Neil Drummond wrote:Dear Vladimir,

One argument for the time-step bias in the energy being linear is that the time-step error in the DMC Green's function is O(tau^2), and hence time-step errors are introduced at a rate O(tau^2)/tau=O(tau) into the mixed wave function f(R,t)=phi(R,t).Psi(R), where Psi(R) is the trial wave function and phi(R,t) is the solution of the imaginary-time Schroedinger equation. At the same time, the DMC algorithm is driving f exponentially towards the ground state phi_0(R).Psi(R), where phi_0 is the fixed-node ground state wave function, at a rate given by the correlation time T_corr. Hence the error Delta f in the mixed wave function is being removed at a rate Delta f / T_corr. In equilibrium the rates at which errors are introduced and removed from f balance, and so Delta f is proportional to the time step tau. The error in f then carries over to other expectation values, including the energy, giving a linear bias.

In this case, could there be some sort of issue with the Gaussian basis set (or perhaps even with the treatment of the nodal surface in the multideterminant wave function) that introduces a new, small length scale into the problem, resulting in a crossover between two different linear bias regimes?

Best wishes,

Neil.

Hello Neil

As I understand, Psi(

R) obeys the e-e and e-n Kato cusp conditions as we set CUSP CORRECTION to TRUE in the input files, but does the phi(

R,

t) have the same properties?

I think that in the case of the zero time step it does, but if we perform the fourier transform of phi_0(

R,

t) and apply low-pass filter (freq lower than 1/tau) than transform back we will get roughly phi(

R,

t).

I think we will break Kato cusp conditions for phi(

R,

t).

Сan we impose Kato cusp conditions for phi(

R,

t) by hands?

Best Vladimir.

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