101210 Lecture 6

101210 Lecture 6 - Welcome to:! Chemistry 120A! Lecture 5!...

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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! What Makes Up a Character Table? Character tables contain informa8on about how func8ons transform in response to the opera8ons of the group Character Tables! What Makes Up a Character Table? Character tables contain informa8on about how func8ons transform in response to the opera8ons of the group Character Character Tables! What Makes Up a Character Table? Character tables contain informa8on about how func8ons transform in response to the opera8ons of the group 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! What Makes Up a Character Table? Character tables contain informa8on about how func8ons transform in response to the opera8ons of the group 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! What Makes Up a Character Table? Character tables contain informa8on about how func8ons transform in response to the opera8ons of the group 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! What Makes Up a Character Table? Character tables contain informa8on about how func8ons transform in response to the opera8ons of the group 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! What Makes Up a Character Table? Character tables contain informa8on about how func8ons transform in response to the opera8ons of the group 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! C1, Cs, Ci EXAMPLES Td , Oh , C∞v , D∞h , Ih H H B H B H A – Cs B – Ci C – D2d D – D2h H H C or S2n Groups D Groups Dnh Cnh Dnd Dn Cnv S2n Cn Character Tables! A – Cs C – D2d B – Ci D – D2h H H H B B H H H Character Tables! A – Cs C – D2d B – Ci D – D2h H H H B B H H H 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 s z px py pz A1 B1 B2 A1 y x ...
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This note was uploaded on 08/15/2011 for the course CHEM 114B taught by Professor Wang during the Spring '09 term at UCSD.

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