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.