Density Functional Calculations of Metal Clusters: Structure, Dynamics, and Reactivity - Metallic Systems: A Quantum Chemist's Perspective - page 310

DFT.calculations.of.neutral.and.anionic.niobium.tri-
mer. monoxides. have. been. performed. [184]. employing.
scalar.quasi-relativistic.effective.core.potentials.(ECPs)..
A. valence. space. of. 6. and. 13. electrons. for. the. oxygen.
and. niobium. atoms. was. employed,. respectively.. The.
topology. and. geometrical. parameters. of. the. obtained.
ground-state.structures.of.Nb 3 O.(top),.Nb 3 O + .(middle),.
and.Nb 3 O − .(bottom).are.reported.in.Figure.9.20..In.this.
igure,.the.calculated.bond.distances.are.reported.in.Å..
As.Figure.9.20.shows,.the.neutral,.cationic,.and.anionic.
ground.states.have.a.C 2v .structure..This.result.is.in.per-
fect. agreement. with. the. experimental. hypothesis. that.
the. neutral. and. anionic. Nb 3 O. clusters. are. planar. with.
doubly.bridging.oxygen.atoms.[128]..Moreover,.we.also.
note.that.the.equilibrium.geometries.of.the.neutral.and.
anionic.ground-state.structures.are.very.similar.(Figure.
9.20).. The. ground-state. structure. of. the. neutral. Nb 3 O.
could. be. assigned. from. our. calculation. to. a. 2 B 2 . state..
We.assigned.a. 1 A 1 .state.as.the.ground-state.structure.of.
the. anionic. system.. Similar. results. were. found. for. the.
ground-state. structure. of. the. neutral. and. anionic. V 3 O.
cluster.[128,183]..Both,.neutral.and.anionic.ground-state.
structures,.are.followed.by.planar.structures.in.the.quar-
tet.( 4 A 1 ).and.triplet.( 3 A 1 ).PES,.respectively..The.quartet.
state. lies. 1.08.eV. above. the. neutral. ground. state. while.
the.energy.difference.between.the.singlet.and.the.triplet.
anionic.states.is.0.49.eV.

Neutral

1.912

2.750

2.297

Cation

1.921

2.723

2.315

Anion

2.772

1.924

2.293

FIGURE 9.20 Ground-
state. structures. of. Nb 3 O.
(top),. Nb 3 O + . (middle),. and.
Nb 3 O − . (bottom). clusters..
All. bond. lengths. are. in. Å..
(Reprinted.from.Calaminici,.
P.. et. al.,. J. Chem. Phys .,.
121(8),. August. 22,. 3558,.
2004..With.permission.)

9.4 VIBRATIONAL ANALYSIS

9.4.1 v 3
In.order.to.assign.the.ground-state.structure.of.the.V 3 .cluster,.we.simulated.its.PFI-
ZEKE.spectrum..For.this.purpose,.we.have.calculated.the.harmonic.frequencies.of.
the. optimized. neutral. and. cationic. ground-state. vanadium. trimer.. For. the. neutral.
2

1 A .state,.we.obtain.a.degenerate.E′.mode.of.255.cm −1 .and.an. A 1 .mode.of.421.cm −1 ..
The.calculated.frequencies.for.the. 4 A 2 .quartet.state.are.144,.259,.and.428.cm −1 ..For.
the.cationic. 3 2

A .ground.state,.we.ind.an.E′.mode.of.253.cm −1 .and.an. A 1 .mode.of.
434.cm −1 .. The. obtained. frequencies. for. the. excited. cationic. 1

1 A . state. are. 266. and.

422.cm −1 .[143].
Figure.9.21.shows.the.experimental.PFI-ZEKE.spectrum.recorded.at.room.tem-
perature.(a).and.the.simulated.one.for.the.transition.from.the.neutral. 2

1 A .to.the.cat-

ionic. 3 2

A .state..The.simulation.was.performed.at.room.temperature.(b).and.at.700.K.
(c).. The. theoretical. frequencies. are. reported. relative. to. the. experimental. adiabatic.
ionization.potential,.which.correspond.to.the.origin.of.the.PFI-ZEKE.spectrum.at.
44,342.cm −1 .