Q1.
(a) State and prove the variation theorem.
(b) Derive the binding energy and wavefunctions for H$_2^+$ molecule in terms of Coulomb (J), exchange (K), and overlap
(S) integrals using a linear combination of atomic orbital and molecular orbital (LCAO-MO) theory.
(c) Write down the valence bond and molecular orbital wavefunctions for the H$_2$ molecule and compare them.
(d) Draw the MO-diagram for a general diatomic molecule. Show the electronic configuration of N$_2$, N$_2^+$, and N$_2^-$ and
predict their relative stabilities.