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Geometry optimization using Krylov subspace method
Date: 2015/07/10 14:58
Name: LK


I have been looking at systems containing several hundred atoms, and comparing geometry optimizations between Cluster and Krylov subspace.

For the cluster eigensolver, for all systems the energy decreases steadily as well as the forces at each step.

For the Krylov algorithm, for smaller systems (say less than 200 atoms) I observe very similar behavior to Cluster. But for systems larger than about 200 atoms, the Krylov optimization had overall increasing energy between optimization steps, as if going to a TS, and the forces often increase/decrease erratically.

I have played with the two keywords orderN.HoppingRanges and orderN.KrylovH.order, but it didn't change the behavior (for example, 9.0 Angs and order 1000).

I have looked at both metallic particles and covalent, large band-gap systems, and I saw the same behavior.

I am wondering whether the forces calculated by the Krylov method have less resolution, or whether there is some other parameter that can converge things tighter (for example, I use 10^-6 energy convergence, and 150Rydberg cutoff).

Thank you for your time.
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Re: Geometry optimization using Krylov subspace method ( No.1 )
Date: 2015/08/06 10:18
Name: T. Ozaki


As we discussed in the paper (PRB 74, 245101), a force calculated by the O(N) Krylov subspace
method is an approximate one. The accuracy of forces can be improved by tightening the
following two parameters:

orderN.HoppingRanges 6.0
orderN.KrylovH.order 400

The other parameters should be always switched on as

orderN.Exact.Inverse.S on
orderN.Recalc.Buffer on
orderN.Expand.Core on

By tightening the two parameters, one can improve the quality of forces as shown
in Fig.12 (PRB 74, 245101).



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