Periodic Systems

The Coulomb energy of a crystal is a sum whose value depends on the order you add it up. Resolving the paradox and Ewald summation.

One orbital and one hopping parameter go a long way. Band structures for the FCC lattice and graphene, and the counting rule that makes most zigzag nanotubes semiconductors.

Two ways to change graphene's band structure. Breaking the sublattice symmetry opens a gap, and stacking a second layer flattens the Dirac cones.

Fitting diamond's energy-volume curve to the Birch-Murnaghan form, and the effect of the HF reference quality on MP2.

Supercells and k-point sampling are the same limit approached two ways. Extrapolating diamond to infinite size, and the Ewald correction's effect on convergence.

The four-index integral is too expensive for crystals. Density fitting, its four flavors in PySCF, and a first benchmark on diamond.