Functional Theory Calculations on Cobalt and Platinum Transition Metal Clusters - Metallic Systems: A Quantum Chemist's Perspective - page 348

above.the.ground.state,.respectively..The.experimental.bond.length.of.the.neighbor-
ing.dimers.Fe 2 .and.Ni 2 .are.1.87.[79].and.2.155.Å.[80],.respectively..Our.calculated.
value.of.2.13.Å.for.Co 2 .is.slightly.less.than.the.Ni 2 .dimer.bond.length.and.in.between.
the.values.obtained.from.Pauling.radius.[71].and.Badger's.rule.[74]..Previous.various.
theoretical.results.for.Co 2 .bond.length.present.values.ranging.from.1.95.to.2.41.Å..We.
calculated.the.IP.of.the.dimer.as.6.84.eV.in.better.(or.similar).agreement.with.experi-
ment.[72].than.previous.theoretical.studies.(see.Table.10.1)..The.ground.spin.multi-
plicity.of.the.Co 2 + .ion.was.calculated.as.the.sextet.state,.which.had.previously.been.
determined.by.ESR.spectroscopy.[81]..The.calculated.bond.length.of.the.dimer.anion.
(Co 2 − ).is.2.19.Å.(sextet.state),.which.exceeds.that.of.the.neutral.dimer.by.0.06.Å..This.
increase.in.bond.length.has.been.estimated.experimentally.as.0.08.±.0.02.Å.[77]..The.
calculated.BE.for.the.Co 2 .dimer.is.1.71.eV.with.respect.to.the.atomic.ground.state.
while. other. theoretical. estimations. span. in. the. larger. range. of. 0.87-5.54.eV.. Our.
calculated.vibrational.frequency.of.329.cm −1 .is.also.closer.to.the.experimental.values.
than.previous.ab.initio.studies.(see.Table.10.1).
Mulliken. population. analysis. gives. a. charge. distribution. of. 3d 7.82 4s 1.18 . for. each.
Co.atom.in.the.neutral.dimer,.which.indicates.that.3d.orbitals.participate.in.bond-
ing..The.symmetry.and.energy.levels.of.the.dimer.molecular.orbitals.are.depicted.
in.Figure.10.3..The.point.group.symmetry.of.the.dimer.was.determined.as. D 4h ..The.
electron.density.isosurfaces.and.the.types.of.the.bonds.of.each.molecular.orbital.are.
given.in.Figure.10.4..It.is.evident.from.Figure.10.4.that.the.hybridization.of.on-site.
4s.and. 3d z 2 .orbitals.constructs.two.s d z 2 .hybrid.atomic.orbitals.(the. z -axis.is.the.bond.
axis).. (These. atomic. orbitals. on. each. of. the. Co. atoms. contribute. to. two. bonding.
(A 1 g ).and.two.antibonding.(A 2 u ).molecular.orbitals.(see.Figure.10.4).The.d xz .and.d yz .
orbitals.form.π.bonds..Since.the.π.bond.formed.by.d xz .orbitals.is.symmetric.to.the.
one.formed.by.d yz .orbitals,.the.dimer.has.the.degenerate.bonding.E u .and.antibonding.
E g .π.molecular.orbitals..Finally,.d xy .and. d x .atomic.orbitals.form.the.δ-bonds: the. 2 2

− y

B 1 u

A 2 u

-0.10

E g

B 2 g

A 2 u

-0.12

A 2 u

-0.14

B 2 u

-0.16

E u

A 1 g

A 2 u

B 1 g

-0.18

B 2 u

E g

-0.20

A 1 g
B 1 g

A 1 g

-0.22

B 1 u

B 2 g

-0.24

E u

A 1 g

-0.26

FIGURE 10.3 Energy.levels.and.symmetries.of.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.)