# dfpt input variables¶

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

## bdeigrf¶

Mnemonics: BanD for second-order EIGenvalues from Response-Function
Mentioned in topic(s): topic_TDepES
Variable type: integer
Dimensions: scalar
Default value: -1
Only relevant if: ieig2rf in [1,2,3,4,5]

Test list (click to open). Moderately used, [15/998] in all abinit tests, [0/117] in abinit tutorials

The variable bdeigrf is the maximum number of bands for which the second- order eigenvalues must be calculated: the full number of bands is still used during the computation of these corrections.

If bdeigrf is set to -1, the code will automatically set bdeigrf equal to nband.

## d3e_pert1_atpol¶

Mnemonics: 3rd Derivative of Energy, mixed PERTurbation 1: limits of ATomic POLarisations
Mentioned in topic(s): topic_nonlinear
Variable type: integer
Dimensions: (2)
Default value: [1, 1]
Only relevant if: optdriver == 5 (non-linear response computations)

Test list (click to open). Moderately used, [27/998] in all abinit tests, [6/117] in abinit tutorials

Controls the range of atoms for which displacements will be considered in non- linear computations (using the 2n+1 theorem), for the 1st perturbation. May take values from 1 to natom, with d3e_pert1_atpol (1)<= d3e_pert1_atpol (2). See rfatpol for additional details.

## d3e_pert1_dir¶

Mnemonics: 3rd Derivative of Energy, mixed PERTurbation 1: DIRections
Mentioned in topic(s): topic_nonlinear
Variable type: integer
Dimensions: (3)
Default value: [0, 0, 0]
Only relevant if: optdriver == 5 (non-linear response computations)

Test list (click to open). Moderately used, [27/998] in all abinit tests, [6/117] in abinit tutorials

Gives the directions to be considered in non-linear computations (using the 2n+1 theorem), for the 1st perturbation. The three elements corresponds to the three primitive vectors, either in real space (atomic displacement), or in reciprocal space (electric field perturbation). See rfdir for additional details.

## d3e_pert1_elfd¶

Mnemonics: 3rd Derivative of Energy, mixed PERTurbation 1: ELectric FielD
Mentioned in topic(s): topic_nonlinear
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 5 (non-linear response computations)

Test list (click to open). Moderately used, [27/998] in all abinit tests, [6/117] in abinit tutorials

Turns on electric field perturbation in non-linear computation, as 1st perturbation. Actually, such calculations requires first the non-self- consistent calculation of derivatives with respect to k, independently of the electric field perturbation itself. See rfelfd for additional details.

## d3e_pert1_phon¶

Mnemonics: 3rd Derivative of Energy, mixed PERTurbation 1: PHONons
Mentioned in topic(s): topic_nonlinear
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 5 (non-linear response computations)

Test list (click to open). Moderately used, [27/998] in all abinit tests, [6/117] in abinit tutorials

Turns on atomic displacement perturbation in non-linear computation, as 1st perturbation. See rfphon for additional details.

## d3e_pert2_atpol¶

Mnemonics: 3rd Derivative of Energy, mixed PERTurbation 2: limits of ATomic POLarisations
Mentioned in topic(s): topic_nonlinear
Variable type: integer
Dimensions: (2)
Default value: [1, 1]
Only relevant if: optdriver == 5 (non-linear response computations)

Test list (click to open). Rarely used, [1/998] in all abinit tests, [0/117] in abinit tutorials

Controls the range of atoms for which displacements will be considered in non- linear computations (using the 2n+1 theorem), for the 2nd perturbation. May take values from 1 to natom, with d3e_pert2_atpol (1) <= d3e_pert2_atpol (2). See rfatpol for additional details.

## d3e_pert2_dir¶

Mnemonics: 3rd Derivative of Energy, mixed PERTurbation 2: DIRections
Mentioned in topic(s): topic_nonlinear
Variable type: integer
Dimensions: (3)
Default value: [0, 0, 0]
Only relevant if: optdriver == 5 (non-linear response computations)

Test list (click to open). Moderately used, [27/998] in all abinit tests, [6/117] in abinit tutorials

Gives the directions to be considered in non-linear computations (using the 2n+1 theorem), for the 2nd perturbation. The three elements corresponds to the three primitive vectors, either in real space (atomic displacement), or in reciprocal space (electric field perturbation). See rfdir for additional details.

## d3e_pert2_elfd¶

Mnemonics: 3rd Derivative of Energy, mixed PERTurbation 2: ELectric FielD
Mentioned in topic(s): topic_nonlinear
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 5 (non-linear response computations)

Test list (click to open). Moderately used, [27/998] in all abinit tests, [6/117] in abinit tutorials

Turns on electric field perturbation in non-linear computation, as 2nd perturbation. Actually, such calculations requires first the non-self- consistent calculation of derivatives with respect to k, independently of the electric field perturbation itself. See rfelfd for additional details.

## d3e_pert2_phon¶

Mnemonics: 3rd Derivative of Energy, mixed PERTurbation 2: PHONons
Mentioned in topic(s): topic_nonlinear
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 5 (non-linear response computations)

Test list (click to open). Rarely used, [1/998] in all abinit tests, [0/117] in abinit tutorials

Turns on atomic displacement perturbation in non-linear computation, as 2nd perturbation. See rfphon for additional details.

## d3e_pert3_atpol¶

Mnemonics: 3rd Derivative of Energy, mixed PERTurbation 3: limits of ATomic POLarisations
Mentioned in topic(s): topic_nonlinear
Variable type: integer
Dimensions: (2)
Default value: [1, 1]
Only relevant if: optdriver == 5 (non-linear response computations)

Test list (click to open). Rarely used, [1/998] in all abinit tests, [0/117] in abinit tutorials

Controls the range of atoms for which displacements will be considered in non- linear computations (using the 2n+1 theorem), for the 3rd perturbation. May take values from 1 to natom, with d3e_pert3_atpol (1)<= d3e_pert3_atpol (2). See rfatpol for additional details.

## d3e_pert3_dir¶

Mnemonics: 3rd Derivative of Energy, mixed PERTurbation 3: DIRections
Mentioned in topic(s): topic_nonlinear
Variable type: integer
Dimensions: (3)
Default value: [0, 0, 0]
Only relevant if: optdriver == 5 (non-linear response computations)

Test list (click to open). Moderately used, [27/998] in all abinit tests, [6/117] in abinit tutorials

Gives the directions to be considered in non-linear computations (using the 2n+1 theorem), for the 3rd perturbation. The three elements corresponds to the three primitive vectors, either in real space (atomic displacement), or in reciprocal space (electric field perturbation). See rfdir for additional details.

## d3e_pert3_elfd¶

Mnemonics: 3rd Derivative of Energy, mixed PERTurbation 3: ELectric FielD
Mentioned in topic(s): topic_nonlinear
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 5 (non-linear response computations)

Test list (click to open). Moderately used, [27/998] in all abinit tests, [6/117] in abinit tutorials

Turns on electric field perturbation in non-linear computation, as 3rd perturbation. Actually, such calculations requires first the non-self- consistent calculation of derivatives with respect to k, independently of the electric field perturbation itself. See rfelfd for additional details.

## d3e_pert3_phon¶

Mnemonics: 3rd Derivative of Energy, mixed PERTurbation 3: PHONons
Mentioned in topic(s): topic_nonlinear
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 5 (non-linear response computations)

Test list (click to open). Rarely used, [1/998] in all abinit tests, [0/117] in abinit tutorials

Turns on atomic displacement perturbation in non-linear computation, as 3rd perturbation. See rfphon for additional details.

## dfpt_sciss¶

Mnemonics: DFPT SCISSor operator
Characteristics: ENERGY
Mentioned in topic(s): topic_DFPT
Variable type: real
Dimensions: scalar
Default value: 0

Test list (click to open). Rarely used, [1/998] in all abinit tests, [0/117] in abinit tutorials

It is the value of the “scissors operator”, the shift of conduction band eigenvalues, used in response function calculations. Can be specified in Ha (the default), Ry, eV or Kelvin, since ecut has the ‘ENERGY‘ characteristics (1 Ha=27.2113845 eV). Typical use is for response to electric field (rfelfd = 3), but NOT for d/dk (rfelfd = 2) and phonon responses.

## efmas¶

Mnemonics: EFfective MASs
Mentioned in topic(s): topic_EffectiveMass
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Rarely used, [6/998] in all abinit tests, [0/117] in abinit tutorials

Turns on effective mass tensor calculations. Such calculations requires the non-self-consistent calculation of derivatives with respect to k, in the same dataset. It must therefore be used with rfelfd = 2 (or 1).

Note

At the present time, both norm-conserving (NC) and PAW calculations are supported. Also, for PAW calculations only, nspinor == 2 and pawspnorb == 1 (i.e. spin-orbit (SO) calculations) is supported. NC SO calculations are NOT currently supported. Also, for both NC and PAW, nspden/=1 and nsppol/=1 are NOT supported.

## efmas_bands¶

Mnemonics: EFfective MASs, BANDS to be treated.
Mentioned in topic(s): topic_EffectiveMass
Variable type: integer
Dimensions: (2,nkpt)
Default value: The full range of band available in the calculation for each k-point.
Only relevant if: efmas == 1

Test list (click to open). Rarely used, [6/998] in all abinit tests, [0/117] in abinit tutorials

This variable controls the range of bands for which the effective mass is to be calculated. If a band is degenerate, all other bands of the degenerate group will automatically be treated, even if they were not part of the user specified range.

## efmas_calc_dirs¶

Mnemonics: EFfective MASs, CALCulate along DIRectionS
Mentioned in topic(s): topic_EffectiveMass
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: efmas == 1

Test list (click to open). Rarely used, [5/998] in all abinit tests, [0/117] in abinit tutorials

Allows the user to calculate the scalar effective mass of all bands specified by efmas_bands along specific directions in reciprocal space. This is particularly useful when considering degenerate bands, which are usually warped, and thus cannot have their dispersion (hessian) and effective mass expressed as a tensor. This allows the user to see the more complex angular behavior of effective masses in these cases, for instance.

When efmas_calc_dirs == 0, no directions are read from the input file (using efmas_dirs) and the effective masses along the 3 cartesian directions are output by default.

When efmas_calc_dirs == 1, 2 or 3, efmas_n_dirs directions are read from efmas_dirs, assuming cartesian, reduced or angular ($\theta$,$\phi$) coordinates, respectively. In the case efmas_calc_dirs == 3, 2 real values per directions are read, whereas 3 real values are read in the two other cases.

## efmas_deg¶

Mnemonics: EFfective MASs, activate DEGenerate formalism
Mentioned in topic(s): topic_EffectiveMass
Variable type: integer
Dimensions: scalar
Default value: 1
Only relevant if: efmas > 0

Test list (click to open). Rarely used, [1/998] in all abinit tests, [0/117] in abinit tutorials

Activate (==1) or not (==0) the treatment of degenerate bands (criterion efmas_deg_tol is used to determine whether bands are degenerate). Also compute the transport equivalent effective mass (see [Mecholsky2014]).

efmas = 0 should only be used for testing purposes.

## efmas_deg_tol¶

Mnemonics: EFfective MASs, DEGeneracy TOLerance
Mentioned in topic(s): topic_EffectiveMass
Variable type: real
Dimensions: scalar
Default value: 1e-05
Only relevant if: efmas_deg == 1

Test list (click to open). Rarely used, [1/998] in all abinit tests, [0/117] in abinit tutorials

Energy difference below which 2 bands are considered degenerate (and treated using the formalism activated with efmas_deg == 1). efmas_deg_tol has the ‘ENERGY‘ characteristics.

## efmas_dim¶

Mnemonics: EFfective MASs, DIMension of the effective mass tensor
Mentioned in topic(s): topic_EffectiveMass
Variable type: integer
Dimensions: scalar
Default value: 3
Only relevant if: efmas == 1

Test list (click to open). Rarely used, [1/998] in all abinit tests, [0/117] in abinit tutorials

For 2D or 1D systems, the band dispersion goes to 0 perpendicular to the system, which causes the inverse effective mass to be singular, i.e. the effective mass to be NaN. This keyword circumvents the problem by eliminating the troublesome dimensions from the inverse effective mass.

In 2D, the Z axis is ignored and, in 1D, the Z and Y axis are ignored.

Also, note that in the 2D degenerate case, a subtlety arises: the ‘transport equivalent’ effective mass does not determine the scale of the transport tensors (conductivity and others). Therefore, for this specific case, the factor by which these transport tensors should be scaled once determined from the ‘transport equivalent’ effective mass tensor is output separately on the line immediately after the effective mass.

## efmas_dirs¶

Mnemonics: EFfective MASs, DIRectionS to be calculated
Mentioned in topic(s): topic_EffectiveMass
Variable type: real
Dimensions: (3 or 2,efmas_n_dirs)
Default value: 0
Only relevant if: efmas_calc_dirs > 0

Test list (click to open). Rarely used, [5/998] in all abinit tests, [0/117] in abinit tutorials

List of efmas_n_dirs directions to be considered according to the value of efmas_calc_dirs. The directions are specified by 3 real values if efmas_calc_dirs == 1 or 2 and by 2 real values if efmas_calc_dirs == 3.

## efmas_n_dirs¶

Mnemonics: EFfective MASs, Number of DIRectionS
Mentioned in topic(s): topic_EffectiveMass
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: efmas_calc_dirs > 0

Test list (click to open). Rarely used, [5/998] in all abinit tests, [0/117] in abinit tutorials

Number of directions in efmas_dirs, to be considered according to efmas_calc_dirs.

## efmas_ntheta¶

Mnemonics: EFfective MASs, Number of points for integration w/r to THETA
Mentioned in topic(s): topic_EffectiveMass
Variable type: integer
Dimensions: scalar
Default value: 1000
Only relevant if: efmas == 1 and efmas_bands == (degenerate band index)

Test list (click to open). Rarely used, [6/998] in all abinit tests, [0/117] in abinit tutorials

When a band is degenerate, the usual definition of effective mass becomes invalid. However, it is still possible to define a ‘transport equivalent mass tensor’ that reproduces the contribution of the band to the conductivity tensor. To obtain this tensor, an integration over the solid sphere is required. The angular variables are sampled using efmas_ntheta points for the theta coordinate, and twice efmas_ntheta points for the phi coordinate. The default value gives a tensor accurate to the 4th decimal in Ge.

## elph2_imagden¶

Mnemonics: ELectron-PHonon interaction at 2nd order: IMAGinary shift of the DENominator
Characteristics: ENERGY
Mentioned in topic(s): topic_TDepES
Variable type: real
Dimensions: scalar
Default value: 0.0
Only relevant if: ieig2rf != 0

Test list (click to open). Moderately used, [19/998] in all abinit tests, [4/117] in abinit tutorials

The variable elph2_imagden determines the imaginary shift of the denominator of the sum-over-states in the perturbation, $(e_{nk}-e_{n'k'}+i$elph2_imagden). One should use a width comparable with the Debye frequency or the maximum phonon frequency. Can be specified in Ha (the default), Ry, eV or Kelvin, since ecut has the ‘ENERGY‘ characteristics (1 Ha=27.2113845 eV).

## esmear¶

Mnemonics: Eigenvalue SMEARing
Characteristics: ENERGY
Mentioned in topic(s): topic_TDepES
Variable type: real
Dimensions: scalar
Default value: 0.01
Only relevant if: smdelta != 0

Test list (click to open). Rarely used, [1/998] in all abinit tests, [0/117] in abinit tutorials

The variable esmear determines the width of the functions approximating the delta function, $\delta(e_{nk}-e_{n'k'})$, present in the expression of the lifetimes. One should use a width comparable with the Debye frequency or the maximum phonon frequency. Can be specified in Ha (the default), Ry, eV or Kelvin, since ecut has the ‘ENERGY‘ characteristics (1 Ha=27.2113845 eV).

## frzfermi¶

Mnemonics: FReeZe FERMI energy
Mentioned in topic(s): topic_DFPT
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Rarely used, [3/998] in all abinit tests, [0/117] in abinit tutorials

Can be used to suppress artificially the first-order change of Fermi energy, in case of Response Function calculation for metals at Q=0. If the input variable frzfermi is set to 1, this contribution is suppressed, even though this is incorrect.

## ieig2rf¶

Mnemonics: Integer for second-order EIGenvalues from Response-Function
Mentioned in topic(s): topic_TDepES
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Moderately used, [26/998] in all abinit tests, [4/117] in abinit tutorials

If ieig2rf is greater then 0, the code will produce a file, named with the trailing suffix _EIGR2D, containing the second-order electronic eigenvalues for the perturbation. These files are used in the calculation of the thermal correction to the electronic eigenvalues.

• If ieig2rf is set to 1, the second-order electronic eigenvalues will be calculated from the DFPT method (Sternheimer).

• If ieig2rf is set to 2, the second-order electronic eigenvalues will be calculated from the Allen-Cardona method (sum over states).

• If ieig2rf is set to 3, the second-order electronic eigenvalues will be calculated from the DFPT method (sum over states) but using a different part of the code. This is equivalent to ieig2rf = 1 [debuging].

• If ieig2rf is set to 4, the second-order electronic eigenvalues will be calculated from the dynamical DFPT method (Sternheimer). The code will generate _EIGR2D.nc files that contain the electron-phonon matrix element squared on the space orthogonal to the active space. The code will also produce _FAN.nc files that contain the electron-phonon matrix elements squared.

• If ieig2rf is set to 5, the second-order electronic eigenvalues will be calculated from the dynamical DFPT method (Sternheimer). The code will generate _EIGR2D.nc files that contain the electron-phonon matrix element square on the space orthogonal to the active space. The code will also produce _GKK.nc files that contain electron-phonon matrix elements. This option is preferable for large system to ieig2rf = 4 as the GKK files take much less disk space and memory (but run a little bit slower).

Note

ieig2rf = 4 and 5 can only be used if Abinit is compiled with NETCDF support.

Related variables: bdeigrf,elph2_imagden,getgam_eig2nkq,smdelta

## ixcrot¶

Mnemonics: Index of the XC ROTation method used to calculate first-order exchange-correlation potential in non-collinear DFPT calculations
Mentioned in topic(s): topic_DFPT, topic_xc
Variable type: integer
Dimensions: scalar
Default value: 3

Test list (click to open). Moderately used, [12/998] in all abinit tests, [0/117] in abinit tutorials

Method of calculation of the 1st order XC potential in non-collinear DFPT calculations. The possible values 1,2 and 3 correspond to the following methods

• If ixcrot=1, the spinor rotation matrix U at each fft point is not calculated explicitly. Instead the needed expressions involving U are derived based on the general properties of the U matrix.
• If ixcrot=2, U is computed explicitly
• If ixcrot=3, the brute force evaluation of the 1st order XC potential as a functional derivative is used. Rotation matrices are not computed.

In theory, all methods give identical results. However, due to different implementation approaches, the round-off errors can lead to slight differences intermediate and final results obtained using methods 1,2 and 3. The choice of the method can also affect the convergence. For more details, see [Ricci2019].

Note

For non-zero perturbation wavevector, only ixcrot=3 implementation is currently available.

## nonlinear_info¶

Mnemonics: Output NON-LINEAR INFOrmation
Mentioned in topic(s): topic_nonlinear
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 5 and usepead == 0, or rf2_dkdk/=0 or rf2_dkde/=0

Test list (click to open). Rarely used, [9/998] in all abinit tests, [0/117] in abinit tutorials

Control the output of the non-linear implementation (only when usepead == 0). The default value, nonlinear_info == 0 does nothing. If nonlinear_info == 1, different contributions of 3rd derivatives of the energy are written in the output file (non time consuming).

Higher values activate some internal tests for checking the implementation correctness (time consuming, not useable in parallel). If nonlinear_info == 2, same effect than 1 and tests are done in non-linear (optdriver==5 and usepead == 0). If nonlinear_info == 3, same effect than 1 and tests are done in rf2_init (rf2_dkdk/=0 or rf2_dkde/=0). If nonlinear_info == 4, same effect than 1 and tests are done in both non-linear and rf2_init. A line containining “NOT PASSED” (and other information) is added to the output file for each test that does not pass, otherwise nothing is printed. However, more information concerning the tests is always printed in the standard output file.

## prepanl¶

Mnemonics: PREPAre Non-Linear response calculation
Mentioned in topic(s): topic_nonlinear
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Moderately used, [26/998] in all abinit tests, [6/117] in abinit tutorials

The computation of third-order derivatives from the 2n+1 theorem requires the first-order wavefunctions and densities obtained from a linear response calculation. The standard approach in a linear response calculation is:

• compute only the irreducible perturbations;
• use symmetries to reduce the number of k-points for the k-point integration.

This approach cannot be applied, presently (v4.1), if the first-order wavefunctions are to be used to compute third-order derivatives. First, for electric fields, the code needs the derivatives along the three directions. Still, in case of phonons, only the irreducible perturbations are required. Second, for both electric fields and phonons, the wavefunctions must be available in half the BZ (kptopt=2), or the full BZ (kptopt=3). During the linear response calculation, in order to prepare a non-linear calculation, one should put prepanl to 1 in order to force ABINIT to compute the electric field perturbation along the three directions explicitly, and to keep the full number of k-points.

In the case of a 2nd derivative of wavefunction (rf2_dkdk or rf2_dkde), prepanl == 1 can be used in order to skip directions of perturbations that will not be used by the non-linear routine (see rf2_dkdk for more details).

## prepgkk¶

Mnemonics: PREPAre GKK calculation
Mentioned in topic(s): topic_ElPhonInt
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Rarely used, [5/998] in all abinit tests, [1/117] in abinit tutorials

The calculation of electron-phonon coupling quantities requires the presence of all the perturbations (all atoms in all directions) for the chosen set of (irreducible) q-points. To impose this and prevent ABINIT from using symmetry to reduce the number of perturbations, set prepgkk to 1. Use in conjunction with prtgkk.

## prtbbb¶

Mnemonics: PRinT Band-By-Band decomposition
Mentioned in topic(s): topic_printing, topic_Output
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Rarely used, [1/998] in all abinit tests, [0/117] in abinit tutorials

If prtbbb is 1, print the band-by-band decomposition of Born effective charges and localization tensor, in case they are computed. See [Ghosez2000].

## prtefmas¶

Mnemonics: PRint EFfective MASs data
Mentioned in topic(s): topic_printing, topic_EffectiveMass
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: efmas == 1

Test list (click to open). Rarely used, [2/998] in all abinit tests, [0/117] in abinit tutorials

If 1, at the end of an effective mass calculation (efmas = 1), create a file *_EFMAS, that contains the generalized second-order k-derivatives, see Eq.(66) in [Laflamme2016], in view of further processing.

## prtfull1wf¶

Mnemonics: PRinT FULL 1st-order WaveFunction
Mentioned in topic(s): topic_DFPT
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Rarely used, [1/998] in all abinit tests, [0/117] in abinit tutorials

If set to 1, the output _1WF files will contain the full 1st-order wavefunctions, for both valence and conduction bands. Otherwise, the _1WF files are not really 1st-order perturbed wavefunctions, but merely a set of perturbed wavefunctions that yield the correct perturbed density. This is used when one expect to perform post-processing of the 1st-order wavefunctions.

## rf2_dkde¶

Mnemonics: Response Function: mixed 2nd Derivative of wavefunctions with respect to K and electric field
Mentioned in topic(s): topic_DFPT
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Rarely used, [9/998] in all abinit tests, [0/117] in abinit tutorials

If is equal to 1, activates computation of mixed second derivatives of wavefunctions with respect to wavevector and electric field (ipert = natom+11 is activated). This is not strictly a response function but is a needed auxiliary quantity in the calculations of 3rd-order derivatives of the energy (non-linear response) if usepead == 0. The directions for the derivatives are determined by rf2_pert1_dir, rf2_pert2_dir and prepanl in the same way than rf2_dkdk.

## rf2_dkdk¶

Mnemonics: Response Function: 2nd Derivative of wavefunctions with respect to K
Mentioned in topic(s): topic_DFPT
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Rarely used, [9/998] in all abinit tests, [0/117] in abinit tutorials

If is equal to 1, activates computation of second derivatives of wavefunctions with respect to wavevectors (ipert = natom+10 is activated). This is not strictly a response function but is a needed auxiliary quantity in the calculations of 3rd-order derivatives of the energy (non-linear response) if usepead == 0. The directions for the derivatives are determined by rf2_pert1_dir and rf2_pert2_dir and prepanl as the following:

The computation of the 2nd derivative of wavefunction with respect to “lambda_1” and “lambda_2” is computed if if rf2_pert1_dir[idir1] AND rf2_pert2_dir[idir2] are equal to 1, where “idir1” (“idir2”) is direction of the perturbation “lambda_1” (“lambda_2”). If ALL directions are activated (default behavior) AND prepanl == 1, then the code automatically selects only the directions that will be used by the non-linear routine (optdriver == 5) using crystal symmetries.

## rf2_pert1_dir¶

Mnemonics: Response Function (2nd order Sternheimer equation): 1st PERTurbation DIRection
Mentioned in topic(s): topic_DFPT
Variable type: integer
Dimensions: (3)
Default value: [1, 1, 1]

Test list (click to open). Rarely used, [0/998] in all abinit tests, [0/117] in abinit tutorials

Gives the directions of the 1st perturbation to be considered when solving the 2nd order Sternheimer equation. The three elements corresponds to the three primitive vectors, either in real space (phonon calculations), or in reciprocal space ($\,d/ \,d k$, homogeneous electric field, homogeneous magnetic field calculations). If equal to 1, the 2nd order wavefunctions, as defined by rf2_dkdk or rf2_dkde, are computed for the corresponding direction. If 0, this direction is not considered. See rf2_dkdk for more details.

## rf2_pert2_dir¶

Mnemonics: Response Function (2nd order Sternheimer equation): 2nd PERTurbation DIRection
Mentioned in topic(s): topic_DFPT
Variable type: integer
Dimensions: (3)
Default value: [1, 1, 1]

Test list (click to open). Rarely used, [0/998] in all abinit tests, [0/117] in abinit tutorials

Gives the directions of the 2nd perturbation to be considered when solving the 2nd order Sternheimer equation. The three elements corresponds to the three primitive vectors, either in real space (phonon calculations), or in reciprocal space ($\,d/ \,d k$, homogeneous electric field, homogeneous magnetic field calculations). If equal to 1, the 2nd order wavefunctions, as defined by rf2_dkdk or rf2_dkde, are computed for the corresponding direction. If 0, this direction is not considered. See rf2_dkdk for more details.

## rfasr¶

Mnemonics: Response Function: Acoustic Sum Rule
Mentioned in topic(s): topic_Phonons
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Rarely used, [4/998] in all abinit tests, [0/117] in abinit tutorials

Control the evaluation of the acoustic sum rule in effective charges and dynamical matrix at Gamma within a response function calculation (not active at the level of producing the DDB, but at the level of the phonon eigenfrequencies output).

• 0 → no acoustic sum rule imposed
• 1 → acoustic sum rule imposed for dynamical matrix at Gamma, and charge neutrality imposed with extra charge evenly distributed among atoms
• 2 → acoustic sum rule imposed for dynamical matrix at Gamma, and charge neutrality imposed with extra charge given proportionally to those atoms with the largest effective charge.

The treatment of the acoustic sum rule and charge neutrality sum rule is finer at the level of the ANADDB utility, with the two independent input variables asr and chneut.

## rfatpol¶

Mnemonics: Response Function: ATomic POLarisation
Mentioned in topic(s): topic_DFPT, topic_Elastic, topic_Phonons
Variable type: integer
Dimensions: (2)
Default value: [1, 1]

Test list (click to open). Moderately used, [179/998] in all abinit tests, [19/117] in abinit tutorials

Control the range of atoms for which displacements will be considered in phonon calculations (atomic polarizations). These values are only relevant to phonon response function calculations. May take values from 1 to natom, with rfatpol(1)<=rfatpol(2). The atoms to be moved will be defined by the do-loop variable iatpol:

For the calculation of a full dynamical matrix, use rfatpol(1)=1 and rfatpol(2)=natom, together with rfdir 1 1 1. For selected elements of the dynamical matrix, use different values of rfatpol and/or rfdir. The name ‘iatpol’ is used for the part of the internal variable ipert when it runs from 1 to natom. The internal variable ipert can also assume values larger than natom, denoting perturbations of electric field or stress type (see the DFPT help file).

## rfddk¶

Mnemonics: Response Function with respect to Derivative with respect to K
Mentioned in topic(s): topic_DFPT
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Moderately used, [10/998] in all abinit tests, [0/117] in abinit tutorials

Activates computation of derivatives of ground state wavefunctions with respect to wavevectors. This is not strictly a response function but is a needed auxiliary quantity in the electric field calculations (see rfelfd). The directions for the derivatives are determined by rfdir.

• 0 → no derivative calculation
• 1 → calculation of first derivatives of wavefunctions with respect to k points ($\,d/ \,d k$ calculation). The exact same functionality is provided by rfelfd = 2.

## rfdir¶

Mnemonics: Response Function: DIRections
Mentioned in topic(s): topic_DFPT, topic_Elastic, topic_Phonons
Variable type: integer
Dimensions: (3)
Default value: [0, 0, 0]

Test list (click to open). Moderately used, [241/998] in all abinit tests, [30/117] in abinit tutorials

Gives the directions to be considered for response function calculations (also for the Berry phase computation of the polarization, see the berryopt input variable). The three elements corresponds to the three primitive vectors, either in real space (phonon calculations), or in reciprocal space ($\,d/ \,d k$, homogeneous electric field, homogeneous magnetic field calculations). So, they generate a basis for the generation of the dynamical matrix or the macroscopic dielectric tensor or magnetic susceptibility and magnetic shielding, or the effective charge tensors. If equal to 1, response functions, as defined by rfddk, rfelfd, rfphon, rfdir and rfatpol, are to be computed for the corresponding direction. If 0, this direction should not be considered.

## rfelfd¶

Mnemonics: Response Function with respect to the ELectric FielD
Mentioned in topic(s): topic_EffectiveMass, topic_DFPT
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Moderately used, [104/998] in all abinit tests, [14/117] in abinit tutorials

Turns on electric field response function calculations. Actually, such calculations requires first the non-self-consistent calculation of derivatives with respect to k, independently of the electric field perturbation itself.

• 0 → no electric field perturbation
• 1 → full calculation, with first the derivative of ground-state wavefunction with respect to k ($\,d / \,d k$ calculation), by a non-self-consistent calculation, then the generation of the first-order response to an homogeneous electric field
• 2 → only the derivative of ground-state wavefunctions with respect to k
• 3 → only the generation of the first-order response to the electric field, assuming that the data on derivative of ground-state wavefunction with respect to k is available on disk.

Note

Because the tolerances to be used for derivatives or homogeneous electric field are different, one often does the calculation of derivatives in a separate dataset, followed by calculation of electric field response as well as phonon. The options 2 and 3 proves useful in that context; also, in case a scissor shift is to be used, it is usually not applied for the $\,d / \,d k$ response).

## rfmagn¶

Mnemonics: Response Function with respect to MAGNetic B-field perturbation
Mentioned in topic(s): topic_DFPT
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Rarely used, [4/998] in all abinit tests, [0/117] in abinit tutorials

rfmagn allows one to run response function calculations with respect to external magnetic field if set to 1. Currently, orbital magnetism is not taken into account and the perturbing potential has Zeeman form. For more details, see [Ricci2019].

## rfmeth¶

Mnemonics: Response Function METHod
Mentioned in topic(s): topic_DFPT
Variable type: integer
Dimensions: scalar
Default value: 1

Test list (click to open). Rarely used, [2/998] in all abinit tests, [0/117] in abinit tutorials

Selects method used in response function calculations. Presently, only abs(rfmeth) = 1 is allowed. This corresponds to storing matrix elements of the 2DTE computed using non-stationary expressions, instead of stationary ones.

The difference between positive and negative values is rather technical. Very often, the symmetries can be used in such a way that some matrix elements can be proven to be zero even without doing any computation. Positive values of rfmeth activate this use of symmetries, while it is denied when rfmeth is negative. There is an indirect additional outcome of this, as a symmetrization of the whole 2DTE is sometimes rendered possible when the additional knowledge of the zero matrix elements is available. Thus, the results obtained for positive and negative values of rfmeth might slightly differ for non-zero elements of the 2DTE, if they are computed in both cases.

## rfphon¶

Mnemonics: Response Function with respect to PHONons
Mentioned in topic(s): topic_DFPT
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Moderately used, [180/998] in all abinit tests, [19/117] in abinit tutorials

It must be equal to 1 to run phonon response function calculations.

## rfstrs¶

Mnemonics: Response Function with respect to STRainS
Mentioned in topic(s): topic_DFPT, topic_Elastic
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Moderately used, [26/998] in all abinit tests, [5/117] in abinit tutorials

Used to run strain response-function calculations (e.g. needed to get elastic constants). Define, with rfdir, the set of perturbations.

• 0 → no strain perturbation
• 1 → only uniaxial strain(s) (ipert=natom+3 is activated)
• 2 → only shear strain(s) (ipert=natom+4 is activated)
• 3 → both uniaxial and shear strain(s) (both ipert=natom+3 and ipert=natom+4 are activated)

See the possible restrictions on the use of strain perturbations, in the respfn help file.

## rfuser¶

Mnemonics: Response Function, USER-defined
Mentioned in topic(s): topic_DFPT
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Rarely used, [0/998] in all abinit tests, [0/117] in abinit tutorials

Available to the developpers, to activate the use of ipert=natom+6 and ipert=natom+7, two sets of perturbations that the developpers can define.

• 0 → no computations for ipert=natom+6 or ipert=natom+7
• 1 → response with respect to perturbation natom+6 will be computed
• 2 → response with respect to perturbation natom+7 will be computed
• 3 → responses with respect to perturbations natom+6 and natom+7 will be computed

Important

In order to define and use correctly the new perturbations, the developper might have to include code lines or additional routines at the level of the following routines: dfpt_cgwf.F90, dfpt_dyout.F90, dfpt_symph.F90, dfpt_dyout.F90, dfpt_etot.F90, littlegroup_pert.F90, dfpt_looppert.F90, dfpt_mkcor.F90, dfpt_nstdy.F90, dfpt_nstwf.F90, respfn.F90, dfpt_scfcv.F90, irreducible_set_pert.F90, dfpt_vloca.F90, dfpt_vtorho.F90, dfpt_vtowfk.F90. In these routines, the developper should pay a particular attention to the rfpert array, defined in the routine respfn (in m_respfn_driver.F90), as well as to the ipert local variable.

## smdelta¶

Mnemonics: SMeared DELTA function
Mentioned in topic(s): topic_TDepES
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Moderately used, [26/998] in all abinit tests, [4/117] in abinit tutorials

When smdelta in non-zero, it will trigger the calculation of the imaginary part of the second-order electronic eigenvalues, which can be related to the electronic lifetimes. The delta function is evaluated using:

• when smdelta == 1, Fermi-Dirac smearing: $
• when smdelta == 2, Cold smearing by Marzari using the parameter $a=-0.5634$ (minimization of the bump): $
• when smdelta == 3, Cold smearing by Marzari using the parameter $a=-0.8165$ (monotonic function in the tail): as 2 but different $a$
• when smdelta == 4, 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 smdelta=2, with different $a$).
• when smdelta == 5, Gaussian smearing: $

## td_maxene¶

Mnemonics: Time-Dependent dft: MAXimal kohn-sham ENErgy difference
Mentioned in topic(s): topic_TDDFT
Variable type: real
Dimensions: scalar
Default value: 0.0

Test list (click to open). Rarely used, [1/998] in all abinit tests, [0/117] in abinit tutorials

The Matrix to be diagonalized in the Casida framework (see [Casida1995]) is a NxN matrix, where, by default, N is the product of the number of occupied states by the number of unoccupied states. The input variable td_maxene allows one to diminish N: it selects only the pairs of occupied and unoccupied states for which the Kohn-Sham energy difference is less than td_maxene. The default value 0.0 means that all pairs are taken into account. See td_mexcit for an alternative way to decrease N.

## td_mexcit¶

Mnemonics: Time-Dependent dft: Maximal number of EXCITations
Mentioned in topic(s): topic_TDDFT
Variable type: real
Dimensions: scalar
Default value: 0

Test list (click to open). Rarely used, [1/998] in all abinit tests, [0/117] in abinit tutorials

The Matrix to be diagonalized in the Casida framework (see [Casida1995]) is a NxN matrix, where, by default, N is the product of the number of occupied states by the number of unoccupied states. The input variable td_mexcit allows one to diminish N: it selects the first td_mexcit pairs of occupied and unoccupied states, ordered with respect to increasing Kohn-Sham energy difference. However, when td_mexcit is zero, all pairs are allowed. See td_maxene for an alternative way to decrease N.

## tim1rev¶

Mnemonics: TIMe 1st order REVersal
Characteristics: DEVELOP
Mentioned in topic(s): topic_DFPT
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Rarely used, [3/998] in all abinit tests, [0/117] in abinit tutorials

Allowed values are 0 or 1.

If tim1rev is equal to 1, the Sternheimer equation is solved simultaneously at +q and -q perturbation wavevectors. The first order potential at -q is taken to be equal to the Hermitian conjugate of the first order potential at +q. The wavefunctions from both +q and -q are then combined to generate the first order density. Relevant in the case of magnetic field perturbation (but will be relevant also in case of non-zero frequency DFPT, when implemented).