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