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( )
2
.
(3.5)
υ
υ
f
=
φ
r
.
where
υ.is.HOMO.or.LUMO
ϕ
υ
(
˙
).is.the.corresponding.Kohn-Sham.frontier.molecular.orbital
If.υ.=.HOMO,.Equation.3.5.quantiies.the.susceptibility.of.the.carbohydrate.toward.
electrophilic.attack..If.υ.=.LUMO,.Equation.3.5.quantiies.the.susceptibility.of.the.
carbohydrate. toward. nucleophilic. attack.. A. measure. of. the. susceptibility. toward.
radical.attacks.is.given.by
(
)
HOMO
LUMO
f
( )
r
+
f
( )
r
.
(3.6)
rad
f
( )
r
=
2
.
A.method.enabling.the.calculation.of.these.indices.based.on.condensing.the.FF.to.a.
particular.atom.
i
.in.the.molecule.was.developed.by.Contreras.et.al..According.to.this.
method,.the.condensed.FF.at.atom.
i
.can.be.calculated.using.[52]
⎡
⎤
AO
AO
∑
∑
2
.
(3.7)
υ
⎢
⎢
⎥
⎥
f
=
c
+
c
c S
i
μυ
μυ
κυ κμ
⎣
⎦
μ
∈
i
κ μ
≠
.
where
c
μυ
.is.the.molecular.orbital.coeficient
AO.is.the.set.of.atomic.orbitals
S
κμ
.is.the.atomic.orbital.overlap.matrix
υ.is.the.frontier.molecular.orbital.(HOMO.or.LUMO)
Analogous.to.Equation.3.6,.the.FF.for.calculating.the.chemical.reactivity.of.the.mol-
ecule.toward.a.radical.is.given.by
(
)
HOMO
LUMO
f
+
f
i
i
.
(3.8)
rad
f
=
i
2
.
Given.that.
f
i
HOMO
.provides.a.quantitative.index.for.the.susceptibility.of.atom.
i
.to.
electrophilic.attack,.we.calculated.the.FF.indices.for.the.chemical.reactions.of.M.
and.
n
Fe
3+
.(with.
n
.=.0,.1,.and.2)..The.condensed.FF.methodology.was.implemented.
in. a. subroutine. within. a. modiied. version. of. the. Gaussian. 03. package. [53].. The.
FFs.were.calculated.using.single.point.calculations.on.optimized.geometries.pre-
viously. obtained. from. our. CPMD. simulations. with. the. gradient-corrected. DFT.
PBE.exchange-correlation.functional.using.the.6-31G**.basis.(B3LYP/6_31G**//
CPMD).
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