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I am wondering how runtime is influenced by a.) the blip multiplicity and b.) the parameters in the Jastrow:

I expect that that the answer to a.) is: runtime is independent of blip multiplicity since each point in space is only contained in 3 B-splines (per dimension) independently of the multiplity. This is also what I observe in my calculations - I just want to make sure this is correct.

Concerning b.): I suppose that the Jastrows have to be calculated each time an electron configuration is moved in DMC. Am I correct in assuming that the calculation time spent to recalculate the Jastrow scales linearly with the number of Parameters and to the third power of the cutoff radius? Or is this nonsense? If it is correct, how expensive are the Jastrows? Might it make sense to use shorter cutoffs, if a larger cutoff doesn't influence the energy significantly?

P.S. sorry for asking so many questions, but I need to shed some light into this still rather gray (not entirely black) box called Casino.

Dear Katharina,

The time should only depend weakly on the blip multiplicity. Usually the time spent evaluating blip orbitals is dominated by the time spent evaluating the blip functions themselves. (On the other hand, the memory requirements will increase rapidly with blip multiplicity.)

The time taken to evaluate the Jastrow generally increases linearly with the number of parameters, although some terms are more expensive than others. It also depends on the cutoff lengths: if the terms are long-range then they will be needed more often.

Usually the u term (pairwise between electrons) has a cutoff length that spans the system, and hence will dominate at large system sizes (the cost per configuration move will be O(N^2)). If you fix the cutoff length of u rather than letting it grow then the cost of evaluating u per configuration move will grow as O(N). The chi and f functions should have cutoff lengths of the order of a bond length, independent of system size, and hence the cost goes as O(N).

If you are doing DMC with a Slater-Jastrow wave function then you can restrict cutoff lengths. It would be best to do this in a systematic fashion for different system sizes.

Best wishes,

Neil.

Dear Neil!

Thank you for your reply!

You say that I can restrict the cutoff in the Jastrow if using the wf in DMC. Wouldn't that make the error in the trial wf larger and thus increas time-step errors and errors in the evaluation of the pseudo-potentials? Or is this effect negligible?

What do you mean by

It would be best to do this in a systematic fashion for different system sizes.

?

Thanks, Katharina

Dear Katharina,

Yes, in principle making the trial wave function slightly worse will make time step, population-control and pseudopotential locality biases slightly worse. However, you are presumably planning to get rid of the former by extrapolating to zero time step. So long as you are sensible with the restriction of the wave function, I wouldn't have thought pseudopotential locality errors would be a big problem.

By "systematic" I mean fixing the cutoff lengths to something sensible at each system size so that the errors you incur are smooth functions of system size. E.g., you could decide to fix the cutoff lengths for chi at 1.5 bond lengths and the cutoff length for u at several bond lengths. Or you could let the cutoff length for u be some fixed fraction of the Wigner-Seitz cell radius.

Best wishes,

Neil.

Got it, thank you, Katharina