Molecule tomic rbital bridied tomic rbital Valence Shell Electron Pair Repulsion Rule Molecular rbital

2 1+ + 1+ 1+ 1+ 2 9+ + 9+ 9+ 9+

2 1+ 1+ 1s 1s

2 9+ 9+ 2p 2p 9+ () 2 (2p ) 2 (2p ) 2 (2p ) 1

Energ 3p l l 2 - + π π 3p π 3p 3p 3p 3p 3p 3p π 3p 1s ε 1s π 3p π 3p valence electrons + + 2 Molecular rbitals M ormation energ E ond rder () 3s 3s l l l l M 3s 3p 2 + 2 2 1-2 ε - ε 1 0.5 3s 2-3 - ε 0.5 l 2 = 1 e 2 4 0 0 l 2 + = 1.5 e 2 + 3 - ε 0.5

Energ - + ψ 2 = c b1 φ 1 + c b2 φ 2 φ 2 + ε + Molecular rbitals M φ 1 E 2 = α - β ε = β E = α ε = β E 1 = α + β ψ 1 = c a1 φ 1 + c a2 φ 2 large 12 = φ 1 φ ˆ 2 dτ 11 = 22 = φ 1 φ ˆ 1 dτ = φ 2 φ ˆ 2 dτ 12 = φ 1 φ ˆ 2 dτ S 12 = φ 1 φ 2 dτ (=0) Energ φ 2 short ψ ε ψ r φ 1 12, S 12 ψ ψ small r r Distance (r) large 12, S 12 small Interaction π Interaction ψ ψ long Energ ψ bonding interaction bonding interaction ψ φ 2 φ 1 ψ antibonding interaction antibonding interaction ε ψ ψ ψ o Interaction large ngle (θ) small

i 2 ~ 2 2 ~ 2 2p 4 u 4 u 4 u 2p 2p 2π g π 2p 2p 2p 2π g π 2p 2p π 2p π 2p 3 g 2p 3 g 2p 2p 1π u π 2p 2π g 2 u 1π u π 2 u 1 g 3 g 2 u π 2p π 2p 1π u 1 g X X X X M X X X X M 2p 2 u 3 g i 2 e 2 2 2 2 2 2 Valence electrons 2 4 6 8 10 12 14 1 g Unpaired electrons 0 0 2 0 0 2 0 1 0 1 2 3 2 1 Distance(X-X), Å 2.673-1.59 1.243 1.098 1.208 1.41 ond formation 101-291 599 942 494 155 energ, kj/mol

2 2 4 u 2π g π UM 4 u 2π g π UM M 2p 2p 2p 2p 2p 2p 2p 2p 2p 3 g 1π u π 2 u 2p 2p M 1π u 3 g π 2p 1 g 2 u 1 g M 2 = 3.0 + 2 = 2.5 M + 2 2-2 2-2 superoide peroide Valence electrons 11 12 13 14 Unpaired electrons 1 2 1 0 2.5 2 1.5 1 Distance(-), Å 1.12 1.21 1.33 1.49 ν-, cm -1 1905 1580 1097 802

Energ φ b s ε - + ψ 2 = c' a φ a - c' b φ b (c' b 2 > c' a2 ) 1s n 2p nonbonding orbital 2p n 2p + ε + Molecular rbitals M φ a s ψ 1 = c a φ a + c b φ b 2 (c b < c a2 ) M ε ε = 1 ( ab ) 2 ( φ ) 2 a φ ˆ b dτ = aa - bb φ a φ ˆ a dτ - φ b φ ˆ b dτ

π (SM) + - 2p 2p π π π π 2p 2p 2p π π π π 2p M VE 10 11 12 unpaired 0 1 2 electrins = 2.5 3 2.5 2 d(-) 1.06 Å 1.15 Å

- R + π (UM) π 2p 2p 2p π π 2p 2p 2p π (M) π π π π π π π M π = 3

2 1+ + 8+ + 1+ 1+ 8+ 1+? = 3 + 3 4 + 4

e e, linear linear e e 180 2 2 trigonal planar trigonal planar angular e 3-3 2-120 e e tetrahedral e e 109.28 tetrahedral e - e 4 trigonal pramidal angular 4 2 + Pl 3 4 Pl 2 S 3 trigonal bipramidal e e e 90 e 120 trigonal e bipramidal reduced epand 3 107.2 P 3 93.2 s 3 92.1 Sb 3 91.6 2 104.45 2 S 92.1 2 Se 90.6 2 Te 90.2 2 + 180 2 132 2-115 SbPh 5, Inl 2-5 (square pramidal) Ter 6 2-, Sbr6 3- (octahedral, stereochemicall inactive pair) octahedral e e e e pentagonal bipramidal e e e e e e e e e 90 90 72 Pl 5 octahedral square pramidal - P 6 S 6 r 5 pentagonal bipramidal I - 6 I 7 butterfl T-shape linear l 3 S 4 r 3 Tel 4 Il - 2 Xe 2 square planar Xe 4 ngew. hem. Int. Ed. Engl., 1996, 35, 495-514

l ( ) + P l 104.3 l 106.5 l 2 3 2 3 4 Pl4 + 101 187 S 87.5 l Xe l l l l l l S 4 Pl 5 Pl - 6 84 I r VE = 7(I)+71() = 14 = 7bp l 3 r 5 I7 l P l Xe Xe 2 Xe 5 l - l P VE = 8(Xe)+41() = 12 = 4bp + 2lp l VE = 5(P)+41(l)-1 = 8 = 4bp VSEPR

sp2 hbridiation p p p p sp 2 T 1 T 2 T 3 T s 1 = (1/3) 1/2 s + (4/6) 1/2 p T 2 = (1/3) 1/2 s - (1/6) 1/2 p + (1/2) 1/2 p T 2 tomic rbital T 3 = (1/3) 1/2 s - (1/6) 1/2 p - (1/2) 1/2 p sp3 hbridiation T 2 T 3 p sp 2 motif T 1 p p p sp 3 T 1 T 1 t 1 t 2 t 3 t 4 T 3 trigonal planar s tomic rbital t 4 t 3 t 1 t2 tetrahedral t 1 = 1/2(s + p + p + p ) t 2 = 1/2(s + p - p - p ) t 3 = 1/2(s - p + p - p ) t 4 = 1/2(s - p - p + p ) p p p sp hbridiation p p p p s tomic rbital D 1 D 2 D 1 D 1 = (1/2) 1/2 (s + p ) D 2 = (1/2) 1/2 (s - p ) sp D 2 D 1 D 2 p sp motif p D 1 linear

sp3 2p 2p 2p 2p 2p 2p sp 3

sp3 6 sp 3 7 sp 3 6 sp 3

sp 3 l 1s 2p 3p 3 3 sp 3 sp 3 sp 3 sp 3 sp 3 2 3 sp 3 sp 3 sp 3 sp 3 3 2

2p sp 2 2p 2p 2p 2p 2p 2p 2p 1 sp 2 3

2p 7 2p 2p sp 2 6 2p 2p 3 sp 2 6 2p sp 2

sp 2 6 2p sp 2 sp 2 sp 2 2p 2p

sp 2 1s sp 2 sp 2 2p p sp 2 p sp 2 sp 2 p sp 2 l 3p 2 = 2 = 2 =

2p sp 2p 2p 2p sp 2p sp 2p 2p 2p 2p 2p 2 sp 2

sp sp 2p 2p sp 2p 2p 6 sp sp sp 2p 2p 2p 2p

l 1s 2p 3p 4p sp 2 p sp 3 p p sp 3 sp 3 sp 3 sp 3 sp 3 sp 3 sp 3 sp 3 r sp 2 sp 2 p sp 2 sp 2 p sp 2 sp

sp2 hbridiation p p p p sp 2 T 1 T 2 T 3 T s 1 = (1/3) 1/2 s + (4/6) 1/2 p T 2 = (1/3) 1/2 s - (1/6) 1/2 p + (1/2) 1/2 p T 2 tomic rbital T 3 = (1/3) 1/2 s - (1/6) 1/2 p - (1/2) 1/2 p sp3 hbridiation T 2 T 3 p sp 2 motif T 1 p p p sp 3 T 1 T 1 t 1 t 2 t 3 t 4 T 3 trigonal planar s tomic rbital t 4 t 3 t 1 t2 tetrahedral t 1 = 1/2(s + p + p + p ) t 2 = 1/2(s + p - p - p ) t 3 = 1/2(s - p + p - p ) t 4 = 1/2(s - p - p + p ) p p p sp hbridiation p p p p s tomic rbital D 1 D 2 D 1 D 1 = (1/2) 1/2 (s + p ) D 2 = (1/2) 1/2 (s - p ) sp D 2 D 1 D 2 p sp motif p D 1 linear

2 sp ds, dp linear 3 sp 2 trigonal planar (e3) S 4 3d sp 3 d 3d from 4 4 sp 3 tetrahedral 5 sp 3 d dsp 3 trigonal bipramidal 5 sp 2 d 2 d 2 sp 2 square pramidal 6 sp 3 d 2 d 2 sp 3 octahedral 6 spd 4 d 4 sp trigonal prism 7 sp 3 d 3 d 3 sp 3, d 5 sp pentagonal bipramidal hpervalent nd compounds np np ns 3p 3p sp 3p 3 d 3s S tomic rbital S (e4) r 5 4d 4d sp 3 d 2 from 5 4p 4p 4p sp 3 d 2 ns tpical elements (n-1)d transition-metal elements r 4s tomic rbital r (e1) 3 from 3 (e2) 2 from 2 (e5) l 3 3d 3d 2p 2p 2p 2p 2p 2p sp 3 d from 3 t 1 t 2 t 3 t 4 t 1 t 2 t 3 t 4 sp 3 sp 3 3p 3p 3p sp 3 d tomic rbital tomic rbital l 3s l tomic rbital

l sp 3 hbridiation from 3 p p p s tomic rbital sp 3 sp 3 sp 3 n 3p 3p 3p l 3s 3 3 3 3 = 1 3 3 l = 1 l (

sp 2 hbridiation p p p s tomic rbital from 2 p sp 2 p sp 2 π π p sp 2 p sp 2 π n π 2p 2p 2p n 2 2 2 2 = 2 +π bonding 2 2 = 2 +π bonding ()

sp hbridiation from p p p π p p p p p π p p p s tomic rbital sp sp π sp sp π (+ ) n 2p 2p 2p = 3 +2π bonding = 3 +2π bonding ()

Γ() E 3 v 3 0 1 χ'(r) a(irr) = (1/h) Σ χ(r)χ'(r) R Γ() R a( 1 ) = (1/6)(13+210+311) = 1 a( 2 ) = (1/6)(13+210+3(-1)1) = 0 a(e) = (1/6)(23+2(-1)0+301) = 1 Γ() = 1 + E D h

2 p p p 1 p

3c,2e Interaction (three center-two electron interaction) D h 2v 3v (D 3h ) Energ n 2 b 1 e 1s 2 1 D h n + + + 180 ~100 60 Walsh Diagram 2v 2 b 1 1 3v (D 3h ) 180 ~100 θ (--) 60 e p 2 n 1s

D3h 2 ' Energ 2 ' 2e' 2a 2 " 2e' 2p (e') 2p (e') 1e" e" a 2 " 2a 2 " π 2p (a 2 ") 1a 2 " e' 1e" n lone pair stabilied ( ') 1e' ' 1e' 1a 2 " π 1 ' 1 ' The p orbitals are drawn with. The three sets of lone pairs of p orbitals are omitted for clarit.

from 2 1.77Å 1.33Å 1.19Å b 2g b 1u D 2h a g * b 3g * b 2g b 1u b 3u sp 3 sp 3 sp 3 b 3u a g 1s () 3c,2e Interaction a g b 3u a g b 3u a g

2v 3 D h 2 g Energ 2b 2 2 u 1s 2 b 2 1b 1 2 2p (b 1 ) 2p (b 2 ) 2p ( ) 1s 2 1π u 2p (b 1 ) 2p ( ) 2p (b 2 ) 1b 2 1 u 1 1 g Walsh Diagram Energ 2 3a g 1 2 u 2b 2 1b 1 2 1π u 1b 2 1 u Estimate structures of 2 -,2, 2, 2, e 2 structures on the basis of the Walsh diagram. 1 1 g 2 (105 ), 2 (103 ), 2 (136 ) 2 (131 ), e 2 (180 ) 104.5 θ 180

3v D3h Energ 3 2e 2 ' 2e' e 2p (e) 2p (e) 2p (e') 2p (e') a 2 " e' 1s 3 2 2p ( ) 2p (a 2 ") ' 1e ( ) ( ') 1e' 1 3 Walsh Diagram 2 ' 1 ' 2e' 2e Energ 2 1e 1 1a 2 " 1e' 1 ' Estimate structures of 3 +,3, 3, 3 +, 3 structures on the basis of the Walsh diagram.

D h 2v 4 2v Energ 2 g 2 u b 2 4 2b 2 2b 2 4 2b 2 3 1π u b 1 3 1b 1 1s 3 n 1b 1 n b 2 1b 1 2 p p p b 2 b 1 b 2 2 1 u 1b 2 2a 1 1b 2 s 1 g 1 1b 2 1 1 87.5 1.698Å 1.598Å l EX) 1) 1s orbitals can be replaced b p orbitals. 2) Think about the structure of l3 on the basis of M diagrams as well as VSEPR rule. 3) Think about the electron deficient bonds involved in l 3 and the potential d orbital effects.

Td tetrahedral D4h square planar 2 2g Energ t 2 e u 2e u 2t 2 e u t 2 2p 2p 2p b 1g 1b 1g 2p e u 2p 1s 4 1t 2 t 2 1s 4 g 1a 2u 2p a 2u 1e u g b 1g 1 g 1g E) Estimate structures of 3 +,3, 3, 3 +, 3 structures on the basis of the Walsh diagram.

2v 2v 4 2v Energ 3 4 2b 1 2b 1 4 2b 1 2b 2 b 2 2b 2 2b 2 2b 2 1s 1b 1 2 b 1 3 2 b 1 n 3 b 2 b 1 3 b 2 p a b 1 1 p b 2 a p 1 b 1 2 b 2 1b 2 2 1b 2 1b 2 1b 1 1b 1 s 1 1 1b 2 1.646Å 101 S 187 1.545Å EX) 1b 1 1 1) 1s orbitals can be replaced b p orbitals. 2) Think about the structure of S4 on the basis of M diagrams as well as VSEPR rule. 3) Think about the electron deficient bonds involved in S 4 and the potential d orbital effects. 1

D4h square planar 4v square pramidap 4 4v square pramidap Energ 2g e 4 2e 2e e 4 2e 2e u 3 3 e 3 1b 1g 1a 2u b 1 1b 1 1s a 1 2 2 1b 1 b 1 b 1 1b 1 2 p p p e 1e u e 1e 1e 1e s 1 Γ = 2 + b 1 + e 1 1g 1 1.68Å 84 r 1.75~1.82Å EX) 1) 1s orbitals can be replaced b p orbitals. 2) Think about the structure of r5 on the basis of M diagrams as well as VSEPR rule. 3) Think about the electron deficient bonds involved in r 5 and the potential d orbital effects.

without d orbitals h with d orbitals h 2e g 1t 2g e g t 2g d 2 d 2-2 d d d Energ e g 2g 2t 1u 2g 2t 1u ver small contribution! t 1u e g 1e g n e g n 1e g t 1u t 1u 1e g g p p p t 1u g p p p t 1u g 1t 1u 1t 1u s g s g 1g 1g EX) 1) 1s orbitals can be replaced b p orbitals. 2) Think about the structure of S6 on the basis of M diagrams as well as VSEPR rule. 3) Think about the potential d orbital effects.

Energ D h 2p π 2p u 2p + u + g 3u 3g 2e 1u 1e 1g 1e 1u 2u 2g 1u 1g π g π u u + g + π g π u + u + g M's 3u 3g 2u 2g 1u 1g 2e 1u 1e 1g 1e 1u π n π n n 2p π 2p u sp + u sp + g D h 3u 3g 2e 1u 1e 1g 1e 1u π g π u + u + g u + g + 2u 2g 1u u + 1g g +

Energ 2p 2p b 2 2p b 1 2v 5 4b 2 2b 1 1a 2 3 1b 1 2b 2 4 3b 2 2 1b 2 1 a 2 b 1 b 2 b 2 b 2 a 2 b 1 b 2 b 2 5 4 2 n n 3 M's 4b 2 2b 2 3b 2 n n 2b 1 1a 2 1b 1 π π n n 1b 1a 2 1

Energ 2v 5 a1 M's 5 Energ 2v 4b 2 b2 M's 2p n 4 4 n 2p n 3b 2 4b 2 n n 3 3a n 1 b 2 2b 2 b 2 b 2 3b 2 2 n 1 2 n 1b 2 b 2 2b 2 n Energ a2 b1 n 1 π 1b 1 2v π 1b 2 n 1a 2 b 1 a 2 2p b 1 2b 1 1a 2 n π 1b 1 π 1b 1