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7. Computational implementation
In this chapter we describe how the corrected penalty functional method
described in section 6.2 has been implemented in a total
energy computer code to perform linearscaling quantummechanical
calculations on arbitrary systems.
As mentioned in section 4.6, the densitymatrix is
represented in the form

(7.1) 
We refer to the contravariant quantity
as the
densitykernel, and the covariant quantities
are localised nonorthogonal support functions, which are themselves
expanded in terms of the sphericalwave basisset of chapter 5:

(7.2) 
We now proceed to express the total energy and penalty functional in
terms of these quantities, and also to calculate gradients with respect
to the densitykernel and expansion coefficients
.
We will also discuss the implementation of the normalisation constraint and
also how the convergence might be improved by the use of a preconditioning scheme for
the gradients.
Subsections
Next: 7.1 Total energy and
Up: thesis
Previous: 6.2 Corrected penalty functional
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Peter Haynes