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1 台灣大學開放式課程化學鍵本著作除另有註明, 所有內容皆採用創用 CC 姓名標示 - 非商業使用 - 相同方式分享 3.0 台灣授權條款釋出

2 Chemical Bonding Lecture 0: MO for AXn system, Multicenter Bonding, VSEPR, Hybridization 5//202 Pictorial Symmetry MO AXn n=3, 4, 5, 6 Spring 202

3 Molecular Orbitals for σ Bonding in AX n Molecules

4 AX4 system-2 (Td) X4 r4 A z r X A set of vectors, r, r2, r3, and r4, representing the four bonds from A to the B atoms in a tetrahedral AB4 molecule. r3 x r2 X2 y ΓA-B = A+T2 A: s T2: px,py,pz & dxy, dxz, dyz X 3 T d E 8C 3 3C 2 6S 4 6σ d A x 2 +y 2 +z 2 A E (2z 2 -x 2 -y 2, x 2 -y 2 ) T (R x, R y, R z ) T (x, y, z) (xy, xz, yz) Γ C-H A + T 2

5 AX4 system-2 (Td) Ψa s (σ + σ 2 + σ 3 + σ 4 ) a Energy s a σ + σ 2 + σ 3 + σ 4 a A atom Ψ b s + (σ + σ 2 + σ 3 + σ 4 ) MOs a X atoms By combining the central s orbital with ligand orbital SALC (symmetry-adapted linear combinations) to give either positive or negative overlap, we get Ψ b and Ψ a, respectively. The expressions written for these are only meant to express this sign relationship; the actual expression for Ψ a and Ψ b contain different coefficients.

6 AX4 system-2 (Td) p p x, p y, p z t2 Energy? t2 A atom MOs X atoms

7 AX4 system-2 (Td) Qualitative representations of the three T 2 type σ MOs for an AX 4 molicule. Consider ligand group orbitals (LGOs) that match with each of the center-atom atomic orbitals Symmetry-adapted linear combination (SALC) Note that s or p along the axis both can form the σ bond

8 AX4 system-2 (Td) Ψ a(t2) Ψ a(a) p t2 Energy s a Ψ b(t2) Ψ b(a) a+ t2 σ+ σ2+ σ3+ σ4 σ σ2+ σ3 σ4 etc. A atom MOs B atoms An MO energy level diagram for a AX 4 molecule showing both the A and T 2 type interaction.

9 Experimental evidence for MO CH 4 A.W. Potts and W. C. Price, Proc. R. Soc. London, A326, 65 (972). The T 2 ionization (~4eV) is more intense than A ionization (~23eV) partly because of the 3: ratio of populations. It is much broader because of a Jahn- Teller effect. Not compatible with the picture of electrons in four equivalent localized bonds.

10 AX4 system- (D4h) XeF4 D 4h E 2C 4 (z) C 2 2C' 2 2C'' 2 i 2S 4 σ h 2σ v 2σ d A g x 2 +y 2, z 2 A 2g R z B g x 2 -y 2 B 2g xy E g (R x, R y ) (xz, yz) A u A 2u z B u B 2u E u (x, y) Γ σ A g + B g + E u Γ π A 2u + B 2u + E g Γ π A 2g + B 2g + E u F y F Xe F F x Γπ : out of plane Γπ : in plane s+dx 2 -y 2 +(px+py) Xe: dsp 2

11 AX4 system- (D4h) The MOs for XeF4 and the Xe orbitals and LGOs from which they are obtained. Xe orbitals LGO (4F) 4 MO * Ag y s x Bg 3 x x y d x 2 y2 2y x x x x Eu y y y y y y Γσ ag + bg + eu

12 AX4 system- (D4h) a g * 5p e u * b g * b 2g (dxy) (a g + b g + b 2g + e g ) 5d e g (dxz,dyz) a g (dz2) e u a 2u a 2u (pz) dsp 2 LGO Symmetry adapted Group orbitals 5s ag a 2g +b 2g +e u +a 2u +b 2u +e g nonbonding a g +b g +e u nonbonding 2p (2) 2s (4) a 2u e u a g b g e u Xe XeF4 4F a g

13 AX5 system (D3h) D 3h E 2C 3 3C 2 σ h 2S 3 3 σ v A x 2 + y 2, z 2 A R z E (x, y) (x 2 -y 2, xy) A A z E (R x,r y ) Γ σ total A + A 2 + E Γ σ ax A + A 2 Γ σ eq A + E F F F P F F Y X Γ total = 2A '+A2"+E' σ A : s, d z2 A 2 : p z E : (p x,py) & (d xy, d x2-y2 )

14 AX5 system (D3h) P orbitals (A) Molecular orbitals for σ bonding in PF5 LGO (5X) MO (AX5) 4 s + d 2 z 5 a 2 s d z a pz a2 5 5 px e py e 3 3 Γσ 2A + E + A2

15 AX5 system (D3h) Determining the equatorial LGO SALC coefficients: Signs of SALC coefficients from overlapping with AOs of the center atom Values of coefficients from normalization & orthogonal conditions LGO energy determined by number of nodal planes

16 AX5 system (D3h) σ MO (AX5) SALC of X A a ' A (axial) = 2 (σ 4 +σ5) ±dz a ' A (equatorial) = (σ +σ 2 +σ3) 3 ± s 5 a2 '' A2 (axial) = 2 (σ 4 σ5) ± pz e e ' E (equatorial) = 6 = 2 (2σ2 σ σ3) (σ σ3) ± px py

17 AX5 system (D3h) 4a 2a2 2e 3a e e a d dz2 e e e a2 px, py pz a s 2a e a2 a P PF5 5F P (5 orbitals) s (5)

18 AX6 system (Oh) O h E 8C 3 6C 2 6C 4 3C 2 ( = C 42 ) i 6S 4 8S 6 3σ h 6 σ d A g x 2 + y 2 +z 2 A 2g E g (2z 2 x 2 y 2, x 2 y 2 ) T g (R x, R y, R z ) T 2g (xy, xz, yz) A u A 2u E u T u (x, y, z) T 2u Γ σ A g + E g +T u Z Γσ = A g + Eg +Tu X A Y A g : s E g : d z2, d x2-y2 T u : p x, p y, p z

19 AX6 system (Oh) A SALC of X s A g = 6 (σ +σ 2 +σ3 +σ 4 +σ5 +σ6) dx 2 -y 2, dz 2 px, py, pz Eg = Tu = 2 2 (2σ5 +2σ6 σ σ 2 σ3 σ 4) = (σ σ 2 +σ3 σ 4) = = (σ σ3) (σ 2 σ 4) (σ5 σ 6)

20 AX6 system (Oh) a g * px py pz t u * e g * s dz 2 dx 2 y 2 t u e g σ SALCs of A g E g, T u Symmetry a g A orbitals MOs 6X orbitals

21 Molecular Orbitals for π Bonding in AX n Molecules

22 σ bonding Character table for D 3h point group D 3h E 2C 3 3C' 2 σ h 2S 3 3σ v A' x 2 +y 2, z 2 A' R z E' (x, y) (x 2 -y 2, xy) A'' A'' z E'' (R x, R y ) (xz, yz) Γ S-O(σ) A + E na' = [ ] = 2 na' 2 = [ ( ) ( )] = 0 2 E ' = [ ( ) ( ) = ] 2 na'' = [ ( ) ( ) + 3 ( )] = 0 2 na'' 2 = [ ( ) + 3 ( ) ( ) + 3 ] = 0 2 E '' = [ ( ) ( 2 + ) = ] 0 2 Γ S-O(σ) A + E

23 π bonding Character table for D 3h point group D 3h E 2C 3 3C' 2 σ h 2S 3 3σ v A' x 2 +y 2, z 2 A' R z E' (x, y) (x 2 -y 2, xy) A'' A'' z E'' (R x, R y ) (xz, yz) Γ S-O(π ) A 2 +E na' = [ ( ) + ( 3) ] = 0 2 na' 2 = [ ( ) ( ) + ( 3) ( )] = 0 2 E ' = [ ( ) + 3 ( ) 0+ ( 3) ( ) = ] 0 2 na'' = [ ( ) + ( 3) ( ) ( ) + 3 ( )] = 0 2 na'' 2 = [ ( ) ( ) + ( 3) ( ) ( ) + 3 ] = 2 E '' = [ ( ) + 3 ( ) 0+ ( 3) ( 2 + ) = ] 2 Γ S-O(π ) A 2 + E

24 π // bonding Character table for D 3h point group D 3h E 2C 3 3C' 2 σ h 2S 3 3σ v A' x 2 +y 2, z 2 A' R z E' (x, y) (x 2 -y 2, xy) A'' A'' z E'' (R x, R y ) (xz, yz) Γ S-O(π//) A 2 + E na' = [ ( ) ( ) ] = 0 2 Γ S-O( π//) na' 2 = [ ( ) ( ) ( ) ( )] = 2 E ' = [ ( ) + 3 ( ) ( ) + 3 ( ) 0] = 2 na'' = [ ( ) + 3 ( ) ( ) + 3 ( ) ( )] = 0 2 na'' 2 = [ ( ) ( ) + 3 ( ) ( ) + 3 ( ) ] = 0 2 E '' = [ ( ) + 3 ( ) 0+ 3 ( 2 + ) ( ) 0 = ] 0 2 A 2 + E

25 AX3 system (D3h) SO3 The resulting representations for the oxygen group orbitals (three orbitals for each type, one from each oxygen atom) are D 3h E 2C 3 3C' 2 σ h 2S 3 3σ v A' x 2 +y 2, z 2 A' R z E' (x, y) (x 2 -y 2, xy) A'' A'' z E'' (R x, R y ) (xz, yz) The representations for the sulfur orbitals S 3s A 3px, 3py E 3pz A2 3O Γ2s Γ2px Γ2py Γ2pz A + E A2 + E A + E A2 + E

26 AX3 system (D3h) The molecular orbitals resulting from combining these orbitals are shown as figure. z z z x z x y y x y y x y direction is along each S=O bond LGO or SALC s A + E Oxygen orbitals px py A2 + E A + E pz A2 + E s A Sulfur orbitals px ; py E pz A2 sσ π// pσ π

27 AX3 system (D3h) Qualitative MO energy-level diagram for SO3 5e 5a 2a2 A2 + E 3p A 3s a2 e a2 4e 3e 2p A + E A2 + E A2 + E pσ π// π 4a S 2e 3a SO3 2s 3O A + E sσ

28 AX4 system-2 (Td) A set of vectors representing the four π-type p orbitals on the four B atoms in a tetrahedral AB4 molecule. Γπ = E+T+T2 E: d z2, d x2-y2 T : None T2: px,py,pz & dxy, dxz, dyz T d E 8C 3 3C 2 6S 4 6σ d A x 2 +y 2 +z 2 A E (2z 2 -x 2 -y 2, x 2 -y 2 ) T (R x, R y, R z ) T (x, y, z) (xy, xz, yz) Γπ E + T + T 2

29 AX4 system-2 (Td) A set of vectors representing the four π-type p orbitals on the four B atoms in a tetrahedral AB4 molecule. Γπ = E+T+T2 E: d z2, d x2-y2 T : None T2: px,py,pz & dxy, dxz, dyz It is impossible to form a complete set of π bonds (i.e. two to each X atom) The π bonding will not be entirely independent of the σ bonding

30 AX4 system-2 (Td) Complete qualitative MO diagram applicable to an MCl 4 2- complex 4p: T2 A atom orbitals Molecular Orbitals T2(σ*, π*) Batom orbitals A(σ*) 4s: A 3d: E, T2 T2(σ*, π*) E(π*) T(π) A(σ), T2(σ), E(π), T2(π) pσ SALC s: A, T2 pπ SALC s: E, T, T2 A(σ), T2(σ) σs SALC s: A, T2 An approximate MO diagram for a tetrahedral AX 4 molecule or complex, where A is a +2 ion from the first transition and X s are O or Cl atoms.

31 AX6 system (Oh) O h E 8C 3 6C 2 6C 4 3C 2 ( = C 42 ) i 6S 4 8S 6 3σ h 6 σ d A g x 2 + y 2 +z 2 A 2g E g (2z 2 x 2 y 2, x 2 y 2 ) T g (R x, R y, R z ) T 2g (xy, xz, yz) A u A 2u E u T u (x, y, z) T 2u Γ π T g + T 2g +T u + T 2u Γπ = Tg+T2g+Tu+T2u Tg : None T2g : dxz, dyz, dxy Tu : px, py, pz T2u : None

32 AX6 system (Oh) p y 2 p x p y 3 p x 5 p x 4 p y 5 p x 2 p x 3 p y 6 p y p y 4 p x 6 T 2g SALC of X atom πorbitals are derived by matching to T 2g orbitals (d xy, d xz, d yz ) on the A atom.

33 AX6 system (Oh) MOs A X An approximate MO diagram for an actahedral AX 6 molecule or ion, where A is a +2 or +3 ion from the transition series and the X s are F, O, or Cl atoms.

34 Molecular Orbitals for Cyclic Molecules and Multicenter Bonding

35 C4H4 (D4h) cyclo-butadiene (C4H4) in D4h C C C C Reducible Representations of C-C σ- and π-bonds of cyclo-butadiene D4h E 2C4 C2 2C'2 2C''2 i 2S4 σh 2σv 2σd Γσ Γπ

36 C4H4 (D4h) cyclo-butadiene (C4H4) in D4h D 4h E 2C 4 (z) C 2 2C' 2 2C'' 2 i 2S 4 σ h 2σ v 2σ d A g x 2 +y 2, z 2 A 2g R z B g x 2 -y 2 B 2g xy E g (R x, R y ) (xz, yz) A u A 2u z B u B 2u E u (x, y) Γ σ A g + B g + E u Γ π E g + A 2u + B 2u Γσ = Ag + B2g + Eu Γπ = Eg + A2u + B2u

37 C4H4 (D4h) Trick: determining MOs by matching to central atomic orbital with proper symmetries Γπ = Eg + A2u + B2u Eg xz, yz A2u z B2u z(x 2 -y 2 )

38 C4H4 (D4h) (e g ) a (e g ) b Energy b 2u e g a 2u a 2u b 2u Sketches of the πmolecular orbitals for planar C 4 H 4

Diborane (D2h) Diborane (B 2 H 6 ) has a planar ethylene-like framework (D 2h ) Total 3+3+6 = 2 electrons 2x4 = 8 electrons forming 4 edge

39 Diborane (D2h) Diborane (B 2 H 6 ) has a planar ethylene-like framework (D 2h ) Total = 2 electrons 2x4 = 8 electrons forming 4 edge B-H bonds 2-8 = 4 electrons in the center square electron deficient Bridge bond: three atoms sharing 2 electrons Three-center two-electron bond

40 Diborane (D2h) σ bridge bonding in diborane H x φ φ 3 y z φ 2 φ 4 H 2 D 2h E C 2 (z) C 2 (y) C 2 (x) i σ(xy) σ(xz) σ(yz) A g B g B 2g B 3g A u B u B 2u B 3u Γ boron = Ag + B2g + Γ H = Ag + B3u Bu + B3u Γ boro n Γ H

41 Diborane (D2h) Qualitative energy-level diagram for the bridge bonding in diborane Γ boron = Ag + B2g + Bu + B3u Γ H = Ag + B3u Four electrons in two bonding orbitals two electron three-center bridge bonds

42 Diborane (D2h) Molecular orbitals for bridge bonding in diborane Γ boron = Ag + B2g + Bu+B3u Γ H = Ag + B3u

43 Tetraborane (C2v) Molecular orbitals for bridge bonding in B 4 H 0. σ v B 4 H 0 σ v

45 VSEPR & Hybrid Orbitals

46 Lewis Theory G.N. Lewis, who introduced it in his 96 article The Molecule and the Atom Lewis stuctures, also called Electron-dot Structures or Electron-dot Diagrams, are diagrams that show the bonding between atoms of a molecule, and the lone pairs of electrons that may exist in the molecule. The Octet Rule Eight electrons in their valence shells, similar to the electronic configuration of a noble gas. Lewis Structures:NaCl, HCl and H2O [Na]+ [ Cl ] H Cl H:O:H Sorce from:

VSEPR Theory The Valence Shell Electron Pair Repulsion Theory or VSEPR is a model in chemistry that aims to generally represent the shapes of individual molecules.

47 VSEPR Theory The Valence Shell Electron Pair Repulsion Theory or VSEPR is a model in chemistry that aims to generally represent the shapes of individual molecules.. Construct a valid Lewis structure that shows all of the bond pairs and the lone pairs of electrons. 2. To predict the molecular geometry based on the total number of pairs around the central atom. Type Shape Examples AXE* Linear HF AX2E0 Linear BeCl2, HgCl2 AX2E Bent SO2, O3 Three types of repulsion : The lone pair-lone pair The lone pair-bonding pair The bonding pair-bonding pair (lp-lp) > (lp-bp) > (bp-bp) repulsion. AX2E2 Bent H2O AX2E3 Linear XeF2 AX3E0 AX3E Trigonal planar Trigonal Pyramidal BF3 NH3 AX3E2 T-shaped ClF3, BrF3 AX4E0 Tetrahedral CH4 AX4E Seesaw SF4 AX4E2 Square Planar XeF4 AXnEm A: central atom; X: bonded ligand; E; lone pairs AX5E0 AX5E AX6E0 AX6E Trigonal Bipyramidal Square Pyramidal Octahedral Pentagonal pyramidal PCl5 BrF5 SF6 XeF6 AX7E0 Pentagonal bipyramidal IF7 Sorce from:

49 Sorce from:

50 Sorce from:

51 Sorce from:

52 Sorce from:

53 Sorce from:

54 Molecular Geometries around atoms with 2,3,4,5 and 6 charge clouds.

55 Molecular Geometries around atoms with 2,3,4,5 and 6 charge clouds.

56 Hybridization --- LCAO from the same atom Hybridization is the mixing of atomic orbitals belonging to a same electron shell to form new orbitals suitable for the qualitative description of atomic bonding properties. Hybridized orbitals are very useful in explaining the shape of molecular orbitals for molecules. Hybridisation is an integral part of the valence shell electron-pair repulsion (VSEPR) theory φ sp3 ; φ 2 sp3 ; φ 3 sp3 ; φ 4 sp3

57 HB Hybridization --- LCAO from the same atom A φi = φ sp φ sp 2 j c ij χ j φ sp2 ; φ 2 sp2 ; φ 3 sp2 Another approach: Hybridization the AOs first Gives Triangular geometry

58 The hybrid orbitals for various electron pair arrangments of A s p x p y The Hybrid orbitals 動畫網站 ( 英文說明 ) ssci/chemistry/essentialche mistry/flash/hybrv8.swf s p x p y p z d z2 s p 3 d z2 d x2-y2

59 Applications of Hybridization in MO Theory Recall H 2 O MOs: H z O x H Hybridization of the two a AOs further stabilized the a bonding MO. 2A +B +B 2 A +B sp-hybridized orbitals

60 Hybridization --- LCAO from the same atom A φ sp φ 2 sp φ HB i = j c ij χ j Linear AH 2 σ * 2σ u 2σg p p y p z p y p z π u s A A.O. sp hybrid sp A Hybrid A.O. σ AH 2 s 2H σ u σ g AH 2

61 Hybridization --- LCAO from the same atom A p σ * Bent AH 2 p z p z φ HB i = j c χ ij j s A sp 2 hybrid sp 2 A σ s 2H AH 2 φ sp2 ; φ 2 sp2 ; φ 3 sp2

62 Hybridization --- LCAO from the same atom A σ * planar AH 3 p p z p z φ HB i = j c χ ij j s A sp 2 hybrid sp 2 A σ s 3H AH 3 φ sp2 ; φ 2 sp2 ; φ 3 sp2 Gives a Triangular geometry

63 Tetrahedral AH 4 σ * p sp 3 s A sp 3 hybrid A σ AH 4 s 4H φ sp3 ; φ 2 sp3 ; φ 3 sp3 ; φ 4 sp3

64 Hybrid orbitals of A AL 2 linear BeH 2 D 2h E C 2 (z) C 2 (y) C 2 (x) i σ(xy) σ(xz) σ(yz) A g x 2, y 2, z 2 B g Rz xy B 2g Ry xz B 3g Rx yz A u B u z B 2u y B 3u x Γ(sp) A g + B u sp Trick: C v (D h ) symmetry use the C 2v (D 2h ) table bent OH 2 C 2v E C 2 (z) σ v (xz) σ v (yz) A z x 2, y 2, z 2 A R z xy B - - x, R y xz B y, R x yz Γ σ A + B sp; p 2 Γ t sp 3 Γ lp A + B 2 sp; p 2

65 AL 3 planar D 3h E 2C 3 3C 2 σ h 2S 3 3 σ v A x 2 + y 2, z 2 A R z E (x, y) (x 2 -y 2, xy) A A z E (R x,r y ) BH 3 Γ A + E sp 2 ; sd 2 ; dp 2 ; d 3 (s; dz2) ((x,y); (dxy, d x2-y2)) bent NH 3 C 3v E 2C 3 3 σ v A z x 2 + y 2, z 2 A 2 - R z E 2-0 (x,y), (R x, R y ) (x2-y2, xy), (xz, yz) Γ 3 0 A + E sd 2,, p 3 ; sp 2 ; pd 2 ; d 3 (s; p s ; d z2 ) ((x,y); (d xy, d x2-y2 ); (d xz, d yz ))

66 Planar AL 4 D 4h E 2C 4 (z) C 2 2C' 2 2C'' 2 i 2S 4 σ h 2σ v 2σ d A g x 2 +y 2, z 2 A 2g R z B g x 2 -y 2 B 2g xy E g (R x, R y ) (xz, yz) A u A 2u z B u B 2u Pt Cl 4 2- E u (x, y) Γ A g + B g + E u p y ) sp 2 d ; p 2 d 2 (s, d z 2 ) (d x 2 y 2 ) (p x

67 AL 4 T d E 8C 3 3C 2 6S 4 6σ d A x 2 + y 2 + z 2 A E (2z 2 - x 2 - y 2, x 2 - y 2 ) T (R x, R y, R z ) T (x, y, z) (xy, xz, yz) CH 4 Γ C-H A + T 2 sp 3 ; sd 3 (s) (p x p y p z ); (d xy d xz d yz )

68 AL 5 D 3h E 2C 3 3C 2 σ h 2S 3 3 σ v A x 2 + y 2, z 2 A R z E (x, y) (x 2 -y 2, xy) A A z E (R x,r y ) PF 5 sp 3 d ; spd 3 ; Γ A + E +A 2 C 4v E 2C 4 C 2 2σ v 2σ d A z x 2 + y 2, z 2 A Rz B x 2 - y 2 B xy E (x, y), (R x, R y ) (xz, yz) XeBr 5 Γ 5 3 2A + B + E sp 3 d ; sp 2 d 2 ; sd 4

69 AL 6 D 4h E 2C 4 (z) C 2 2C' 2 2C'' 2 i 2S 4 σ h 2σ v 2σ d A g x 2 +y 2, z 2 A 2g R z B g x 2 -y 2 B 2g xy E g (R x, R y ) (xz, yz) A u A 2u z B u B 2u E u (x, y) Γ eq A g + B g + E u Γ ax A g + A 2u sp 2 d pd sp 3 d 2

70 AL 6 O h E 8C 3 6C 2 6C 4 3C 2 ( = C 42 ) i 6S 4 8S 6 3σ h 6 σ d A g x 2 + y 2 +z 2 A 2g E g (2z 2 x 2 y 2, x 2 y 2 ) T g (R x, R y, R z ) T 2g (xy, xz, yz) A u A 2u E u T u (x, y, z) T 2u Γ σ A g + E g +T u sp 3 d 2

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Lewis Dot Structures for Methane, CH 4 The central C atom is bonded by single bonds (-) to 4 individual H atoms

Lewis Dot Structures for Methane, CH 4 The central C atom is bonded by single bonds (-) to 4 individual H atoms Chapter 10 (Hill/Petrucci/McCreary/Perry Bonding Theory and Molecular Structure This chapter deals with two additional approaches chemists use to describe chemical bonding: valence-shell electron pair

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