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-BnHn

2-.

• 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-BnHn

2-.

B

H

z

B5 B6 B7 B8 B12

22 e 26 e 30 e 34 e 50 e

the total electron count for dianionic BnHn2-

42 e

B10

trigonal bipyramid

octahedron

pentagonal bipyramid

dodecahedron dicapped square antiprism

icosahedron

38 e

tricapped trigonal prism

B9

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).

• 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 BmHm

6- with the total electron count of 4m+6 (3rd Mingos’s rule).

B4 B5 B6 B10

B4 B5 B6 B7 B11

20e 24e 28e 32e 48e

the total electron count for anions BmHm4- is given

40 e

B9

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 non-transition 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.

B

H

C

H

BH CC

B

BBB

B

HC

CH

HC BCH

B

H

H

H

H

H

H

H

HH

22 e 30 e 48 e

the total electron count is given

2-

closo-B3C2H5 closo-B5C2H7 nido-[B9C2H11]2-

4n+2 4n+2 4n+4

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-, Ge9

2-, Ge94-, Sn5

2-, Sn86-, Sn9

4-, Pb52-, Pb9

4-. 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

the total electron count is given

38 e

closo-Ge92-

nido-Ge94-

40 e

trigonal bipyramid tricapped trigonal prism monocapped tetragonal antiprism

4n+2 4n+2 4n+4

arachno-Sn86-

38 e

4n+6