Lanczos Parameters

Several parameters related to the Lanczos ( Friesner-Pollard) method are given. Generically:

             LANCZOS PARAMETER [N=n]
                ncycle  nkrylov  nblock  tolerance
                drhomax(2)    tolerance(n)
                  .....
                  .....
                drhomax(n)    tolerance(n)

$Ncycle$ can always be safely set to 50. Similarly, $Nkrylov=8$ is almost always a good choice. Exceptionally, for certain d-metallic systems, increasing $nkrylov=16$ may be more efficient. $Nblock$ is the dimension of the blocking in the evaluation of $H[\psi_1,...,\psi_{nblock}]$ . $Nblock$ should be a divisor of $NSTATE$ and recommended values lie in the range of 20-100. The $tolerance$ specifies the accuracy to be achieved in the Lanczos method. States are considered converged if

$$\vert H\psi-\epsilon\psi\vert^2 < tolerance$$ (274)

For efficient calculations, the tolerance should vary according to closeness to self-consistency (as measured by DRHOMAX). During initial stages of the self-consistency cycle, the tolerance can be loose, and then one should gradually tighten it when getting closer to self-consistency . An example of this might be:

             LANCZOS PARAMETER N=5
                50  8  20 1.D-9
                0.05      1.D-11
                0.01      1.D-13
                0.0025    1.D-16
                0.001     1.D-18

For accurate forces, a final tolerance of at least 1.D-16 is recommended, although accurate energies can be achieved using a lower tolerance. It is worth experimenting how best to tighten the tolerance - it is system dependent.