A brief summary on the electronic structures ofmolecules wehavelearnt(MO & VB)2) Ifm>n,VB: (m-n) lone pairs & (2n-m)/2 2c-2e bonds:MO: (m-n) nonbonding MOs & (2n-m)/2 bonding MOsThen if necessary can electron delocalization be consideredH,O: 4 VAOs(O) + 2 1s(H) + 8VE →> VB: 2 LPs & 2 -bonds MO:2 nonbonding,2 o-bondingMOs (occupied)&2 antibondingMOs (unoccupied!)3)If m < n, ? (to be learnt in this chapter)
2) If m > n, VB: (m-n) lone pairs & (2n-m)/2 2c-2e bonds; MO: (m-n) nonbonding MOs & (2n-m)/2 bonding MOs. A brief summary on the electronic structures of molecules we have learnt (MO & VB) 3) If m < n, ? (to be learnt in this chapter). H2O: 4 VAOs(O) + 2 1s(H) + 8VE VB: 2 LPs & 2 s-bonds. MO: 2 nonbonding, 2 s-bonding MOs (occupied) & 2 antibonding MOs (unoccupied!) Then if necessary can electron delocalization be considered
6.1Multi-centerbondsinelectron-deficientsystems6.1.1Boranes andtheirrelativesi.B2H6HHBRVAO = 4 (B) x2 + 1(H) x6 = 14HHVE = 3 (B) x2 + 1(H) x6 =12·Anethane-likestructurehaving72c-2ebondsneeds14VEsLack of two VEs!:To make full use of all VAOs,two three-center two-electron(3c-2e) B-H-B bonds are formedH*131pmHO1/2+1/2+1/21/21/21/2HBBRBRBHResonancestructuresof3c-2ebondHin diborane (VB description)83119pm
B H H H B H H H i. B2H6 • An ethane-like structure having 7 2c-2e bonds needs 14 VEs. VAO = 4 (B) x2 + 1(H) x6 = 14 6.1.1 Boranes and their relatives 6.1 Multi-center bonds in electrondeficient systems VE = 3 (B) x2 + 1(H) x6 = 12 Lack of two VEs! • To make full use of all VAOs, two three-center two-electron (3c-2e) B-H-B bonds are formed. Resonance structures of 3c-2e bond in diborane (VB description)
three-center two-electron B-H-B bond:i.BH6B: sp3hybridization,H : ls orbitalLocalized MO descriptionHy=CaVBI +CVH +CaB2BBits HMO secular equation is :0βE -EBHHββ=0E -EHH0βE-EE, = E +cβ(bonding )For a B atom: sp3-hybridizationE, =Eb(E, >E.)(non - bonding 2VEsusedby2terminalB-E, =Ep-c'β(anti - bondingH bonds(VB +2H +B2)y,21OneVE&HOis usedtoform(B1 -B2)2J2a B-H-Bbond witha H 1sand a HO of another B atom!(VB1 - ~2H +B2)
i. B2H6 ( 2 ) 2 1 ( ) 2 1 ( 2 ) 2 1 ' (anti - bonding ) ( ) (non - bonding ) (bonding ) 3 1 2 2 1 2 1 1 2 3 2 2 1 B H B B B B H B B B H H E E c E E E E E E c For a B atom: sp3 -hybridization 0 0 E - E E - E E - E 0 its HMO secular equation is : 1 B H B 1 2 3 Ca B Cb H Ca B B sp hybridization H s orbital three-center two-electron B-H-B bond: Localized MO description : , : • 2 VEs used by 2 terminal BH bonds • One VE&HO is used to form a B-H-B bond with a H 1s and a HO of another B atom!
B,He:canonical valence molecular orbitalsMO-NICS(O)2B(2p)+4H(1s)tV+15.0 (+5.3) [+7.1]b1g科2a+0.2 (+1.4) [+1.5]Mainly2B(2p)b2u9.5 (-1.9) [-2.1]+ minor 2Hs(1s)4+minor 4H(1s)6.4 (+4.4) [+1.6]E-5.3 (-3.2)[4.3]03uDSkeletal MOs:lablugNICS(0)tot = -26.0 (-9.9) [-15.3]2)Termial B-HMOs1ag-tl18.4 (-14.7) [-14.9]b3u, b2u, 2ag, bigMainly 2B(2s)2B(2p,) + 2Hs(1s)2B(2s)+2Hb(1s)+minor 4H(1s)Note: The CMOs can be transformed into LMOs, two of which arethe 3c2e LMOs!
B2H6：canonical valence molecular orbitals 2B(2s)+2HB (1s) 2B(2pz ) + 2HB (1s) Mainly 2B(2py ) + minor 2HB (1s) +minor 4H(1s) 2B(2px )+4H(1s) Mainly 2B(2s) +minor 4H (1s) 1) Skeletal MOs: 1ag , b1u 2) Termial B-H MOs: b3u, b2u, 2ag , b1g Note: The CMOs can be transformed into LMOs, two of which are the 3c2e LMOs!
Three-centertwo-electron(3c-2e)B-H-Bbond:UVBIWB2Y2YH11yy· B,He, actually having 14 VAOsRand 12 VEs, has to form two 3c-2eBHBbondstoinvolveallVAOsHinto bonding MOs
B1 B2 H 1 2 3 B H H H H H H B Three-center two-electron (3c-2e) B-H-B bond: • B2H6 , actually having 14 VAOs and 12 VEs, has to form two 3c-2e BHB bonds to involve all VAOs into bonding MOs