The Jahn-Teller Theorem

"The Jahn-Teller (J-T) theorem states that in molecules/ ions that have a degenerate ground-state, the molecule/ion will distort to remove the degeneracy. This is a fancy way of saying that when orbitals in the same level are occupied by different numbers of electrons, this will lead to distortion of the molecule. For us, what is important is that if the two orbitals of the eg level have different numbers of electrons, this will  lead to J-T distortion. Cu(II) with its d9 configuration is degenerate and has J-T distortion."

In Quantum point of view, electrons are dynamically hoping between different orbitals. To form a unequal occupation between two degenerate orbitals, a fluctuation is required. So this is like the van der Waals interaction, is essentially a Casimir effect.
However, to distort the lattice, maybe we need to have ion lattice relaxation time is shorter than the hoping/fluctuation time.

Is this the correct picture? 

Crystal Binding

1 The attractive electrostatic interaction between the negative charges of the electrons and the positive charges of the nuclei is entirely responsible for the cohesion of solids. Magnetic forces have only a weak effect on cohesion.

2 The melting T and bulk modulii vary roughly as the cohesive energies.

3 The repulsive interaction in binding in large part stems from the Pauli exclusion principle (PEP). Image that two atoms approach to each other, electron orbits will overlap. Because of PEP, if the orbit is full, some electrons have to go to higher energy orbits.

4 Van der Waals type inert gas crystals are favor close pack structure because there is no preferred interaction orientation.

5 Zero-point motion of the atom affect the accuracy of the Lennard-Jones potential model. The heavier the atom the less affection on the model.

6 Ionic crystal structures are mostly relatively empty packed. I guess the reason is the same charge interactions.

7 In ionic crystal, instead of Van der Waals potential, the total potential is sum of central field potential (short range) and coulomb potential (long range).

Definitions:

1 Cohesive energy (usually single element crystal): the energy that must be added to the crystal to separate its components into neutral free atoms at rest, at infinite separation, with the same electronic configuration. In theory, it is determined from total potential at equilibrium lattice constant.

2 Lattice energy (ionic crystals): the energy that must be added to the crystal to separate its component ions into free ions at rest at infinite separation.

3 Van der Waals-London Interaction: two electric dipole oscillators with coulomb interactions. See Kittel P-53. It is quantum interaction because the resulted attractive interaction comes from the ground state energy of two oscillators. (In classical model, ground state energy of oscillator is 0.)

4 Lennard-Jones potential: mostly applied to inert gases or molecules, it is the added up of Van der Waals-London Interaction and Repulsive Interaction.

5 Madelung constant: is the sum of all coulomb interactions on one site in an ionic crystal. Typical values: NaCl 1.75; CsCl 1.76; ZnS 1.64.