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dimers. and. trimers. by. negative. ion. photodetachment. spectroscopy. and. Eberhardt.
and. coworkers. [85]. obtained. the. valence-. and. core-level. photoemission. spectra. of.
mass-selected. monodisperse. Pt
n
. (
n
= 1.-.6). clusters.. In. a. recent. theoretical. calcula-
tion,. we. studied. bare. and. hydrogenated. Pt
n
H
m
. (
n
= 1.-.5,.
m
= 0.-.2). clusters. within.
the. scalar-relativistic. DFT. formalism. [39].. Relevant. literature. can. be. found. in. the.
literature.[39].for.previous.experimental.and.theoretical.investigations..In.addition,.
Saenz. et. al.. [86]. worked. on. the. interaction. of. Pt. clusters. with. molecular. oxygen..
Futschek.et.al..[87].presented.ab.initio.density.functional.studies.of.structural.and.
magnetic. isomers. of. Ni
n
. and. Pt
n
. clusters. with. up. to. 13. atoms.. Seivane. and. Ferrer.
[88].analyzed.the.impact.of.the.magnetic.anisotropy.on.the.geometric.structure.and.
magnetic.ordering.of.small.atomic.clusters.of.palladium,.iridium,.platinum,.and.gold.
from.two.to.ive,.six,.or.seven.atoms.depending.on.the.element..Bhattacharyya.and.
Majumder. [89]. reported. the. growth. pattern. and. bonding. trends. in. Pt
n
. (
n
= 2.-.13).
clusters.and.concluded.in.their.irst.principles.study.that.small.Pt
n
.clusters.have.pla-
nar. geometries. and. that. a. structural. transition. to. nonplanar. geometries. occurs. at.
n
= 10..Similarly,.Huda.et.al..[90].predicted.that.SO.coupling.leads.to.planar.struc-
tures.of.small.Pt.clusters.
10.3.1 c
omPutational
d
etailS
We. used. [91]. the. NWChem. 5.0. program. package. [67]. to. perform. geometry. opti-
mizations. and. total. energy. calculations. using. DFT.. The. CRENBL. [92]. basis. set,.
ECPs,.and.the.spin.orbit.(SO).operator.for.Pt.were.employed.where.the.outermost.
18. electrons. of. the. free. Pt. atom. (5s
2
5p
6
5d
9
6s
1
). are. treated. as. valence. electrons..
The. generalized. gradient. approximation. exchange. functional. of. Becke. [93]. and.
the. Lee-Yang-Parr. correlation. functional. [70]. (B3LYP). was. chosen. as. the. hybrid.
xc. functional.. In. our. calculations. with. SO. operator,. the. chosen. hybrid. functional.
produced.better.results.for.small.Pt.clusters.than.the.GGA.functional..The.default.
convergence.criteria.1.μE
h
.for.energy.and.0.5.mE
h
/Bohr.for.geometry.optimization.
were.used..Geometries.were.optimized.without.imposing.any.symmetry.constraints..
Spin-polarized.calculations.were.performed.for.the.irst.ive.spin.multiplicities.(from.
singlet.to.nonet)..The.SO.coupling.DFT.calculations.were.performed.in.a.Kramers-
unrestricted.approach,.which.means.that.spinors.do.not.have.to.have.the.same.spinor.
energy.
10.3.2 r
eSultS
and
d
iScuSSion
10.3.2.1 Pt and Pt
2
First,. we.discuss.the.properties.of.Pt.and.Pt
2
.to.assess.the.accuracy.of.the.chosen.
B3LYP/CRENBL.method..The.ground-state.Pt.atom.was.found.in.the.triplet.state.
(5d
9
6s
1
). for. the. non-SO. coupling. case. in. agreement. with. the. experimental. results.
[94]..The.excitation.energy.of.the.singlet.(5d
10
6s
0
).state.was.calculated.as.0.510.eV.
(neglecting.SO.coupling),.which.can.be.compared.with.a.spin-averaged.experimental.
value.of.0.478.eV.[94]..By.including.SO.effects,.the.excitation.energy.of.the.closed-
shell.coniguration.is.0.881.eV.compared.with.an.experimental.value.of.0.761.eV.[94]..
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