Aqueous Solutions of Metal Ions - Metallic Systems: A Quantum Chemist's Perspective - page 115

agreement.with.the.recent.studies.of.Swaddle.et.al.,.a.hexa-coordinate.AlOH 2+ .ion.is.
formed.via.the.removal.of.a.single.proton.from.the.Al(H 2 O) 3+ .structure.in.water.[76]..
The. penta-coordinate. Al(H 2 O) 4 OH 2+ . complex. was. obtained. from. the. hexa-coordi-
nate.Al(H 2 O) 5 OH 2+ .structure.during.the.course.of.our.simulation.(see.Section.4.3.for.
details).. In. order. to. study. the. polymerization. reaction. mechanism. of. two. Al 3+ . ions.
in.water.in.detail,.we.performed.separate.CPMD.simulations.of.two.Al(OH)(H 2 O) 2+ .
species.with.118.water.molecules.for.60.ps.with.initial.trigonal.bipyramidal.Al(OH)
(H 2 O) 2+ .structures.obtained.from.our.CPMD.simulations.(see.Section.4.3.for.details)..
To.study.the.thermodynamic.preference.of.Al 3+ .polymerization.in.water,.the.perturba-
tion.method.was.used.with.CPMD.simulations.utilizing.Equation.4.2..For.determin-
ing.the.free.energy.difference.in.the.formation.of.Al 2 .species.via.the.distance.between.
the.metal.centers.of.two.Al(OH)(H 2 O) 2+ .ions.in.water.using.the.perturbation.method,.
the.perturbations.were.broken.into.a.series.of.intermediates.with.a. Δλ .value.of.0.05.
Ab.initio.calculations.on.geometries.extracted.from.trajectories.obtained.from.our.
CPMD.simulations.were.performed.using.the.GAMESS.program.utilizing.COSMO..
The.irst.phase.of.our.studies.focused.on.the.calculations.of.the.hydrated.Al 3+ .ion.in.
the.gas.phase.and.we.computed.the.gas.phase.enthalpy.of.formation,.Δ E f , .from.the.
chemical.reaction.[1]

3+ ) +

Al + 6 H O → Al (H O

.

2 2 6

The. results. obtained. using. various. irst. principles. methods. utilizing. the. cc-pVTZ.
basis.set.are.given.in.Table.4.1.
Calculations.of.the.gas.phase.enthalpy.were.made.using

) .

(4.3)

Δ H = Δ E + Δ E + T c Δ + ( Δ RT

f ZPE v

.

where
Δ E ZPE is.the.zero.point.energy
T Δ c v .is.the.heat.capacity.contribution
Δ( RT ).is.the.work.term

TABLE 4.1
Thermodynamic Properties of Al(H 2 O) 3+ Ion
in the Gas Phase and in Aqueous Solution
Using a Continuum Model for Water via
Employing the PBE Method with the cc-pVTZ
Basis Set

Property (kJ mol −1 ) Gas Phase Aqueous Solution

Δ E o .=.Δ E f .+.Δ E ZPE −2861.7 −4639.7

Δ E 298.15 −2886.8 −4655.2

Δ H −2903.5 −4671.8

ZPE .denotes.zero.point.energy.