CASINO manual - Theory of Condensed Matter

ENVMC v0.60: Script to extract VMC energies from CASINO output files.
Usage: envmc [-kei] [-ti] [-fisq] [-pe] [-vee] [-vei] [-vnl] [-nc]
[-vr] [-rel] [-ct] [-nf ] [files]
File: ./out
(energies in au, variances in au)
E = -0.49999(4) ; var = 0.000083(4)
Total CASINO CPU time ::: 3.3700 seconds
If any warnings are present in the output file, then envmc will print them out, but there shouldn’t be
in this case. Note that, because of the stochastic nature of the method, the energy has an associated
error bar (users of DFT, etc., may find this disconcerting!). The true HF energy of the hydrogen atom
is exactly −0.5 a.u., so we have seemingly correctly performed our first VMC calculation!
A point about parallel machines: if you try to run this calculation on your machine then you may
get a slightly different answer. The numbers above were obtained on a single processing core; if your
computer has more than one core (these days, most new machines do) and your CASINO ARCH is a
parallel one, then the runqmc script will automatically detect the number of cores on your machine
and run casino in parallel using that number. If you wish to reproduce the single-core result, you
may use runqmc -p 1.
For example, my (=MDT) personal machine has dual hex-core processors (i.e., 12 cores in total),
though if I interrogate it using a command like
cat /proc/cpuinfo 2> /dev/null | grep -cE "ˆprocessor"
it thinks it has 24. This is because these are Intel chips with hyperthreading enabled, i.e., for each
processor core that is physically present, the operating system addresses two virtual processors, and
shares the workload between them when possible. This is not really useful for casino, so by default
runqmc will ignore this, hence we have 12 cores.
So if I execute runqmc then I get the following 12-core result:
ENVMC v0.60: Script to extract VMC energies from CASINO output files.
Usage: envmc [-kei] [-ti] [-fisq] [-pe] [-vee] [-vei] [-vnl] [-nc]
[-vr] [-rel] [-ct] [-nf ] [files]
File: ./out
(energies in au, variances in au)
E = -0.50000(4) ; var = 0.000088(7)
Total CASINO CPU time ::: 0.4309 seconds
Note the behaviour here. The second run is a lot faster but gives roughly the same error bar as the
first one. This is because vmc nstep gives the total number of configuration space samples—in this
case 100,000—not (as was the case with early versions of casino using the old nmove keyword) the
number of samples done by each core. Giving the total number is better since it means that the input
files are then independent of the number of processors on which the job is run. With 12 cores, the
100000 samples to be taken will be divided by 12 (to give 8333.333). Because this is not an integer,
this number is rounded up to 8334, and so 8334×12=100008 samples will actually be done in total.
Because each processor is doing less work, the calculation as a whole is much faster (not exactly 12
times faster because the setup is a significant fraction of such a short calculation). The answer will
be different, however, because 12 short random walks initialized with different random number seeds
sample the space differently to 1 long random walk.
Next, look in the out file. We see a complete report of the calculation and at the end we see the total
energy and its components. Just before the total energy, we see the ‘acceptance ratio’ which should
be around 50% (the acceptance ratio depends on the VMC time step, and we have set opt dtvmc to
1 to automagically adjust the time step so that the acceptance ratio of 50% is achieved). 2 .
Next, look at the file vmc.hist (see Sec. 7.10). This contains mainly energy data produced at each
step of the random walk (you can average over successive steps using the vmc ave period keyword
2 If the time step is small then the electrons only attempt to move very short distances at each step of the random
walk. Although the acceptance ratio is therefore high, the electrons are likely to bumble about in one corner of the
configuration space, and serial correlation is likely to be significant. If the time step is large then the electrons attempt
very large jumps—which are likely to be to regions of lower probability—and are thus likely to be rejected by the
Metropolis algorithm. Hence the electrons don’t move very much, and the serial correlation is again large. This is the
reason why an acceptance ratio of 50% usually implies nearly optimal sampling efficiency.
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