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7.3 Penalty functional and electron number
The penalty functional is defined by
The derivative with respect to the densitykernel is then

(7.38) 
The penalty functional depends implicitly upon the support functions
though the overlap matrix:

(7.39) 
so that

(7.40) 
For the sake of completeness, we now describe the expressions for the
electron number and its derivatives.

(7.41) 

(7.42) 

(7.43) 
Next: 7.4 Physical interpretation
Up: 7. Computational implementation
Previous: 7.2 Energy gradients
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Peter Haynes