CASINO manual - Theory of Condensed Matter

– Variational Monte Carlo (including optimization of wave functions by minimization of variance,
energy, or the mean absolute deviation of local energies from the median (madmin);
there is a super-fast variance-minimization method available for optimizing linear Jastrow
parameters).
– Diffusion Monte Carlo (branching DMC and pure DMC).
• Systems:
– Atoms, molecules, polymers, slabs and solids (the latter three having periodic boundary
conditions in one, two, and three dimensions, respectively).
– 1D/2D/3D electron and electron–hole phases with fluid or crystal wave functions, with
arbitrary cell shape/spin polarization/density (including excited-state capability). Can
simulate 2D bilayers and 1D biwires.
– Pseudopotentials or all-electron calculations.
– Can use particles of any charge or mass.
• Wave functions:
– Slater-Jastrow wave functions, where the Slater part may consist of multiple determinants
of spin orbitals and the Jastrow factor is a sum of selectable, very flexible terms capable of
describing complicated electronic correlations. Alternative specially-crafted wave function
forms are available for excitonic and positronic systems.
– Orbitals expanded in Gaussian basis sets (s, sp, p, d, f or g functions centred on atoms or
elsewhere) produced by the following programs (using DFT, HF, or various multideterminant
methods): crystal9X/03/06/09 [1, 2], gaussian9X/03/09 [3, 4], gamess-us and
turbomole. Optimizable functions may be added to these.
– Orbitals expanded in plane waves produced by pwscf/quantum espresso [5], abinit
[6], gp, castep [7], mcexx, and k207.
– Orbitals expanded in ‘blip’ (B-spline) functions, usually generated by post-processing planewave
orbitals though they can be produced directly by pwscf/quantum espresso).
– Orbitals interpolated from a radial grid for atomic calculations. Optimizable functions may
be added to these.
– Slater-type orbitals produced by adf [8]. Optimizable functions may be added to these.
– Use of flexible inhomogeneous backflow functions to give highly accurate trial wave functions.
– Localized orbitals and basis functions for improved scaling with system size. casino scales
quadratically with system size to evaluate the total energy to a specified error bar (a
capability sometimes referred to as ‘linear scaling’ in the literature).
– Complex wave functions and twisted boundary conditions can be used to reduce singleparticle
finite-size errors. Twist averaging can be performed wholly within casino for
electron(–hole) fluid phases (and with the aid of other codes to regenerate the wave function
files it can be done for real systems containing atoms).
• Expectation values:
• Other:
– Computation of excitation energies corresponding to the promotion, addition or subtraction
of electrons.
– Computation of various expectation values: density, spin-density, noncollinear spin-density
matrix, one-body and two-body density matrices, condensate fraction, reciprocal space
and spherical real space pair correlation functions, localization tensor, structure factor and
spherically averaged structure factor.
– Calculation of electron–electron interactions using either Ewald and/or our model periodic
Coulomb interaction, which is faster and has smaller Coulomb finite-size effects.
– Corrections to the finite-system kinetic energy from the long-ranged two-body Jastrow
factor and to the interaction energy from the structure factor can be calculated for periodic
systems.
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