ABINIT, basic input variables:

• angdeg(1) is the angle between the 2nd and 3rd vectors,
• angdeg(2) is the angle between the 1st and 3rd vectors,
• angdeg(3) is the angle between the 1st and 2nd vectors,

R1=( a  ,           0,c)
R2=(-a/2, sqrt(3)/2*a,c)
R3=(-a/2,-sqrt(3)/2*a,c)

• R1=(1,0,0)
• R2=(a,b,0)
• R3=(c,d,e)

Usually one runs at least several calculations at various ecut to investigate the convergence needed for reliable results.

For k-points whose coordinates are build from 0 or 1/2, the implementation of time-reversal symmetry that links coefficients of the wavefunctions in reciprocal space has been realized. See the input variable istwfk. If activated (which corresponds to the Default mode), this input variable istwfk will allow to divide the number of plane wave (npw) treated explicitly by a factor of two. Still, the final result should be identical with the 'full' set of plane waves.

• =1 => get the largest eigenvalue of the SCF cycle
  (DEVELOP option, used with irdwfk=1 or irdwfq=1)
• =2 => SCF cycle, simple mixing
• =3 => SCF cycle, anderson mixing
• =5 => SCF cycle, CG based on the minim. of the energy
• Other positive, including zero values, are not allowed.

• = -2 => a non-self-consistent calculation is to be done; in this case an electron density rho(r) on a real space grid (produced in a previous calculation) will be read from a disk file (automatically if ndtset=0, or according to the value of getden if ndtset/=0).
  The name of the density file must be given as indicated in the section 4 of abinis_help. iscf=-2 would be used for band structure calculations, to permit computation of the eigenvalues of occupied and unoccupied states at arbitrary k points in the fixed self consistent potential produced by some integration grid of k points.
  To compute the eigenvalues (and wavefunctions) of unoccupied states in a separate (non-selfconsistent) run, the user should save the self-consistent rho(r) and then run iscf=-2 for the intended set of k-points and bands.
  To prepare a run with iscf=-2, a density file can be produced using the parameter prtden (see its description). When a self-consistent set of wavefunctions is already available, abinit can be used with nstep=0 (see Test_v2/t47.in), and the adequate value of prtden.
• = -3 => like -2, but initialize occ and wtk, directly or indirectly (using ngkpt or kptrlatt) depending on the value of occopt.
  For GS, this option might be used to generate Density-of-states (thanks to prtdos), or to produce STM charge density map (thanks to prtstm).
  For RF, this option is needed to compute the response to ddk perturbation.
• = -1 => like -2, but the non-self-consistent calculation is followed by the determination of excited states within TDDFT. This is only possible for nkpt=1, kpt=0 0 0, nsppol=1. Note that the oscillator strength needs to be defined with respect to an origin of coordinate, thanks to the input variable boxcenter. The maximal number of Kohn-Sham excitations to be used to build the excited state TDDFT matrix can be defined by td_mexcit, or indirectly by the maximum Kohn-Sham excitation energy td_maxene.

• 0=> NO xc;

• 1=> LDA or LSD, Teter Pade parametrization (4/93, published in S. Goedecker, M. Teter, J. Huetter, Phys.Rev.B54, 1703 (1996)), which reproduces Perdew-Wang (which reproduces Ceperley-Alder!).
• 2=> LDA, Perdew-Zunger-Ceperley-Alder (no spin-polarization)
• 3=> LDA, old Teter rational polynomial parametrization (4/91) fit to Ceperley-Alder data (no spin-polarization)
• 4=> LDA, Wigner functional (no spin-polarization)
• 5=> LDA, Hedin-Lundqvist functional (no spin-polarization)
• 6=> LDA, "X-alpha" functional (no spin-polarization)
• 7=> LDA or LSD, Perdew-Wang 92 functional
• 8=> LDA or LSD, x-only part of the Perdew-Wang 92 functional
• 9=> LDA or LSD, x- and RPA correlation part of the Perdew-Wang 92 functional

• 11=> GGA, Perdew-Burke-Ernzerhof GGA functional
• 12=> GGA, x-only part of Perdew-Burke-Ernzerhof GGA functional
• 13=> GGA potential of van Leeuwen-Baerends, while for energy, Perdew-Wang 92 functional
• 14=> GGA, revPBE of Y. Zhang and W. Yang, Phys. Rev. Lett. 80, 890 (1998)
• 15=> GGA, RPBE of B. Hammer, L.B. Hansen and J.K. Norskov, Phys. Rev. B 59, 7413 (1999)
• 16=> GGA, HTCH of F.A. Hamprecht, A.J. Cohen, D.J. Tozer, N.C. Handy, J. Chem. Phys. 109, 6264 (1998)

• 20=> Fermi-Amaldi xc ( -1/N Hartree energy, where N is the number of electrons per cell ; G=0 is not taken into account however), for TDDFT tests. No spin-pol. Does not work for RF.
• 21=> same as 20, except that the xc-kernel is the LDA (ixc=1) one, for TDDFT tests.
• 22=> same as 20, except that the xc-kernel is the Burke-Petersilka-Gross hybrid, for TDDFT tests.

• to determine which input variables are specific to each dataset, since the variable names for this dataset will be made from the bare variable name concatenated with this index, and only if such a composite variable name does not exist, the code will consider the bare variable name, or even, the Default;
• to characterize output variable names, if their content differs from dataset to dataset;
• to characterize output files ( root names appended with _DSx where 'x' is the dataset index ).

Often, the k points will form a lattice in reciprocal space. In this case, one will also aim at initializing input variables that give the reciprocal of this k-point lattice, as well as its shift with respect to the origin: ngkpt or kptrlatt, as well as on nshiftk and shiftk.

• 0=> read directly nkpt, kpt, kptnrm and wtk (corresponds to the usage before version 2.1)
  One can use the kptgen utility to produce these input data.
• 1=> rely on ngkpt or kptrlatt, as well as on nshiftk and shiftk to set up the k points. Take fully into account the symmetry to generate the k points in the Irreducible Brillouin Zone only.
  (This is the usual mode for GS calculations)
• 2=> rely on ngkpt or kptrlatt, as well as on nshiftk and shiftk to set up the k points. Take into account only the time-reversal symmetry : k points will be generated in half the Brillouin zone.
  (This is to be used when preparing or executing a RF calculation at q=(0 0 0) )
• 3=> rely on ngkpt or kptrlatt, as well as on nshiftk and shiftk to set up the k points. Do not take into account any symmetry : k points will be generated in the full Brillouin zone.
  (This is to be used when preparing or executing a RF calculation at non-zero q )
• (4=> has been replaced by negative values in version 2.3 )
• A negative value => rely on kptbounds, and ndivk to set up a band structure calculation along different lines (allowed only for iscf==-2). The absolute value of kptopt gives the number of segments of the band structure.

If nspinor is 2, nband must be even for each k point.

When nshiftk=1, kptrlatt is initialized as a diagonal (3x3) matrix, whose diagonal elements are the three values ngkpt(1:3). When nshiftk is greater than 1, ABINIT will try to generate kptrlatt on the basis of the primitive vectors of the k-lattice: the number of shifts might be reduced, in which case kptrlatt will not be diagonal anymore.

If nkpt is zero, the code deduces from other input variables (see the list in the description of kptopt) the number of k points, which is possible only when kptopt/=0. If kptopt/=0 and the input value of nkpt/=0, then ABINIT will check that the number of k points generated from the other input variables is exactly the same than nkpt.

If kptopt is positive, nkpt must be coherent with the values of kptrlatt, nshiftk and shiftk.
For ground state calculations, one should select the k point in the irreducible Brillouin Zone (obtained by taking into account point symmetries and the time-reversal symmetry).
For response function calculations, one should select k points in the full Brillouin zone, if the wavevector of the perturbation does not vanish, or in a half of the Brillouin Zone if q=0. The code will automatically decrease the number of k points to the minimal set needed for each particular perturbation.

If nsppol=1, one has an unpolarized calculation (nspinor=1, nspden=1) or an antiferromagnetic system (nspinor=1, nspden=2), or a calculation in which spin up and spin down cannot be disantengled (nspinor=2), non-collinear magnetism or presence of spin-orbit coupling, for which one needs spinor wavefunctions.

If nsppol=2, one has a spin-polarized calculation with separate and different wavefunctions for up and down spin electrons for each band and k point. Compatible only with nspinor=1, nspden=2.

In the present status of development, with nsppol=1, all values of ixc are allowed, while with nsppol=2, only ixc=0, 1, 7 and 11 are allowed.

SYMMETRY FINDER mode (Default mode). If nsym is 0, all the atomic coordinates must be explicitely given (one cannot use the geometry builder and the symmetrizer): the code will then find automatically the symmetry operations that leave the lattice and each atomic sublattice invariant. It also checks whether the cell is primitive (see chkprim).
Note that the tolerance on symmetric atomic positions and lattice is rather stringent : for a symmetry operation to be admitted, the lattice and atomic positions must map on themselves within 1.0e-8 .

• occopt=0:
  All k points have the same number of bands and the same occupancies of bands. nband is given as a single number, and occ(nband) is an array of nband elements, read in by the code.
  The k point weights in array wtk(nkpt) are automatically normalized by the code to add to 1.
• occopt=1:
  Same as occopt=0, except that the array occ is automatically generated by the code, to give a semiconductor.
  An error occurs when filling cannot be done with occupation numbers equal to 2 or 0 in each k-point (non-spin-polarized case), or with occupation numbers equal to 1 or 0 in each k-point (spin-polarized case).
• occopt=2:
  k points may optionally have different numbers of bands and different occupancies. nband( nkpt*nsppol) is given explicitly as an array of nkpt*nsppol elements. occ() is given explicitly for all bands at each k point, and eventually for each spin -- the total number of elements is the sum of nband(ikpt) over all k points and spins. The k point weights wtk (nkpt) are NOT automatically normalized under this option.
• occopt=3, 4, 5, 6 and 7
  Metallic occupation of levels, using different occupation schemes (see below). The corresponding thermal broadening, or cold smearing, is defined by the input variable tsmear (see below : the variable xx is the energy in Ha, divided by tsmear)
  Like for occopt=1, the variable occ is not read
  All k points have the same number of bands, nband is given as a single number, read by the code.
  The k point weights in array wtk(nkpt) are automatically normalized by the code to add to 1.
• occopt=3:
  Fermi-Dirac smearing (finite-temperature metal) Smeared delta function : 0.25d0/(cosh(xx/2.0d0)**2)
• occopt=4:
  "Cold smearing" of N. Marzari (see his thesis work), with a=-.5634 (minimization of the bump)
  Smeared delta function :
  exp(-xx²)/sqrt(pi) * (1.5d0+xx*(-a*1.5d0+xx*(-1.0d0+a*xx)))
• occopt=5:
  "Cold smearing" of N. Marzari (see his thesis work), with a=-.8165 (monotonic function in the tail)
  Same smeared delta function as occopt=4, with different a.
• occopt=6:
  Smearing of Methfessel and Paxton (PRB40,3616(1989)) with Hermite polynomial of degree 2, corresponding to "Cold smearing" of N. Marzari with a=0 (so, same smeared delta function as occopt=4, with different a).
• occopt=7:
  Gaussian smearing, corresponding to the 0 order Hermite polynomial of Methfessel and Paxton.
  Smeared delta function : 1.0d0*exp(-xx**2)/sqrt(pi)

• R1p(i)=rprim(i,1)*acell(1) for i=1,2,3 (x,y,and z)
• R2p(i)=rprim(i,2)*acell(2) for i=1,2,3
• R3p(i)=rprim(i,3)*acell(3) for i=1,2,3.

Alternatively to rprim, directions of dimensionless primitive vectors can be specified by using the input variable angdeg. This is especially useful for hexagonal lattices (with 120 or 60 degrees angles). Indeed, in order for symmetries to be recognized, rprim must be symmetric up to 10 digits, inducing a specification such as

rprim  0.86602540378  0.5  0.0
      -0.86602540378  0.5  0.0
       0.0            0.0  1.0

angdeg 90 90 120

• R1p(i)=rprimd(i,1)=rprim(i,1)*acell(1) for i=1,2,3 (x,y,and z)
• R2p(i)=rprimd(i,2)=rprim(i,2)*acell(2) for i=1,2,3
• R3p(i)=rprimd(i,3)=rprim(i,3)*acell(3) for i=1,2,3

The user might rely on ABINIT to suggest suitable and efficients combinations of kptrlatt and shiftk. The procedure to be followed is described with the input variables kptrlen. In what follows, we suggest some interesting values of the shifts, to be used with even values of ngkpt. This list is much less exhaustive than the above-mentioned automatic procedure.

1) When the primitive vectors of the lattice do NOT form a FCC or a BCC lattice, the usual (shifted) Monkhorst-Pack grids are formed by using nshiftk=1 and shiftk 0.5 0.5 0.5 . This is often the preferred k point sampling. For a non-shifted Monkhorst-Pack grid, use nshiftk=1 and shiftk 0.0 0.0 0.0 , but there is little reason to do that.

The FCC k point sampling defined with nshiftk=4 and shiftk

        0.5 0.5 0.5
        0.5 0.0 0.0
        0.0 0.5 0.0
        0.0 0.0 0.5

2) When the primitive vectors of the lattice form a FCC lattice, with rprim

        0.0 0.5 0.5
        0.5 0.0 0.5
        0.5 0.5 0.0

        0.5 0.5 0.5
        0.5 0.0 0.0
        0.0 0.5 0.0
        0.0 0.0 0.5

3) When the primitive vectors of the lattice form a BCC lattice, with rprim

       -0.5  0.5  0.5
        0.5 -0.5  0.5
        0.5  0.5 -0.5

        0.25  0.25  0.25
       -0.25 -0.25 -0.25

  < nk|(H-E)2|nk >,    E = < nk|H|nk >,

  typat 1 2 3 3 3