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Efficient single band eigenvalue-minimization

A very efficient scheme for the calculation of the lowest eigenvalues, might be obtained by increasing the basis set mentioned in the previous section in each iteration step, i.e.: At the step N solve the eigenvalue problem

$\displaystyle \langle b_i \vert {\bf H} - \epsilon {\bf S} \vert b_j \rangle = 0

with the basis set

$\displaystyle b_{i,i=1,N-1} = \{ \phi_{n} / g^1_{n} / g^2_{n} / g^3_{n} / ...\}.

The lowest eigenvector of the eigenvalue problem is used to calculate a new (possibly preconditioned) search vector $ g^N_{n}$.

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