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Consider the Hydrogen molecule ion $\bgroup\color{col1}$ H_2^+$\egroup$ .

a) Write down the Hamiltonian for the electronic part of $\bgroup\color{col1}$ H_2^+$\egroup$ , including the repulsion energy of the protons.

b) Briefly explain (one or two sentences) what LCAO means.

c) Write down the molecular orbitals (MO) for the lowest bonding and antibonding state in $\bgroup\color{col1}$ H_2^+$\egroup$ in terms of atomic orbitals.

d) Briefly explain the spatial symmetry of the bonding and antibonding MO in $\bgroup\color{col1}$ H_2^+$\egroup$ .

e) Sketch the effective potentials for the nuclei $\bgroup\color{col1}$ E_{\pm}(R)$\egroup$ as a function of their distance $\bgroup\color{col1}$ R$\egroup$ for the bonding and the antibonding state. Very briefly explain why the bonding state is called `bonding'.

Tobias Brandes 2005-04-26