qðXÞ ¼ Z X À NðXÞ with NðXÞ ¼
Z
X
qðXÞdr
ð10:1Þ
In Fig. 10.2a, the charge density of the Ag and V centers of the [AgO 6 ] 1 ,
[AgO 6 ] 2 , and [VO 4 ] clusters is depicted as a function of the number of electrons
added to α-AgVO 3 . The average bond distances of Ag–Ag as a function of the
number of electrons added are presented in Fig. 10.2b. An analysis of the results
presented in Fig. 10.2 shows that the Ag atoms of the [AgO 6 ] clusters are more
prone to be reduced than V atoms (that form [VO 4 ] clusters), since the Ag coordination changes to 4 at N = 2 and to 2 at N = 3 and 4. Above N = 2, charge density
differences between [AgO 6 ] 1 and [AgO 6 ] 2 start to be sensed, being Ag3/Ag4 more
prone to be reduced than Ag1/Ag2 (by 0.12 units). This result is related to the major
Ag–O distance obtained for the completely reduced Ag3/Ag4 (2.548 Å) compared
to the Ag1/Ag2 (2.333 Å) for N = 4 (see Table 10.1). In addition, Ag1–Ag3
(a)
(b)
Fig. 10.2 a Charge density
of the Ag and V centers in
[AgO 6 ] 1 , [AgO 6 ] 2 , and [VO 4 ]
clusters, b average Ag–Ag
distances, as a function of the
number of electrons added for
α-AgVO 3
10 Quantum Chemical Topology Approach …
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