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Qualitative MO-theory Why is the Hartree-Fock approximation important? HF gives quite reasonable estimates for the bond energies. HF is a starting point for many methods that try to improve on its results. HF is a prototype for various theories of the chemical bond.

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Qualitative MO-theory (continued) bond energy: total energy (kJ/mol) experimental bond energy (kJ/mol) calculated bond energy (kJ/mol)

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Qualitative MO-theory (continued) Rule II: Two orbitals that interact form two new orbitals. The one with the lower energy is called a bonding orbital, the one with higher energy an anti-bonding orbital. The stabilization of the bonding orbital is smaller than the destabilization of the anti-bonding orbital.

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Qualitative MO-theory (continued) bonding level anti-bonding level This is relevant for repulsion. It holds only if overlap is not neglected.

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Qualitative MO-theory (continued) Rule III: The (de)stabilization of the (anti-)bonding orbital is smaller when the difference of the energies of the orbitals, from which the bonding and anti-bonding orbital are formed, is larger.

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Qualitative MO-theory (continued)

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covalent bond ionic bond

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Qualitative MO-theory (continued) Rule IV: The (de)stabilization of the (anti-)bonding orbital is smaller when the overlap of the orbitals, from which the bonding and anti-bonding orbital are formed, is smaller.

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Qualitative MO-theory (continued) secular equation: assume: case 1:case 2:

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Qualitative MO-theory (continued) Basis for Li 2 : Li 2 Li is large; no interaction between 1s and 2s (rule III). The 1s’s are compact; little overlap; neglegible (de)stabilization (rule IV). core orbitals valence orbitals

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Qualitative MO-theory (continued) Basis for Be 2 : Be 2 Be Be 2 is not stable (rule II).

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Qualitative MO-theory (continued) Rule I: Transform the basis functions to symmetry-adapted functions.

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AB Qualitative MO-theory (continued) Basis for H 2 : A B A B

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Qualitative MO-theory (continued) secular equation:

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Qualitative MO-theory (continued) secular equation:

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Qualitative MO-theory (continued) Non-diagonal matrix elements may vanish because of symmetry.

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I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=

I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=

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