CASINO manual - Theory of Condensed Matter

6.3.3 How to a ‘madmin’ calculation
‘Madmin’ is a variant of variance minimization where a measure of the spread of local energies other
than the variance is minimized, one that is less sensitive to outliers (e.g., divergent local energies).
This measure is the mean absolute deviation (MAD) from the median energy,
MAD = 1 ∑
∣
N C
R
∣E {α}
L
(R) − Ēm∣ , (1)
where Ēm is the median of the set of local energies {E L }. This actually works very well, and minimizing
the MAD generally gives a lower energy than minimizing the variance. Having a ‘robust’ measure of
the spread turns out to be important when e.g., optimizing parameters that affect the nodal surface
where Ψ = 0 (such as multideterminant expansion coefficients, parameters in orbitals and backflow
functions). Optimization of such parameters is difficult because the local energy diverges where the
wave function is zero, and so the unreweighted variance diverges whenever the nodal surface moves
through a configuration.
To use this method, you do essentially the same procedure as in a varmin calculation but set
opt method = ‘madmin’.
6.4 How to do a DMC calculation
DMC calculations are the main point of doing QMC. They are generally extremely accurate—
comparable to or better than the best quantum chemistry correlated wave-function techniques—and
yet remain applicable to very large systems. However, they require an accurate trial wave function in
order to be efficient. This is normally taken to be a Slater-Jastrow wave function with the parameters
in the Jastrow factor optimized by one or more of the above minimization procedures.
So we begin by assuming we have an input file, an xwfn.data file containing the determinantal
part of the wave function and an optimized correlation.data file containing the Jastrow factor.
A DMC calculation then consists of three basic steps: (i) VMC configuration generation; (ii) DMC
equilibration; and (iii) DMC statistics accumulation.
The wave function in DMC is not represented analytically, but by the time-dependent distribution of
a set of configurations (or ‘walkers’). The shape of the many-electron wave function in configuration
space is built up by moving, killing or duplicating individual walkers according to certain rules, and
thus the population of walkers fluctuates.
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