CASINO manual - Theory of Condensed Matter
CASINO manual - Theory of Condensed Matter
CASINO manual - Theory of Condensed Matter
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0.5 0.5 0.0<br />
particle 1 det 1 : 9 orbitals free<br />
particle 2 det 1 : 9 orbitals free<br />
k_<strong>of</strong>fset 0.1 0.2 0.3<br />
%endblock free_particles<br />
Note that ground-state calculations for electron(-hole) fluids with real wave functions must have<br />
‘magic’ numbers <strong>of</strong> electrons, such that there are no partially filled shells <strong>of</strong> k vectors. If the wave<br />
functions is complex, however, then any number <strong>of</strong> electrons may be used. This reflects the fact that<br />
for general twisted boundary conditions each shell contains just one k vector.<br />
Anyway, to specify that twist averaging is to be used in VMC, set vmc ntwist to the required<br />
number <strong>of</strong> twist angles to sample. After each change <strong>of</strong> the k-vector <strong>of</strong>fset, vmc reequil nstep VMC<br />
equilibration moves will be carried out. Note that vmc reequil nstep can be much smaller than<br />
vmc equil nstep, because the distribution <strong>of</strong> configurations obtained at different k-vector <strong>of</strong>fsets<br />
should be similar. A typical value for vmc reequil nstep might be 100.<br />
To specify that twist averaging is to be used in DMC, set dmc ntwist to the desired number <strong>of</strong><br />
twist angles to sample. In the statistics-accumulation phase <strong>of</strong> DMC the following process will<br />
occur dmc ntwist times: (i) a random k-vector <strong>of</strong>fset will be chosen, (ii) dmc reequil nstep<br />
DMC equilibration moves will be carried out, but no data will be written to dmc.hist and (iii)<br />
dmc stats nstep statistics-accumulation moves will be carried out. So the total amount <strong>of</strong> data<br />
generated is dmc ntwist × dmc stats nstep. Note that the number <strong>of</strong> post-twist-change equilibration<br />
moves dmc reequil nstep can be much less than the number <strong>of</strong> equilibration moves<br />
dmc reequil nstep because the configuration distribution at one twist angle is a reasonably good<br />
approximation to the configuration distribution at another.<br />
Obviously, if twist averaging is to be used in either VMC or DMC then complex wf should be<br />
set to T. The twist-averaged HF energy <strong>of</strong> the HEG will be calculated and written to the out<br />
file for single-determinant ground-state calculations. One can check that vmc reequil nstep and<br />
dmc reequil nstep are sufficiently large by setting use jastrow, backflow and ibran to F and<br />
comparing the VMC and DMC energies with the twist-averaged HF value (they should be the same).<br />
Note that one cannot expect to find a plateau when performing reblocking analysis until the block<br />
length is greater than the number <strong>of</strong> data points between changes <strong>of</strong> twist angle, i.e., greater than<br />
vmc nstep for VMC data and dmc stats nstep for DMC data.<br />
28.3.2 Real systems<br />
For real systems one can perform the DFT/HF wave-function generation calculations at arbitrary grids<br />
<strong>of</strong> k points, then use the wave-function converters (including blip) in the usual fashion to generate<br />
casino input files, then read in and use those wave functions in casino, provided that complex wf<br />
is set to T. This functionality is not yet available for Gaussian orbitals, however.<br />
We provide a couple <strong>of</strong> scripts which quasi-automate this procedure: twistav pwscf for use with the<br />
pwscf plane-wave DFT code, and twistav castep for use on conjunction with the castep planewave<br />
DFT code, the castep2casino utility and the blip utility. Note that these scripts just produce<br />
the correct data files for you to analyse <strong>manual</strong>ly; they do not analyse the results themselves. How<br />
you want to analyse the data is up to you. Do you (i) just average the QMC energies and include<br />
the random error from twist averaging with the statistical error or (ii) do you use the DFT energies<br />
to correct the QMC energies before averaging or (iii) some other way. . . As an example, in Ref. [78]<br />
option (ii) was chosen.<br />
It is not generally necessary to re-optimize the Jastrow factor and backflow functions for the different<br />
twists; just a single correlation.data file should be supplied.<br />
28.3.3 Monte Carlo twist averaging for real systems using <strong>CASINO</strong> and CASTEP<br />
This is automated with the twistav castep utility. This script repeatedly <strong>of</strong>fsets the grid <strong>of</strong> k vectors<br />
in the castep .cell file and runs castep, then castep2casino, then blip and then casino. The<br />
castep and casino output files are put in directories called twist0001, twist0002, etc. The progress<br />
<strong>of</strong> the calculations is reported in a file called STATUS. All the necessary castep and casino input<br />
files must be set up in the directory in which the calculation is run. The complete list <strong>of</strong> k vectors<br />
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