ABINIT, ground-state calculation variables:

Used for the generation of alchemical pseudopotentials, that is, when ntypalch is non-zero.

Give the algorithm to be used to generate the ntypalch alchemical potentials from the different npspalch pseudopotentials dedicated to this use.

Presently, algalch can only have the value 1, that is :

• the local potentials are mixed, thanks to the mixalch mixing coefficients
• the form factors of the non-local projectors are all preserved, and all considered to generate the alchemical potential
• the scalar coefficients of the non-local projectors are multiplied by the proportion of the corresponding type of atom that is present in mixalch
• the characteristic radius for the core charge is a linear combination of the characteristic radii of the core charges, build with the mixalch mixing coefficients
• the core charge function f(r/rc) is a linear combination of the core charge functions, build with the mixalch mixing coefficients

Used for non-zero values of berryopt.

Give the lower band and the upper band of the set of bands for which the Berry phase must be computed. Irrelevant if nberry is not positive. When nsppol is 1 (no spin-polarisation), only the two first numbers, giving the lower and highest bands, are significant. Their occupation number is assumed to be 2. When nsppol is 2 (spin-polarized calculation), the two first numbers give the lowest and highest bands for spin up, and the third and fourth numbers give the lowest and highest bands for spin down. Their occupation number is assumed to be 1 .

• 0 => no computation of expressions relying on a Berry phase (default)
• 1 => the computation of Berry phases is activated (berryphase routine)
• 2 => the computation of derivatives with respect to the wavevector, thanks to the Berry phase finite-difference formula, is activated (uderiv routine)
• 3 => same as option 1 and 2 together
• 4 => finite electric field calculation
• -1 => alternative computation of Berry phases (berryphase_new routine)
• -2 => alternative computation of derivatives with respect to the wavevector, thanks to the Berry phase finite-difference formula (berryphase_new routine)
• -3 => same as option -1 and -2 together

The other related input variables are :

• in case of berryopt=1,2, or 3 : bdberry and kberry; also, nberry must be larger than 0;
• in case of berryopt=-1,-2, or -3 : the variable rfdir must be used to specify the primitive vector along which the projection of the polarization or the ddk will be computed. For example if berryopt=1 and rfdir=1 0 0, the projection of the polarization along the reciprocal lattice vector G_1 is computed. In case rfdir=1 1 1, ABINIT computes the projection of P along G_1, G_2 and G_3 and transforms the results to cartesian coordinates;
• efield, rfdir in case of berryopt=4 ;

If chkexit=0, the check is not performed at all

If chkexit=1, the check is not performed frequently (after each SCF step)

             (     1        + dielng2 * K2 )  
diel(K)= --------------------------------------------
             ( 1/diemac + dielng2 * K2 ) * diemix

References for the calculation under electric field (based on multi k point Berry phase) :

• Nunes and Vanderbilt, PRL 73, 712 (1994) : real-space version of the finite-field Hamiltonian
• Nunes and Gonze, PRB 63, 155197 (2001) : reciprocal-space version of the finite-field Hamiltonian (the one presently implemented), and extensive theoretical analysis
• Souza, Iniguez and Vanderbilt, PRL 89, 117602 (2003) : implementation of the finite-field Hamiltonian (reciprocal-space version)

• 0=>print eigenvalues in hartree;
• 1=>print eigenvalues in eV;
• 2=>print eigenvalues in both hartree and eV.

• 0=> phonon frequencies in Hartree and cm-1;
• 1=> phonon frequencies in eV and THz;
• 2=> phonon frequencies in hartree, eV, cm-1, Thz and Kelvin.

• 0 => model dielectric function described by diemac, dielng and diemix.
• larger or equal to 21 => will compute the dielectric matrix according to diecut, dielam, diegap.
• Between 21 and 29 => for the first few steps uses the same as option 0 then compute RPA dielectric function, and use it as such.
• Between 31 and 39 => for the first few steps uses the same as option 0 then compute RPA dielectric function, and use it, with the mixing factor diemix.
• Between 41 and 49 => compute the RPA dielectric matrix at the first step, and recompute it at a later step, and take into account the mixing factor diemix.
• Between 51 and 59 => same as between 41 and 49, but compute the RPA dielectric matrix by another mean
• Between 61 and 69 => same as between 41 and 49, but compute the electronic dielectric matrix instead of the RPA one.

Used for non-zero values of berryopt.

This array defines, for each Berry phase calculation (the number of such calculations is defined by nberry), the difference of wavevector between k points for which the overlap matrix must be computed. The polarisation vector will be projected on the direction of that wavevector, and the result of the computation will be the magnitude of this projection. Doing more than one wavevector, with different independent direction, allows to find the full polarisation vector. However, note that converged results need oriented grids, denser along the difference wavevector than usual Monkhorst-Pack grids.

The values kptrlatt(1:3,1), kptrlatt(1:3,2), kptrlatt(1:3,3) are the coordinates of three vectors in real space, expressed in the rprim coordinate system (reduced coordinates). They defines a super-lattice in real space. The k point lattice is the reciprocal of this super-lattice, eventually shifted (see shiftk).

Preliminary explanation :
The k point lattice defined by ngkpt or kptrlatt is used to perform integrations of periodic quantities in the Brillouin Zone, like the density or the kinetic energy. One can relate the error made by replacing the continuous integral by a sum over k point lattice to the Fourier transform of the periodic quantity. Erroneous contributions will appear only for the vectors in real space that belong to the reciprocal of the k point lattice, except the origin. Moreover, the expected size of these contributions usually decreases exponentially with the distance. So, the length of the smallest of these real space vectors is a measure of the accuracy of the k point grid.

When either ngkpt or kptrlatt is defined, kptrlen is not used as an input variable, but the length of the smallest vector will be placed in this variable, and echoed in the output file.

On the other hand, when neither ngkpt nor kptrlatt are defined, ABINIT will automatically generate a large set of possible k point grids, and select among this set, the grids that give a length of smallest vector LARGER than kptrlen, and among these grids, the one that, when used with kptopt=1, reduces to the smallest number of k points. Note that this procedure can be time-consuming. It is worth to do it once for a given unit cell and set of symmetries, but not use this procedure by default. The best is then to set prtkpt=1, in order to get a detailed analysis of the set of grids.

Used for the generation of alchemical pseudoatoms, that is, when ntypalch is non-zero.

This array gives, for each type of alchemical pseudatom (there are ntypalch such pseudoatoms), the mixing coefficients of the basic npspalch pseudopotentials for alchemical use. For each type of alchemical pseudoatom, the sum of the mixing coefficients must equal 1.

The actual use of the mixing coefficients is defined by the input variable algalch.

Example 1. Suppose that we want to describe Ba(0.25) Sr(0.75) Ti O3.
The input variables related to the construction of the alchemical Ba(0.25) Sr(0.75) potential will be :

npsp   4                 ! 4 pseudopotentials should be read.
znucl  8 40 56 38        ! The nuclear charges. Note that the two
                         ! atoms whose pseudopotentials are to be mixed
                         ! are mentioned at the end of the series.
ntypat  3                ! There will be three types of atoms.
ntypalch   1             ! One pseudoatom will be alchemical.
                         ! Hence, there will be ntyppure=2 pure pseudoatoms,
                         ! with znucl 8 (O) and 40 (Ti), corresponding to 
                         ! the two first pseudopotentials. Out of the
                         ! four pseudopotentials, npspalch=2 are left
                         ! for alchemical purposes, with znucl 56 (Ba) 
                         ! and 38 (Sr).
mixalch    0.25  0.75    ! For that unique pseudoatom to be
                         ! generated, here are the mixing coeeficients,
                         ! to be used to combine the Ba and Sr pseudopotentials.

Example 2. More complicated, and illustrate some minor drawback of the design of input variables. Suppose that one wants to generate Al(0.25)Ga(0.75) As(0.10)Sb(0.90).
The input variables will be :

npsp  4                  ! 4 pseudopotentials should be read
znucl  13 31 33 51       ! The atomic numbers. All pseudopotentials
                         ! will be used for some alchemical purpose
ntypat  2                ! There will be two types of atoms.
ntypalch   2             ! None of the atoms will be "pure".
                         ! Hence, there will be npspalch=4 pseudopotentials
                         !  to be used for alchemical purposes.
mixalch    0.25  0.75 0.0  0.0   ! This array is a (4,2) array, arranged in the
           0.0   0.0  0.1  0.9   ! usual Fortran order.

In non-self-consistent GS calculations (iscf<0), the highest levels might be difficult to converge, if they are degenerate with another level, that does not belong to the set of bands treated. Then, it might take extremely long to reach tolwfr, although the other bands are already extremely well-converged, and the energy of the highest bands (whose residual are not yet good enough), is also rather well converged.
In response to this problem, for non-zero nbdbuf, the largest residual (residm), to be later compared with tolwfr, will be computed only in the set of non-buffer bands (this modification applies for non-self-consistent as well as self-consistent calculation, for GS as well as RF calculations).
For a GS calculation, with iscf<0, supposing nbdbuf is not initialized in the input file, then ABINIT will overcome the default nbdbuf value, and automatically set nbdbuf to 2.

In metallic RF calculations, in the conjugate gradient optimisation of first-order wavefunctions, there is an instability situation when the q wavevector of the perturbation brings the eigenenergy of the highest treated band at some k point higher than the lowest untreated eigenenergy at some k+q point. If one accept a buffer of frozen states, this instability can be made to disappear. Frozen states receive automatically a residual value of -0.1d0.
For a RF calculation, with 3<=occopt<=7, supposing nbdbuf is not initialized in the input file, then ABINIT will overcome the default nbdbuf value, and automatically set nbdbuf to 2. This value might be too low in some cases.

Used for non-zero values of berryopt.

Gives the number of Berry phase computations of polarisation, or finite-difference estimations of the derivative of wavefunctions with respect to the wavevector, each of which might be characterized by a different change of wavevector kberry.

When equal to 0, no Berry phase calculation of polarisation is performed. The maximal value of nberry is 20.

Note that the computation of the polarisation for a set of bands having different occupation numbers is meaningless (although in the case of spin-polarized calculations, the spin up bands might have an identical occupation number, that might differ from the identical occupation number of spin down bands). Although meaningless, ABINIT will perform such computation, if required by the user. The input variable bdberry governs the set of bands for which a Berry phase is computed.

For example, suppose that the number of segment is just one (kptopt=-1), a value ndivk=4 will lead to the computation of points with relative coordinates 0.0, 0.25, 0.5, 0.75 and 1.0 , along the segment in consideration.

Now, suppose that there are two segments (kptopt=-2), with ndivk(1)=4 and ndivk(2)=2, the computation of the eigenvalues will be done at 7 points, 5 belonging to the first segment, with relative coordinates 0.0, 0.25, 0.5, 0.75 and 1.0, the last one being also the starting point of the next segment, for which two other points must be computed, with relative coordinates 0.5 and 1.0 .

Internally, ngfft is an array of size 18. The present components are stored in ngfft(1:3), while

• ngfft(4:6) contains slightly different (larger) values, modified for efficiency of the FFT
• ngfft(7) is fftalg
• ngfft(8) is fftcache
• ngfft(9) is set to 0 if the parallelization of the FFT is not activated, while it is set to 1 if it is activated.
• ngfft(10) is the number of processors of the FFT group
• ngfft(11) is the index of the processor in the group of processors
• ngfft(12) is n2proc, the number of x-z planes, in reciprocal space, treated by the processor
• ngfft(13) is n3proc, the number of x-y planes, in real space, treated by the processor
• ngfft(14) is mpi_comm_fft, the handle on the MPI communicator in charge of the FFT parallelisation
• ngfft(15:18) are not yet used

If nspden=2, scalar magnetization (the axis is arbitrarily fixed in the z direction) : the density matrix is diagonal, with different values for spin-up and spin-down (compatible with nspinor=1, either with nsppol=2 -general collinear magnetisation- or nsppol=1 -antiferromagnetism)

If nspden=4, vector magnetization : the density matrix is full, with allowed x, y and z magnetisation (useful only with nspinor=2 and nsppol=1, either because there is spin-orbit without time-reversal symmetry - and thus spontaneous magnetization, or with spin-orbit, if one allows for spontaneous non-collinear magnetism). Not yet available for forces, stresses, response functions.

If nspinor=2, the wavefunction is a spinor (compatible with nsppol=1, with nspden=1 or 4, but not with nsppol=2)

Used for the generation of alchemical pseudopotentials : when ntypalch is non-zero, alchemical mixing will be used.

Among the ntypat types of atoms, the last ntypalch will be "alchemical" pseudoatoms, while only the first ntyppure will be uniquely associated with a pseudopotential (the ntyppure first of these, actually). The ntypalch types of alchemical pseudoatoms are to be made from the remaining npspalch pseudopotentials.

The choice is between :
optdriver=0 : ground-state calculation (GS), routine "gstate"
optdriver=1 : response-function calculation (RF), routine "respfn"
optdriver=2 : susceptibility calculation (SUS), routine "suscep"
optdriver=3 : susceptibility and dielectric matrix calculation (CHI), routine "screening"
(see the input variables ecutwfn, ecuteps, plasfrq, getkss, as well as nbandkss and nband)
optdriver=4 : self-energy calculation (SIG), routine "sigma"
optdriver=5 : non-linear response functions, using the 2n+1 theorem, routine "nonlinear"

Note that if nspden=2, the z-component must be given for each atom, in triplets (0 0 z-component).
For example, the electron of an hydrogen atom can be spin up (0 0 1.0) or spin down (0 0 -1.0).

This information might be used to generate k-point grids, if kptopt=0 and neither ngkpt nor kptrlatt are defined (see explanations with the input variable prtkpt).
It will allow to select a zero-, one-, two- or three-dimensional grid of k points. The coordinate of the k points along vacuum directions is automatically set to zero.