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

$\langle b_{i}|{\bf {H}}-\epsilon {\bf {S}}|b_{j}\rangle =0$

with the basis set

$b_{i,i=1,N-1}=\{\phi _{n}/g_{n}^{1}/g_{n}^{2}/g_{n}^{3}/...\}.$

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

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