Chemistry Reference
In-Depth Information
To.calculate.the.hydration.enthalpy.for.the.Al(H
2
O)
3+
.ion.and.to.compare.with.the.
available.experimental.data,.we.used.the.Born-Haber.cycle.presented.in.Equation.
4.4.[1]
∆
H
gas
Al
3+
(gas) + 6H
2
O (gas)
Al(H
2
O)
3+
(gas)
6
∆
H
vap
∆
H
solv
.
(4.4)
∆
H
hyd
Al
3+
(gas) + 6H
2
O (aq)
Al(H
2
O)
3+
(aq)
.
The.values.computed.using.this.cycle.are.presented.in.Table.4.1..The.solvation.energy.
for.water.obtained.in.these.calculations.is.−38.5.and.−37.9.kJ.mol
−1
.using.the.PBE/cc-
pVTZ.and.MP2/cc-pVTZ.methods,.respectively..These.values.are.slightly.larger.than.
the.experimental.value.(−44.1.kJ.mol
−1
),.but.are.in.better.agreement.with.the.experi-
mental.data.than.an.earlier.theoretical.study,.which.reported.values.of.−28.6.kJ.mol
−1
.
using. the. BLYP/SVP. method. and. the. PCM. (Polarizable. Continuum. Model). model.
for.water..The.experimental.hydration.enthalpy.of.−4668.3.kJ.mol
−1
.agrees.well.with.
our.calculated.value.of.−4671.8.kJ.mol
−1
..Free.energies.calculated.in.aqueous.solution.
can.be.sensitive.to.the.radius.of.the.cavity.surrounding.the.ions.embedded.in.the.con-
tinuum..We.performed.calculations.for.itting.the.van.der.Waals.radius.of.the.Al
3+
.ion.
to.the.experimental.free.energy.value.of.−4619.1.kJ.mol
−1
..In.these.calculations,.the.
van.der.Waals.radius.was.it.such.that
Δ
G
⎣
Al
3
+
⎦
=
Δ
G
⎣
Al
3
+
,
r
⎦
−
Δ
G
⎣
Al
3
+
,
r
⎦
.
(4.5)
water
gas
.
where.
r
.is.the.van.der.Waals.radius.of.the.Al
3+
.ion..The.optimized.van.der.Waals.
radius.is.1.33.Å,.in.good.agreement.with.the.studies.of.Saukkoriipi.et.al..[74]..Our.
benchmark.studies.show.that.the.PBE.method.using.the.cc-pVTZ.basis.set.with.an.
optimized.van.der.Waals.radius.of.1.33.Å.for.the.Al.ion.with.the.COSMO.method.
reproduces.the.experimental.hydration.enthalpy.(see.Equation.4.4).for.this.system.
4.3 RESULTS AND DISCUSSION
The.structures.of.hydrated.metal.ions,.mechanisms.of.water.dissociation.in.the.vicinity.
of.transition.metal.ions,.and.the.structural.and.thermodynamic.properties.of.aqua.ion.
(Zundel.and.Eigen).complexes.formed.in.the.vicinity.of.the.metal.ion.in.aqueous.solu-
tion.were.predicted.utilizing.various.CPMD.simulations.along.with.TPS.calculations.
4.3.1 S
tudieS
of
the
m
echaniSm
of
W
ater
d
iSSociation
in
a
queouS
S
olutionS
of
f
e
3+
and
c
r
3+
i
onS
The.mechanisms.of.water.dissociation.around.Cr
3+
.and.Fe
3+
.ions.obtained.from.our.
simulations.are.depicted.in.Figure.4.1..In.these.simulations,.we.observe.an.elongation.
of.the.O-H.bond.in.the.irst.hydration.shell.(Figure.4.1A)..It.is.this.event.that.initiates.
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