StructureofCarboranes1,5-C,B3H,1,2-C,B4He1,6-C,B4H2,4-C,B,H3 isomers of C,B1oH2 (with hydrogen omitted)Note:Herein the topological atom-atom linkage does not meanthepresence of a 2c-2e o-bond! (3D aromaticity!)
Structure of Carboranes 1,5-C2B3H5 1,2-C2B4H6 1,6-C2B4H6 2,4-C2B5H7 3 isomers of C2B10H12 (with hydrogen omitted) Note: Herein the topological atom-atom linkage does not mean the presence of a 2c-2e s-bond! (3D aromaticity!)
Tang's ruleFora closo-borane/carborane with a n-vertice triangularpolyhedral structure, its total bonding MOs amount to BMo =4n - F, with F = f + 3(s+1)(fisthenumberoffacesinthepolyhedron,sisthenumberofdefected vertices.For a closo-structure, s=O)e.g., for octahedral B.H.2-, F=8 + 3 =11, BMO = 4x6-11=13(6 B-H bonds, 7 skeletal bonding MOs.)This rulealso works for nido-and arachno-boranes bysupposingthe number of defected verticesbeing1and2,respectively.e.g. nido-CsHg, f = 8, s = -1, F = 8, BMO = 4x5-8 = 125 B-H bonds, 7 skeletal BMOs (i.e., 4 BHB 3c2e bonds, 3BBB 3c2e bonds)
Tang’s rule • For a closo-borane/carborane with a n-vertice triangular polyhedral structure, its total bonding MOs amount to BMO = 4n – F, with F = f + 3(s+1). (f is the number of faces in the polyhedron, s is the number of defected vertices. For a closo-structure, s=0). e.g., for octahedral B6H6 2- , F=8 + 3 =11, BMO = 4x6-11=13. (6 B-H bonds, 7 skeletal bonding MOs.) • This rule also works for nido- and arachno-boranes by supposing the number of defected vertices being 1 and 2, respectively. e.g. nido-C5H9 , f = 8, s = -1, F = 8, BMO = 4x5-8 = 12 5 B-H bonds, 7 skeletal BMOs ( i.e., 4 BHB 3c2e bonds, 3 BBB 3c2e bonds)
"Nido" series - formula B,H(n+4)BMO = 4n- F.Total valence electrons(VEC) = 3n (B) +F = f +3(s+1).n(H) + 4 (extra H) = 4n + 4Numberofskeletalelectrons·Frameworkelectrons(NFE)=2n+4to make the structure stable:(i.e.,n+2 pairs)2n+2 wheren=theClosonumberof surface.The structure of the“nido”compound isatoms present in thebased onthe"closo”polyhedronwithonecluster,i.e.n=Nmore vertexthan the“nido"compoundmissing surfaceatomoncluster2n+4NowN=n+(sothe number of elec-NidoArachno" series -formula B.H(n+6)trons =2n'+2 wheren'=n+l)·Total valenceelectrons(VEC)=4n+6Frameworkelectrons(NFE)=2n+6(i.e., n+3 pairs)Arachno2n+6NowN=n+2(sothenumberofelec-.The structure of the“nido”compound istronsis still 2n"+2based onthe"closo”polyhedronwithtwowhweren=n+2)more verticesthan the“nido”compoundElectron-deficientmulti-centerbonds
“Nido” series – formula BnH(n+4) •Total valence electrons(VEC) = 3n (B) + n(H) + 4 (extra H) = 4n + 4 •Framework electrons (NFE) = 2n + 4 (i.e., n+2 pairs). •The structure of the “nido” compound is based on the “closo” polyhedron with one more vertex than the “nido” compound. “Arachno” series – formula BnH(n+6) •Total valence electrons(VEC) = 4n + 6 •Framework electrons (NFE) = 2n + 6 (i.e., n+3 pairs). •The structure of the “nido” compound is based on the “closo” polyhedron with two more vertices than the “nido” compound. Electron-deficient multi-center bonds BMO = 4n – F F = f +3(s+1)
Electron-deficientmulti-centerbonds6.1.4 otherelectron-deficientcompoundsBorongroupB、Al、Ga、In、TIH3CCH3H3.9470°120°AlAl2..14CH3CH3CH3Gas-phase:monomerSolid state:dimerorpolymerCHCHACHOH
6.1.4 other electron-deficient compounds Electron-deficient multi-center bonds 120º 70º B、Al、Ga、In、Tl Gas-phase: monomer Solid state: dimer or polymer Boron group H3C Al H3C Al C CH3 H3 CH3 CH3
Alkalimetalandalkaliearthmetalalkylides[Li(CH3)]4FHilll.-BeBHBeB2H:CH,R(Li-Li)= 2.68 AR(Li-CH,) = 2.31 ABe(CH3) 2H313BeBeBe-BeBeBeBeBeBeH3C-CH3CH3H3C-H3HH--polymerdimertrimerMulticenter bond can also exist intransition-metal cluster compounds!
Alkali metal and alkali earth metal alkylides Li CH3 polymer [Li(CH3 )]4 Be(CH3 ) 2 dimer trimer Be H3 C C H3 Be C H3 H3 C Be H3 C C H3 Be Be H3 C H3C C H3 Be C H3 H3 C Be CH3 Be H3 C H3C C H3 Be CH3 BeB2H8 R(Li-Li) = 2.68 Å R(Li-CH3 ) = 2.31 Å Multicenter bond can also exist in transition-metal cluster compounds!