CASINO manual - Theory of Condensed Matter

ATOM BASIS TYPE The basis used to represent the orbitals: ‘plane-wave’, ‘gaussian’,
‘slater-type‘, ‘blip’, ‘numerical’, ‘dimer’ or ‘none’ (the last option is for HEGs, etc.);
• Important VMC keywords:
VMC EQUIL NSTEP Number of equilibration steps;
VMC NSTEP Number of VMC energy-evaluation steps;
VMC DECORR PERIOD Number of steps between VMC energy-evaluation moves.
VMC NCONFIG WRITE Number of VMC configurations stored for later use in DMC or
optimization;
DTVMC VMC time step (size of trial steps in random walk);
• Important optimization keywords:
OPT CYCLES Number of optimization+VMC cycles to perform.
OPT METHOD Optimization method to use: variance minimization (‘varmin’), energy minimization
(‘emin’), etc.
• Important DMC keywords:
DMC TARGET WEIGHT Target number of configurations in DMC;
DMC EQUIL NSTEP Number of DMC steps in equilibration;
DMC STATS NSTEP Number of DMC steps in statistics accumulation;
DTDMC DMC time step.
6.1.4 Correlation parameter file
If you run a casino VMC calculation using a trial wave function consisting of only a single determinant
of orbitals (referred to as an ‘HFVMC’ calculation), then the result will be the HF energy. If the
orbitals were generated using a HF calculation, then the HFVMC energy should agree with the
HF energy from the generating code. This is a good check that everything is being done correctly.
Obviously, if the determinant is made up of Kohn–Sham orbitals from a DFT calculation then the total
energies will not agree, because the DFT program adds an XC energy deduced from the self-consistent
charge density; however, the kinetic energies should still be in agreement.
The full Slater-Jastrow trial function normally used in QMC requires the determinantal part of the
wave function stored in xwfn.data to be multiplied by a separate ‘Jastrow factor’, which defines the
functional form of explicit interparticle correlations. In a typical VMC calculation one might recover
60–80% of the correlation energy using such a wave function. This is not really enough to be generally
useful, and in practice the main use of VMC is to prepare an accurate trial wave function to be given
as input to a DMC calculation. The DMC energy does not in principle depend on the Jastrow factor,
since the Jastrow factor is positive definite and the DMC energy depends only on the nodal surface
(the set of points in configuration space where the many-electron wave function is zero). However, it
makes the calculation vastly more efficient, and in general Jastrow factors should always be used.
The Jastrow factor is stored in a file called correlation.data. Again, you should look at the
examples to see what these look like. The various parameters in the files are defined in Sec. 7.4.2.
The adjustable parameters in the file must be optimized for a specific system, and this is the purpose
of the variance-minimization procedure.
The correlation.data files may also contain other optimizable parameters not contained in the
Jastrow factor (for example, ‘backflow’ parameters, or the coefficients in a determinant expansion)
but you don’t need to know about these yet.
6.1.5 The MPC data file
If, for a two- or three-dimensionally periodic system, you want to use the model periodic Coulomb
(MPC) interaction to calculate the electron–electron energies instead of (or as well as) the standard
Ewald interaction, then you need to generate an extra file for the given geometry before you start
doing VMC/DMC calculations. This is called mpc.data and contains the Fourier transform of the 1/r
interaction and the Fourier transform of the charge density. The mpc.data file should be prepared
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