Chemistry Reference
In-Depth Information
those.obtained.for.λ.=.1.→.λ.=.0..We.also.compared.the.PMF.results.obtained.from.
500,.600,.and.700.ps.simulations.for.each.window..The.PMF.results.do.not.deviate.
from. each. other. using. CMD. simulations,. indicating. that. the. systems. were. equili-
brated.with.CPMD.as.well.as.with.CMD.simulations.
The.perturbation.method.was.employed.and.the.Gibbs.free.energy.change.(Δ
G
).
between.states.
i
.and.
i
.+.1.with.the.corresponding.Hamiltonians.
H
i
.and.
H
i
+1
.were.cal-
culated.using.Equation.3.2.[46-48]:
(
)
= −
Δ
G
λ
+
−
λ
kT
ln exp
⎣
−
(
H
−
H kT
)/
⎦
.
(3.2)
i
1
i
λ
λ
i
+
1
i
.
λ
i
where
λ.is.a.continuous.coupling.parameter.that.represents.the.initial.(λ.=.0).and.inal.
(λ.=.1).states
k
.is.the.Boltzmann.constant
T
.is.the.temperature
Perturbations. were. broken. into. 20. windows. with. a. Δλ. value. of. 0.05.. Gibbs. free.
energy.values.were.compared.to.those.calculated.using.the.PMF.method.
3.3 CHEMICAL REACTIVITY CALCULATIONS
In.order.to.predict.the.reactive.sites.of.M.with.respect.to.binding.a.Fe
3+
.ion.in.the.gas.
phase.and.in.aqueous.solution,.we.performed.chemical.reactivity.analysis.of.these.
systems.based.on.Fukui.reactivity.indices.[49]..The.Fukui.functions.(FF),.
f
(
˙
),.pro-
vide.a.robust.and.eficient.way.to.capture.the.physics.governing.chemical.reactivity..
Within.the.DFT.formalism,.FF.can.be.described.via.Equation.3.3.[49]:
=
⎢
δμ
δυ
⎥
⎥
f r
( )
.
(3.3)
⎢
( )
r
.
N
where
μ.is.the.chemical.potential
υ(
˙
).is.the.external.potential
and.the.derivative.is.taken.at.a.ixed.total.number.of.electrons,.
N
..Applying.Maxwell's.
relations.and.assuming.that.the.total.energy.of.a.molecular.system.is.a.function.of.
N
,.
Equation.3.3.becomes.[50,51]
⎢
⎢
∂
∂
ρ
r
N
( )
⎥
⎥
f r
( )
=
.
(3.4)
.
υ
where.ρ(
˙
).is.the.electron.density..Within.the.frozen.orbital.approximation,.the.FF.
becomes.equal.to.the.Kohn-Sham.frontier.orbital.density,.and.the.following.func-
tions.can.be.deined.as.[50,51]
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