Chapter 5 Bonding in polyatomic molecules Polyatomic species: contains three or more atoms Three approaches to bonding in diatomic molecules 1.Lewis structures 2.Valence bond theory 3.Molecular orbital theory Directionalities of atomic orbitals are not compatible with the H-O-H bond angle. 1 Orbital hybridization - sp 1 ( ) sp _ hybrid 2 2s 2 px 1 ( ) sp _ hybrid 2 2s 2 px Hybrid orbitals – generated by mixing the characters of atomic orbitals sp hybridized valence state is a formalism and is not a ‘real’ observation 2 Orbital hybridization – sp2 1 2 sp2 _ hybrid 3 2s 3 2 p x 1 1 1 sp2_ hybrid 2s 2 p 2 p 3 6 x 2 y 1 1 1 sp2_ hybrid 3 2s 6 2 px 2 2 py Trigonal planar molecule, BH3 Each B-H interaction is formed by the overlap of one B sp2 hybrid orbital with the 1s atomic orbital of an H atom 3 sp3 hybrid orbitals – one s and three p atomic orbitals mix to form a set of four orbitals with different directional properties 1 1 sp3_ hybrid 2s 2 p 2 p 2 p sp3_ hybrid 2 2s 2 px 2 py 2 pz 2 x y z 1 1 sp3_ hybrid 2s 2 p 2 p 2 p sp3_ hybrid 2s 2 p 2 p 2 p 2 x y z 2 x y z sp3d hybrid orbitals – one s, three p, and one d atomic orbitals mix to form a set of five orbitals with different directional properties 3- [Ni(CN)5] 4 Valence bond theory – multiple bonding in polyatomic molecules Valence bond theory – multiple bonding in polyatomic molecules 5 Valence bond theory – multiple bonding in polyatomic molecules Molecular orbital theory: ligand group orbital approach in triatomic molecules 6 MO diagram is constructed by allowing interactions between orbitals of the same symmetry. 7 8 The bonding is described by a consideration of all three bonding MOs 9 NH3 10 CH4 Td 11 Derive the symmetries of the valence orbitals and symmetries for the ligand group orbitals (LGOs) to derive a qualitative MO diagram for BF3. Determine the composition of each LGO in terms of the individual wavefunctions ψ1, ψ2, … and sketch the resulting LGO. D3h E 2C3 3C2 h 2S3 3v 6m2 A1 1 1 1 1 1 1 A2 1 1 –1 1 1 –1 E 2 –1 0 2 –1 0 A1 1 1 1 –1 –1 –1 A2 1 1 –1 –1 –1 1 E 2 –1 0 –2 1 0 Molecular orbital theory: BF3 12 Consider the S3 operation (=C3·σh) on the pz orbitals in the F3 fragment. 2 C3 ψ ψ 2 1 ψ3 S3 S3 ψ3 ψ2 ψ ψ ψ 1 1 3 ψ2 Unique, ‘S3’ S3 σh S3 C3 ψ1 ψ3 ψ2 S3 S3 ψ ψ1 2 ψ3 ψ3 ψ2 ψ1 2 Unique, ‘S3 ’ 2 The resulting wavefunction contributions from the S3 and S3 operations are –ψ3 and –ψ2, respectively. 13 Partial MO diagram that illustrates the formation of delocalized CO -bonds 14 SF6 15 5 Find number of unchanged radial 2p 2 orbitals that are unchanged under each Oh symmetry operation. 3 C2 Note the C2 axis bisect the planes containing 4 p orbitals. The C axis 1 2 contains no 2p orbitals. 4 C2 6 E C3 C2 C4 C2 i S4 S6 h d 2 (C4 ) 6 0 0 2 2 0 0 0 4 2 Use the reduction formula to find the resulting symmetries: a1g, t1u, eg Could derive the equations for the LGOs for the F6 fragment. 1 (a ) 1g 6 1 2 3 4 5 6 1 (t ) 1u 1 2 1 6 1 (t ) 1u 2 2 2 4 1 (t1u )3 3 5 12 (e ) 2 2 g 1 12 1 2 3 4 5 6 1 (e ) g 2 2 2 3 4 5 16 Three-center two- electron interactions 17 B2H6 18 19.