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H 2, He 2, and HeH Step 1: A basis for H 2 : AB AB
Step 2: Write down the Roothaan-equation H 2, He 2, and HeH (continued)
Step 3: Solve the Roothaan-equation ABAB H 2, He 2, and HeH (continued)
AB AB AB Step 3: Solve the Roothaan-equation
H2H2 H H 2, He 2, and HeH (continued) H
bond energy: energy of electron in lower MOenergy of electron in 1s H (H 2 is stable.) neglect of overlap:
H 2, He 2, and HeH (continued) Intermezzo: MO-diagrams and energy-levels central column of an MO-diagram (MO-energy) energy of the whole system (total energy)
He 2 : H 2, He 2, and HeH (continued)
He 2 He H 2, He 2, and HeH (continued) He
H 2, He 2, and HeH (continued) bond energy: energy of electron in lower MO energy of electron in 1s He (He 2 is not stable.) Overlap should not be neglected here. energy of electron in upper MO
HeH: H 2, He 2, and HeH (continued)
H 2, He 2, and HeH (continued) He level shifted downwards H level shifted upwards ordering: The average of the levels increases.
H 2, He 2, and HeH (continued) The lower MO resembles the 1s orbital of He. The upper MO resembles the 1s orbital of H.
HeHHe H 2, He 2, and HeH (continued) H
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= the matrix for T relative to the standard basis is a basis for R 2. B is the matrix for T relative to To find B, complete:
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