Molecular Basis Sets Adaptation for Periodic Systems

3 Molecular Basis Sets Adaptation for Periodic Systems 

In the periodic systems the basis sets are chosen in such a way that they satisfy the Bloch theorem. Let a finite number of contracted GTFs be attributed to the atom A with coordinate in the reference unit cell. The same GTFs are then formally associated with all translationally equivalent atoms in the crystal occupying positions rA + (In (In is the direct lattice translation vector). For the crystal main region of N primitive unit cells there are N tha Gaussian-type Bloch functions (GTBF) 

The total number M of GTBFs equals M = X) where the summation is made 

The product of two polynomial GTF, of degree p and v and located at points A and B is therefore another polynomial GTF located at C of degree p + v m xc, yc and za, which can be expressed as a short expansion of one-center Gaussians  

We follow [458] in discussion of optimization strategies for the basis sets given in the libraries mentioned and also the adaptation of molecular bases for various types of solids. First, a number of general principles are given that should be taken into account when choosing a basis set for a periodic system. 

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