set8 - g = 2 2 SAB A B 1 2 u = 2 2 SAB A B 1 2 u A B g...

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Diatomic molecules From Li 2 to F 2 ψ g = 2 + 2 S AB ( ) 1/2 φ A + B ( ) u = 2 2 S AB ( ) 1/2 A −φ B ( ) Molecular ground and excited state orbital from atomic orbitals A B u g
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The simplest diatomics Electron confgura.ons No± bonding – an.bonding electrons Equilibrium distance Å Dissocia.on energy kJ/mol H 2 + (1σ g ) 1 1 1.06 256 H 2 (1σ g ) 2 2 0.74 432 He + 2 (1σ g ) 2 (1σ u ) 1 1 1.08 ~300 He 2 (1σ g ) 2 (1σ u ) 2 0 1 σ g = 1 s A + 1 s B 1 u = 1 s A 1 s B (ignoring normalizaNon factors….)
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Going to principal number n=2 and discovering new orbitals 2 σ g = 2 s A + 2 s B 2 u = 2 s A 2 s B 1 π u x , y ( ) = 2 p x , yA + 2 p x , yB 1 g x , y ( ) = 2 p x , yA 2 p x , yB 3 g = 2 p zA + 2 p zB 3 u = 2 p zA 2 p zB
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Molecular orbitals for diatomics g u g u (x) u (y) g (x) g (y) u Order of 3σ g and 1π u not always as shown
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Diatomic molecule energy diagrams
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Electronic confguraNons oF diatomics Molecule Electron confgura.on Excess oF bonding electrons No± oF unpair electrons Bond length Å Dissocia.on energy kJ/mol Li 2 (2σ g ) 2 2 0 2.67 107 Be 2 (2σ g ) 2 (2σ u ) 2 0 0 B 2 [Be](1π u ) 2 2 2 1.59 291 C 2 [Be] (1π u ) 4 4 0 1.24 590 ± 2 [Be] (1π u ) 4 (3σ g ) 2 6 0 1.09 942 O 2 [Be] (1π u ) 4 (3σ g ) 2 (1π g ) 2 4 2 1.21 494 ² 2 [Be] (1π u ) 4 (3σ g ) 2 (1π g ) 4 2 0 1.44 154
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Hueckel theory of π systems We assume that the σ electrons that provide the scaFold to organic molecules are Separated from the P electrons (or the π system). Consider for example ethene: C C H H H H
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The secular determinant of P orbitals situated on carbon atoms and normal to the plane that includes the hydrogens α− E β− ES ES ES
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set8 - g = 2 2 SAB A B 1 2 u = 2 2 SAB A B 1 2 u A B g...

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