101410 Lecture 10

101410 Lecture 10 - Welcome to:! Chemistry 120A! Lecture...

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Unformatted text preview: Welcome to:! Chemistry 120A! Lecture 10! Even More SALCʼs ! and Molecular Orbital Diagrams! Prof. Joshua Figueroa ! Another Example: Character Tables! Character summary for a p ­block atom in D3h symmetry. Molecule has two sets of dissymmetric off ­origin atoms H H H P H H D3h! Central Phosphorus Atom! Character summary for a p ­block atom in D3h symmetry s z py px pz H H H x P H y A1’ E’ E’ A2” H E Mulliken Symbol means ʻDoubly Degenerateʼ ! The orbitals transform together under the operation! Symmetry Adapted Linear Combinations of Orbitals! SALCʼs! We know how the phosphorus atom transforms within D3h point symmetry, but what do we do with the hydrogen atoms? Break up into two ! dissymmetric sets: ! Equatorial and axial! H H H P H H We must determine the symmetry properGes of a ‘group orbitals’ and construct ‘symmetry adapted linear combinaGons’ (SALC’s) of orbitals SALCʼs for Equatorial Set! DeterminaGon of the symmetry character for Group Orbitals: If the symmetry operaGon DOES NOT CHANGE the orbital posiGon = +1 If the symmetry operaGon CHANGES the orbital posiGon = 0 If the symmetry operaGon DOES NOT CHANGE the orbital posiGon, but INVERTS its sign =  ­1 Z c X a P b Y D3h E 2C3 3C2 σh 2S 3 3σv re d 3 0 1 3 0 1 SALCʼs for Equatorial Set! DeterminaGon of the symmetry character for Group Orbitals: If the symmetry operaGon DOES NOT CHANGE the orbital posiGon = +1 If the symmetry operaGon CHANGES the orbital posiGon = 0 If the symmetry operaGon DOES NOT CHANGE the orbital posiGon, but INVERTS its sign =  ­1 Z c X a P b Y D3h E 2C3 3C2 σh 2S 3 3σv re d 3 0 1 3 0 1 SALCʼs for Equatorial Set! DeterminaGon of the symmetry character for Group Orbitals: If the symmetry operaGon DOES NOT CHANGE the orbital posiGon = +1 If the symmetry operaGon CHANGES the orbital posiGon = 0 If the symmetry operaGon DOES NOT CHANGE the orbital posiGon, but INVERTS its sign =  ­1 Z c X a P b Y D3h E 2C3 3C2 σh 2S 3 3σv re d 3 0 1 3 0 1 SALCʼs for Equatorial Set! DeterminaGon of the symmetry character for Group Orbitals: If the symmetry operaGon DOES NOT CHANGE the orbital posiGon = +1 If the symmetry operaGon CHANGES the orbital posiGon = 0 If the symmetry operaGon DOES NOT CHANGE the orbital posiGon, but INVERTS its sign =  ­1 Z c X a P b Y D3h E 2C3 3C2 σh 2S 3 3σv re d 3 0 1 3 0 1 SALCʼs for Equatorial Set! DeterminaGon of the symmetry character for Group Orbitals: If the symmetry operaGon DOES NOT CHANGE the orbital posiGon = +1 If the symmetry operaGon CHANGES the orbital posiGon = 0 If the symmetry operaGon DOES NOT CHANGE the orbital posiGon, but INVERTS its sign =  ­1 Z c X a P b Y D3h E 2C3 3C2 σh 2S 3 3σv re d 3 0 1 3 0 1 SALCʼs for Equatorial Set! DeterminaGon of the symmetry character for Group Orbitals: If the symmetry operaGon DOES NOT CHANGE the orbital posiGon = +1 If the symmetry operaGon CHANGES the orbital posiGon = 0 If the symmetry operaGon DOES NOT CHANGE the orbital posiGon, but INVERTS its sign =  ­1 Z c X a P b Y D3h E 2C3 3C2 σh 2S 3 3σv re d 3 0 1 3 0 1 SALCʼs for Equatorial Set! DeterminaGon of the symmetry character for Group Orbitals: If the symmetry operaGon DOES NOT CHANGE the orbital posiGon = +1 If the symmetry operaGon CHANGES the orbital posiGon = 0 If the symmetry operaGon DOES NOT CHANGE the orbital posiGon, but INVERTS its sign =  ­1 Z c X a P b Y D3h E 2C3 3C2 σh 2S 3 3σv re d 3 0 1 3 0 1 Reduction Formula for Irreducible Representations! # of irreducible Representa6ons = 1 order Of a given type Σ R Character of # opera6ons X Reducible In class representa6on Character of X Irreducible representa6on Z c a X P b Y D3h E 2C3 3C2 σh 2S 3 3σv re d 3 0 1 3 0 1 nA1’ = 1/12[(3)(1) + (2)(0)(1) + (3)(1)(1) + (1)(3)(1) + (2)(0)(1) + (3)(1)(1)] = 1 Reduction Formula for Irreducible Representations! # of irreducible Representa6ons = 1 order Of a given type Σ R Character of # opera6ons X Reducible In class representa6on Character of X Irreducible representa6on Z c a X P b Y D3h E 2C3 3C2 σh 2S 3 3σv re d 3 0 1 3 0 1 nA1’ = 1/12[(3)(1) + (2)(0)(1) + (3)(1)(1) + (1)(3)(1) + (2)(0)(1) + (3)(1)(1)] = 1 nE’ = 1/12[(3)(2) + (2)(0)(-1) + (3)(1)(0) + (1)(3)(2) + (2)(0)(-1) + (3)(1)(0)] = 1 Reduction Formula for Irreducible Representations! # of irreducible Representa6ons = 1 order Of a given type Σ R Character of # opera6ons X Reducible In class representa6on Z c X a P b Y D3h E 2C3 re d 3 A1' E' 3C2 σh 2S 3 3σv 0 1 3 0 1 1 1 1 1 1 1 2 -1 0 2 -1 0 Character of X Irreducible representa6on Symmetry Adapted Linear Combinations SALCʼs! We now know that the equitorial H 1s orbitals transform as A1’ and E’ SALC’s, but what do these look like? D3h E 2C3 re d 3 A1' E' 3C2 σh 2S 3 3σv 0 1 3 0 1 1 1 1 1 1 1 2 -1 0 2 -1 0 c a c c a P P P b b b A1’ E’ E’ Ψ = ψ(Fa) + ψ(Fb) + ψ(Fc) Ψ = (1/61/2)[ 2ψ(Fa) – ψ(Fb) – ψ(Fc)] Ψ = ψ(Hb)  ­ ψ(Hc) SALCʼs for Axial Set! DeterminaGon of the symmetry character for Group Orbitals: If the symmetry operaGon DOES NOT CHANGE the orbital posiGon = +1 If the symmetry operaGon CHANGES the orbital posiGon = 0 If the symmetry operaGon DOES NOT CHANGE the orbital posiGon, but INVERTS its sign =  ­1 Z d P X Y e D3h E 2C3 red 2 2 3C2 σh 2S 3 3σv 0 0 0 2 SALCʼs for Axial Set! DeterminaGon of the symmetry character for Group Orbitals: If the symmetry operaGon DOES NOT CHANGE the orbital posiGon = +1 If the symmetry operaGon CHANGES the orbital posiGon = 0 If the symmetry operaGon DOES NOT CHANGE the orbital posiGon, but INVERTS its sign =  ­1 Z d P X Y e D3h E 2C3 red 2 2 3C2 σh 2S 3 3σv 0 0 0 2 SALCʼs for Axial Set! DeterminaGon of the symmetry character for Group Orbitals: If the symmetry operaGon DOES NOT CHANGE the orbital posiGon = +1 If the symmetry operaGon CHANGES the orbital posiGon = 0 If the symmetry operaGon DOES NOT CHANGE the orbital posiGon, but INVERTS its sign =  ­1 Z d P X Y e D3h E 2C3 red 2 2 3C2 σh 2S 3 3σv 0 0 0 2 SALCʼs for Axial Set! DeterminaGon of the symmetry character for Group Orbitals: If the symmetry operaGon DOES NOT CHANGE the orbital posiGon = +1 If the symmetry operaGon CHANGES the orbital posiGon = 0 If the symmetry operaGon DOES NOT CHANGE the orbital posiGon, but INVERTS its sign =  ­1 Z d P X Y e D3h E 2C3 red 2 2 3C2 σh 2S 3 3σv 0 0 0 2 SALCʼs for Axial Set! DeterminaGon of the symmetry character for Group Orbitals: If the symmetry operaGon DOES NOT CHANGE the orbital posiGon = +1 If the symmetry operaGon CHANGES the orbital posiGon = 0 If the symmetry operaGon DOES NOT CHANGE the orbital posiGon, but INVERTS its sign =  ­1 Z d P X Y e D3h E 2C3 red 2 2 3C2 σh 2S 3 3σv 0 0 0 2 SALCʼs for Axial Set! DeterminaGon of the symmetry character for Group Orbitals: If the symmetry operaGon DOES NOT CHANGE the orbital posiGon = +1 If the symmetry operaGon CHANGES the orbital posiGon = 0 If the symmetry operaGon DOES NOT CHANGE the orbital posiGon, but INVERTS its sign =  ­1 Z d P X Y e D3h E 2C3 red 2 2 3C2 σh 2S 3 3σv 0 0 0 2 SALCʼs for Axial Set! DeterminaGon of the symmetry character for Group Orbitals: If the symmetry operaGon DOES NOT CHANGE the orbital posiGon = +1 If the symmetry operaGon CHANGES the orbital posiGon = 0 If the symmetry operaGon DOES NOT CHANGE the orbital posiGon, but INVERTS its sign =  ­1 Z d P X Y e D3h E 2C3 red 2 2 3C2 σh 2S 3 3σv 0 0 0 2 Reduction Formula for Irreducible Representations! # of irreducible Representa6ons = 1 order Of a given type Σ R Character of # opera6ons X Reducible In class representa6on Character of X Irreducible representa6on Z d P X Y e D3h E 2C3 red 2 2 3C2 σh 2S 3 3σv 0 0 0 2 nA2” = 1/12[(2)(1) + (2)(2)(1) + (3)(0)(-1) + (1)(0)(-1) + (2)(0)(-1) + (3)(2)(1)] = 1 Reduction Formula for Irreducible Representations! # of irreducible Representa6ons = 1 order Of a given type Σ R Character of # opera6ons X Reducible In class representa6on Character of X Irreducible representa6on Z d P X Y e D3h E 2C3 red 2 2 3C2 σh 2S 3 3σv 0 0 0 2 nA2” = 1/12[(2)(1) + (2)(2)(1) + (3)(0)(-1) + (1)(0)(-1) + (2)(0)(-1) + (3)(2)(1)] = 1 nA1’ = 1/12[(2)(1) + (2)(2)(1) + (3)(0)(1) + (1)(0)(1) + (2)(0)(1) + (3)(2)(1)] = 1 Reduction Formula for Irreducible Representations! # of irreducible Representa6ons = 1 order Of a given type Character of # opera6ons X Reducible In class representa6on Σ R Z d P X Y e D3h E 2C3 red 2 A1' A2" 3C2 σh 2S 3 3σv 2 0 0 0 2 1 1 1 1 1 1 1 1 -1 -1 -1 1 Character of X Irreducible representa6on Symmetry Adapted Linear Combinations SALCʼs! We now know that the axial H 1s orbitals transform as A1’ and A2” SALC’s, but what do these look like? D3h E 2C3 red 2 A1' A2" 3C2 σh 2S 3 3σv 2 0 0 0 2 1 1 1 1 1 1 1 1 -1 -1 -1 1 d d P P e e A1’ A2” Ψ = ψ(Hd) + ψ(He) Ψ = ψ(Hd)  ­ ψ(He) Symmetry Adapted Linear Combinations SALCʼs! For all H atoms! c a a P P P b b b E’ E’ A1’ d d P A1’ c c P e e A2” Symmetry Adapted Linear Combinations SALCʼs! For all H atoms! c a a P P P b b b E’ E’ A1’ d d P A1’ c c P e e A2” and the P atom! A1’ E’ E’ A2” Molecular Orbital Diagram for PH5 in D3h Symmetry! 3a1' z x 2e' y 2a2" 3px 3py 3pz E' E' 2a1' A2" 5H 1s 2A1' + A2" +E' d d e e 1a2" c 2s A1' a 1e' b c c a b 1a1' b Molecular Orbital Diagram for PH5 in D3h Symmetry! 3a1' z x 2e' y 2a2" Non ­bonding e ­ pair 3px 3py 3pz E' E' 2a1' A2" 5H 1s 2A1' + A2" +E' d d e e 1a2" c 2s A1' a 1e' b c c a b 1a1' b Molecular Orbital Diagram for PH5 in D3h Symmetry! d 3a1' z c a b 3a1' x e 2e' y c c a 2e' b b d 2a2" Non ­bonding e ­ pair 2a2" e d c a 3px 3py 3pz E' E' b 2a1' A2" 2a1' 5H 1s 2A1' + A2" +E' d d d 1a2" 1a2" e e e a a 1e' b c b c 1a1' b 1e' d a b c c c 2s A1' e c b 1a1' a b e Molecular Orbital Diagram for PH5 in D3h Symmetry! d 3a1' z c a b 3a1' x e 2e' y c c a 2e' b b d 2a2" Non ­bonding e ­ pair 2a2" e d c a 3px 3py 3pz E' E' b 2a1' A2" 2a1' 5H 1s 2A1' + A2" +E' d d d 1a2" 1a2" e e e a a 1e' b c b c 1a1' b 1e' d a b c c c 2s A1' e c b 1a1' a b e Molecular Orbital Diagram for PH5 in D3h Symmetry! d 3a1' z c a b 3a1' x e 2e' y c c a 2e' b b d 2a2" Non ­bonding e ­ pair 2a2" e d c a 3px 3py 3pz E' E' b 2a1' A2" 2a1' 5H 1s 2A1' + A2" +E' d d d 1a2" 1a2" e e e a a 1e' b c b c 1a1' b 1e' d a b c c c 2s A1' e c b 1a1' a b e Another Example: Character Tables! Character summary for a p ­block atom in C4v symmetry. Molecule has two sets of dissymmetric off ­origin atoms H H P H H H C4v! Character summary for a p ­block atom in C4v symmetry. Molecule has two sets of dissymmetric off ­origin atoms Z H H H X P H H Y ...
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