The variance minimisation procedure in Eq.(
) is stable
for systems containing small numbers of electrons, but gradually
becomes unstable as the numbers of electrons increases. The problem
arises because the reweighting factors, 
, in
Eq.() deviate greatly from unity at the beginning of the
optimisation process when the changes in the parameters are large due
to the poor quality of the initial guess of the trial wavefunction.
Note that for a small change, 
, in the function, the
local energy 
changes by an amount
proportional to 
, where N is the number of electrons,
but the reweighting factor is multiplied by a factor which is
exponential in . For large N, this behaviour of the
reweighting factors dominates the optimisation process. One way to
counteract this is to increase the number of configurations used, but
this rapidly becomes impractical and it was found that it is better to
reduce the importance of the reweighting factor. For 
and
above, the reweighting factors were set to unity and several sets of
configurations were generated with successively better functions,
until the procedure converged. This works because as the procedure
converges the reweighting factors approach unity. At each iteration
only limited variations of the parameters were allowed, which promotes
the smooth convergence of the process. This optimisation is perfectly
stable even up to the largest number of electrons studied (N=338).