in PBC, there is one extra derivative of energy with reference to the system geometry, this is the derivative of cell energy with respect to cell dimension (see for example: H. Teramae, et al. Chem. Phys. Lett. 101, 149 (1983); P. J. Feibelman, Phys. Rev. B. 44, 3916 (1991))
Choice of basis function is always dependent on type of calculation. In general The basis set must satisfy the same
boundary conditions applied for your system. E.g. for an infinite crystal, the basis must satisfy periodic boundary conditions; for a molecule or a cluster, basis functions must
go to zero at infinity.
Periodic Boundary Conditions are one of the basic things you need to learn about when doing Materials Simulation:
http://en.wikipedia.org/wiki/Periodic_boundary_conditions
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