Aqueous Solutions of Metal Ions - Metallic Systems: A Quantum Chemist's Perspective - page 113

molecules. is. used. in. all. simulations. studies. to. facilitate. meaningful. comparison.
of. the. results). with. periodic. boundary. conditions.. In. each. of. these. simulations,.
the. water. density. corresponds. to. 1.g. cm −3 .. We. used. the. White. and. Bird. param-
eterization.(PBE96).of.the.Perdew-Burke-Ernzerhof.functional.that.has.proved.to.
be. eficient. in. describing. metal-water. interactions. and. Hamann. pseudopotentials.
[65,66]..The.electronic.wave.functions.were.expanded.in.a.plane.wave.basis.set.with.
a.kinetic.energy.cutoff.of.140.Ry..A.time.step.of.0.1.fs.was.used.and.the.electronic.
mass.was.set.to.750.au..A.homogeneous.background.charge.was.applied.to.compen-
sate.the.ionic.charge..The.simulations.were.performed.at.300.K.and.at.a.pressure.
of.0.1.MPa.using.the.Nose-Hoover.thermostat.for.40.ps;.statistics.were.collected.for.
the.last.30.ps..Long-range.interactions.were.treated.with.the.Ewald.mesh.method..
The.tunneling.and.zero-point.motion.should.not.affect.the.qualitative.nature.of.the.
coordinates.as.discussed.previously.by.Geissler.et.al..and.by.Marx.and.coworkers.
[24,41].
The. timescale. on. which. water. autoionization. or. dissociation. occurs. greatly.
exceeds. the. capabilities. of. state-of-the-art. computers. and. algorithms.. Thus,. to.
observe. the. dissociation. of. water. using. CPMD,. a. sampling. method. that. is. able. to.
locate.and.focus.on.rare.events.is.needed..TPS.is.capable.of.precisely.this.type.of.
sampling,.and.we.discuss.some.of.the.features.of.this.method..TPS.calculations.can.
be.applied.without.prior.knowledge.of.the.dissociation.mechanism,.as.demonstrated.
by. Chandler. and. coworkers. and. the. present. authors. [79-88].. CPMD. simulations.
were.used.to.generate.trajectories..Attention.was.restricted.to.trajectories.on.a.200.fs.
timescale.. We. took. the. neutral. and. charged. states. of. water. as. two. stable. states. as.
required. by. the. TPS. algorithm.. TPS. focuses. on. the. transition. between. these. two.
states.in.which.the.system.jumps.from.one.state.to.the.other.by.some.pathway..Given.
the.large.number.of.degrees.of.freedom.in.a.solvated.system.like.we.consider.here,.
many.pathways.that.join.the.two.stable.states.are.possible..After.assigning.a.prob-
ability.to.each.of.the.transition.pathways,.a.Monte.Carlo.method.is.used.along.the.
path. to. generate. an. ensemble. of. all. transition. paths.. All. structural. and. thermody-
namic. properties. can. be. calculated. from. these. ensembles,. such. as. the. Gibbs. free.
energy. and. rates. of. chemical. reactions. [80].. It. is. also. possible. to. extract. reaction.
mechanisms. from. these. calculations.. The. TPS. method. is. detailed.and. specialized.
and.the.interested.reader.is.encouraged.to.refer.to.the.literature.for.additional.details.
of.its.implementation.and.application.[65,66,80].
In. our. studies,. the. initial. state. is. deined. as. the. neutral. state. of. water. and. the.
product.is.deined.as.water.ions.coordinate.to.a.metal.ion..Thus,.pathways.involving.
a.transition.from.neutral.water.to.separated.water.ions.are.accepted.during.the.course.
of.the.simulation..Details.can.be.found.in.Ref..[80]..In.this.study,.60.trial.pathways.
per.time.step.were.used.for.each.metal.ion.solution.[65].
Structural.studies.of.hydrated.metal.ions.in.water.and.of.aqua.ions.(Zundel.and.
Eigen.complexes).are.performed.via.bond.distance.and.bond.angle.calculations.using.
trajectories.obtained.from.CPMD.simulations.coupled.with.TPS.calculations..Radial.
distribution.functions.of.metal-water.oxygen.and.metal-water.hydrogen.were.calcu-
lated. using. trajectories. obtained. from. our. simulations.. The. coordination. numbers.
(CNs).of.water.molecules.in.the.irst.and.second.hydration.shells.are.calculated.as.
integrals.over.correlation.functions.using.[89,90]