## DMC energy

General discussion of quantum Monte Carlo in electronic structure theory

### Re: DMC energy

Dear Vladimir,

The optimised VMC time step is generally determined by the most important length scale, not necessarily the longest length scale in the system being studied.

Fitting a sum of exponential decays to the DMC energy could in principle tell you about excited-state energies. However, these are excited states subject to the boundary condition of being zero on the nodes of the (ground state) trial wave function, and are not necessarily excited states of interest. Furthermore, fitting to determine the exponents of multiple terms would require colossal amounts of data (i.e., a vast configuration population).

I'm not sure about your conclusion about 1/x being a better fit than a sum of exponentials... The chi^2 values aren't that different.

Best wishes,

Neil.
Neil Drummond

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### Re: DMC energy

Neil Drummond wrote:Dear Vladimir,

The optimised VMC time step is generally determined by the most important length scale, not necessarily the longest length scale in the system being studied.

Fitting a sum of exponential decays to the DMC energy could in principle tell you about excited-state energies. However, these are excited states subject to the boundary condition of being zero on the nodes of the (ground state) trial wave function, and are not necessarily excited states of interest. Furthermore, fitting to determine the exponents of multiple terms would require colossal amounts of data (i.e., a vast configuration population).

I'm not sure about your conclusion about 1/x being a better fit than a sum of exponentials... The chi^2 values aren't that different.

Best wishes,

Neil.

I agree with you Neil, I tested several other molecules such as AlCl3, Cl, B with different initial JASTROW optimizations, actually 1/x not always better. I would say that the accuracy of 1/x and exp is comparable at the level of errors.
Thanks for the understandable explanation.

UPD
In general one can write any differential equation in form of y' = F(y), solve it with Wolfram and fit DMC equilibration data with this solution.
For example y' + C*y = 0 solution give exponential decay, y' + C*y^2 = 0 solution give 1/x decay. Should y' = C1*y+C2*y^2+C3*y^3 fits better.

Best, Vladimir.
In Soviet Russia Casino play you.
Vladimir_Konjkov

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