Chemistry Reference
In-Depth Information
Table 1 Descriptors defined within conceptual DFT as energy derivatives
Symbol
Descriptor
Energy derivative
m
Chemical potential
@E
@
N
v
r
ðÞ
w
Electronegativity
@
E
@
N
v ðÞ
r
(
r
)
Electron density
dE
dv
ðÞ
N
w
(
r
,
r
0
)
Linear response function
d
2
E
dv ðÞdv r ðÞ
dr
ðÞ
dv ðÞ
N
¼
N
v ðÞ
¼
Chemical hardness
@
2
E
@m
@
@
N
2
N
v ðÞ
S
Chemical softness
1
¼
@
N
@m
v
r
ðÞ
f
(
r
)
Fukui function
d@
E
@r ðÞ
@
¼
dv
ðÞ@
N
N
v ðÞ
potential with respect to a perturbation in the external potential. One distinguishes
between left- and right-hand derivatives of the electron density with respect to
N
:
þ
@
r
ðÞ
@
f
þ
¼
r
Nþ
1
ðÞr
N
ðÞ
(60)
N
v
r
ðÞ
@
r
ðÞ
@
f
¼
r
N
ðÞr
N
1
ðÞ;
(61)
N
v
r
ðÞ
where
f
+
describes a nucleophilic and
f
an electrophilic attack. Both can be appro-
ximated by a finite differences formula, expressing them as differences of the
electron density of the system in the initial state and after the addition or subtraction
of an electron (at the geometry of the neutral system). Other approaches for the
calculation of the Fukui function can be found in [
133
,
134
].
Because the chemical reactivity descriptors (especially the Fukui function)
are useful tools in the analysis of chemical reactions also for those mediated by
heavy metal containing catalysts [
135
], it is important to investigate the influence
of relativistic effects on them. For the Fukui function, i.e., for the reactivity
toward nucleophilic and electrophilic attacks, such a study was carried out by De,
Krishnamurty, and Pal [
136
], who investigated two gold clusters (Au
19
and Au
20
),
focusing on relativistic effects on vibrational frequencies and on the Fukui function.
The authors used effective core potentials (ECPs) to replace the core electrons of the
gold atoms in both the relativistic and the nonrelativistic calculations. They find that
the incorporation of relativistic effects results in minor changes of the Fukui function.
