Question

50. The molecular orbital may be written as the superposition of atomic orbitals: We can use the variation theorem to find the optimal values of Ca and Cb that would yield the expectation value of energy to be the closest to the real energy eigenvalue of the system. Solving the variational integral and differentiating (W) with respect to Ca and Cb, we obtain secular equations of the kind Ca (Haa-) + Cb(Hab - Sab)=0 Ca (Hab - Sab) + Cb(Hbb-)=0 Solve this system of secular equations for the case of homonuclear diatomic molecules in terms of the integrals Haa, Hab, Sab, i.e. the case when Haa = Hbb.

          50. The molecular orbital may be written as the superposition of atomic orbitals:
We can use the variation theorem to find the optimal values of Ca and Cb that would yield the expectation value of energy to be the closest to the real energy eigenvalue of the system.
Solving the variational integral and differentiating (W) with respect to Ca and Cb, we obtain secular equations of the kind
Ca (Haa-) + Cb(Hab - Sab)=0
Ca (Hab - Sab) + Cb(Hbb-)=0
Solve this system of secular equations for the case of homonuclear diatomic molecules in terms of the integrals Haa, Hab, Sab, i.e. the case when Haa = Hbb.

Added by Joan S.

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