When I was reading through the ADF-BAND tutorials, one of the toy systems presented was a 1-D periodic structure involving 3 collinear hydrogen atoms. The tutorial pointed out that, topologically speaking, this is cylindrically symmetrical (more specifically, it's ring symmetrical).
In the instance of a 2-D structure, can the calculation be considered a model for the surface of a torus (this seems logical), a sphere (I doubt this because if you fit a rectilinear grid to a sphere you end up with two poles and dissimilar meridians and parallels), or other?
Bonus questions: Has anyone used periodic calculations to model electronic structure/chemistry on the surface of a sphere or torus? Can you introduce a curvature term to account for these structures having a finite size?