Bonding in cluster compounds Polyhedral skeletal electron pair theory

molecular-orbital (mo) diagram of b2h6. atoms , corresponding orbitals colored same. green mos symbolize bonding, while red symbolize anti-bonding.



the bonding in diborane best described treating each b sp-hybridized. 2 sp-hybrid orbitals on each boron form bonds terminal hydrogens. remaining sp-orbitals create bonds bridging hydrogens. because angles in diborane structure not tetrahedral orbitals contain sp character.



closo-b

6h2−

6


mo diagram of b

6h2−

6 showing orbitals responsible forming cluster. pictorial representations of orbitals shown; mo sets of t , e symmetry each have 2 or 1 additional pictorial representation, respectively, not shown here.



the boron atoms lie on each vertex of octahedron , sp hybridized. 1 sp-hybrid radiates away structure forming bond hydrogen atom. other sp-hybrid radiates center of structure forming large bonding molecular orbital @ center of cluster. remaining 2 unhybridized orbitals lie along tangent of sphere structure creating more bonding , antibonding orbitals between boron vertices. orbital diagram breaks down follows:




the 18 framework molecular orbitals, (mos), derived 18 boron atomic orbitals are:

1 bonding mo @ center of cluster , 5 antibonding mos 6 sp-radial hybrid orbitals
6 bonding mos , 6 antibonding mos 12 tangential p-orbitals.




the total skeletal bonding orbitals therefore 7, i.e. n + 1.



main group atom clusters
the bonding in other main group cluster compounds follow similar rules described boron cluster bonding. atoms @ vertex hybridize in way allows lowest energy structure form.


the 18 framework molecular orbitals, (mos), derived 18 boron atomic orbitals are:

1 bonding mo @ center of cluster , 5 antibonding mos 6 sp-radial hybrid orbitals
6 bonding mos , 6 antibonding mos 12 tangential p-orbitals.


the total skeletal bonding orbitals therefore 7, i.e. n + 1.

transition metal clusters

transition metal clusters use d orbitals bonding have 9 bonding orbitals, instead of 4 present in boron , main group clusters. there more bonding flexibility in transition metal clusters depending on whether vertex metal electron pairs involved in cluster bonding or appear lone pairs. cluster chlorides , carbonyls of transition metals briefly discussed here represent opposite ends of spectrochemical series , show important features of differences between transition metal clusters different ligands. in chloride clusters energy splitting of valence d orbitals increases upon formation of cluster. number , symmetry of these orbitals dependent upon type , structure of each individual cluster complex. conversely in carbonyl clusters energy splitting of valence d orbitals greater before formation of cluster.

mo diagram clusters metal chlorides , metal carbonyls