S6Structuresofpolyatomicmolecules(ll)Introduction:In chapter 5, we focused on the (localized and delocalized) -and π-bonds within polyatomic molecules in terms of hybridorbital theory (VB) and MO theory as well as the symmetry rulesfor chemical reactions ofpolyatomicmoleculesIn this chapter, we will discuss multi-center bonds in electron-deficient molecules (e.g., boranes and carboranes) and thechemical bonds in coordination compounds
§6 Structures of polyatomic molecules (II) Introduction: • In chapter 5, we focused on the (localized and delocalized) sand p-bonds within polyatomic molecules in terms of hybrid orbital theory (VB) and MO theory as well as the symmetry rules for chemical reactions of polyatomic molecules. • In this chapter, we will discuss multi-center bonds in electrondeficient molecules (e.g., boranes and carboranes) and the chemical bonds in coordination compounds
$6Structures ofpolyatomic molecules (ll)6.1Multi-centerbondsin electron-deficientsystems6.2 Chemical bonds in coordinationcompounds6.3Ligand Field Theory(LFT)6.4 Transition-metal cluster compounds6.5Carbonclustersand nanotubes
6.1 Multi-center bonds in electron-deficient systems 6.2 Chemical bonds in coordination compounds 6.3 Ligand Field Theory (LFT) 6.4 Transition-metal cluster compounds 6.5 Carbon clusters and nanotubes §6 Structures of polyatomic molecules (II)
Qualitative description of Chemicalbonding within a molecule: VB vs. MOVB: Valence AOs or hybridized orbitals of each atom(s)> Forming 2c-2e -/元-bonds with AOs of surrounding atoms> If necessary, resonance of VB structures are used to accountfor electron delocalization (e.g., the II.6 bond in benzene)!MO: LCAO-MO→ Formation of bonding & nonbonding MOs? Both hybridization & electron delocalization (e.g., II,b bond)are inherently taken into account.A molecule/an aggregate of atoms can have several isomers.How to quickly predict its structure/bonding pattern?
Qualitative description of Chemical bonding within a molecule: VB vs. MO • VB: Valence AOs or hybridized orbitals of each atom(s) Forming 2c-2e s-/p-bonds with AOs of surrounding atoms. If necessary, resonance of VB structures are used to account for electron delocalization (e.g., the 6 6 bond in benzene)! • MO: LCAO-MO Formation of bonding & nonbonding MOs. * Both hybridization & electron delocalization (e.g., a b bond) are inherently taken into account. A molecule/an aggregate of atoms can have several isomers. How to quickly predict its structure/bonding pattern?
Qualitative description of Chemicalbonding within a molecule: VB vs. MOA molecule/an aggregate of atoms can have several isomers.How can one quickly predict its structure/bonding pattern?Chemical bondings occur between the valence atomicorbitals (VAOs)(and valence electrons (VEs)) of theconstituent atoms within a molecule2.The more VEs and VAOs involved in chemical bondingsthe more stable is a molecule> A molecule prefers the bonding pattern/structure thatinvolves as many bonding VEs & VAOs as possible
Qualitative description of Chemical bonding within a molecule: VB vs. MO 1. Chemical bondings occur between the valence atomic orbitals (VAOs) (and valence electrons (VEs)) of the constituent atoms within a molecule. 2. The more VEs and VAOs involved in chemical bondings, the more stable is a molecule. A molecule prefers the bonding pattern/structure that involves as many bonding VEs & VAOs as possible! A molecule/an aggregate of atoms can have several isomers. How can one quickly predict its structure/bonding pattern?
A brief summary on the electronic structures ofmolecules we have learnt(MO & VB)A polyatomic molecule with a closed-shell electronicconfiguration has m(=even) VEs and n VAOsIfm=n,VB: n/2 2c-2e (α-/元-) bonds ( first);MO: n/2 bonding MOs (occupied!)& n/2 antibonding MOsThen if necessary can electron delocalization be consideredC,H2: 10 VAOs/VEs = 2x4 (C) + 2x1(H)> VB: 3 o-bonds & 2 π-bond> MO: 3 - & 2 元-bonding MOs
A polyatomic molecule with a closed-shell electronic configuration has m(=even) VEs and n VAOs. 1) If m = n, VB: n/2 2c-2e (s-/p-) bonds (s first!); MO: n/2 bonding MOs (occupied!) & n/2 antibonding MOs. A brief summary on the electronic structures of molecules we have learnt (MO & VB) C2H2 : 10 VAOs/VEs = 2x4 (C) + 2x1(H) VB: 3 s-bonds & 2 p-bond. MO: 3 s- & 2 p-bonding MOs . Then if necessary can electron delocalization be considered
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