The configurations used in in the optimisation procedure Eqn.(
)
are generated by periodically storing the positions
of all the electrons (a configuration) after a certain number
of moves of all the electrons in a VMC calculation. To keep the
computation time for generating the configurations to a minimum,
the number of moves required to produce independent configurations
(i.e. the correlation length in time) was investigated by a procedure
based on that used by Jacucci and Rahman [12] which works
as follows.
A series of N sequential configurations and their energies were
generated by a VMC calculation.
The N energies were divided up into b blocks
each containing 
energies. The average value for each block and
the variance of the block averages are then given by.
When the block size is large enough such that the individual block
averages 
can be considered as being independent,
the value of 
might be expected to be inversely
proportional to 
.
This is because the individual error in the mean, 
is proportional to 
. In an attempt to calculate
this constant of proportionality, the
statistical inefficiency, s is defined as
It is possible to calculate a value for s from the N energies by
plotting the value of s for a series of block sizes.
Finally, from the definition of the
variance in the mean for a series of N values and a correlation
length 
,
It is clear that for the case of a single block that
constitutes the whole sample (i.e. 
) s is equivalent
to 
in ().
For the energies produced in a VMC calculation the value of s proved
to be much smaller than expected, about 2.8. This meant that every
third move of all the electrons could be written out as a configuration.
Where results are
presented later in this report for fitting with 1000 configurations, this
required a 3000 move VMC calculation and 30,000 moves were required to
generate 10,000 configurations.
