Varmin and emin energies

[varelse]

When I run emin calculation, the energy in first iteration is usually different then the initial energy in varmin and madmin. Is that wrong? They both start from empty Jastrow (no parameters in the Taylor expansions), so the starting point should be similar.

[Mike Towler]

Hi Blazej,

Note first that having an empty Jastrow factor is not the same as having no Jastrow at all (there is a cusp present even if all the parameters are zero). See the formulae for the various Jastrow terms in section 22 of the manual.

The difference you see between emin and varmin for the total energy following the first VMC configuration run is not wrong - it is entirely as expected in CASINO wave function optimizations. In a varmin (vmc_opt) calculation the Jastrow is turned off entirely (equivalent to 'use_jastrow=F' in input) during the first VMC config generation run -- so that the initial HF configurations match the supposed starting wave function. In emin (vmc_opt) by contrast the 'empty Jastrow' with the cusp is used in the first config generation -- equivalent to 'use_jastrow = T' -- since this makes the energy minimization work better (for technical reasons I won't bore you with).

Mike

[Sweyn Asleifsson]

When should one use emin rather than varmin (and vice versa)?

Thanks,

S.

[Neil Drummond]

If you are doing a "typical" QMC project in which you are interested in DMC energies obtained with Slater-Jastrow trial wave functions then I suggest you stick to variance minimisation. In particular, the varmin_linjas method allows you to carry out optimisations relatively cheaply. The resulting wave functions also seem to be less likely to result in instability in DMC than wave functions optimised by energy minimisation.

If you are optimising parameters that affect the nodal surface then the final stage of your optimisation process should be emin. If optimising a Slater-Jastrow-backflow wave function then I usually optimise the Jastrow factor quickly by varmin_linjas without a backflow function, then add a backflow function and optimise everything together by emin.

Note that emin struggles to optimise cutoff lengths in the Jastrow factor and backflow function. If you want to optimise these then use varmin or madmin.

[Mike Towler]

Note added later: the default behaviour for empty Jastrows in emin (referred to above) was changed in CASINO v2.13.94, so that it now does the following:

"If one is studying a homogeneous system, or a 3D-periodic system or is using
energy minimisation using the CASINO standard Jastrow factor, a simple default
for u will be chosen that satisfies the Kato cusp conditions; otherwise, only
the Slater wave function will be used for the first configuration generation
run when performing wave-function optimization" (varmin, madmin, or emin)."

Mike