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H2, He2, and HeH Step 1: A basis for H2: A B A B

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**H2, He2, and HeH (continued)**

Step 2: Write down the Roothaan-equation

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**H2, He2, and HeH (continued)**

reflection: A B s

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**H2, He2, and HeH (continued)**

Step 3: Solve the Roothaan-equation A B A B

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**H2, He2, and HeH (continued)**

Step 3: Solve the Roothaan-equation A B A B A B

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**H2, He2, and HeH (continued)**

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**H2, He2, and HeH (continued)**

energy of electron in lower MO energy of electron in 1sH bond energy: (H2 is stable.) neglect of overlap:

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**H2, He2, and HeH (continued)**

Intermezzo: MO-diagrams and energy-levels central column of an MO-diagram (MO-energy) energy of the whole system (total energy)

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**H2, He2, and HeH (continued)**

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**H2, He2, and HeH (continued)**

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**H2, He2, and HeH (continued)**

energy of electron in lower MO energy of electron in upper MO bond energy: energy of electron in 1sHe (He2 is not stable.) Overlap should not be neglected here.

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**H2, He2, and HeH (continued)**

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**H2, He2, and HeH (continued)**

small overlap:

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**H2, He2, and HeH (continued)**

He level shifted downwards H level shifted upwards ordering: The average of the levels increases.

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**H2, He2, and HeH (continued)**

The lower MO resembles the 1s orbital of He. The upper MO resembles the 1s orbital of H.

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**H2, He2, and HeH (continued)**

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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.

Qualitative MO-theory Why is the Hartree-Fock approximation important? HF gives quite reasonable estimates for the bond energies. HF is a starting point.

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