Density Functional Theory Calculations on Cobalt and Platinum Transition Metal Clusters - Metallic Systems: A Quantum Chemist's Perspective - page 357

TABLE 10.4
Relative Stability of Pt 4 Isomers Predicted Utilizing Non-SO and
SO DFT Calculations

Non-SO SO

Spin
Moment (μ B )

Spin
Moment (μ B )

Isomer Structure Δ E (eV) Δ E (eV)

(4-1) Tetrahedron 2 0.000 1.84 0.026

4 0.109 a 3.64 0.000

6 1.110 3.64

8 2.239 3.64

(4-2) Rhombus 0 0.576 2.08 0.133

2 0.471 2.11

4 0.206 2.10

6 0.945 2.09

(4-3) Square 0 0.232 0.00 0.357

2 0.321 1.77 0.493

(4-4) Y-like 0 1.410 0.54 0.410

2 0.892 1.50 0.458

4 0.551 3.51 0.354

6 1.134 3.47 0.337

Source: . Reprinted.from. Phys. Chem. Chem. Phys .,.354,.Sebetci,.A.,.Does.spin.orbit.cou-
pling. effects. favour. planar. structures. for. small. platinum. clusters,. 921-925,.
Copyright.(2009)..With.permission.from.The.Royal.Chemical.Society.
a. Saddle.point.

account,.tetramers.with.quintet,.septet,.and.nonet.initial.spin.multiplicity.converge.
to.the.same.spin.moment.of.3.64.μ B .and.this.state.is.26.meV.lower.in.energy.than.the.
state.with.a.1.84.μ B .spin.moment..The.point.group.symmetry.of.the.optimized.struc-
ture.in.this.case.is. D 2d ..Our.prediction.of.a.tetrahedron.as.the.ground-state.geometry.
differs.from.those.reported.in.the.literature.[89,90,106]..A.common.feature.of.these.
studies.is.that.they.employ.plane.wave.codes.(Refs..[89,90].employ.the.PAW.method.
of.the.code.VASP.and.Refs..[106,107].employ.the.code.CPMD.[108])..These.studies.
predict.that.the.rhombus.isomer.is.the.lowest.energy.structure.with.a.spin.multiplic-
ity.of.5..However,.Futschek.et.al..[87].obtained.a.distorted.tetrahedron.similar.to.our.
results.using.VASP.so.the.source.of.the.discrepancy.is.not.clear..According.to.the.
present.calculations.on.the.non-SO.case,.the.quintet.state.is.the.ground.magnetic.state.
of.the.rhombus,.but.its.total.energy.is.0.206.eV.higher.than.that.of.the.tetrahedron..
For.the.SO.case,.the.rhombus.whose.singlet,.triplet,.quintet,.and.septet.initial.spin.
multiplicities. converge. to. a. spin. moment. between. 2.08. and. 2.11.μ B . has. an. energy.
of. 0.133.eV. higher. than. the. tetrahedron.. The. optimized. structures. of. the. rhombus.
in.both.non-SO.and.SO.cases.have. C 2v .symmetry..As.in.the.case.of.the.dimer,.SO.
effects. slightly. stretch. the. bond. lengths.. Both. of. these. structures. are. out. of. plane.
where. the. angles. between. the. triangular. planes. are. 113°. (non-SO). and. 105°. (SO)..