7. Given a heteronuclear diatomic AB. Following the LCAO procedure with a guess wave function of the form $psi_g(r) = C_Apsi_{2s(Z=Z_A)}(r) + C_Bpsi_{2s(Z=Z_B)}(r)$ prove that the coefficients $C_A$ and $C_B$ are related by $frac{C_A}{C_B} = frac{H_{AA} - H_{BB}}{2H_{AB}} pm sqrt{frac{(H_{AA} - H_{BB})^2}{4H_{AB}^2} + 1}$
Added by Brian W.
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First, we need to write the Hamiltonian operator for the heteronuclear diatomic AB molecule. The Hamiltonian operator is given by: H = - (h^2/2μ) (∂^2/∂r^2) - (h^2/2μr^2) (∂^2/∂θ^2) - (h^2/2μr^2sin^2θ) (∂^2/∂φ^2) + V(r) where h is Planck's constant, μ is the Show more…
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