ssp_3y - 1 Chemical binding structure, properties 1.1...

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1-1 1 Chemical binding structure, properties 1.1 Covalent binding Molecule made up of 2 atoms, 1 bound electron (e.g., H 2 + ) (more electrons exchange interaction (see Chpt. 7)) R e ZZ r e Z r Ze m B A 0 2 0 2 0 2 2 4 4 4 2 πε + = h H (1.1) Fig.1.1. Explanation of the quantities used in equation (1.1). Approach: Find molecular orbital Ψ Mo with HE Mo Mo Ψ = (1.2) Approximation: =+ cc AA BB (1.3) i atomic wave functions
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1-2 Expected value: E Hd r dr E * * =≥ ΨΨ 3 3 (1.4) (1.3) in (1.4) E cH ccH c c ccS A AA B BB A B AB AB A B = ++ 22 2 2 with Sd r = *3 (overlap integral) HH d r AA A A = (atomic eigenvalue) d r AB A B = E E c i : =⇒ 0 E E S E S E AA A BA B B BB B () ( ) ( ) ’’ −+ = = 0 0 0 ) ( ) )( (H 0 . 2 AA = = S E H E H E Det AB BB secular equations Minimization of
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1-3 H molecule: = E 2 1 + ± ⇒= ± ± HH S AA BB AB (1.5) Bonding m.o.: Ψ Mo A B ∝+ Increase of 2 between atom cores Antibonding m.o.: A B ∝− Reduction of 2 between atom cores Fig.1.2. Bonding and antibonding molecular orbitals of an electron in the H 2 + molecule. (a) see Fig.1.1. (b) Course of Ψ () r . (c) Energy levels. Note: Bonding only occurs between partially filled atomic orbitals. Then only the binding molecular orbitals are occupied. If the atomic orbitals are filled the resulting 4 electrons also have to occupy the antibinding states because of the Pauli principle, and no net bonding occurs. Fig.1.3. Illustration of the directional covalent bonding:(left) no bonding. (right) bonding.
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1-4 Hybridization 2 , 2 , 2 , 1 : 1 1 2 2 y x p p s s C Hybridization (1-electron picture) 1 1 1 1 2 2 , 2 , 2 , 2 , 1 z y x p p p s s New linear combinations for optimum overlap Ψ ΨΨ 1 2 3 4 =+ + + + + αΨ β Sx y z y z y z y
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This note was uploaded on 01/19/2010 for the course MATERIALS M504 taught by Professor Adelung during the Spring '02 term at Uni Kiel.

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ssp_3y - 1 Chemical binding structure, properties 1.1...

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