Localized Orbitals for Valence Bands LCAO approximation

3 Localized Orbitals for Valence Bands LCAO approximation 

The method of the localized WF generation for occupied energy bands was suggested in [53,63,64] and implemented with the CRYSTAL code for LCAO calculations of periodic systems. In this method, WFs are sought in the form of a linear combination of atomic orbitals (AO)  

index A runs over atoms in a cell, multipliers pa,s are equal to unity only for those atoms on which the Muthken populations of WF W(s(r) are more than the, fixed in advance, chosen threshold (for other atoms they are supposed to be equal to zero), and the vector Ga,s defines a cell in which this population is maximal. Thus, 

At the second stage termed by localization , the linear combination of WF, belonging to one cell is searched  

Here is a point of lTi (r) centering (centroid position). In other words, this 

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