### DMC timestep bias asymptotic

Posted:

**Fri Mar 09, 2018 6:27 am**Hello everyone who does DMC calculations.

I calculated the time step bias dependence for simple full electron systems like H-Cl atoms and some diatomic.

I've found that small time step asymptotic is rather quadratic than linear whereas large time step asymptotic is linear in some cases.

For example Be atom with 4 determinant WFN which is known to give the correct nodal surface

For example B atom with 3 determinant WFN which is known to give the correct nodal surface

For comparition F atom and F2 molecules the slopes match exactly

As for single determinant Be and B atoms and Be2 molecule which nodal surface is not exact asymptotic is not linear.

So is there any equation which describe DMC time step bias asymptotic behavior arising from different sources of nodal surface non-ideality or the finiteness of the time step itself?

Best Vladimir

I calculated the time step bias dependence for simple full electron systems like H-Cl atoms and some diatomic.

I've found that small time step asymptotic is rather quadratic than linear whereas large time step asymptotic is linear in some cases.

For example Be atom with 4 determinant WFN which is known to give the correct nodal surface

For example B atom with 3 determinant WFN which is known to give the correct nodal surface

For comparition F atom and F2 molecules the slopes match exactly

As for single determinant Be and B atoms and Be2 molecule which nodal surface is not exact asymptotic is not linear.

So is there any equation which describe DMC time step bias asymptotic behavior arising from different sources of nodal surface non-ideality or the finiteness of the time step itself?

Best Vladimir