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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 πε πε + = h H (1.1) Fig.1.1. Explanation of the quantities used in equation (1.1). Approach: Find molecular orbital Ψ Mo with H E Mo Mo Ψ Ψ = (1.2) Approximation: Ψ Ψ Ψ = + c c A A B B (1.3) Ψ i atomic wave functions
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1-2 Expected value: E H d r d r E * * = Ψ Ψ Ψ Ψ 3 3 (1.4) (1.3) in (1.4) E c H c H c c H c c c c S A AA B BB A B AB A B A B = + + + + 2 2 2 2 2 2 with S d r A B = Ψ Ψ * 3 (overlap integral) H H d r AA A A = Ψ Ψ * 3 (atomic eigenvalue) H H d r AB A B = Ψ Ψ * 3 E E c i : = 0 c H E c H E S c H E S c H E A AA B AB A AB B BB ( ) ( ) ( ) ( ) + = + = 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 + ± = ± ± H H H H S AA BB AA AB (1.5) Bonding m.o.: Ψ Ψ Ψ Mo A B + Increase of Ψ 2 between atom cores Antibonding m.o.: Ψ Ψ Ψ Mo A B Reduction of Ψ 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.
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