Transcript Slide 1

Lecture 19
Electron count in cluster compounds
1) Electron count in boron cages. Wade’s and Mingos’s rules
•
The cluster electron count in closo-polyboranes: BnHn (n = 5, … 12) have n+1 cluster
bonding MO’s. As a result, the most stable electron configuration of these species is 2n+2
cluster electrons (1st Wade’s rule). Therefore, the closo-BnHn which has only 2n cluster
electrons is expected to add 2 e’s to form stable dianion closo-BnHn2-.
•
The total electron count in closo-polyboranes: each BH fragment contributes 3+1 = 4
electrons into the total electron count of BnHn. Therefore, BnHn itself has 4n electrons in
total. The number of the bonding MO’s in it is n (BH bonds) + n+1 (cluster bonding MO’s) =
2n+1. Thus, to be stable the closo-BnHn should have the total electron count of 4n+2
(Mingos’s rule), which corresponds to dianionic closo-BnHn2-.
H
B6
B5
B
22 e
z
B7
26 e
trigonal bipyramid
B9
B8
30 e
34 e
38 e
B12
42 e
dodecahedron
the total electron count for dianionic BnHn2-
50 e
icosahedron
tricapped trigonal prism
pentagonal bipyramid
octahedron
B10
dicapped square antiprism
2) Electron count in boron cages. Wade’s and Mingos’s rules
•
In the case of nido-polyboranes BmHm one vertex of the parent closo-BnHn is missing,
m=n-1, but the number of the bonding core orbitals is m+2, the same as in the parent
closo-BnHn (2nd Wade’s rule).
B5
B4
20e
B6
24e
B7
28e
B11
B9
32e
40 e
48e
the total electron count for anions BmHm4- is given
•
nido-Polyboranes form stable tetraanions, BmHm4- and neutral BmH(m+4) with the total
electron count of 4m+4 (2nd Mingos’s’ rule).
•
arachno-Polyboranes BmHm with two vertices of the parent closo-BnHn missing, m=n-2,
also have the same number of the cluster bonding MO’s, m+3, (3rd Wade’s rule) and
form stable anions BmHm6- with the total electron count of 4m+6 (3rd Mingos’s rule).
B4
B5
B6
B10
3) Electron count in heteronuclear boron-based cages
•
•
Using analogy with boron cages, it turned out to be possible to rationalize
composition and shape of heteronuclear boron cages and some nontransition element clusters.
Consider first some carboranes, where BH is substituted by CH. Each C
contributes into the cage MO’s the same number of AO’s and one electron
more than B. As a result, the charge of the related anion decreases by the
number of CH groups present.
H
B
B
B
H
H
H
B
B
HC
H
H
B
H
H
nido-[B 9C2H11]2-
H
H
C
B
H
closo-B5C2H7
closo-B3C2H5
B
C
C
CH
H
C
H
B
H
C
22 e
30 e
48 e
4n+2
4n+2
4n+4
the total electron count is given
2-
4) Electron count in main group element clusters
•
So-called Zintl phases produced by reduction of Si, Ge, Sn or Pb with alkali metals
contain cluster anions Si94-, Ge92-, Ge94-, Sn52-, Sn86-, Sn94-, Pb52-, Pb94-. Wade’s rule
allows to rationalize their structure.
•
Compare BH fragment which contributes 2 electrons into cage MO’s and Si, Ge, Sn
or Pb which also contribute 2 electrons in it with 2 electrons remaining in their shell as
a lone pair.
closo-Sn52-
22 e
4n+2
trigonal bipyramid
closo-Ge92-
nido-Ge94-
38 e
40 e
4n+2
tricapped trigonal prism
4n+4
monocapped tetragonal
antiprism
the total electron count is given
arachno-Sn86-
38 e
4n+6