101410 Lecture 9

101410 Lecture 9 - Welcome to:! Chemistry 120A! Lecture 9!...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Welcome to:! Chemistry 120A! Lecture 9! More SALCʼs ! and Molecular Orbital Diagrams! Prof. Joshua Figueroa ! Another Example: Character Tables! Character summary for a p ­block atom in C3v symmetry N H C3v! H H Another Example: Character Tables! Character summary for a p ­block atom in C3v symmetry s z px py pz N y H x A1 E E A1 E Mulliken Symbol means ʻDoubly Degenerateʼ ! The orbitals transform together under the operation! H H Symmetry Adapted Linear Combinations of Orbitals! SALCʼs! N We know how the oxygen atoms transform within C3v point symmetry, but what do we with the hydrogen atoms? z N H x H H H H H z y y x 1s orbitals of hydrogen We must determine the symmetry properBes of a ‘group orbitals’ and construct ‘symmetry adapted linear combinaBons’ (SALC’s) of orbitals Symmetry Adapted Linear Combinations SALCʼs! DeterminaBon of the symmetry character for Group Orbitals: If the symmetry operaBon DOES NOT CHANGE the orbital posiBon = +1 If the symmetry operaBon CHANGES the orbital posiBon = 0 If the symmetry operaBon DOES NOT CHANGE the orbital posiBon, but INVERTS its sign =  ­1 z y C A x B C3v Γ E 2C3 3σv Symmetry Adapted Linear Combinations SALCʼs! DeterminaBon of the symmetry character for Group Orbitals: If the symmetry operaBon DOES NOT CHANGE the orbital posiBon = +1 If the symmetry operaBon CHANGES the orbital posiBon = 0 If the symmetry operaBon DOES NOT CHANGE the orbital posiBon, but INVERTS its sign =  ­1 z y C A x B C3v E Γ 3 2C3 3σv Symmetry Adapted Linear Combinations SALCʼs! DeterminaBon of the symmetry character for Group Orbitals: If the symmetry operaBon DOES NOT CHANGE the orbital posiBon = +1 If the symmetry operaBon CHANGES the orbital posiBon = 0 If the symmetry operaBon DOES NOT CHANGE the orbital posiBon, but INVERTS its sign =  ­1 z y C A x B C3v E 2C3 Γ 3 0 3σv Symmetry Adapted Linear Combinations SALCʼs! DeterminaBon of the symmetry character for Group Orbitals: If the symmetry operaBon DOES NOT CHANGE the orbital posiBon = +1 If the symmetry operaBon CHANGES the orbital posiBon = 0 If the symmetry operaBon DOES NOT CHANGE the orbital posiBon, but INVERTS its sign =  ­1 z y C A x B C3v 2C3 Γ UNIQUE OPERATION ONLY E 3 0 3σv Symmetry Adapted Linear Combinations SALCʼs! DeterminaBon of the symmetry character for Group Orbitals: If the symmetry operaBon DOES NOT CHANGE the orbital posiBon = +1 If the symmetry operaBon CHANGES the orbital posiBon = 0 If the symmetry operaBon DOES NOT CHANGE the orbital posiBon, but INVERTS its sign =  ­1 z y C A x B C3v E 2C3 Γ 3 0 3σv 1 Symmetry Adapted Linear Combinations SALCʼs! DeterminaBon of the symmetry character for Group Orbitals: If the symmetry operaBon DOES NOT CHANGE the orbital posiBon = +1 If the symmetry operaBon CHANGES the orbital posiBon = 0 If the symmetry operaBon DOES NOT CHANGE the orbital posiBon, but INVERTS its sign =  ­1 z y C A x B C3v 2C3 Γ UNIQUE OPERATION ONLY E 3 0 3σv 1 Symmetry Adapted Linear Combinations SALCʼs! DeterminaBon of the symmetry character for Group Orbitals: If the symmetry operaBon DOES NOT CHANGE the orbital posiBon = +1 If the symmetry operaBon CHANGES the orbital posiBon = 0 If the symmetry operaBon DOES NOT CHANGE the orbital posiBon, but INVERTS its sign =  ­1 z y C A x B C3v 2C3 Γ UNIQUE OPERATION ONLY E 3 0 3σv 1 How do we! reduce this?! How do we handle E! Representations?! Reduction Formula for Irreducible Representations! # of irreducible Representa<ons = 1 order Of a given type Σ R Character of # opera<ons X Reducible In class representa<on Character of X Irreducible representa<on Reduction Formula for Irreducible Representations! # of irreducible Representa<ons = 1 order Of a given type z Σ R y C A B x C3v E 2C3 Γ 3 0 3σv 1 Character of # opera<ons X Reducible In class representa<on Character of X Irreducible representa<on Reduction Formula for Irreducible Representations! # of irreducible Representa<ons = 1 order Of a given type z Σ R Character of # opera<ons X Reducible In class representa<on Character of X Irreducible representa<on y C A B x C3v E 2C3 Γ 3 0 3σv 1 nA1 = 1/6[(3)(1) + (2)(0)(1) + (3)(1)(1)] = 1 Reduction Formula for Irreducible Representations! # of irreducible Representa<ons = 1 order Of a given type z Σ R Character of # opera<ons X Reducible In class representa<on Character of X Irreducible representa<on y C A B x C3v E 2C3 Γ 3 0 3σv 1 nA1 = 1/6[(3)(1) + (2)(0)(1) + (3)(1)(1)] = 1 nA2 = 1/6[(3)(1) + (2)(0)(1) + (3)(1)(-1)] = 0 nE = 1/6[(3)(2) + (2)(0)(-1) + (3)(1)(0)] = 1 Reduction Formula for Irreducible Representations! # of irreducible Representa<ons = 1 order Of a given type z Σ R Character of # opera<ons X Reducible In class representa<on Character of X Irreducible representa<on y C A B x nA1 = 1/6[(3)(1) + (2)(0)(1) + (3)(1)(1)] = 1 C3v E 2C3 Γ 3 0 1 A1 1 1 1 z E 2  ­1 0 x,y 3σv nA2 = 1/6[(3)(1) + (2)(0)(1) + (3)(1)(-1)] = 0 nE = 1/6[(3)(2) + (2)(0)(-1) + (3)(1)(0)] = 1 Symmetry Adapted Linear Combinations SALCʼs! We now know that the hydrogen 1s orbitals transform as A1 and E SALC’s, but what do these look like? C3v E 2C3 Γ 3 0 1 A1 1 1 1 z E 2  ­1 0 x,y 3σv z y C A B x A1 Ψ = ψ(Ha) + ψ(Hb) + ψ(Hc) Symmetry Adapted Linear Combinations SALCʼs! We now know that the hydrogen 1s orbitals transform as A1 and E SALC’s, but what do these look like? C3v E 2C3 Γ 3 0 1 A1 1 1 1 z E 2  ­1 0 x,y 3σv y C A B x A1 z z z y y A C x B E A C B x E Ψ = ψ(Ha) + ψ(Hb) + ψ(Hc) Ψ = (1/61/2)[ 2ψ(Ha)  ­ ψ(Hb)  ­ ψ(Hc)] Ψ = ψ(Hb)  ­ ψ(Hc) Construction of a Molecular Orbital Diagram for NH3! 3a1 3a1 2e 2e E A1 2a1 2px 2py E 2a1 2pz E 1s A1 1e 1e 2s A1 1a1 1a1 Construction of a Molecular Orbital Diagram for NH3! 3a1 3a1 2e Lone Pair A1 2a1 2px 2py E Lone Pair 1s 2a1 2pz E 2e E A1 1e 1e 2s A1 1a1 1a1 Inversion at Nitrogen! 2a1 2a1 Higher Symmetry Point Groups Lets consider some other point groups: What do these other symbols mean? A – B – E – T – Higher Symmetry Point Groups Lets consider some other point groups: What do these other symbols mean? A – Singly Degenerate (only one orbital transforms): Symmetric With respect to the primary rota<on axis B – Singly Degenerate (only one orbital transforms): An5 ­Symmetric With respect to the primary rota<on axis E – T – Higher Symmetry Point Groups Lets consider some other point groups: What do these other symbols mean? A – Singly Degenerate (only one orbital transforms): Symmetric With respect to the primary rota<on axis B – Singly Degenerate (only one orbital transforms): An5 ­Symmetric With respect to the primary rota<on axis E – Doubly Degenerate (Two orbitals transform together) T – Higher Symmetry Point Groups An Example of Doubly Degenerate Orbitals z F B x Point Group = D3h F F y z z C3 x x y y z Not on axis z C3 x y x y Higher Symmetry Point Groups An Example of Doubly Degenerate Orbitals z z C3 x x y y z Not on axis z C3 x y x y Higher Symmetry Point Groups Lets consider some other point groups: What do these other symbols mean? A – Singly Degenerate (only one orbital transforms): Symmetric With respect to the primary rota<on axis B – Singly Degenerate (only one orbital transforms): An5 ­Symmetric With respect to the primary rota<on axis E – Doubly Degenerate (Two orbitals transform together) T – Triply Degenerate (Three orbitals transform together) Higher Symmetry Point Groups Lets consider some other point groups: What do these other symbols mean? g – Symmetric with respect to inversion u – Anit ­Symmetric with respect to inversion z x y z z x x y y Higher Symmetry Point Groups Lets consider some other point groups: What do these other symbols mean? Subscript 1 – Symmetric with respect to perpendicular C2 axis Subscript 2 – Anit ­Symmetric with respect to perpendicular C2 axis Higher Symmetry Point Groups Lets consider some other point groups: What do these other symbols mean? ‘ (prime) – Symmetric with respect to σh ‘’ (double prime) – Anit ­Symmetric with respect to to σh Another Example: Character Tables! Character summary for a p ­block atom in D3h symmetry The π-system in BF3!! F F B F D3h! Another Example: Character Tables! Character summary for a p ­block atom in D3h symmetry The π-system in BF3!! F F B F D3h! Another Example: Character Tables! Character summary for a p ­block atom in C3v symmetry s z px py pz F F x y B F A1’ E’ E’ A2” E Mulliken Symbol means ʻDoubly Degenerateʼ ! The orbitals transform together under the operation! Another Example: Character Tables! Character summary for a p ­block atom in C3v symmetry s z px py pz F F x y B F A1’ E’ E’ A2” E Mulliken Symbol means ʻDoubly Degenerateʼ ! The orbitals transform together under the operation! Symmetry Adapted Linear Combinations of Orbitals! SALCʼs! N We know how the oxygen atoms transform within D3h point symmetry, but what do we with the hydrogen atoms? H H H Z F F B F F F X B F Y 2p orbitals of Fluorine We must determine the symmetry properBes of a ‘group orbitals’ and construct ‘symmetry adapted linear combinaBons’ (SALC’s) of orbitals Symmetry Adapted Linear Combinations SALCʼs! DeterminaBon of the symmetry character for Group Orbitals: If the symmetry operaBon DOES NOT CHANGE the orbital posiBon = +1 If the symmetry operaBon CHANGES the orbital posiBon = 0 If the symmetry operaBon DOES NOT CHANGE the orbital posiBon, but INVERTS its sign =  ­1 Z C A F F X B F B Y D3h E 2C3 3C2 !h 2S3 3! v red 3 0 -1 -3 0 1 Symmetry Adapted Linear Combinations SALCʼs! DeterminaBon of the symmetry character for Group Orbitals: If the symmetry operaBon DOES NOT CHANGE the orbital posiBon = +1 If the symmetry operaBon CHANGES the orbital posiBon = 0 If the symmetry operaBon DOES NOT CHANGE the orbital posiBon, but INVERTS its sign =  ­1 Z C A F F X B F B Y D3h E 2C3 3C2 !h 2S3 3! v red 3 0 -1 -3 0 1 Symmetry Adapted Linear Combinations SALCʼs! DeterminaBon of the symmetry character for Group Orbitals: If the symmetry operaBon DOES NOT CHANGE the orbital posiBon = +1 If the symmetry operaBon CHANGES the orbital posiBon = 0 If the symmetry operaBon DOES NOT CHANGE the orbital posiBon, but INVERTS its sign =  ­1 Z C A F F X B F B Y D3h E 2C3 3C2 !h 2S3 3! v red 3 0 -1 -3 0 1 Symmetry Adapted Linear Combinations SALCʼs! DeterminaBon of the symmetry character for Group Orbitals: If the symmetry operaBon DOES NOT CHANGE the orbital posiBon = +1 If the symmetry operaBon CHANGES the orbital posiBon = 0 If the symmetry operaBon DOES NOT CHANGE the orbital posiBon, but INVERTS its sign =  ­1 Z C A F F X B F B Y D3h E 2C3 3C2 !h 2S3 3! v red 3 0 -1 -3 0 1 Symmetry Adapted Linear Combinations SALCʼs! DeterminaBon of the symmetry character for Group Orbitals: If the symmetry operaBon DOES NOT CHANGE the orbital posiBon = +1 If the symmetry operaBon CHANGES the orbital posiBon = 0 If the symmetry operaBon DOES NOT CHANGE the orbital posiBon, but INVERTS its sign =  ­1 Z C A F F X B F B Y D3h E 2C3 3C2 !h 2S3 3! v red 3 0 -1 -3 0 1 Symmetry Adapted Linear Combinations SALCʼs! DeterminaBon of the symmetry character for Group Orbitals: If the symmetry operaBon DOES NOT CHANGE the orbital posiBon = +1 If the symmetry operaBon CHANGES the orbital posiBon = 0 If the symmetry operaBon DOES NOT CHANGE the orbital posiBon, but INVERTS its sign =  ­1 Z C A F F X B F B Y D3h E 2C3 3C2 !h 2S3 3! v red 3 0 -1 -3 0 1 Symmetry Adapted Linear Combinations SALCʼs! DeterminaBon of the symmetry character for Group Orbitals: If the symmetry operaBon DOES NOT CHANGE the orbital posiBon = +1 If the symmetry operaBon CHANGES the orbital posiBon = 0 If the symmetry operaBon DOES NOT CHANGE the orbital posiBon, but INVERTS its sign =  ­1 Z C A F F X B F B Y D3h E 2C3 3C2 !h 2S3 3! v red 3 0 -1 -3 0 1 Reduction Formula for Irreducible Representations! # of irreducible Representa<ons = 1 order Of a given type Character of # opera<ons X Reducible In class representa<on Σ R Z Character of X Irreducible representa<on F X A F C B F B Y D3h E 2C3 3C2 !h 2S3 3! v red 3 0 -1 -3 0 1 nA2” = 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 Representa<ons = 1 order Of a given type Character of # opera<ons X Reducible In class representa<on Σ R Z Character of X Irreducible representa<on F X A F C B F B Y D3h E 2C3 3C2 !h 2S3 3! v red 3 0 -1 -3 0 1 nA2” = 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 Representa<ons = 1 order Of a given type Σ R Z Character of # opera<ons X Reducible In class representa<on F X A F C B F Y B D3h E 2C3 3C2 !h 2S3 3! v red 3 0 -1 -3 0 1 A2" 1 1 -1 -1 -1 1 E" 2 -1 0 -2 1 0 Character of X Irreducible representa<on Symmetry Adapted Linear Combinations SALCʼs! We now know that the F 2pz orbitals transform as A2” and E” SALC’s, but what do these look like? D3h E 2C3 3C2 !h 2S3 3! v red 3 0 -1 -3 0 1 A2" 1 1 -1 -1 -1 1 E" 2 -1 0 -2 1 0 F A F B A FF B BB F C F FB A F F BB FF C A2” E FF B F F C E Ψ = ψ(Fa) + ψ(Fb) + ψ(Fc) Ψ = (1/61/2)[ 2ψ(Fa) – ψ(Fb) – ψ(Fc)] Ψ = ψ(Hb)  ­ ψ(Hc) Symmetry Adapted Linear Combinations SALCʼs! We now know that the F 2pz orbitals transform as A2” and E” SALC’s, but what do these look like? D3h E 2C3 3C2 !h 2S3 3! v red 3 0 -1 -3 0 1 A2" 1 1 -1 -1 -1 1 E" 2 -1 0 -2 1 0 nodes F A F B A FF B BB F C F FB A F F BB FF C A2” E FF B F F C E Ψ = ψ(Fa) + ψ(Fb) + ψ(Fc) Ψ = (1/61/2)[ 2ψ(Fa) – ψ(Fb) – ψ(Fc)] Ψ = ψ(Hb)  ­ ψ(Hc) Construction of a Molecular Orbital Diagram ! for BF3 π-system! F B F F (a2")* F F B F pz F F B F F 3pz e" A2" B F A2" + E" F F B F F a2" F B F F Construction of a Molecular Orbital Diagram ! for BF3 π-system! π* F B F F (a2")* F F B F pz F F B F F 3pz e" A2" B F A2" + E" F F π B F F a2" F B F F ...
View Full Document

This note was uploaded on 08/15/2011 for the course CHEM 114B taught by Professor Wang during the Spring '09 term at UCSD.

Ask a homework question - tutors are online