Re: Cutoff lengths in the Jastrow factor
Posted: Fri Oct 25, 2013 9:31 pm
Dear Varelse,
The cutoff length behaviour you describe seems a bit unusual; nevertheless every system is unique and, if the energy expectation value is going down, one cannot argue with the variational principle. If you are looking at similar systems then I would certainly make use of what you have learned in this case when choosing initial cutoff lengths.
The DMC energy is in principle independent of the Jastrow factor, because the Jastrow factor does not affect the nodal surface. If you have a poor wave function then the time-step bias, population-control bias, etc. will be larger. Nevertheless, for an all-electron system, if you extrapolate to zero time step, you should get exactly the same DMC energy without a Jastrow factor as you do with a Jastrow factor (optimal or otherwise). If you are performing pseudopotential calculations then there is an additional pseudopotential locality approximation that is second order in the error in the wave function, so the DMC energy has a slight dependence on the Jastrow factor.
So, while a good Jastrow factor is undoubtedly helpful (and bad trial wave functions are responsible for most problems encountered in QMC calculations), it should nevertheless be the case that optimisation is a small fraction of your total CPU time - if you find you are using more core hours on optimisation than on the subsequent DMC then you are probably overdoing the optimisation.
If you have DMC results you can judge the quality of your Jastrow factor by evaluating (E_HFVMC - E_VMC)/(E_HFVMC - E_DMC), where E_HFVMC is the VMC energy without a Jastrow factor, E_VMC is the VMC energy with a Jastrow factor and E_DMC is the DMC energy. For single atoms and electron gases this should be about 95% or more; for molecules and crystals with pseudopotentials this should be more than, say, 85-90%; for all-electron systems it should be more than, say, 80-85%.
Best wishes,
Neil.
The cutoff length behaviour you describe seems a bit unusual; nevertheless every system is unique and, if the energy expectation value is going down, one cannot argue with the variational principle. If you are looking at similar systems then I would certainly make use of what you have learned in this case when choosing initial cutoff lengths.
The DMC energy is in principle independent of the Jastrow factor, because the Jastrow factor does not affect the nodal surface. If you have a poor wave function then the time-step bias, population-control bias, etc. will be larger. Nevertheless, for an all-electron system, if you extrapolate to zero time step, you should get exactly the same DMC energy without a Jastrow factor as you do with a Jastrow factor (optimal or otherwise). If you are performing pseudopotential calculations then there is an additional pseudopotential locality approximation that is second order in the error in the wave function, so the DMC energy has a slight dependence on the Jastrow factor.
So, while a good Jastrow factor is undoubtedly helpful (and bad trial wave functions are responsible for most problems encountered in QMC calculations), it should nevertheless be the case that optimisation is a small fraction of your total CPU time - if you find you are using more core hours on optimisation than on the subsequent DMC then you are probably overdoing the optimisation.
If you have DMC results you can judge the quality of your Jastrow factor by evaluating (E_HFVMC - E_VMC)/(E_HFVMC - E_DMC), where E_HFVMC is the VMC energy without a Jastrow factor, E_VMC is the VMC energy with a Jastrow factor and E_DMC is the DMC energy. For single atoms and electron gases this should be about 95% or more; for molecules and crystals with pseudopotentials this should be more than, say, 85-90%; for all-electron systems it should be more than, say, 80-85%.
Best wishes,
Neil.