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# basic input variables¶

This document lists and provides the description of the name (keywords) of the basic input variables to be used in the input file for the abinit executable.

## accuracy¶

Mnemonics: ACCURACY
Mentioned in topic(s): topic_Planewaves, topic_SCFControl
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Moderately used, [16/973] in all abinit tests, [3/118] in abinit tutorials

Allows to tune the accuracy of a calculation by setting automatically the variables according to the following table:

accuracy 1 2 3 4 5 6
ecut E_min E_med E_med E_max E_max E_max
pawecutdg ecut ecut 1.2 * ecut 1.5 * ecut 2 * ecut 2 * ecut
fband 0.5 0.5 0.5 0.5 0.75 0.75
boxcutmin 1.5 1.8 1.8 2.0 2.0 2.0
bxctmindg 1.5 1.8 1.8 2.0 2.0 2.0
pawxcdev 1 1 1 1 2 2
pawmixdg 0 0 0 0 1 1
pawovlp 10 7 7 5 5 5
pawnhatxc 0 1 1 1 1 1
tolvrs 1.0d-3 1.0d-5 1.0d-7 1.0d-9 1.0d-10 1.0d-12
tolmxf 1.0d-3 5.0d-4 1.0d-4 5.0d-5 1.0d-6 1.0d-6
optforces 1 1 2 2 2 2
timopt 0 0 1 1 1 1
npulayit 4 7 7 7 15 15
nstep 30 30 30 30 50 50
prteig 0 0 1 1 1 1
prtden 0 0 1 1 1 1

For a parallel calculation, timopt is enforced to be 0. E_min, E_med and E_max may be read from the pseudopotential file (available only for XML PAW atomic data files). If E_min, E_med and E_max are not given in the pseudopotential file, ecut must be given in the input file and E_max=E_med=E_max=ecut. The values in bold font are the default values of ABINIT. accuracy=4 corresponds to the default tuning of ABINIT. It is already a very accurate tuning. If the user wants to modify one of the input variable automatically tuned by accuracy, he must put it in the input file. The other input variables automatically tuned by accuracy will not be affected. accuracy=0 means that this input variable is deactivated.

## acell¶

Mnemonics: CELL lattice vector scaling
Characteristics: EVOLVING, LENGTH
Mentioned in topic(s): topic_UnitCell
Variable type: real
Dimensions: (3)
Commentdims: represented internally as acell(3,nimage)
Default value: 3 * 1

Test list (click to open). Very frequently used, [972/973] in all abinit tests, [118/118] in abinit tutorials

Gives the length scales by which dimensionless primitive translations (in rprim) are to be multiplied. By default, given in Bohr atomic units (1 Bohr=0.5291772108 Angstroms), although Angstrom can be specified, if preferred, since acell has the ‘LENGTH‘ characteristics. See further description of acell related to the rprim input variable, the scalecart input variable, and the associated internal %rprimd input variable.

Note that acell is NOT the length of the conventional orthogonal basis vectors, but the scaling factors of the primitive vectors. Use scalecart to scale the cartesian coordinates.

## angdeg¶

Mnemonics: ANGles in DEGrees
Characteristics: INPUT_ONLY
Mentioned in topic(s): topic_UnitCell
Variable type: real
Dimensions: (3)
Default value: None
Comment: deduced from ‘rprim

Test list (click to open). Moderately used, [59/973] in all abinit tests, [1/118] in abinit tutorials

Gives the angles between directions of primitive vectors of the unit cell (in degrees), as an alternative to the input array rprim. Will be used to set up rprim, that, together with the array acell, will be used to define the primitive vectors.

• 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,

If the three angles are equal within 1.0d-12 (except if they are exactly 90 degrees), the three primitive vectors are chosen so that the trigonal symmetry that exchange them is along the z cartesian axis:

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


where a 2 +c 2 =1.0d0 If the angles are not all equal (or if they are all 90 degrees), one will have the following generic form:

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

where each of the vectors is normalized, and form the desired angles with the others.

## ecut¶

Mnemonics: Energy CUToff
Characteristics: ENERGY
Mentioned in topic(s): topic_Planewaves
Variable type: real
Dimensions: scalar
Default value: None

Test list (click to open). Very frequently used, [973/973] in all abinit tests, [118/118] in abinit tutorials

Used for kinetic energy cutoff which controls number of planewaves at given k point by: (½)[(2 Pi)*(k+Gmax)] 2 =ecut for Gmax.

All planewaves inside this “basis sphere” centered at k are included in the basis (except if dilatmx is defined). Can be specified in Ha (the default), Ry, eV or Kelvin, since ecut has the ‘ENERGY‘ characteristics. (1 Ha=27.2113845 eV) This is the single parameter which can have an enormous effect on the quality of a calculation; basically the larger ecut is, the better converged the calculation is. For fixed geometry, the total energy MUST always decrease as ecut is raised because of the variational nature of the problem.

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 ½, 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.

See the input variable ecutsm, for the smoothing of the kinetic energy, needed to optimize unit cell parameters.

## einterp¶

Mnemonics: Electron bands INTERPolation
Mentioned in topic(s): topic_ElecBandStructure, topic_SelfEnergy
Variable type: real
Dimensions: (4)
Default value: [0, 0, 0, 0]

Test list (click to open). Rarely used, [2/973] in all abinit tests, [0/118] in abinit tutorials

This variable activates the interpolation of the electronic eigenvalues. It can be used to interpolate KS eigenvalues at the end of the GS run or to interpolate GW energies in sigma calculations (optdriver = 4). The k-path can be specified with kptbounds and nkpath. einterp consists of 4 entries. The first element specificies the interpolation method.

• 0 → No interpolation (default)
• 1 → Star-function interpolation (Shankland-Koelling-Wood Fourier interpolation scheme, see [Pickett1988]
• 2 → B-spline interpolation.

The meaning of the other entries depend on the interpolation technique selected. In the case of star-function interpolation:

• einterp(2): Number of star-functions per ab-initio k-point
• einterp(3): If non-zero, activate Fourier filtering according to Eq 9 of [Uehara2000]. In this case, rcut is given by einterp(2) * Rmax where Rmax is the maximum length of the lattice vectors included in the star expansion
• einterp(4): Used if einterp(2) /= 0. It defines rsigma in Eq 9

For B-spline interpolation: einterp(2:4): Order of B-spline for the three reduced directions. Cubic spline (3) is the recommended value.

## iscf¶

Mnemonics: Integer for Self-Consistent-Field cycles
Mentioned in topic(s): topic_SCFAlgorithms, topic_TDDFT, topic_ElecBandStructure
Variable type: integer
Dimensions: scalar
Default value: 17 if %usepaw==1, 0 if usewvl==1, 7 otherwise.

Test list (click to open). Moderately used, [300/973] in all abinit tests, [42/118] in abinit tutorials

Controls the self-consistency. Positive values → this is the usual choice for doing the usual ground state (GS) calculations or for structural relaxation, where the potential has to be determined self-consistently. The choice between different algorithms for SCF is possible:

*=0 → SCF cycle, direct minimization scheme on the gradient of the wavefunctions. This algorithm is faster than diagonalisation and mixing but is working only for systems with a gap. It is implemented only on the wavelet basis set, when usewvl=1. * 1 → get the largest eigenvalue of the SCF cycle (DEVELOP option, used with irdwfk=1 or irdwfq=1)

• 2 → SCF cycle, simple mixing of the potential with the preconditioned potential residual (in the usual case, the latter is defined by diemix, diemac and dielng)
• 3 → SCF cycle, Anderson mixing of the potential
• 4 → SCF cycle, Anderson mixing of the potential based on the two previous iterations
• 5 → SCF cycle, CG based on the minim. of the energy with respect to the potential
• 7 → SCF cycle, Pulay mixing of the potential based on the npulayit previous iterations
• 12 → SCF cycle, simple mixing of the density
• 13 → SCF cycle, Anderson mixing of the density
• 14 → SCF cycle, Anderson mixing of the density based on the two previous iterations
• 15 → SCF cycle, CG based on the minim. of the energy with respect to the density
• 17 → SCF cycle, Pulay mixing of the density based on the npulayit previous iterations

Warning

Other positive values, including zero ones, are not allowed.

Such algorithms for treating the “SCF iteration history” should be coupled with accompanying algorithms for the SCF “preconditioning”. See the input variable iprcel. The default value iprcel=0 is often a good choice, but for inhomogeneous systems, you might gain a lot with iprcel=45.

(Warning: if iscf>10, at present (v4.6), the energy printed at each SCF cycle is not variational - this should not affect the other properties, and at convergence, all values are OK)

• In the norm-conserving case, the default option is iscf=7, which is a compromise between speed and reliability. The value iscf= 2 is safer but slower.
• In the PAW case, default option is iscf=17. In PAW you have the possibility to mix density/potential on the fine or coarse FFT grid (see pawmixdg).
• Note that a Pulay mixing (iscf=7 or 17) with npulayit =1 (resp. 2) is equivalent to an Anderson mixing with iscf=3 or 13 (resp. 4 or 14).
• Also note that:
• when mixing is done on potential (iscf <10), total energy is computed by “direct” decomposition.
• when mixing is done on density (iscf >=10), total energy is computed by “double counting” decomposition. “Direct” and “double counting” decomposition of energy are equal when SCF cycle is converged. Note that, when using GGA XC functionals, these decompositions of energy can be slightly different due to imprecise computation of density gradients on FFT grid (difference decreases as size of FFT grid increases - see ecut for NC pseudopotentials, pawecutdg for PAW).

Other (negative) options:

• = -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 th density file must be given as indicated here. 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. Due to this typical use, ABINIT insist that either prtvol>2 or prteig does not vanish when there are more than 50 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, with kpt=0 0 0. 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.

## ixc¶

Mnemonics: Index of eXchange-Correlation functional
Mentioned in topic(s): topic_xc, topic_Hybrids, topic_TDDFT
Variable type: integer
Dimensions: scalar
Default value: 1
Comment: Default corresponds to Teter parametrization. However, if all the pseudopotentials have the same value of pspxc, the initial value of ixc will be that common value

Test list (click to open). Moderately used, [386/973] in all abinit tests, [45/118] in abinit tutorials

Controls the choice of exchange and correlation (xc). The list of XC functionals is given below. Positive values are for ABINIT native library of XC functionals, while negative values are for calling the much wider set of functionals from the ETSF LibXC library (by M. Marques), available at the LibXC home page Note that the choice made here should preferably agree with the choice made in generating the original pseudopotential, except for ixc=0 (usually only used for debugging). A warning is issued if this is not the case. Unfortunately, pseudopotential (or PAW) generators for hybrid functionals and mGGA are currently under development, so that one usually uses GGA or LDA pseudopotentials instead. The error should be limited when GGA or LDA pseudopotentials with semi-core states are used. Still this is a non- controlled error.. Moreover, the choices ixc=1, 2, 3 and 7 are fits to the same data, from Ceperley-Alder, and are rather similar, at least for spin- unpolarized systems. The choice between the non-spin-polarized and spin-polarized case is governed by the value of nsppol (see below).

Native ABINIT XC functionals

NOTE: in the implementation of the spin-dependence of these functionals, and in order to avoid divergences in their derivatives, the interpolating function between spin-unpolarized and fully-spin-polarized function has been slightly modified, by including a zeta rescaled by 1.d0-1.d-6. This should affect total energy at the level of 1.d-6Ha, and should have an even smaller effect on differences of energies, or derivatives. The value ixc=10 is used internally: gives the difference between ixc=7 and ixc=9, for use with an accurate RPA correlation energy.

• 0 → NO xc;

• 1 → LDA or LSD, Teter Pade parametrization (4/93, published in [Goedecker1996], which reproduces Perdew-Wang (which reproduces Ceperley-Alder!).

• 2 → LDA, Perdew-Zunger-Ceperley-Alder (no spin-polarization) [Perdew1981]
• 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, HTCH93 of F.A. Hamprecht, A.J. Cohen, D.J. Tozer, N.C. Handy, J. Chem. Phys. 109, 6264 (1998)
• 17 → GGA, HTCH120 of A.D. Boese, N.L. Doltsinis, N.C. Handy, and M. Sprik, J. Chem. Phys 112, 1670 (1998) - The usual HCTH functional.
• 18 → (NOT AVAILABLE: used internally for GGA BLYP pseudopotentials from M. Krack, see Theor. Chem. Acc. 114, 145 (2005), available from the CP2K repository - use the LibXC instead, with ixc=-106131.
• 19 → (NOT AVAILABLE: used internally for GGA BP86 pseudopotentials from M. Krack, see Theor. Chem. Acc. 114, 145 (2005), available from the CP2K repository - use the LibXC instead, with ixc=-106132.

• 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.
• 23 → GGA of Z. Wu and R.E. Cohen, Phys. Rev. 73, 235116 (2006).
• 24 → GGA, C09x exchange of V. R. Cooper, PRB 81, 161104(R) (2010).
• 26 → GGA, HTCH147 of A.D. Boese, N.L. Doltsinis, N.C. Handy, and M. Sprik, J. Chem. Phys 112, 1670 (1998).
• 27 → GGA, HTCH407 of A.D. Boese, and N.C. Handy, J. Chem. Phys 114, 5497 (2001).
• 28 → (NOT AVAILABLE: used internally for GGA OLYP pseudopotentials from M. Krack, see Theor. Chem. Acc. 114, 145 (2005), available from the CP2K repository - use the LibXC instead, with ixc=-110131.

• 40 → Hartree-Fock

• 41 → PBE0, J.P. Perdew, M. Ernzerhof and K. Burke, J. Chem. Phys. 105, 9982 (1996)
• 42 → PBE0-⅓, C.A. Guido, E. Bremond, C. Adamo and P. Cortona, J. Chem. Phys. 138, 021104 (2013)

ETSF Lib XC functionals

Note that you must compile ABINIT with the LibXC plug-in in order to be able to access these functionals. The LibXC functionals are accessed by negative values of ixc. The LibXC contains functional forms for either exchange-only functionals, correlation-only functionals, or combined exchange and correlation functionals. Each of them is to be specified by a three-digit number. In case of a combined exchange and correlation functional, only one such three-digit number has to be specified as value of ixc, with a minus sign (to indicate that it comes from the LibXC). In the case of separate exchange functional (let us represent its identifier by XXX) and correlation functional (let us represent its identified by CCC), a six-digit number will have to be specified for ixc, by concatenation, be it XXXCCC or CCCXXX. As an example, ixc=-020 gives access to the Teter93 LDA, while ixc=-101130 gives access to the PBE GGA. In version 0.9 of LibXC (December 2008), there are 16 three-dimensional (S)LDA functionals (1 for X, 14 for C, 1 for combined XC), and there are 41 three-dimensional GGA (23 for X, 8 for C, 10 for combined XC). Note that for a meta-GGA, the kinetic energy density is needed. This means having usekden=1.

(S)LDA functionals (do not forget to add a minus sign, as discussed above)

• 001 → XC_LDA_X [PAM Dirac, Proceedings of the Cambridge Philosophical Society 26, 376 (1930); F Bloch, Zeitschrift fuer Physik 57, 545 (1929) ]
• 002 → XC_LDA_C_WIGNER Wigner parametrization [EP Wigner, Trans. Faraday Soc. 34, 678 (1938) ]
• 003 → XC_LDA_C_RPA Random Phase Approximation [M Gell-Mann and KA Brueckner, Phys. Rev. 106, 364 (1957) ]
• 004 → XC_LDA_C_HL Hedin & Lundqvist [L Hedin and BI Lundqvist, J. Phys. C 4, 2064 (1971) ]
• 005 → XC_LDA_C_GL ! Gunnarson & Lundqvist [O Gunnarsson and BI Lundqvist, PRB 13, 4274 (1976) ]
• 006 → XC_LDA_C_XALPHA ! Slater’s Xalpha ]
• 007 → XC_LDA_C_VWN ! Vosko, Wilk, & Nussair [SH Vosko, L Wilk, and M Nusair, Can. J. Phys. 58, 1200 (1980) ]
• 008 → XC_LDA_C_VWN_RPA ! Vosko, Wilk, & Nussair (RPA) [SH Vosko, L Wilk, and M Nusair, Can. J. Phys. 58, 1200 (1980) ]
• 009 → XC_LDA_C_PZ ! Perdew & Zunger [Perdew1981]
• 010 → XC_LDA_C_PZ_MOD ! Perdew & Zunger (Modified) [Perdew1981] Modified to improve the matching between the low and high rs part ]
• 011 → XC_LDA_C_OB_PZ ! Ortiz & Ballone (PZ) [G Ortiz and P Ballone, Phys. Rev. B 50, 1391 (1994); G Ortiz and P Ballone, Phys. Rev. B 56, 9970(E) (1997); [Perdew1981] ]
• 012 → XC_LDA_C_PW ! Perdew & Wang [JP Perdew and Y Wang, Phys. Rev. B 45, 13244 (1992) ]
• 013 → XC_LDA_C_PW_MOD ! Perdew & Wang (Modified) [JP Perdew and Y Wang, Phys. Rev. B 45, 13244 (1992); Added extra digits to some constants as in the PBE routine see https://www.chem.uci.edu/~kieron/dftold2/pbe.php (at some point it was available at http://dft.uci.edu/pbe.php) ]
• 014 → XC_LDA_C_OB_PW ! Ortiz & Ballone (PW) [G Ortiz and P Ballone, Phys. Rev. B 50, 1391 (1994); G Ortiz and P Ballone, Phys. Rev. B 56, 9970(E) (1997); JP Perdew and Y Wang, Phys. Rev. B 45, 13244 (1992) ]
• 017 → XC_LDA_C_vBH ! von Barth & Hedin [U von Barth and L Hedin, J. Phys. C: Solid State Phys. 5, 1629 (1972) ]
• 020 → XC_LDA_XC_TETER93 ! Teter 93 parametrization [S Goedecker, M Teter, J Hutter, PRB 54, 1703 (1996) ]
• 022 → XC_LDA_C_ML1 ! Modified LSD (version 1) of Proynov and Salahub [EI Proynov and D Salahub, Phys. Rev. B 49, 7874 (1994) ]
• 023 → XC_LDA_C_ML2 ! Modified LSD (version 2) of Proynov and Salahub [EI Proynov and D Salahub, Phys. Rev. B 49, 7874 (1994) ]
• 024 → XC_LDA_C_GOMBAS ! Gombas parametrization [P. Gombas, Pseudopotentials (Springer-Verlag, New York, 1967) ]
• 025 → XC_LDA_C_PW_RPA ! Perdew & Wang fit of the RPA [JP Perdew and Y Wang, Phys. Rev. B 45, 13244 (1992) ]
• 027 → XC_LDA_C_RC04 ! Ragot-Cortona [S Ragot and P Cortona, J. Chem. Phys. 121, 7671 (2004) ]
• 028 → XC_LDA_C_VWN_1 ! Vosko, Wilk, & Nussair (1) [SH Vosko, L Wilk, and M Nusair, Can. J. Phys. 58, 1200 (1980) ]
• 029 → XC_LDA_C_VWN_2 ! Vosko, Wilk, & Nussair (2) [SH Vosko, L Wilk, and M Nusair, Can. J. Phys. 58, 1200 (1980) ]
• 030 → XC_LDA_C_VWN_3 ! Vosko, Wilk, & Nussair (3) [SH Vosko, L Wilk, and M Nusair, Can. J. Phys. 58, 1200 (1980) ]
• 031 → XC_LDA_C_VWN_4 ! Vosko, Wilk, & Nussair (4) [SH Vosko, L Wilk, and M Nusair, Can. J. Phys. 58, 1200 (1980) ]

GGA functionals (do not forget to add a minus sign, as discussed above)

• 84 → XC_GGA_C_OP_XALPHA ! one-parameter progressive functional (G96 version) [T Tsuneda, T Suzumura, and K Hirao, J. Chem. Phys. 111, 5656 (1999) ]
• 85 → XC_GGA_C_OP_G96 ! one-parameter progressive functional (G96 version) [T Tsuneda, T Suzumura, and K Hirao, J. Chem. Phys. 111, 5656 (1999) ]
• 86 → XC_GGA_C_OP_PBE ! one-parameter progressive functional (PBE version) [T Tsuneda, T Suzumura, and K Hirao, J. Chem. Phys. 111, 5656 (1999) ]
• 87 → XC_GGA_C_OP_B88 ! one-parameter progressive functional (B88 version) [T Tsuneda, T Suzumura, and K Hirao, J. Chem. Phys. 111, 5656 (1999) ]
• 88 → XC_GGA_C_FT97 ! Filatov & Thiel correlation [M Filatov & W Thiel, Int. J. Quant. Chem. 62, 603-616 (1997); M Filatov & W Thiel, Mol Phys 91, 847 (1997) ] WARNING: this functional is not tested. Use at your own risks.
• 89 → XC_GGA_C_SPBE ! PBE correlation to be used with the SSB exchange [M Swart, M Sola, and FM Bickelhaupt, J. Chem. Phys. 131, 094103 (2009) ]
• 90 → XC_GGA_X_SSB_SW ! Swarta, Sola and Bickelhaupt correction to PBE [M Swart, M Sola, and FM Bickelhaupt, J. Comp. Meth. Sci. Engin. 9, 69 (2009) ]
• 91 → XC_GGA_X_SSB ! WARNING: This functional gives NaN on IBM (XG20130608). Swarta, Sola and Bickelhaupt [M Swart, M Sola, and FM Bickelhaupt, J. Chem. Phys. 131, 094103 (2009) ]
• 92 → XC_GGA_X_SSB_D ! WARNING: This functional gives NaN on IBM (XG20130608). Swarta, Sola and Bickelhaupt dispersion [M Swart, M Sola, and FM Bickelhaupt, J. Chem. Phys. 131, 094103 (2009) ]
• 93 → XC_GGA_XC_HCTH_407P ! HCTH/407+ [AD Boese, A Chandra, JML Martin, and Dominik Marx, J. Chem. Phys. 119, 5965 (2003) ]
• 94 → XC_GGA_XC_HCTH_P76 ! HCTH p=7/6 [G Menconi, PJ Wilson, and DJ Tozer, J. Chem. Phys. 114, 3958 (2001) ]
• 95 → XC_GGA_XC_HCTH_P14 ! HCTH p=¼ [G Menconi, PJ Wilson, and DJ Tozer, J. Chem. Phys. 114, 3958 (2001) ]
• 96 → XC_GGA_XC_B97_GGA1 ! Becke 97 GGA-1 [AJ Cohen and NC Handy, Chem. Phys. Lett. 316, 160-166 (2000) ]
• 97 → XC_GGA_XC_HCTH_A ! HCTH-A [FA Hamprecht, AJ Cohen, DJ Tozer, and NC Handy, J. Chem. Phys. 109, 6264 (1998) ]
• 98 → XC_GGA_X_BPCCAC ! BPCCAC (GRAC for the energy) [E Bremond, D Pilard, I Ciofini, H Chermette, C Adamo, and P Cortona, Theor Chem Acc 131, 1184 (2012) ]
• 99 → XC_GGA_C_REVTCA ! Tognetti, Cortona, Adamo (revised) [V Tognetti, P Cortona, and C Adamo, Chem. Phys. Lett. 460, 536-539 (2008) ]
• 100 → XC_GGA_C_TCA ! Tognetti, Cortona, Adamo [V Tognetti, P Cortona, and C Adamo, J. Chem. Phys. 128, 034101 (2008) ]
• 101 → XC_GGA_X_PBE ! Perdew, Burke & Ernzerhof exchange [JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996); JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 78, 1396(E) (1997) ]
• 102 → XC_GGA_X_PBE_R ! Perdew, Burke & Ernzerhof exchange (revised) [Y Zhang and W Yang, Phys. Rev. Lett 80, 890 (1998) ]
• 103 → XC_GGA_X_B86 ! Becke 86 Xalfa,beta,gamma [AD Becke, J. Chem. Phys 84, 4524 (1986) ]
• 104 → XC_GGA_X_HERMAN ! Herman Xalphabeta GGA [F Herman, JP Van Dyke, and IB Ortenburger, Phys. Rev. Lett. 22, 807 (1969); F Herman, IB Ortenburger, and JP Van Dyke, Int. J. Quantum Chem. Symp. 3, 827 (1970) ]
• 105 → XC_GGA_X_B86_MGC ! Becke 86 Xalfa,beta,gamma (with mod. grad. correction) [AD Becke, J. Chem. Phys 84, 4524 (1986); AD Becke, J. Chem. Phys 85, 7184 (1986) ]
• 106 → XC_GGA_X_B88 ! Becke 88 [AD Becke, Phys. Rev. A 38, 3098 (1988) ]
• 107 → XC_GGA_X_G96 ! Gill 96 [PMW Gill, Mol. Phys. 89, 433 (1996) ]
• 108 → XC_GGA_X_PW86 ! Perdew & Wang 86 [JP Perdew and Y Wang, Phys. Rev. B 33, 8800 (1986) ]
• 109 → XC_GGA_X_PW91 ! Perdew & Wang 91 [JP Perdew, in Proceedings of the 21st Annual International Symposium on the Electronic Structure of Solids, ed. by P Ziesche and H Eschrig (Akademie Verlag, Berlin, 1991), p. 11.; JP Perdew, JA Chevary, SH Vosko, KA Jackson, MR Pederson, DJ Singh, and C Fiolhais, Phys. Rev. B 46, 6671 (1992); JP Perdew, JA Chevary, SH Vosko, KA Jackson, MR Pederson, DJ Singh, and C Fiolhais, Phys. Rev. B 48, 4978(E) (1993) ]
• 110 → XC_GGA_X_OPTX ! Handy & Cohen OPTX 01 [NC Handy and AJ Cohen, Mol. Phys. 99, 403 (2001) ]
• 111 → XC_GGA_X_DK87_R1 ! dePristo & Kress 87 (version R1) [AE DePristo and JD Kress, J. Chem. Phys. 86, 1425 (1987) ]
• 112 → XC_GGA_X_DK87_R2 ! dePristo & Kress 87 (version R2) [AE DePristo and JD Kress, J. Chem. Phys. 86, 1425 (1987) ]
• 113 → XC_GGA_X_LG93 ! Lacks & Gordon 93 [DJ Lacks and RG Gordon, Phys. Rev. A 47, 4681 (1993) ]
• 114 → XC_GGA_X_FT97_A ! Filatov & Thiel 97 (version A) [M Filatov and W Thiel, Mol. Phys 91, 847 (1997) ]
• 115 → XC_GGA_X_FT97_B ! Filatov & Thiel 97 (version B) [M Filatov and W Thiel, Mol. Phys 91, 847 (1997) ]
• 116 → XC_GGA_X_PBE_SOL ! Perdew, Burke & Ernzerhof exchange (solids) [JP Perdew, et al, Phys. Rev. Lett. 100, 136406 (2008) ]
• 117 → XC_GGA_X_RPBE ! Hammer, Hansen & Norskov (PBE-like) [B Hammer, LB Hansen and JK Norskov, Phys. Rev. B 59, 7413 (1999) ]
• 118 → XC_GGA_X_WC ! Wu & Cohen [Z Wu and RE Cohen, Phys. Rev. B 73, 235116 (2006) ]
• 119 → XC_GGA_X_mPW91 ! Modified form of PW91 by Adamo & Barone [C Adamo and V Barone, J. Chem. Phys. 108, 664 (1998) ]
• 120 → XC_GGA_X_AM05 ! Armiento & Mattsson 05 exchange [R Armiento and AE Mattsson, Phys. Rev. B 72, 085108 (2005); AE Mattsson, R Armiento, J Paier, G Kresse, JM Wills, and TR Mattsson, J. Chem. Phys. 128, 084714 (2008) ]
• 121 → XC_GGA_X_PBEA ! Madsen (PBE-like) [G Madsen, Phys. Rev. B 75, 195108 (2007) ]
• 122 → XC_GGA_X_MPBE ! Adamo & Barone modification to PBE [C Adamo and V Barone, J. Chem. Phys. 116, 5933 (2002) ]
• 123 → XC_GGA_X_XPBE ! xPBE reparametrization by Xu & Goddard [X Xu and WA Goddard III, J. Chem. Phys. 121, 4068 (2004) ]
• 125 → XC_GGA_X_BAYESIAN ! Bayesian best fit for the enhancement factor [JJ Mortensen, K Kaasbjerg, SL Frederiksen, JK Norskov, JP Sethna, and KW Jacobsen, Phys. Rev. Lett. 95, 216401 (2005) ]
• 126 → XC_GGA_X_PBE_JSJR ! PBE JSJR reparametrization by Pedroza, Silva & Capelle [LS Pedroza, AJR da Silva, and K. Capelle, Phys. Rev. B 79, 201106(R) (2009) ]
• 130 → XC_GGA_C_PBE ! Perdew, Burke & Ernzerhof correlation [JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996); JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 78, 1396(E) (1997) ]
• 131 → XC_GGA_C_LYP ! Lee, Yang & Parr [C Lee, W Yang and RG Parr, Phys. Rev. B 37, 785 (1988) B Miehlich, A Savin, H Stoll and H Preuss, Chem. Phys. Lett. 157, 200 (1989) ]
• 132 → XC_GGA_C_P86 ! Perdew 86 [JP Perdew, Phys. Rev. B 33, 8822 (1986) ]
• 133 → XC_GGA_C_PBE_SOL ! Perdew, Burke & Ernzerhof correlation SOL [JP Perdew, et al, Phys. Rev. Lett. 100, 136406 (2008) ]
• 134 → XC_GGA_C_PW91 ! Perdew & Wang 91 [JP Perdew, JA Chevary, SH Vosko, KA Jackson, MR Pederson, DJ Singh, and C Fiolhais, Phys. Rev. B 46, 6671 (1992) ]
• 135 → XC_GGA_C_AM05 ! Armiento & Mattsson 05 correlation [ R Armiento and AE Mattsson, Phys. Rev. B 72, 085108 (2005); AE Mattsson, R Armiento, J Paier, G Kresse, JM Wills, and TR Mattsson, J. Chem. Phys. 128, 084714 (2008) ]
• 136 → XC_GGA_C_XPBE ! xPBE reparametrization by Xu & Goddard [X Xu and WA Goddard III, J. Chem. Phys. 121, 4068 (2004) ]
• 137 → XC_GGA_C_LM ! Langreth and Mehl correlation [DC Langreth and MJ Mehl, Phys. Rev. Lett. 47, 446 (1981) ]
• 138 → XC_GGA_C_PBE_JRGX ! JRGX reparametrization by Pedroza, Silva & Capelle [LS Pedroza, AJR da Silva, and K. Capelle, Phys. Rev. B 79, 201106(R) (2009) ]
• 139 → XC_GGA_X_OPTB88_VDW ! Becke 88 reoptimized to be used with vdW functional of Dion et al [J Klimes, DR Bowler, and A Michaelides, J. Phys.: Condens. Matter 22, 022201 (2010) ]
• 140 → XC_GGA_X_PBEK1_VDW ! PBE reparametrization for vdW [J Klimes, DR Bowler, and A Michaelides, J. Phys.: Condens. Matter 22, 022201 (2010) ]
• 141 → XC_GGA_X_OPTPBE_VDW ! PBE reparametrization for vdW [J Klimes, DR Bowler, and A Michaelides, J. Phys.: Condens. Matter 22, 022201 (2010) ]
• 142 → XC_GGA_X_RGE2 ! Regularized PBE [A Ruzsinszky, GI Csonka, and G Scuseria, J. Chem. Theory Comput. 5, 763 (2009) ]
• 143 → XC_GGA_C_RGE2 ! Regularized PBE [A Ruzsinszky, GI Csonka, and G Scuseria, J. Chem. Theory Comput. 5, 763 (2009) ]
• 144 → XC_GGA_X_RPW86 ! refitted Perdew & Wang 86 [ED Murray, K Lee and DC Langreth, J. Chem. Theory Comput. 5, 2754-2762 (2009) ]
• 145 → XC_GGA_X_KT1 ! Keal and Tozer version 1 [TW Keal and DJ Tozer, J. Chem. Phys. 119, 3015 (2003) ]
• 146 → XC_GGA_XC_KT2 ! WARNING: This functional gives NaN on IBM (XG20130608). Keal and Tozer version 2 [TW Keal and DJ Tozer, J. Chem. Phys. 119, 3015 (2003) ]
• 147 → XC_GGA_C_WL ! Wilson & Levy [LC Wilson and M Levy, Phys. Rev. B 41, 12930 (1990) ]
• 148 → XC_GGA_C_WI ! Wilson & Ivanov [LC Wilson & S Ivanov, Int. J. Quantum Chem. 69, 523-532 (1998) ]
• 149 → XC_GGA_X_MB88 ! Modified Becke 88 for proton transfer [V Tognetti and C Adamo, J. Phys. Chem. A 113, 14415-14419 (2009) ]
• 150 → XC_GGA_X_SOGGA ! Second-order generalized gradient approximation [Y Zhao and DG Truhlar, J. Chem. Phys. 128, 184109 (2008); http://comp.chem.umn.edu/mfm/index.html ]
• 151 → XC_GGA_X_SOGGA11 ! Second-order generalized gradient approximation 2011 [R Peverati, Y Zhao, and DG Truhlar, J. Phys. Chem. Lett. 2, 1911-1997 (2011); http://comp.chem.umn.edu/mfm/index.html ]
• 152 → XC_GGA_C_SOGGA11 ! Second-order generalized gradient approximation 2011 [R Peverati, Y Zhao, and DG Truhlar, J. Phys. Chem. Lett. 2, 1911-1997 (2011); http://comp.chem.umn.edu/mfm/index.html ]
• 153 → XC_GGA_C_WI0 ! Wilson & Ivanov initial version [LC Wilson & S Ivanov, Int. J. Quantum Chem. 69, 523-532 (1998) ]
• 154 → XC_GGA_XC_TH1 ! Tozer and Handy v. 1 [DJ Tozer and NC Handy, J. Chem. Phys. 108, 2545 (1998) ] WARNING: this functional is not tested. Use at your own risks.
• 155 → XC_GGA_XC_TH2 ! Tozer and Handy v. 2 [DJ Tozer and NC Handy, J. Phys. Chem. A 102, 3162 (1998) ]
• 156 → XC_GGA_XC_TH3 ! Tozer and Handy v. 3 [DJ Tozer and NC Handy, Mol. Phys. 94, 707 (1998) ]
• 157 → XC_GGA_XC_TH4 ! Tozer and Handy v. 4 [DJ Tozer and NC Handy, Mol. Phys. 94, 707 (1998) ]
• 158 → XC_GGA_X_C09X ! C09x to be used with the VdW of Rutgers-Chalmers [VR Cooper, PRB 81, 161104(R) (2010) ]
• 159 → XC_GGA_C_SOGGA11_X ! To be used with hyb_gga_x_SOGGA11-X [R Peverati and DG Truhlar, J. Chem. Phys. 135, 191102 (2011); http://comp.chem.umn.edu/mfm/index.html ]
• 161 → XC_GGA_XC_HCTH_93 ! HCTH functional fitted to 93 molecules [FA Hamprecht, AJ Cohen, DJ Tozer, and NC Handy, J. Chem. Phys. 109, 6264 (1998) ]
• 162 → XC_GGA_XC_HCTH_120 ! HCTH functional fitted to 120 molecules [AD Boese, NL Doltsinis, NC Handy, and M Sprik, J. Chem. Phys. 112, 1670 (2000) ]
• 163 → XC_GGA_XC_HCTH_147 ! HCTH functional fitted to 147 molecules [AD Boese, NL Doltsinis, NC Handy, and M Sprik, J. Chem. Phys. 112, 1670 (2000) ]
• 164 → XC_GGA_XC_HCTH_407 ! HCTH functional fitted to 407 molecules [AD Boese, and NC Handy, J. Chem. Phys. 114, 5497 (2001) ]
• 165 → XC_GGA_XC_EDF1 ! Empirical functionals from Adamson, Gill, and Pople [RD Adamson, PMW Gill, and JA Pople, Chem. Phys. Lett. 284 6 (1998) ]
• 166 → XC_GGA_XC_XLYP ! XLYP functional [X Xu and WA Goddard, III, PNAS 101, 2673 (2004) ]
• 167 → XC_GGA_XC_B97 ! Becke 97 [AD Becke, J. Chem. Phys. 107, 8554-8560 (1997) ]
• 168 → XC_GGA_XC_B97_1 ! Becke 97-1 [FA Hamprecht, AJ Cohen, DJ Tozer, and NC Handy, J. Chem. Phys. 109, 6264 (1998); AD Becke, J. Chem. Phys. 107, 8554-8560 (1997) ]
• 169 → XC_GGA_XC_B97_2 ! Becke 97-2 [AD Becke, J. Chem. Phys. 107, 8554-8560 (1997) ]
• 170 → XC_GGA_XC_B97_D ! Grimme functional to be used with C6 vdW term [S Grimme, J. Comput. Chem. 27, 1787 (2006) ]
• 171 → XC_GGA_XC_B97_K ! Boese-Martin for Kinetics [AD Boese and JML Martin, J. Chem. Phys., Vol. 121, 3405 (2004) ]
• 172 → XC_GGA_XC_B97_3 ! Becke 97-3 [TW Keal and DJ Tozer, J. Chem. Phys. 123, 121103 (2005) ]
• 173 → XC_GGA_XC_PBE1W ! Functionals fitted for water [EE Dahlke and DG Truhlar, J. Phys. Chem. B 109, 15677 (2005) ]
• 174 → XC_GGA_XC_MPWLYP1W ! Functionals fitted for water [EE Dahlke and DG Truhlar, J. Phys. Chem. B 109, 15677 (2005) ]
• 175 → XC_GGA_XC_PBELYP1W ! Functionals fitted for water [EE Dahlke and DG Truhlar, J. Phys. Chem. B 109, 15677 (2005) ]
• 176 → XC_GGA_XC_SB98_1a ! Schmider-Becke 98 parameterization 1a [HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998) ]
• 177 → XC_GGA_XC_SB98_1b ! Schmider-Becke 98 parameterization 1b [HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998) ]
• 178 → XC_GGA_XC_SB98_1c ! Schmider-Becke 98 parameterization 1c [HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998) ]
• 179 → XC_GGA_XC_SB98_2a ! Schmider-Becke 98 parameterization 2a [HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998) ]
• 180 → XC_GGA_XC_SB98_2b ! Schmider-Becke 98 parameterization 2b [HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998) ]
• 181 → XC_GGA_XC_SB98_2c ! Schmider-Becke 98 parameterization 2c [HL Schmider and AD Becke, J. Chem. Phys. 108, 9624 (1998) ]
• 183 → XC_GGA_X_OL2 ! Exchange form based on Ou-Yang and Levy v.2 [P Fuentealba and O Reyes, Chem. Phys. Lett. 232, 31-34 (1995); H Ou-Yang, M Levy, Int. J. of Quant. Chem. 40, 379-388 (1991) ]
• 184 → XC_GGA_X_APBE ! mu fixed from the semiclassical neutral atom [LA Constantin, E Fabiano, S Laricchia, and F Della Sala, Phys. Rev. Lett. 106, 186406 (2011) ]
• 186 → XC_GGA_C_APBE ! mu fixed from the semiclassical neutral atom [LA Constantin, E Fabiano, S Laricchia, and F Della Sala, Phys. Rev. Lett. 106, 186406 (2011) ]
• 191 → XC_GGA_X_HTBS! Haas, Tran, Blaha, and Schwarz [P Haas, F Tran, P Blaha, and K Schwarz, Phys. Rev. B 83, 205117 (2011) ]
• 192 → XC_GGA_X_AIRY ! Constantin et al based on the Airy gas [LA Constantin, A Ruzsinszky, and JP Perdew, Phys. Rev. B 80, 035125 (2009) ]
• 193 → XC_GGA_X_LAG ! Local Airy Gas [L Vitos, B Johansson, J Kollar, and HL Skriver, Phys. Rev. B 62, 10046-10050 (2000) ]
• 194 → XC_GGA_XC_MOHLYP ! Functional for organometallic chemistry [NE Schultz, Y Zhao, DGJ Truhlar, Phys. Chem. A, 109, 11127 (2005) ]
• 195 → XC_GGA_XC_MOHLYP2 ! Functional for barrier heights [J Zheng, Y Zhao, DGJ Truhlar, Chem. Theory. Comput. 5, 808 (2009) ]
• 196 → XC_GGA_XC_TH_FL ! Tozer and Handy v. FL [DJ Tozer, NC Handy, amd WH Green, Chem. Phys. Lett. 273, 183-194 (1997) ]
• 197 → XC_GGA_XC_TH_FC ! Tozer and Handy v. FC [DJ Tozer, NC Handy, amd WH Green, Chem. Phys. Lett. 273, 183-194 (1997) ]
• 198 → XC_GGA_XC_TH_FCFO ! Tozer and Handy v. FCFO [DJ Tozer, NC Handy, amd WH Green, Chem. Phys. Lett. 273, 183-194 (1997) ]
• 199 → XC_GGA_XC_TH_FCO ! Tozer and Handy v. FCO [DJ Tozer, NC Handy, amd WH Green, Chem. Phys. Lett. 273, 183-194 (1997) ]
• 200 → XC_GGA_C_OPTC ! Optimized correlation functional of Cohen and Handy [AJ Cohen and NC Handy, Mol. Phys. 99, 607-615 (2001) ]
• 524 → XC_GGA_X_WPBEH ! short-range version of the PBE [J Heyd, GE Scuseria, and M Ernzerhof, J. Chem. Phys. 118, 8207 (2003) ]
• 525 → XC_GGA_X_HJS_PBE ! HJS screened exchange PBE version [TM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008) ]
• 526 → XC_GGA_X_HJS_PBE_SOL ! HJS screened exchange PBE_SOL version [TM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008) ]
• 527 → XC_GGA_X_HJS_B88 ! HJS screened exchange B88 version [TM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008) ] WARNING: this functional is not tested. Use at your own risks.
• 528 → XC_GGA_X_HJS_B97X ! HJS screened exchange B97x version [TM Henderson, BG Janesko, and GE Scuseria, J. Chem. Phys. 128, 194105 (2008) ]
• 529 → XC_GGA_X_ITYH ! short-range recipe for exchange GGA functionals [H Iikura, T Tsuneda, T Yanai, and K Hirao, J. Chem. Phys. 115, 3540 (2001) ] WARNING: this functional is not tested. Use at your own risks.

MetaGGA functionals (do not forget to add a minus sign, as discussed above). See Sun et al, PRB 84, 035117 (2011) for the formulas.

• 202 → XC_MGGA_X_TPSS ! Tao, Perdew, Staroverov & Scuseria [J Tao, JP Perdew, VN Staroverov, and G Scuseria, Phys. Rev. Lett. 91, 146401 (2003); JP Perdew, J Tao, VN Staroverov, and G Scuseria, J. Chem. Phys. 120, 6898 (2004) ]
• 203 → XC_MGGA_X_M06L ! Zhao, Truhlar exchange [Y Zhao and DG Truhlar, JCP 125, 194101 (2006); Y Zhao and DG Truhlar, Theor. Chem. Account 120, 215 (2008) ]
• 204 → XC_MGGA_X_GVT4 ! GVT4 (X part of VSXC) from van Voorhis and Scuseria [T Van Voorhis and GE Scuseria, JCP 109, 400 (1998) ]
• 205 → XC_MGGA_X_TAU_HCTH ! tau-HCTH from Boese and Handy [AD Boese and NC Handy, JCP 116, 9559 (2002) ]
• 207 → XC_MGGA_X_BJ06 ! Becke & Johnson correction to Becke-Roussel 89 [AD Becke and ER Johnson, J. Chem. Phys. 124, 221101 (2006) ] WARNING: this Vxc-only mGGA can only be used with a LDA correlation, typically Perdew-Wang 92.
• 208 → XC_MGGA_X_TB09 ! Tran-blaha - correction to Becke & Johnson correction to Becke-Roussel 89 [F Tran and P Blaha, Phys. Rev. Lett. 102, 226401 (2009) ] WARNING: this Vxc-only mGGA can only be used with a LDA correlation, typically Perdew-Wang 92.
• 209 → XC_MGGA_X_RPP09 ! Rasanen, Pittalis, and Proetto correction to Becke & Johnson [E Rasanen, S Pittalis & C Proetto, arXiv:0909.1477 (2009) ] WARNING: this Vxc-only mGGA can only be used with a LDA correlation, typically Perdew-Wang 92.
• 232 → XC_MGGA_C_VSXC ! VSxc from Van Voorhis and Scuseria (correlation part) [T Van Voorhis and GE Scuseria, JCP 109, 400 (1998) ]

Hybrid functionals (do not forget to add a minus sign, as discussed above).

• 402 → XC_HYB_GGA_XC_B3LYP ! The (in)famous B3LYP [PJ Stephens, FJ Devlin, CF Chabalowski, MJ Frisch, J. Phys. Chem. 98 11623 (1994) ]
• 406 → XC_HYB_GGA_XC_PBEH ! PBEH (PBE0) [C Adamo and V Barone, J. Chem. Phys. 110, 6158 (1999); M. Ernzerhof, G. E. Scuseria, J. Chem. Phys. 110, 5029 (1999) ]
• 427 → XC_HYB_GGA_XC_HSE03 ! The 2003 version of the screened hybrid HSE (in this case one should use omega^HF = 0.15/sqrt(2) and omega^PBE = 0.15*(2.0)**⅓) 428 → XC_HYB_GGA_XC_HSE06 ! The 2006 version of the screened hybrid HSE (in this case one should use omega^HF = omega^PBE = 0.11) (The following section is taken from the LibXC sources. In ABINIT, we stick to the LibXC choice.) Note that there is an enormous mess in the literature concerning the values of omega in HSE. This is due to an error in the original paper that stated that they had used omega=0.15. This was in fact not true, and the real value used was omega^HF = 0.15/sqrt(2) ~ 0.1061 and omega^PBE = 0.15*(2.0)**⅓ ~ 0.1890. In 2006 Krukau et al [JCP 125, 224106 (2006)] tried to clarify the situation, and called HSE03 to the above choice of parameters, and called HSE06 to the functional where omegaHF=omegaPBE. By testing several properties for atoms they reached the conclusion that the best value for omega=0.11. Of course, codes are just as messy as the papers. In espresso HSE06 has the value omega=0.106. VASP, on the other hand, uses for HSE03 the same value omega^HF = omega^PBE = 0.3 (A^-1) ~ 0.1587 and for HSE06 omega^HF = omega^PBE = 0.2 (A^-1) ~ 0.1058. [J Heyd, GE Scuseria, and M Ernzerhof, J. Chem. Phys. 118, 8207 (2003); J Heyd, GE Scuseria, and M Ernzerhof, J. Chem. Phys. 124, 219906 (2006); AV Krukau, OA Vydrov, AF Izmaylov, and GE Scuseria, J. Chem. Phys. 125, 224106 (2006) ]

• 456 → XC_HYB_GGA_XC_PBE0_13 ! PBE0-⅓ [P Cortona, J. Chem. Phys. 136, 086101 (2012) ]

## jdtset¶

Mnemonics: index -J- for DaTaSETs
Characteristics: NO_MULTI
Mentioned in topic(s): topic_multidtset
Variable type: integer
Dimensions: (ndtset)
Default value: [ {‘start’: 1, ‘stop’: ‘ndtset’}; ->

Test list (click to open). Moderately used, [91/973] in all abinit tests, [11/118] in abinit tutorials

Gives the dataset index of each of the datasets. This index will be used:

• 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 ).

The allowed index values are between 1 and 9999. An input variable name appended with 0 is not allowed. When ndtset==0, this array is not used, and moreover, no input variable name appended with a digit is allowed. This array might be initialized thanks to the use of the input variable udtset. In this case, jdtset cannot be used.

## kpt¶

Mnemonics: K - PoinTs
Mentioned in topic(s): topic_k-points
Variable type: real
Dimensions: (3,nkpt)
Default value: [0, 0, 0]
Comment: Adequate for one molecule in a supercell

Test list (click to open). Very frequently used, [969/973] in all abinit tests, [118/118] in abinit tutorials

Contains the k points in terms of reciprocal space primitive translations (NOT in cartesian coordinates!). Needed ONLY if kptopt=0, otherwise deduced from other input variables.

It contains dimensionless numbers in terms of which the cartesian coordinates would be: k_cartesian = k1*G1+k2*G2+k3*G3 where (k1,k2,k3) represent the dimensionless “reduced coordinates” and G1, G2, G3 are the cartesian coordinates of the primitive translation vectors. G1,G2,G3 are related to the choice of direct space primitive translation vectors made in rprim. Note that an overall norm for the k points is supplied by kptnrm. This allows one to avoid supplying many digits for the k points to represent such points as (1,1,1)/3. Note: one of the algorithms used to set up the sphere of G vectors for the basis needs components of k-points in the range [-1,1], so the remapping is easily done by adding or subtracting 1 from each component until it is in the range [-1,1]. That is, given the k point normalization kptnrm described below, each component must lie in [ -kptnrm, kptnrm ]. Note: a global shift can be provided by %qptn Not read if kptopt/=0.

## kptnrm¶

Mnemonics: K - PoinTs NoRMalization
Mentioned in topic(s): topic_k-points
Variable type: real
Dimensions: scalar
Default value: 1

Test list (click to open). Moderately used, [109/973] in all abinit tests, [0/118] in abinit tutorials

Establishes a normalizing denominator for each k point. Needed only if kptopt<=0, otherwise deduced from other input variables. The k point coordinates as fractions of reciprocal lattice translations are therefore kpt(mu,ikpt)/kptnrm. kptnrm defaults to 1 and can be ignored by the user. It is introduced to avoid the need for many digits in representing numbers such as ⅓. It cannot be smaller than 1.0d0

## kptopt¶

Mnemonics: KPoinTs OPTion
Mentioned in topic(s): topic_k-points, topic_ElecBandStructure
Variable type: integer
Dimensions: scalar
Default value: 4 if nspden==4, 1 otherwise.

Test list (click to open). Very frequently used, [801/973] in all abinit tests, [69/118] in abinit tutorials

Controls the set up of the k-points list. The aim will be to initialize, by straight reading or by a preprocessing approach based on other input variables, the following input variables, giving the k points, their number, and their weight: kpt, kptnrm, nkpt, and, for iscf/=-2, wtk.

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.

A global additional shift can be provided by %qptn

• 0 → read directly nkpt, kpt, kptnrm and wtk.
• 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, with the appropriate weights. (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, with the appropriate weights. (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, with the appropriate weights. (This is to be used when preparing or executing a RF calculation at non-zero q)

• 4 → rely on ngkpt or kptrlatt, as well as on nshiftk and shiftk to set up the k points. Take into account all the symmetries EXCEPT the time-reversal symmetry to generate the k points in the Irreducible Brillouin Zone, with the appropriate weights. This has to be used when performing calculations with non-collinear magnetism allowed (nspden=4)

• 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. Weights are usually irrelevant with this option, and will be left to their default value.

In the case of a grid of k points, the auxiliary variables kptrlen, ngkpt and prtkpt might help you to select the optimal grid.

## natom¶

Mnemonics: Number of ATOMs
Mentioned in topic(s): topic_crystal, topic_SmartSymm
Variable type: integer
Dimensions: scalar
Default value: 1

Test list (click to open). Very frequently used, [973/973] in all abinit tests, [118/118] in abinit tutorials

Gives the total number of atoms in the unit cell. Default is 1 but you will obviously want to input this value explicitly. Note that natom refers to all atoms in the unit cell, not only to the irreducible set of atoms in the unit cell (using symmetry operations, this set allows to recover all atoms). If you want to specify only the irreducible set of atoms, use the symmetriser, see the input variable natrd.

## nband¶

Mnemonics: Number of BANDs
Mentioned in topic(s): topic_BandOcc
Variable type: integer
Dimensions: scalar
Default value: None
Comment: the estimated number of occupied bands +1 (TODO provide the mathematical formulation)

Test list (click to open). Very frequently used, [850/973] in all abinit tests, [100/118] in abinit tutorials

Gives number of bands, occupied plus possibly unoccupied, for which wavefunctions are being computed along with eigenvalues. Note: if the parameter occopt (see below) is not set to 2, nband is a scalar integer, but if the parameter occopt is set to 2, then nband must be an array nband(nkpt* nsppol) giving the number of bands explicitly for each k point. This option is provided in order to allow the number of bands treated to vary from k point to k point. For the values of occopt not equal to 0 or 2, nband can be omitted. The number of bands will be set up thanks to the use of the variable fband. The present Default will not be used.

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

In the case of a GW calculation (optdriver=3 or 4), nband gives the number of bands to be treated to generate the screening (susceptibility and dielectric matrix), as well as the self-energy. However, to generate the _KSS file (see kssform) the relevant number of bands is given by nbandkss.

## nbandhf¶

Mnemonics: Number of BANDs for (Hartree)-Fock exact exchange
Mentioned in topic(s): topic_Hybrids
Variable type: integer
Dimensions: scalar
Default value: None
Comment: the estimated number of occupied bands (TODO: provide the mathematical formulation)

Test list (click to open). Rarely used, [8/973] in all abinit tests, [0/118] in abinit tutorials

Gives the maximum number of occupied bands with which Fock exact exchange is being computed for the wavefunctions.

## ndtset¶

Mnemonics: Number of DaTaSETs
Characteristics: NO_MULTI
Mentioned in topic(s): topic_multidtset
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Very frequently used, [655/973] in all abinit tests, [75/118] in abinit tutorials

Gives the number of data sets to be treated. If 0, means that the multi-data set treatment is not used, so that the root filenames will not be appended with _DSx, where ‘x’ is the dataset index defined by the input variable jdtset, and also that input names with a dataset index are not allowed. Otherwise, ndtset=0 is equivalent to ndtset=1.

## ngkpt¶

Mnemonics: Number of Grid points for K PoinTs generation
Characteristics: INPUT_ONLY
Mentioned in topic(s): topic_k-points
Variable type: integer
Dimensions: (3)
Default value: [0, 0, 0]
Only relevant if: kptopt >=0,
The use of this variable forbids the use of: specified(kptrlatt)

Test list (click to open). Very frequently used, [549/973] in all abinit tests, [99/118] in abinit tutorials

Used when kptopt>=0, if kptrlatt has not been defined (kptrlatt and ngkpt are exclusive of each other). Its three positive components give the number of k points of Monkhorst-Pack grids (defined with respect to primitive axis in reciprocal space) in each of the three dimensions. ngkpt will be used to generate the corresponding kptrlatt input variable. The use of nshiftk and shiftk, allows to generate shifted grids, or Monkhorst-Pack grids defined with respect to conventional unit cells.

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.

Monkhorst-Pack grids are usually the most efficient when their defining integer numbers are even. For a measure of the efficiency, see the input variable kptrlen.

## nkpath¶

Mnemonics: Number of K-points defining the PATH
Mentioned in topic(s): topic_k-points
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Rarely used, [2/973] in all abinit tests, [0/118] in abinit tutorials

This variable is used to define the number of high-symmetry k-points in the kptbounds array when kptopt > 0. Historically, kptbounds is used in conjuction with a negative value of kptopt when performing a NSCF band structure calculation. In this case, the number of k-points in kptbounds is given by abs(kptopt) + 1. There are, however, other cases in which one has to specify a k-path in the input file in order to activate some kind of post- processing tool. Typical examples are the interpolation of the GW corrections at the end of the sigma run or the interpolation of the KS eigenvalues along a path at the end of the SCF run (see also einterp) In a nutshell, nkpath replaces kptopt when we are not performing a NSCF calculation. Note that, unlike kptopt, nkpath represents the total number of points in the kptbounds array.

## nkpt¶

Mnemonics: Number of K - Points
Mentioned in topic(s): topic_k-points
Variable type: integer
Dimensions: scalar
Default value: 1 if kptopt==0, 0 otherwise.

Test list (click to open). Very frequently used, [496/973] in all abinit tests, [29/118] in abinit tutorials

If non-zero, nkpt gives the number of k points in the k point array kpt. These points are used either to sample the Brillouin zone, or to build a band structure along specified lines.

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 kptopt is negative, nkpt will be the sum of the number of points on the different lines of the band structure. For example, if kptopt=-3, one will have three segments; supposing ndivk is 10 12 17, the total number of k points of the circuit will be 10+12+17+1(for the final point)=40.

## nkpthf¶

Mnemonics: Number of K - Points for (Hartree) Fock exact exchange
Mentioned in topic(s): topic_Hybrids
Variable type: integer
Dimensions: scalar
Default value: None

Test list (click to open). Rarely used, [8/973] in all abinit tests, [0/118] in abinit tutorials

nkpthf gives the number of k points used to sample the full Brillouin zone for the Fock exact exchange contribution. It is obtained from the specification of the wavefunction k point grid (see kptopt), possibly downfolded as specified by fockdownsampling.

## nshiftk¶

Mnemonics: Number of SHIFTs for K point grids
Mentioned in topic(s): topic_k-points
Variable type: integer
Dimensions: scalar
Default value: 1

Test list (click to open). Moderately used, [469/973] in all abinit tests, [91/118] in abinit tutorials

This parameter gives the number of shifted grids to be used concurrently to generate the full grid of k points. It can be used with primitive grids defined either from ngkpt or kptrlatt. The maximum allowed value of nshiftk is 8. The values of the shifts are given by shiftk.

## nsppol¶

Mnemonics: Number of SPin POLarization
Mentioned in topic(s): topic_spinpolarisation
Variable type: integer
Dimensions: scalar
Default value: 1

Test list (click to open). Moderately used, [182/973] in all abinit tests, [18/118] in abinit tutorials

Give the number of INDEPENDENT spin polarisations, for which there are non- related wavefunctions. Can take the values 1 or 2.

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 disentangled (nspinor=2), that is, either non-collinear magnetism or presence of spin- orbit coupling, for which one needs spinor wavefunctions.

If nsppol=2, one has a spin-polarized (collinear) 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. If nsppol=2, one usually uses a metallic value for occopt, in order to let ABINIT find the magnetization. On the contrary, if occopt==1 is used, the user has to impose the magnetization, using spinmagntarget, except for the case of a single isolated Hydrogen atom.

In the present status of development, with nsppol=1, all values of ixc are allowed, while with nsppol=2, some values of ixc might not be allowed (e.g. 2, 3, 4, 5, 6, 20, 21, 22 are not allowed).

See also the input variable nspden for the components of the density matrix with respect to the spin-polarization.

## nstep¶

Mnemonics: Number of (non-)self-consistent field STEPS
Mentioned in topic(s): topic_SCFControl
Variable type: integer
Dimensions: scalar
Default value: 30

Test list (click to open). Very frequently used, [925/973] in all abinit tests, [110/118] in abinit tutorials

Gives the maximum number of cycles (or “iterations”) in a SCF or non-SCF run. Full convergence from random numbers is usually achieved in 12-20 SCF iterations. Each can take from minutes to hours. In certain difficult cases, usually related to a small or zero bandgap or magnetism, convergence performance may be much worse. When the convergence tolerance tolwfr on the wavefunctions is satisfied, iterations will stop, so for well converged calculations you should set nstep to a value larger than you think will be needed for full convergence, e.g. if using 20 steps usually converges the system, set nstep to 30. For non-self-consistent runs ( iscf < 0) nstep governs the number of cycles of convergence for the wavefunctions for a fixed density and Hamiltonian.

NOTE that a choice of nstep=0 is permitted; this will either read wavefunctions from disk (with irdwfk=1 or irdwfq=1, or non-zero getwfk or getwfq in the case of multi-dataset) and compute the density, the total energy and stop, or else (with all of the above vanishing) will initialize randomly the wavefunctions and compute the resulting density and total energy. This is provided for testing purposes. Also NOTE that nstep=0 with irdwfk=1 will exactly give the same result as the previous run only if the latter is done with iscf<10 (potential mixing). One can output the density by using prtden. The forces and stress tensor are computed with nstep=0.

## nsym¶

Mnemonics: Number of SYMmetry operations
Mentioned in topic(s): topic_crystal, topic_GW
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Moderately used, [359/973] in all abinit tests, [12/118] in abinit tutorials

Gives number of space group symmetries to be applied in this problem. Symmetries will be input in array “symrel” and (nonsymmorphic) translations vectors will be input in array “tnons”. If there is no symmetry in the problem then set nsym to 1, because the identity is still a symmetry. In case of a RF calculation, the code is able to use the symmetries of the system to decrease the number of perturbations to be calculated, and to decrease of the number of special k points to be used for the sampling of the Brillouin zone. After the response to the perturbations have been calculated, the symmetries are used to generate as many as possible elements of the 2DTE from those already computed.

Symmetry finder mode (Default mode). If nsym is 0, all the atomic coordinates must be explicitely given (one cannot use the atom manipulator neither the smart 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.

The user is allowed to set up systems with non-primitive unit cells (i.e. conventional FCC or BCC cells, or supercells without any distortion). In this case, pure translations will be identified as symmetries of the system by the symmetry finder. Then, the combined “pure translation + usual rotation and inversion” symmetry operations can be very numerous. For example, a conventional FCC cell has 192 symmetry operations, instead of the 48 ones of the primitive cell. A maximum limit of 384 symmetry operations is hard-coded. This corresponds to the maximum number of symmetry operations of a 2x2x2 undistorted supercell. Going beyond that number will make the code stop very rapidly. If you want nevertheless, for testing purposes, to treat a larger number of symmetries, change maxnsym.

For GW calculation, the user might want to select only the symmetry operations whose non-symmorphic translation vector tnons is zero. This can be done with the help of the input variable symmorphi

## ntypat¶

Mnemonics: Number of TYPes of AToms
Characteristics: NO_MULTI
Mentioned in topic(s): topic_AtomTypes, topic_PseudosPAW, topic_crystal
Variable type: integer
Dimensions: scalar
Default value: 1

Test list (click to open). Very frequently used, [963/973] in all abinit tests, [118/118] in abinit tutorials

Gives the number of types of atoms. E.g. for a homopolar system (e.g. pure Si) ntypat is 1.

The code tries to read the same number of pseudopotential files. The first pseudopotential is assigned type number 1, and so on…

There is an exception in the case of alchemical mixing of potentials, for which there is a different number of pseudopotentials atomic types. See mixalch.

## occopt¶

Mnemonics: OCCupation OPTion
Mentioned in topic(s): topic_BandOcc, topic_STM
Variable type: integer
Dimensions: scalar
Default value: 1

Test list (click to open). Very frequently used, [528/973] in all abinit tests, [55/118] in abinit tutorials

Controls how input parameters nband, occ, and wtk are handled.

• 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). If nsppol=2 and occopt==1 is used, the user has to impose the magnetization, using spinmagntarget, except for the case of a single isolated Hydrogen atom.

• occopt=2: k points may optionally have different numbers of bands and different occupancies. nband(nkptnsppol) is given explicitly as an array of nkptnsppol 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(-xx 2 )/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 [Methfessel1989] 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)

• occopt=8: Uniform smearing (the delta function is replaced by a constant function of value one over ]-½,½[ (with one-half value at the boundaries). Used for testing purposes only.

WARNING: one can use metallic occupation of levels in the case of a molecule, in order to avoid any problem with degenerate levels. However, it is advised NOT to use occopt=6 (and to a lesser extent occopt=4 and 5), since the associated number of electron versus the Fermi energy is NOT guaranteed to be a monotonic function. For true metals, AND a sufficiently dense sampling of the Brillouin zone, this should not happen, but be cautious ! As an indication of this problem, a small variation of input parameters might lead to a jump of total energy, because there might be two or even three possible values of the Fermi energy, and the bissection algorithm finds one or the other.

## rprim¶

Mnemonics: Real space PRIMitive translations
Characteristics: EVOLVING
Mentioned in topic(s): topic_UnitCell
Variable type: real
Dimensions: (3,3)
Commentdims: Internally, it is represented as rprim(3,3,nimage)
Default value: [[1, 0, 0], [0, 1, 0], [0, 0, 1]]

Test list (click to open). Very frequently used, [793/973] in all abinit tests, [112/118] in abinit tutorials

Give, in columnwise entry, the three dimensionless primitive translations in real space, to be rescaled by acell and scalecart. It is EVOLVING only if ionmov==2 and optcell/=0, otherwise it is fixed. If the Default is used, that is, rprim is the unity matrix, the three dimensionless primitive vectors are three unit vectors in cartesian coordinates. Each will be (possibly) multiplied by the corresponding acell value, then (possibly) stretched along the cartesian coordinates by the corresponding scalecart value, to give the dimensional primitive vectors, called %rprimd. In the general case, the dimensional cartesian coordinates of the crystal primitive translations R1p, R2p and R3p, see %rprimd, are

where i=1,2,3 is the component of the primitive translation (i.e. x, y, and z).

The rprim variable, scaled by scalecart, is thus used to define directions of the primitive vectors, that will be multiplied (so keeping the direction unchanged) by the appropriate length scale acell(1), acell(2), or acell(3), respectively to give the dimensional primitive translations in real space in cartesian coordinates. Presently, it is requested that the mixed product (R1xR2).R3 is positive. If this is not the case, simply exchange a pair of vectors. To be more specific, keeping the default value of scalecart=1 to simplify the matter, rprim 1 2 3 4 5 6 7 8 9 corresponds to input of the three primitive translations R1=(1,2,3) (to be multiplied by acell(1)), R2=(4,5,6) (to be multiplied by acell(2)), and R3=(7,8,9) (to be multiplied by [acell). Note carefully that the first three numbers input are the first column of rprim, the next three are the second, and the final three are the third. This corresponds with the usual Fortran order for arrays. The matrix whose columns are the reciprocal space primitive translations is the inverse transpose of the matrix whose columns are the direct space primitive translations.

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 tolsym (10 digits by default), inducing a specification such as

  rprim  0.86602540378  0.5  0.0
-0.86602540378  0.5  0.0
0.0            0.0  1.0


that can be avoided thanks to angdeg:

  angdeg 90 90 120


Although the use of scalecart or acell is rather equivalent when the primitive vectors are aligned with the cartesian directions, it is not the case for non-orthogonal primitive vectors. In particular, beginners often make the error of trying to use acell to define primitive vectors in face- centered tetragonal lattice, or body-centered tetragonal lattice, or similarly in face or body-centered orthorhombic lattices. Let us take the example of a body-centered tetragonal lattice, that might be defined using the following (“a” and “c” have to be replaced by the appropriate conventional cell vector length):

  rprim  "a"      0        0
0      "a"       0
"a/2"   "a/2"    "c/2"
acell 3*1     scalecart 3*1    !  ( These are default values)


The following is a valid, alternative way to define the same primitive vectors:

  rprim   1        0       0
0        1       0
1/2      1/2     1/2
scalecart  "a"  "a"  "c"
acell 3*1    !  ( These are default values)


Indeed, the cell has been stretched along the cartesian coordinates, by “a”, “a” and “c” factors.

At variance, the following is WRONG:

  rprim   1       0       0
0       1       0
1/2     1/2     1/2
acell  "a"  "a"  "c"    !   THIS IS WRONG
scalecart 3*1    !  ( These are default values)


Indeed, the latter would correspond to:

  rprim  "a"      0       0
0      "a"      0
"c/2"   "c/2"   "c/2"
acell 3*1     scalecart 3*1    !  ( These are default values)


Namely, the third vector has been rescaled by “c”. It is not at all in the center of the tetragonal cell whose basis vectors are defined by the scaling factor “a”. As another difference between scalecart or acell, note that scalecart is INPUT_ONLY: its content will be immediately applied to rprim, at parsing time, and then scalecart will be set to the default values (3*1). So, in case scalecart is used, the echo of rprim in the output file is not the value contained in the input file, but the value rescaled by scalecart.

## rprimd¶

Mnemonics: Real space PRIMitive translations, Dimensional
Characteristics: INTERNAL_ONLY, EVOLVING
Mentioned in topic(s): topic_UnitCell
Variable type: real
Dimensions: (3,3)
Commentdims: Internally, it is represented as rprimd(3,3,nimage).
Default value: None

This internal variable gives the dimensional real space primitive vectors, computed from acell, scalecart, and rprim.

It is EVOLVING only if ionmov==2 and optcell/=0, otherwise it is fixed.

## scalecart¶

Mnemonics: SCALE CARTesian coordinates
Characteristics: INPUT_ONLY
Mentioned in topic(s): topic_UnitCell
Variable type: real
Dimensions: (3)
Default value: 3 * 1

Test list (click to open). Rarely used, [1/973] in all abinit tests, [0/118] in abinit tutorials

Gives the scaling factors of cartesian coordinates by which dimensionless primitive translations (in “rprim”) are to be multiplied. rprim input variable, the acell input variable, and the associated internal %rprimd internal variable. Especially useful for body-centered and face-centered tetragonal lattices, as well as body-centered and face-centered orthorhombic lattices, see %rprimd. Note that this input variable is INPUT_ONLY: its content will be immediately applied to rprim, at parsing time, and then scalecart will be set to the default values. So, it will not be echoed.

## shiftk¶

Mnemonics: SHIFT for K points
Mentioned in topic(s): topic_k-points
Variable type: real
Dimensions: (3,nshiftk)
Default value: None if nshiftk>1, [0.5, 0.5, 0.5] otherwise.

Test list (click to open). Very frequently used, [520/973] in all abinit tests, [92/118] in abinit tutorials

It is used only when kptopt>=0, and must be defined if nshiftk is larger than 1. shiftk(1:3,1:nshiftk) defines nshiftk shifts of the homogeneous grid of k points based on ngkpt or kptrlatt. The shifts induced by shiftk corresponds to the reduced coordinates in the coordinate system defining the k-point lattice. For example, if the k point lattice is defined using ngkpt, the point whose reciprocal space reduced coordinates are ( shiftk(1,ii)/ngkpt(1) shiftk(2,ii)/ngkpt(2) shiftk(3,ii)/ngkpt(3) ) belongs to the shifted grid number ii.

The user might rely on ABINIT to suggest suitable and efficient 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 default (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, as the shift improves the sampling efficiency. However, it can also break symmetry, if the 111 direction is not an axis of rotation, e.g. in tetragonal or hexagonal systems. Abinit will complain about this breaking, and you should adapt shiftk. For a non-shifted Monkhorst-Pack grid, use nshiftk=1 and shiftk 0.0 0.0 0.0, which will be compatible with all symmetries, and is necessary for some features such as k-point interpolation.

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


the (very efficient) usual Monkhorst-Pack sampling will be generated by using 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


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


the usual Monkhorst-Pack sampling will be generated by using nshiftk= 2 and shiftk

  0.25  0.25  0.25
-0.25 -0.25 -0.25


However, the simple sampling nshiftk=1 and shiftk 0.5 0.5 0.5 is excellent.

4) For hexagonal lattices with hexagonal axes, e.g. rprim

  1.0  0.0       0.0
-0.5  sqrt(3)/2 0.0
0.0  0.0       1.0


one can use nshiftk= 1 and shiftk 0.0 0.0 0.5

In rhombohedral axes, e.g. using angdeg 3*60., this corresponds to shiftk 0.5 0.5 0.5, to keep the shift along the symmetry axis.

## symrel¶

Mnemonics: SYMmetry in REaL space
Mentioned in topic(s): topic_crystal
Variable type: integer
Dimensions: (3,3,nsym)
Default value: [[1, 0, 0], [0, 1, 0], [0, 0, 1]] if nsym==1, None otherwise.

Test list (click to open). Moderately used, [185/973] in all abinit tests, [1/118] in abinit tutorials

Gives “nsym” 3x3 matrices expressing space group symmetries in terms of their action on the direct (or real) space primitive translations. It turns out that these can always be expressed as integers. Always give the identity matrix even if no other symmetries hold, e.g. symrel 1 0 0 0 1 0 0 0 1 Also note that for this array as for all others the array elements are filled in a columnwise order as is usual for Fortran. The relation between the above symmetry matrices symrel, expressed in the basis of primitive translations, and the same symmetry matrices expressed in cartesian coordinates, is as follows. Denote the matrix whose columns are the primitive translations as R, and denote the cartesian symmetry matrix as S. Then symrel = R(inverse) * S * R where matrix multiplication is implied. When the symmetry finder is used (see nsym), symrel will be computed automatically.

## tnons¶

Mnemonics: Translation NON-Symmorphic vectors
Mentioned in topic(s): topic_crystal
Variable type: real
Dimensions: (3,nsym)
Default value: None

Test list (click to open). Moderately used, [165/973] in all abinit tests, [2/118] in abinit tutorials

Gives the (nonsymmorphic) translation vectors associated with the symmetries expressed in “symrel”. These may all be 0, or may be fractional (nonprimitive) translations expressed relative to the real space primitive translations (so, using the “reduced” system of coordinates, see “xred”). If all elements of the space group leave 0 0 0 invariant, then these are all 0. When the symmetry finder is used (see nsym), tnons is computed automatically.

## toldfe¶

Mnemonics: TOLerance on the DiFference of total Energy
Characteristics: ENERGY
Mentioned in topic(s): topic_SCFControl
Variable type: real
Dimensions: scalar
Default value: 0.0
Comment: The default value implies that this stopping condition is ignored. For the SCF case, one and only one of the input tolerance criteria tolwfr, toldff, tolrff, toldfe or tolvrs must differ from zero.
The use of this variable forbids the use of: specified(tolwfr) or specified(toldff) or specified(tolrff) or specified(tolvrs)

Test list (click to open). Moderately used, [313/973] in all abinit tests, [48/118] in abinit tutorials

Sets a tolerance for absolute differences of total energy that, reached TWICE successively, will cause one SCF cycle to stop (and ions to be moved). Can be specified in Ha (the default), Ry, eV or Kelvin, since toldfe has the ‘ENERGY‘ characteristics. (1 Ha=27.2113845 eV) If set to zero, this stopping condition is ignored. Effective only when SCF cycles are done (iscf>0). Because of machine precision, it is not worth to try to obtain differences in energy that are smaller than about 1.0d-12 of the total energy. To get accurate stresses may be quite demanding. When the geometry is optimized (relaxation of atomic positions or primitive vectors), the use of toldfe is to be avoided. The use of toldff or tolrff is by far preferable, in order to have a handle on the geometry characteristics. When all forces vanish by symmetry (e.g. optimization of the lattice parameters of a high-symmetry crystal), then place toldfe to 1.0d-12, or use (better) tolvrs. Since toldfe, toldff, tolrff, tolvrs and tolwfr are aimed at the same goal (causing the SCF cycle to stop), they are seen as a unique input variable at reading. Hence, it is forbidden that two of these input variables have non-zero values for the same dataset, or generically (for all datasets). However, a non-zero value for one such variable for one dataset will have precedence on the non-zero value for another input variable defined generically.

## toldff¶

Mnemonics: TOLerance on the DiFference of Forces
Mentioned in topic(s): topic_SCFControl, topic_ForcesStresses
Variable type: real
Dimensions: scalar
Default value: 0.0
Comment: The default value implies that this stopping condition is ignored. For the SCF case, one and only one of the input tolerance criteria tolwfr, toldff, tolrff, toldfe or tolvrs must differ from zero.
The use of this variable forbids the use of: specified(tolwfr) or specified(toldfe) or specified(tolrff) or specified(tolvrs)

Test list (click to open). Moderately used, [92/973] in all abinit tests, [10/118] in abinit tutorials

Sets a tolerance for differences of forces (in hartree/Bohr) that, reached TWICE successively, will cause one SCF cycle to stop (and ions to be moved). If set to zero, this stopping condition is ignored. Effective only when SCF cycles are done (iscf>0). This tolerance applies to any particular cartesian component of any atom, INCLUDING fixed ones. This is to be used when trying to equilibrate a structure to its lowest energy configuration (ionmov=2), or in case of molecular dynamics (ionmov=1) A value ten times smaller than tolmxf is suggested (for example 5.0d-6 hartree/Bohr). This stopping criterion is not allowed for RF calculations. Since toldfe, toldff, tolrff, tolvrs and tolwfr are aimed at the same goal (causing the SCF cycle to stop), they are seen as a unique input variable at reading. Hence, it is forbidden that two of these input variables have non-zero values for the same dataset, or generically (for all datasets). However, a non-zero value for one such variable for one dataset will have precedence on the non-zero value for another input variable defined generically.

## tolrff¶

Mnemonics: TOLerance on the Relative diFference of Forces
Mentioned in topic(s): topic_SCFControl, topic_ForcesStresses
Variable type: real
Dimensions: scalar
Default value: 0.0
Comment: The default value implies that this stopping condition is ignored. For the SCF case, one and only one of the input tolerance criteria tolwfr, toldff, tolrff, toldfe or tolvrs must differ from zero.
The use of this variable forbids the use of: specified(tolwfr) or specified(toldfe) or specified(toldff) or specified(tolvrs)’

Test list (click to open). Rarely used, [9/973] in all abinit tests, [0/118] in abinit tutorials

Sets a tolerance for the ratio of differences of forces (in hartree/Bohr) to maximum force, that, reached TWICE successively, will cause one SCF cycle to stop (and ions to be moved): diffor < tolrff * maxfor. If set to zero, this stopping condition is ignored. Effective only when SCF cycles are done (iscf>0). This tolerance applies to any particular cartesian component of any atom, INCLUDING fixed ones. This is to be used when trying to equilibrate a structure to its lowest energy configuration (ionmov=2), or in case of molecular dynamics (ionmov=1) A value of 0.02 is suggested. This stopping criterion is not allowed for RF calculations. Since toldfe, toldff, tolrff, tolvrs and tolwfr are aimed at the same goal (causing the SCF cycle to stop), they are seen as a unique input variable at reading. Hence, it is forbidden that two of these input variables have non-zero values for the same dataset, or generically (for all datasets). However, a non-zero value for one such variable for one dataset will have precedence on the non-zero value for another input variable defined generically.

## tolvrs¶

Mnemonics: TOLerance on the potential V(r) ReSidual
Mentioned in topic(s): topic_SCFControl
Variable type: real
Dimensions: scalar
Default value: 0.0
Comment: The default value implies that this stopping condition is ignored. For the SCF case, one and only one of the input tolerance criteria tolwfr, toldff, tolrff, toldfe or tolvrs must differ from zero.
The use of this variable forbids the use of: specified(tolwfr) or specified(toldfe) or specified(toldff) or specified(tolrff)’

Test list (click to open). Moderately used, [302/973] in all abinit tests, [53/118] in abinit tutorials

Sets a tolerance for potential residual that, when reached, will cause one SCF cycle to stop (and ions to be moved). If set to zero, this stopping condition is ignored. Effective only when SCF cycles are done (iscf>0). To get accurate stresses may be quite demanding. For simple materials with internal positions determined by symmetries, a value of tolvrs=10^-12 empirically leads to a very approximate 10^-6 atomic unit accuracy for the optimized lattice parameter.

Additional explanation: the residual of the potential is the difference between the input potential and the output potential, when the latter is obtained from the density determined from the eigenfunctions of the input potential. When the self-consistency loop is achieved, both input and output potentials must be equal, and the residual of the potential must be zero. The tolerance on the potential residual is imposed by first subtracting the mean of the residual of the potential (or the trace of the potential matrix, if the system is spin-polarized), then summing the square of this function over all FFT grid points. The result should be lower than tolvrs. Since toldfe, toldff, tolrff, tolvrs and tolwfr are aimed at the same goal (causing the SCF cycle to stop), they are seen as a unique input variable at reading. Hence, it is forbidden that two of these input variables have non-zero values for the same dataset, or generically (for all datasets). However, a non-zero value for one such variable for one dataset will have precedence on the non-zero value for another input variable defined generically.

## tolwfr¶

Mnemonics: TOLerance on WaveFunction squared Residual
Mentioned in topic(s): topic_SCFControl
Variable type: real
Dimensions: scalar
Default value: 0.0
Comment: The default value implies that this stopping condition is ignored. For the SCF case, one and only one of the input tolerance criteria tolwfr, toldff, tolrff, toldfe or tolvrs must differ from zero.
The use of this variable forbids the use of: specified(toldfe) or specified(toldff) or specified(tolrff) or specified(tolvrs)

Test list (click to open). Moderately used, [454/973] in all abinit tests, [40/118] in abinit tutorials

The signification of this tolerance depends on the basis set. In plane waves, it gives a convergence tolerance for the largest squared “residual” (defined below) for any given band. The squared residual is:

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


which clearly is nonnegative and goes to 0 as the iterations converge to an eigenstate. With the squared residual expressed in Hartrees 2 (Hartrees squared), the largest squared residual (called residm) encountered over all bands and k points must be less than tolwfr for iterations to halt due to successful convergence. Note that if iscf>0, this criterion should be replaced by those based on toldfe (preferred for ionmov==0), toldff tolrff (preferred for ionmov/=0), or tolvrs (preferred for theoretical reasons!). When tolwfr is 0.0, this criterion is ignored, and a finite value of toldfe, toldff or tolvrs must be specified. This also imposes a restriction on taking an ion step; ion steps are not permitted unless the largest squared residual is less than tolwfr, ensuring accurate forces. To get accurate stresses may be quite demanding. Note that the preparatory GS calculations before a RF calculations must be highly converged. Typical values for these preparatory runs are tolwfr between 1.0d-16 and 1.0d-22.

Note that tolwfr is often used in the test cases, but this is tolwfr purely for historical reasons: except when iscf <0, other critera should be used.

In the wavelet case (see usewvl = 1), this criterion is the favoured one. It is based on the norm 2 of the gradient of the wavefunctions. Typical values range from 5*10 -4 to 5*10 -5.

Since toldfe, toldff, tolrff, tolvrs and tolwfr are aimed at the same goal (causing the SCF cycle to stop), they are seen as a unique input variable at reading. Hence, it is forbidden that two of these input variables have non-zero values for the same dataset, or generically (for all datasets). However, a non-zero value for one such variable for one dataset will have precedence on the non-zero value for another input variable defined generically.

## typat¶

Mnemonics: TYPe of AToms
Mentioned in topic(s): topic_crystal, topic_AtomTypes
Variable type: integer
Dimensions: [3, ‘natrd’] if natrd<natom, [3, ‘natom’] otherwise.

Default value: 1 if natom==1, None otherwise.

Test list (click to open). Very frequently used, [973/973] in all abinit tests, [118/118] in abinit tutorials

Array giving an integer label to every atom in the unit cell to denote its type. The different types of atoms are constructed from the pseudopotential files. There are at most ntypat types of atoms. As an example, for BaTiO3, where the pseudopotential for Ba is number 1, the one of Ti is number 2, and the one of O is number 3, the actual value of the typat array might be:

  typat 1 2 3 3 3


The array typat has to agree with the actual locations of atoms given in xred, xcart or xangst, and the input of pseudopotentials has to be ordered to agree with the atoms identified in typat. The nuclear charge of the elements, given by the array znucl, also must agree with the type of atoms designated in “typat”. The array typat is not constrained to be increasing. An internal representation of the list of atoms, deep in the code (array atindx), groups the atoms of same type together. This should be transparent to the user, while keeping efficiency.

## udtset¶

Mnemonics: Upper limit on DaTa SETs
Mentioned in topic(s): topic_multidtset
Variable type: integer
Dimensions: (2)
Default value: None
Comment: It is not used when it is not defined

Test list (click to open). Moderately used, [42/973] in all abinit tests, [11/118] in abinit tutorials