The self-interaction correction (SIC) included in the CP package is based on the Constrained Local-Spin-Density approach proposed my F. Mauri and coworkers (M. D'Avezac et al. PRB 71, 205210 (2005)). It was used for the first time in QUANTUM ESPRESSO by F. Baletto, C. Cavazzoni and S.Scandolo (PRL 95, 176801 (2005)).
This approach is a simple and nice way to treat ONE, and only one, excess charge. It is moreover necessary to check a priori that the spin-up and spin-down eigenvalues are not too different, for the corresponding neutral system, working in the Local-Spin-Density Approximation (setting nspin = 2). If these two conditions are satisfied and you are interest in charged systems, you can apply the SIC. This approach is a on-the-fly method to correct the self-interaction with the excess charge with itself.
Briefly, both the Hartree and the XC part have been corrected to avoid the interaction of the excess charge with tself.
For example, for the Boron atoms, where we have an even number of electrons (valence electrons = 3), the parameters for working with the SIC are:
&system nbnd= 2, total_magnetization=1, sic_alpha = 1.d0, sic_epsilon = 1.0d0, sic = 'sic_mac', force_pairing = .true., &ions ion_dynamics = 'none', ion_radius(1) = 0.8d0, sic_rloc = 1.0, ATOMIC_POSITIONS (bohr) B 0.00 0.00 0.00 0 0 0 1The two main parameters are:
force_pairing = .true., which forces the paired electrons to be the same;Remember to add an extra-column in ATOMIC_POSITIONS with "1" to activate SIC for those atoms.
sic='sic_mac', which instructs the code to use Mauri's correction.
Warning: This approach has known problems for dissociation mechanism driven by excess electrons.
Comment 1:
Two parameters, sic_alpha and sic_epsilon', have been introduced
following the suggestion of M. Sprik (ICR(05)) to treat the radical
(OH)-H2
Comment 2:
When you apply this SIC scheme to a molecule or to an atom, which are neutral,
remember to add the correction to the energy level as proposed by Landau:
in a neutral system, subtracting the self-interaction, the unpaired electron
feels a charged system, even if using a compensating positive background.
For a cubic box, the correction term due to the Madelung energy is approx.
given by
1.4186/Lbox -1.047/(Lbox)3
The ensemble-DFT (eDFT) is a robust method to simulate the metals in the
framework of ''ab-initio'' molecular dynamics. It was introduced in 1997
by Marzari et al.
The specific subroutines for the eDFT are in
CPV/src/ensemble_dft.f90 where you
define all the quantities of interest. The subroutine
CPV/src/inner_loop_cold.f90
called by cg_sub.f90, control the inner loop, and so the minimization of
the free energy A
To select a eDFT calculations, the user has to set:
The input for an Al surface is:
All the other parameters have the same meaning in the usual CP input,
and they are discussed above.
The cutoff ecutrho defines the resolution on the real space FFT mesh (as expressed
by nr1, nr2 and nr3, that the code left on its own sets automatically).
In the USPP case we refer to this mesh as the "hard" mesh, since it
is denser than the smooth mesh that is needed to represent the square
of the non-norm-conserving wavefunctions.
On this "hard", fine-spaced mesh, you need to determine the size of the
cube that will encompass the largest of the augmentation charges - this
is what nr1b, nr2b, nr3b are. hey are independent
of the system size, but dependent on the size
of the augmentation charge (an atomic property that doesn't vary
that much for different systems) and on the
real-space resolution needed by augmentation charges (rule of thumb:
ecutrho is between 6 and 12 times ecutwfc).
The small boxes should be set as small as possible, but large enough
to contain the core of the largest element in your system.
The formula for estimating the box size is quite simple:
The core charge is in principle finite only at the core region (as defined
by some Rrcut
4.4.2 ensemble-DFT
calculation = 'cp'
occupations= 'ensemble'
tcg = .true.
passop= 0.3
maxiter = 250
to use the CG procedure. In the eDFT it is also the outer loop, where the
energy is minimized with respect to the wavefunction keeping fixed the
occupation matrix. While the specific parameters for the inner loop.
Since eDFT was born to treat metals, keep in mind that we want to describe
the broadening of the occupations around the Fermi energy.
Below the new parameters in the electrons list, are listed.
NOTE: degauss is in Hartree, while in PWscfis in Ry (!!!).
The typical range is 0.01-0.02 Ha.
&CONTROL
calculation = 'cp',
restart_mode = 'from_scratch',
nstep = 10,
iprint = 5,
isave = 5,
dt = 125.0d0,
prefix = 'Aluminum_surface',
pseudo_dir = '~/UPF/',
outdir = '/scratch/'
ndr=50
ndw=51
/
&SYSTEM
ibrav= 14,
celldm(1)= 21.694d0, celldm(2)= 1.00D0, celldm(3)= 2.121D0,
celldm(4)= 0.0d0, celldm(5)= 0.0d0, celldm(6)= 0.0d0,
nat= 96,
ntyp= 1,
nspin=1,
ecutwfc= 15,
nbnd=160,
input_dft = 'pbe'
occupations= 'ensemble',
smearing='cs',
degauss=0.018,
/
&ELECTRONS
orthogonalization = 'Gram-Schmidt',
startingwfc = 'random',
ampre = 0.02,
tcg = .true.,
passop= 0.3,
maxiter = 250,
emass_cutoff = 3.00,
conv_thr=1.d-6
n_inner = 2,
lambda_cold = 0.03,
niter_cold_restart = 2,
/
&IONS
ion_dynamics = 'verlet',
ion_temperature = 'nose'
fnosep = 4.0d0,
tempw = 500.d0
/
ATOMIC_SPECIES
Al 26.89 Al.pbe.UPF
NOTA1 remember that the time step is to integrate the ionic dynamics,
so you can choose something in the range of 1-5 fs.
NOTA2 with eDFT you are simulating metals or systems for which the
occupation number is also fractional, so the number of band, nbnd, has to
be chosen such as to have some empty states. As a rule of thumb, start
with an initial occupation number of about 1.6-1.8 (the more bands you
consider, the more the calculation is accurate, but it also takes longer.
The CPU time scales almost linearly with the number of bands.)
NOTA3 the parameter emass_cutoff is used in the preconditioning
and it has a completely different meaning with respect to plain CP.
It ranges between 4 and 7.
4.4.3 Free-energy surface calculations
Once CP is patched with PLUMED plug-in, it becomes possible to turn-on most of the PLUMED functionalities
running CP as: ./cp.x -plumed plus the other usual CP arguments. The PLUMED input file has to be located in the specified outdir with
the fixed name plumed.dat.
4.4.4 Treatment of USPPs
nr1b =
2Rc/Lx x
and the like, where Rcut
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Contents
Layla Martin-Samos Colomer
2012-11-21