120A lecture 6- SALCS, MO diagrams

120A lecture 6- SALCS, MO diagrams - Welcome to:! Chemistry...

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Unformatted text preview: Welcome to:! Chemistry 120A! Lecture 5! Character Tables,! SALCʼs and Molecular Orbital Prof. Joshua Figueroa ! Diagrams! Character Tables! Character tables contain informa8on about how func8ons transform in response to the opera8ons of the group What Makes Up a Character Table? Character Tables! Character tables contain informa8on about how func8ons transform in response to the opera8ons of the group What Makes Up a Character Table? Character Character Tables! Character tables contain informa8on about how func8ons transform in response to the opera8ons of the group What Makes Up a Character Table? Five Parts of a Character Table 1 ­ At the upper le, is the symbol for the point group 2  ­ The top row shows the opera:ons of the point group, organized into classes 3  ­ The le, column gives the Mulliken symbols for each of the irreducible representa:ons 4  ­ The rows at the center of the table give the characters of the irreducible representa:ons (these can not be reduced further) 5  ­ Listed at right are certain func:ons, showing the irreducible representa:on for which the func:on can serve as a basis Character Character Tables! Character tables contain informa8on about how func8ons transform in response to the opera8ons of the group What Makes Up a Character Table? Five Parts of a Character Table 1 ­ At the upper le, is the symbol for the point group 2  ­ The top row shows the opera:ons of the point group, organized into classes 3  ­ The le, column gives the Mulliken symbols for each of the irreducible representa:ons 4  ­ The rows at the center of the table give the characters of the irreducible representa:ons (these can not be reduced further) 5  ­ Listed at right are certain func:ons, showing the irreducible representa:on for which the func:on can serve as a basis Character Character Tables! Character tables contain informa8on about how func8ons transform in response to the opera8ons of the group What Makes Up a Character Table? Five Parts of a Character Table 1 ­ At the upper le, is the symbol for the point group 2  ­ The top row shows the opera:ons of the point group, organized into classes 3  ­ The le, column gives the Mulliken symbols for each of the irreducible representa:ons 4  ­ The rows at the center of the table give the characters of the irreducible representa:ons (these can not be reduced further) 5  ­ Listed at right are certain func:ons, showing the irreducible representa:on for which the func:on can serve as a basis Character Character Tables! Character tables contain informa8on about how func8ons transform in response to the opera8ons of the group What Makes Up a Character Table? Five Parts of a Character Table 1 ­ At the upper le, is the symbol for the point group 2  ­ The top row shows the opera:ons of the point group, organized into classes 3  ­ The le, column gives the Mulliken symbols for each of the irreducible representa:ons 4  ­ The rows at the center of the table give the characters of the irreducible representa:ons (these can not be reduced further) 5  ­ Listed at right are certain func:ons, showing the irreducible representa:on for which the func:on can serve as a basis Character Character Tables! Character tables contain informa8on about how func8ons transform in response to the opera8ons of the group What Makes Up a Character Table? Five Parts of a Character Table 1 ­ At the upper le, is the symbol for the point group 2  ­ The top row shows the opera:ons of the point group, organized into classes 3  ­ The le, column gives the Mulliken symbols for each of the irreducible representa:ons 4  ­ The rows at the center of the table give the characters of the irreducible representa:ons (these can not be reduced further) 5  ­ Listed at right are certain func:ons, showing the irreducible representa:on for which the func:on can serve as a basis Determining Molecular! Point Groups! EXAMPLES H H H B H B H H C1, Cs, Ci Td , Oh , C∞v , D∞h , Ih D Groups C or S2n Groups A – Cs C – D2d B – Ci Dnh Dnd Dn Cnh Cnv S2n Cn D – D2h Character Tables! A – Cs C – D2d B – Ci H H H B H B H H D – D2h Character Tables! A – Cs C – D2d B – Ci H H H B H B H H D – D2h Character Tables! How do they work? Character Character Tables! Transforma8on Proper8es of an s Orbital in C2v What happens when the E opera8on is applied? Character Character Tables! Transforma8on Proper8es of an s Orbital in C2v What happens when the E opera8on is applied? The E opera8on is a rota8on by 360 about an arbitrary axis The result of this corresponds to a character of 1 (The Orbital is Unchanged AQer the Opera8on) Character Character Tables! Transforma8on Proper8es of an s Orbital in C2v What happens when the C2 opera8on is applied? Character Character Tables! Transforma8on Proper8es of an s Orbital in C2v What happens when the C2 opera8on is applied? The C2 opera8on is a rota8on by 180 about the z axis The result of this corresponds to a character of 1 (The Orbital is Unchanged AQer the Opera8on) Character Character Tables! Transforma8on Proper8es of an s Orbital in C2v What happens when the σv(xz) opera8on is applied? Character Character Tables! Transforma8on Proper8es of an s Orbital in C2v What happens when the σv(xz) opera8on is applied? The σv(xz) opera8on is a reflec8on through the xz plane The result of this corresponds to a character of 1 (The Orbital is Unchanged AQer the Opera8on) Character Character Tables! Transforma8on Proper8es of an s Orbital in C2v What happens when the σv’(yz) opera8on is applied? Character Character Tables! Transforma8on Proper8es of an s Orbital in C2v What happens when the σv’(yz) opera8on is applied? The σv’(yz) opera8on is a reflec8on through the yz plane The result of this corresponds to a character of 1 (The Orbital is Unchanged AQer the Opera8on) Character Tables! Transforma8on Proper8es of an s Orbital in C2v: All 1’s Returned The s orbital “belongs to" or “serves as a basis for" the totally symmetric irreducible representa8on (A1) The totally symmetric irreducible representa8on is always singly degenerate (No other component transforms with it) Consider an s orbital located on a central atom in a molecule An example of a central atom is O in the case of water, or N in the case of ammonia Character Tables! Transforma8on Proper8es of an s Orbital in C2v: All 1’s Returned The s orbital “belongs to" or “serves as a basis for" the totally symmetric irreducible representa8on (A1) The totally symmetric irreducible representa8on is always singly degenerate (No other component transforms with it) Consider an s orbital located on a central atom in a molecule An example of a central atom is O in the case of water, or N in the case of ammonia Character Character Tables! Transforma8on Proper8es of a px Orbital in C2v What happens when the E opera8on is applied? The E opera8on is a rota8on by 360 about an arbitrary axis The result of this corresponds to a character of 1 (The Orbital is Unchanged AQer the Opera8on) Character Character Tables! Transforma8on Proper8es of a px Orbital in C2v What happens when the C2 opera8on is applied? The C2 opera8on is a rota8on by 180 about the z axis The result of this corresponds to a character of  ­1 (The C2 Opera8on Inverts the phase of the px orbital) Character Character Tables! Transforma8on Proper8es of a px Orbital in C2v What happens when the σv(xz) opera8on is applied? The σv(xz) opera8on is a reflec8on through the xz plane The result of this corresponds to a character of 1 (The Orbital is Unchanged AQer the Opera8on) Character Character Tables! Transforma8on Proper8es of a px Orbital in C2v What happens when the σv’(yz) opera8on is applied? The σv’(yz) opera8on is a reflec8on through the yz plane The result of this corresponds to a character of  ­1 (The σv’(yz) Opera8on Inverts the phase of the px orbital) Character Character Tables! Transforma8on Proper8es of a px Orbital in C2v The opera8ons generated the following characters: 1,  ­1, 1,  ­1 This row of characters in the C2v character table is labeled B1 Any orbital having these transforma8on proper8es in C2v is said to have B1 symmetry Character Character Tables! Transforma8on Proper8es of a py Orbital in C2v What happens when the E opera8on is applied? The E opera8on is a rota8on by 360 about an arbitrary axis The result of this corresponds to a character of 1 (The Orbital is Unchanged AQer the Opera8on) Character Character Tables! Transforma8on Proper8es of a py Orbital in C2v What happens when the C2 opera8on is applied? The C2 opera8on is a rota8on by 180 about the z axis The result of this corresponds to a character of  ­1 (The C2 Opera8on Inverts the phase of the px orbital) Character Character Tables! Transforma8on Proper8es of a py Orbital in C2v What happens when the σv(xz) opera8on is applied? The σv(xz) opera8on is a reflec8on through the xz axis The result of this corresponds to a character of  ­1 (The σv(xz) Opera8on Inverts the phase of the px orbital) Character Character Tables! Transforma8on Proper8es of a py Orbital in C2v What happens when the σv’(yz) opera8on is applied? The σv’(yz) opera8on is a reflec8on through the yz plane The result of this corresponds to a character of 1 (The Orbital is Unchanged AQer the Opera8on) Character Character Tables! Transforma8on Proper8es of a px Orbital in C2v The opera8ons generated the following characters: 1,  ­1,  ­1, 1 This row of characters in the C2v character table is labeled B2 Any orbital having these transforma8on proper8es in C2v is said to have B2 symmetry Character Character Tables! Transforma8on Proper8es of a pz Orbital in C2v What happens when the E opera8on is applied? The E opera8on is a rota8on by 360 about an arbitrary axis The result of this corresponds to a character of 1 (The Orbital is Unchanged AQer the Opera8on) Character Character Tables! Transforma8on Proper8es of a pz Orbital in C2v What happens when the C2 opera8on is applied? The E opera8on is a rota8on by 180 about the z axis The result of this corresponds to a character of 1 (The Orbital is Unchanged AQer the Opera8on) Character Character Tables! Transforma8on Proper8es of a pz Orbital in C2v What happens when the σv(xz) opera8on is applied? The σv(xz) opera8on is a reflec8on through the xz plane The result of this corresponds to a character of 1 (The Orbital is Unchanged AQer the Opera8on) Character Character Tables! Transforma8on Proper8es of a pz Orbital in C2v What happens when the σv’(yz) opera8on is applied? The σv’(yz) opera8on is a reflec8on through the xz plane The result of this corresponds to a character of 1 (The Orbital is Unchanged AQer the Opera8on) Character Character Tables! Transforma8on Proper8es of a px Orbital in C2v The opera8ons generated the following characters: 1, 1, 1, 1 This row of characters in the C2v character table is labeled A1 Any orbital having these transforma8on proper8es in C2v is said to have A1 symmetry Character Tables! Character summary for a p ­block atom in C2v symmetry z s y px py pz x A1 B1 B2 A1 Character Tables! Character summary for a p ­block atom in C2v symmetry z s y px py pz x A1 B1 B2 A1 Symmetry Restric8ons on AO’s and MO’s Only orbital of the same character (symmetry can mix) Orbitals of the same symmetry" belong to the same irreducible representa8on Any valid molecular orbital must transform according to one of the irreducible representa8ons of the molecular point group Character Tables! Character summary for a p ­block atom in C2v symmetry z s y px py pz x A1 B1 B2 A1 Symmetry Restric8ons on AO’s and MO’s Only orbital of the same character (symmetry can mix) Orbitals of the same symmetry" belong to the same irreducible representa8on Any valid molecular orbital must transform according to one of the irreducible representa8ons of the molecular point group Character Tables! Character summary for a p ­block atom in C2v symmetry z s y px py pz x A1 B1 B2 A1 These AO’s could represent the oxygen atom in water O H C2v H Lets consider this further and construct an MO diagram for water Symmetry Adapted Linear Combinations of Orbitals! SALCʼs! We know how the oxygen atoms transform within C2v point symmetry, but what do we with the hydrogen atoms? O H H Symmetry Adapted Linear Combinations of Orbitals! SALCʼs! We know how the oxygen atoms transform within C2v point symmetry, but what do we with the hydrogen atoms? O H z H z O H x y y H x 1s orbitals of hydrogen We must determine the symmetry proper8es of a ‘group orbitals’ and construct ‘symmetry adapted linear combina8ons’ (SALC’s) of orbitals Symmetry Adapted Linear Combinations SALCʼs! Determina8on of the symmetry character for Group Orbitals: If the symmetry opera8on DOES NOT CHANGE the orbital posi8on = +1 If the symmetry opera8on CHANGES the orbital posi8on = 0 If the symmetry opera8on DOES NOT CHANGE the orbital posi8on, but INVERTS its sign =  ­1 Symmetry Adapted Linear Combinations SALCʼs! Determina8on of the symmetry character for Group Orbitals: If the symmetry opera8on DOES NOT CHANGE the orbital posi8on = +1 If the symmetry opera8on CHANGES the orbital posi8on = 0 If the symmetry opera8on DOES NOT CHANGE the orbital posi8on, but INVERTS its sign =  ­1 z y x Symmetry Adapted Linear Combinations SALCʼs! Determina8on of the symmetry character for Group Orbitals: If the symmetry opera8on DOES NOT CHANGE the orbital posi8on = +1 If the symmetry opera8on CHANGES the orbital posi8on = 0 If the symmetry opera8on DOES NOT CHANGE the orbital posi8on, but INVERTS its sign =  ­1 z y x C2v E C2 σv(xz) σv’(yz) E Opera8on? Γ Symmetry Adapted Linear Combinations SALCʼs! Determina8on of the symmetry character for Group Orbitals: If the symmetry opera8on DOES NOT CHANGE the orbital posi8on = +1 If the symmetry opera8on CHANGES the orbital posi8on = 0 If the symmetry opera8on DOES NOT CHANGE the orbital posi8on, but INVERTS its sign =  ­1 z y x C2v E 2 C2 σv(xz) σv’(yz) C2 Opera8on? Γ Symmetry Adapted Linear Combinations SALCʼs! Determina8on of the symmetry character for Group Orbitals: If the symmetry opera8on DOES NOT CHANGE the orbital posi8on = +1 If the symmetry opera8on CHANGES the orbital posi8on = 0 If the symmetry opera8on DOES NOT CHANGE the orbital posi8on, but INVERTS its sign =  ­1 z y x C2v E 2 C2 0 σv(xz) σv’(yz) σv(xz) Opera8on? Γ Symmetry Adapted Linear Combinations SALCʼs! Determina8on of the symmetry character for Group Orbitals: If the symmetry opera8on DOES NOT CHANGE the orbital posi8on = +1 If the symmetry opera8on CHANGES the orbital posi8on = 0 If the symmetry opera8on DOES NOT CHANGE the orbital posi8on, but INVERTS its sign =  ­1 z y x C2v E 2 C2 0 σv(xz) 0 σv’(yz) σv’(yz) Opera8on? Γ Symmetry Adapted Linear Combinations SALCʼs! Determina8on of the symmetry character for Group Orbitals: If the symmetry opera8on DOES NOT CHANGE the orbital posi8on = +1 If the symmetry opera8on CHANGES the orbital posi8on = 0 If the symmetry opera8on DOES NOT CHANGE the orbital posi8on, but INVERTS its sign =  ­1 z y x Reducible Representa8on C2v Γ E 2 C2 0 σv(xz) 0 σv’(yz) 2 Symmetry Adapted Linear Combinations SALCʼs! Determina8on of the symmetry character for Group Orbitals: If the symmetry opera8on DOES NOT CHANGE the orbital posi8on = +1 If the symmetry opera8on CHANGES the orbital posi8on = 0 If the symmetry opera8on DOES NOT CHANGE the orbital posi8on, but INVERTS its sign =  ­1 z y x Reducible Representa8on Irreducible Representa8ons C2v Γ A1 B2 E 2 1 1 C2 0 1  ­1 σv(xz) 0 1  ­1 σv’(yz) 2 1 1 z y Symmetry Adapted Linear Combinations SALCʼs! We now know that the hydrogen 1s orbitals make transform as A1 and B2 SALC’s, but what do these look like? C2v Γ A1 B2 E 2 1 1 C2 0 1  ­1 σv(xz) 0 1  ­1 σv’(yz) 2 1 1 z y Symmetry Adapted Linear Combinations SALCʼs! We now know that the hydrogen 1s orbitals make transform as A1 and B2 SALC’s, but what do these look like? C2v Γ A1 B2 E 2 1 1 C2 0 1  ­1 σv(xz) 0 1  ­1 σv’(yz) 2 1 1 z y z A1 (Ha + Hb) x y Symmetry Adapted Linear Combinations SALCʼs! We now know that the hydrogen 1s orbitals make transform as A1 and B2 SALC’s, but what do these look like? C2v Γ A1 B2 E 2 1 1 C2 0 1  ­1 σv(xz) 0 1  ­1 σv’(yz) 2 1 1 z y z z A1 (Ha + Hb) x y B2 y (Ha  ­ Hb) x Construction of a Molecular Orbital Diagram for H2O! 2b2 2b2 3a1 3a1 B2 A1 b1 2px B1 2py B2 2pz A1 2a1 2a1 1s b1 1b2 1b2 2s A1 1a1 1a1 Construction of a Molecular Orbital Diagram for H2O! 2b2 2b2 3a1 Lone Pair B2 A1 b1 2px B1 2py B2 2pz A1 2a1 1s 3a1 Lone Pair b1 2a1 1b2 1b2 2s A1 Lone Pair 1a1 1a1 Lone Pair ...
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This note was uploaded on 01/23/2011 for the course CHEM 120A taught by Professor Figueroa during the Spring '10 term at UCSD.

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