Chemistry Reference
In-Depth Information
9.6 REACTIONS
In.this.inal.section,.we.will.review.briely.two.studies.in,.arguably,.the.most.dificult.
area. of. all,. namely,. the. direct. calculation. of. chemical. reactions. involving. TM. spe-
cies..The.irst.example,.aimed.at.understanding.the.gas-phase.synthesis.of.benzene.
from. acetylene. on. small. iron. clusters,. was. performed. some. 7. or. 8. years. ago,. and.
it.highlights.both.the.promise.and.the.dificulty.of.DFT.calculations.on.even.small.
TM. clusters.. Modern. techniques. for. locating. transition. states. were. not. available. in.
deMon. at. that. time.. The. second. example. involves. iron. oxide. clusters. reacting. with.
carbon.monoxide,.and.it.beneits.from.the.improvements.that.are.now.implemented.
in.deMon2k.
9.6.1 f
ormation
of
B
enzene
from
a
cetylene
on
S
mall
(
n
= 1-4) f
e
c
luSterS
We.will.review.briely.three.papers.by.Chrétien.and.Salahub.that.together.provide.
considerable.insight.into.the.complex.systems.and.reactions.involved.in.making.even.
a.“simple”.molecule.like.benzene.using.iron.clusters.as.the.catalyst.
The.study.was.motivated.by.early.experimental.work.by.Irion.and.collaborators.
[216]. who. found. in. beam. experiments. that. benzene. could. be. produced. from. Fe
+
,.
Fe
4
+
,.and.
Fe
5
+
,.but.not.from.
Fe
2
+
,.
Fe
3
+
,.or.larger.clusters.(up.to.
Fe
1
+
)..The.small.size.
of.the.active.clusters.seemed.very.attractive.for.a.theoretical.study,.even.though.we.
were. well. aware. of. the. potential. structural. and. electronic. complexity. of. a. small.
cluster.such.as.
Fe
4
+
.
The.irst.paper.[198].treated.the.isolated.iron.clusters.and.involved.an.extensive.
series.of.calculations.on.
Fe
n
+
,.Fe
n
,.and.
Fe
n
−
.clusters..Careful.attention.was.paid.to.all.
of. the. computational. parameters. (exchange-correlation. potentials,. basis. sets,. inte-
gration.grids,.number.of.unpaired.spins,.starting.geometries,.SCF.convergence,.etc.),.
and.we.tried.to.establish.reasonable.(conservative).error.bars.for.the.calculations..In.
the.end,.comparing.available.calculations.and.experimental.values,.we.proposed.that.
an.error.bar.on.the.relative.energy.of.the.various.states.should.be.set.at.around.50.kJ/
mol.(12.kcal/mol),.and.we.have.kept.all.states.within.this.error.bar.of.the.computed.
ground.state.in.the.subsequent.studies.of.the.reactions.
Table.IV.of.Ref..[198].reproduced.here.as.Table.9.2.will.give.the.reader.a.sense.of.
the.extent.of.the.calculations.for.Fe
4
,.
Fe
4
+
,.and.
Fe
4
−
..Table.9.3.summarizes.the.avail-
able.experimental.results.for.D
0
,.IP,.and.EA.of.all.of.the.clusters.up.to.the.tetramer..
While. the. agreement. is. “reasonable”. in. particular. concerning. trends. with. cluster.
size,.it.is.clear.that.quantitative. agreement.is.still.beyond.the.reach.of.GGA.DFT..
While. our. approach. is. not. perfect. (see. Ref.. [198]. for. a. discussion. on. the. limiting.
factors),.there.is.enough.encouragement.in.the.performance.of.the.methodology.to.
allow.the.study.of.reactions.on.the.clusters,.provided.that.the.quantitative.limitations.
are.kept.in.mind.
The. second. paper. from. Chrétien. and. Salahub. [217]. looks. at. the. adsorption. of.
acetylene.and.vinylidene.on.the.clusters.and.has,.as.the.end.result,.the.elimination.of.
vinylidene.as.a.reactant,.thus.greatly.simplifying.the.computational.task.when.three.
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