Density Functional Calculations of Metal Clusters: Structure, Dynamics, and Reactivity - Metallic Systems: A Quantum Chemist's Perspective - page 297

the.deMon2k.code.and.can.be.downloaded.directly.from.the.deMon2k.web.page.at.
http://www.demon-software.com/public_html/download.html#basissets
The. experimental. PFI-ZEKE. spectrum. was. simulated. using. multidimensional.
Franck-Condon.factors.calculated.from.the.geometries.and.harmonic.frequencies.of.
the.obtained.structures.of.V 3 .and. V 3 + ..The.comparison.between.the.experimental.and.
theoretical. PFI-ZEKE. spectra. establishes. unequivocally. the. ground-state. structure.
of.the.V 3 .cluster.as.an.equilateral.doublet..This.represented.the.irst.work.in.which.
the.structure.of.a.pure.TM.metal.cluster.has.been.determined.from.the.combination.
of.DFT.calculations,.Franck-Condon.simulations,.and.ZEKE.photoelectron.spectros-
copy. [143].. Figure. 9.8. summarizes. our. restricted. open. shell. Kohn-Sham. (ROKS).
optimized.V 3 .and. V 3 + .structures..For.neutral.V 3 ,.we.ind.an.equilateral.triangle. 2 1 A .
ground.state..The.optimized.bond.distance.is.2.17.Å..Our.D 3h .vanadium.trimer.ground.
state.differs.from.the.C 2v .structures.reported.in.previous.DFT.studies.[140,141]..This.
is. due. to. the. different. orbital. ordering. at. the. Fermi. level.. In. fact,. with. the. VWN-
optimized.DZVP.basis.set.[46],.we.obtain.an.acute.triangle.doublet.ground.state.for.
the.vanadium.trimer..Only.0.03.eV.above.the. 2 1 A .ground.state,.we.ind.an.acute.tri-
angle. 4 A 2 .state.(Figure.9.8)..The. 4 A 2 .quartet.is.formed.by.the.excitation.of.one.of.the.
e″.electrons.into.an.unoccupied.e′.orbital..As.a.result,.a.Jahn-Teller.distortion.into.C 2v .
symmetry.occurs..Other.structures.with.higher.spin.multiplicities.such.as.the.sextet.
depicted.in.Figure.9.8.are.energetically.well.separated.from.these.two.structures.
Similar.to.the.neutral.trimer,.we.ind.an.equilateral.triangle.ground.state.for. V 3 + ..
This.structure.can.be.assigned.to.a. 3 2 A .state..Wu.and.Ray.also.found.in.their.calcula-

tions.[141].the.same. V 3 + .ground.state..The.optimized.bond.distances.of.2.18.Å.in.the.
cationic.ground.state.are.very.close.to.those.of.the.neutral.trimer.(see.Figure.9.8).
The.calculated.adiabatic.ionization.potential.is.5.61.eV.in.good.agreement.with.
the.experimental.value.of.5.49.eV.[112,120]..Above.the. 3 A .state,.we.ind.a. 1

A .sin-

2 1

glet..This.singlet.is,.at.0.18.eV,.reasonably.well.separated.from.the. 3 2

A .ground.state..
Higher. spin. multiplicities,. like. the. quintet. (0.52.eV. above. the. 3 2

A . ground. state).
depicted. in. Figure. 9.8. are. considerably. higher. in. energy.. Therefore,. the. assign-
ment.of.the. V 3 + .ground.state.to.the. 3 2 A .state.depends.less.critically.on.the.choice.of.

the.exchange-correlation.functional.and.basis.set..The.MO.analysis.shows.that.the.
assignment.of.the.V 3 .ground.state.depends.on.the.ordering.of.the. d . �

a 1 .and.e′.orbitals.

2 A 1 4 A 2

6 A 1

2.335

(a) 2.169 1.964 2.256

3 A 2 1 A 1 5 A 1

2.323

(b) 2.180 2.211 2.141

FIGURE 9.8 Ground-state.structures.of.V 3 .(a).and. V 3 + .(b).clusters..Bond.lengths.are.in.Å..
(Reprinted. from. Calaminici,. P.. et. al.,. J. Chem. Phys .,. 114(9),. March. 1,. 4036,. 2001.. With.
permission.)