Help file for the Anaddb utility of the ABINIT package.

• 0 => no ASR for interatomic force constants is imposed.
• 1 or 2 => the ASR for interatomic force constants is imposed by modifying the on-site interatomic force constants, in a symmetric way (asr=2), or in the more general case, unconstrained way (asr=1).

More detailed explanations : the total energy should be invariant under translation of the crystal as a whole. This would garantee that the three lowest phonon modes at Gamma have zero frequency (Acoustic Sum Rule - ASR). Unfortunately, the way the DDB is generated (presence of a discrete grid of points for the evaluation of the exchange-correlation potential and energy) slightly breaks the translational invariance. Well, in some pathological cases, the breaking can be rather important.

Two quantities are affected : the interatomic forces (or dynamical matrices), and the effective charges. The ASR for the effective charges is called the charge neutrality sum rule, and will be dealt with by the variable chneut. The ASR for the interatomic forces can be restored, by modifying the interatomic force of the atom on itself, (called self-IFC), as soon as the dynamical matrix at Gamma is known. This quantity should be equal to minus the sum of all interatomic forces generated by all others atoms (action-reaction law!), which is determined by the dynamical matrix at Gamma.

So, if asr is non-zero, the correction to the self-force will be determined, and the self-force will be imposed to be consistent with the ASR. This correction will work if IFCs are computed (ifcflag/=0), as well as if the IFCs are not computed (ifcflag==0). In both cases, the phonon frequencies will not be the same as the ones determined by the output of abinit, RF case. If you want to check that the DDB is correct, by comparing phonon frequencies from abinit and anaddb, you should turn off both asr and chneut.

Until now, we have not explained the difference between asr=1 and asr=2. This is rather subtle. In some local low-symmetry cases (basically the effective charges should be anisotropic), when the dipole-dipole contribution is evaluated and subtracted, the ASR cannot be imposed without breaking the symmetry of the on-site interatomic forces. That explains why two options are given : the second case (asr=2, sym) does not entirely impose the ASR, but simply the part that keeps the on-site interatomic forces symmetric (which means that the acoustic frequencies do not go to zero exactly), the first case (asr=1, asym) imposes the ASR, but breaks the symmetry. asr=2 is to be preferred for the analysis of the interatomic force constant in real space, while asr=1 should be used to get the phonon band structure.

• 1 => all the lattices (including FCC, BCC and hexagonal)
• 2 => specific for Face Centered lattices
• 3 => specific for Body Centered lattices
• 4 => specific for the Hexagonal lattice

Note that in the latter case, the rprim of the unit cell have to be 1.0 0.0 0.0 -.5 sqrt(3)/2 0.0 0.0 0.0 1.0 in order for the code to work properly.

• chneut=0 => no ASR for effective charges is imposed
• chneut=1 => the ASR for effective charges is imposed by giving to each atom an equal portion of the missing charge.
• chneut=2 => the ASR for effective charges is imposed by giving to each atom a portion of the missing charge proportional to the screening charge already present.

• 0 => No dielectric tensor is calculated.
• 1 => The frequency-dependent dielectric tensor is calculated. The frequencies are defined by the nfreq, frmin, frmax variables. Also, the generalized Lyddane-Sachs-Teller relation will be used as an independent check of the dielectic tensor at zero frequency (this for the directions defined in the phonon list 2. See nph2l).
• 2 => Only the electronic dielectric tensor is calculated. It corresponds to a zero-frequency homogeneous field, with quenched atomic positions. For large band gap materials, this quantity is measurable because the highest phonon frequency is on the order of a few tenths of eV, and the band gap is larger than 5eV.
• 3 => Compute and print the relaxed-ion dielectric tensor. Requirements for preceding response-function DDB generation run: electric-field and full atomic-displacement responses. Set rfstrs = 1, 2, or 3 (preferably 3). Set rfatpolrfatpol and rfdir to do a full calculation of phonons at Q=0 (needed because the inverse of force-constant tensor is required). Note that the relaxed-ion dielectric tensor computed here can also be obtained as the zero-frequency limit of the frequency-dependent dielectric tensor using input variables dieflag=1 and frmin=0.0. (The results obtained using these two approaches should agree to good numerical precision.) The ability to compute and print the static dielectric tensor here is provided for completeness and consistency with the other tensor quantities that are computed in this section of the code.

• 0 => the dipole-dipole interaction is not handled separately in the treatment of the interatomic forces. This option is available for testing purposes or if effective charge and/or dielectric tensor is not available in the derivative database. It gives results much less accurate than dipdip=1.
• 1 => the dipole-dipole interaction is subtracted from the dynamical matrices before Fourier transform, so that only the short-range part is handled in real space. Of course, it is reintroduced analytically when the phonon spectrum is interpolated, or if the interatomic force constants have to be analysed in real space.

• 0 => do not write the phonon eigenvectors;
• 1 => write the phonon eigenvectors;
• 2 => write the phonon eigenvectors, the dynamical matrix is symmetrized;
• 3 => write the phonon eigenvectors, in the lwf-formatted file;
• 4 => generate output files for band2eps (drawing tool for the phonon band structure);

• 0 => No elastic or compliance tensor will be calculated.
• 1 => Only clamped-ion elastic and compliance tensors will be calculated. Requirements for preceding response-function DDB generation run: Strain perturbation. Set rfstrs to 1, 2, or 3. Note that rfstrs=3 is recommended so that responses to both uniaxial and shear strains will be computed.
• 2 => Both relaxed- and clamped-ion elastic and compliance tensor will be calculated, but only the relaxed-ion quantities will be printed. The input variable instrflag should also be set to 1, because the internal-strain tensor is needed to compute the relaxed-ion corrections. Requirements for preceding response-function DDB generation run: Strain and atomic-displacement responses at Q=0. Set rfstrs = 1, 2, or 3 (preferably 3). Set rfatpolrfatpol and rfdir to do a full calculation of phonons at Q=0 (needed because the inverse of force-constant tensor is required).
• 3 => Both relaxed and clamped-ion elastic and compliance tensors will be printed out. The input variable instrflag should also be set to 1. Requirements for preceding response-function DDB generation run: Same as for elaflag=2'.

• 0 => Hartree and cm-1;
• 1 => meV and Thz;
• 2 => Hartree, cm-1, meV, Thz, and Kelvin.

• 0 => no analysis of interatomic force constants;
• 1 => analysis of interatomic force constants.

• 0 => do all calculations directly from the DDB, without the use of the interatomic force constant.
• 1 => calculate and use the interatomic force constants for interpolating the phonon spectrum and dynamical matrices at every q wavevector, and eventually analyse the interatomic force constants, according to the informations given by atifc, dipdip, ifcana, ifcout, natifc, nsphere.

• 0 => No internal-strain calculation.
• 1 => Print out both force-response and displacement-response internal-strain tensor. Requirements for preceding response-function DDB generation run: Strain and full atomic-displacement responses. Set rfstrs = 1, 2, or 3 (preferably 3). Set rfatpol and rfdir to do a full calculation of phonons at Q=0.

• 1 -> xx
• 2 -> yy
• 3 -> zz
• 4 -> yz & zy
• 5 -> xz & zx
• 6 -> xy & yx

• 0 => do not compute non-linear properties ;
• 1 => the electrooptic tensor, Raman susceptibilities and non-linear optical susceptibilities are calculated;
• 2 => only the non-linear optical susceptibilities and first-order changes of the dielectric tensor induced by an atomic displacement are calculated;

• 0 => No piezoelectric tensor will be calculated.
• 1 => Only the clamped-ion piezoelectric tensor is computed and printed. Requirements for preceding response-function DDB generation run: Strain and electric-field responses. For the electric-field part, one needs results from a prior 'ddk perturbation' run. Note that even if only a limited number of piezoelectric tensor terms are wanted (as determined by rfstrs and rfdir in this calculation) it is necessary to set rfdir = 1 1 1 in the d/dk calculation for most structures. The only obvious exception to this requirement is cases in which the primitive lattice vectors are all aligned with the cartesian axes. The code will omit terms in the output piezoelectric tensor for which the available d/dk set is incomplete. Thus: Set rfstrs to 1, 2, or 3i (preferably 3)
• 2 => Both relaxed- and clamped-ion elastic and compliance tensor will be calculated, but only the relaxed-ion quantities will be printed. The input variable instrflag should also be set to 1, because the internal-strain tensor is needed to compute the relaxed-ion corrections. Requirements for preceding response-function DDB generation run: Strain, electric-field and full atomic-displacement responses at Q=0. Set rfstrs = 1, 2, or 3 (preferably 3). Set rfelfd = 3. Set rfatpol and rfdir to do a full calculation of phonons at Q=0 (needed because the inverse of force-constant tensor is required).
• 3 => Both relaxed and clamped-ion piezoelectric tensors will be printed out. The input variable instrflag should also be set to 1. Requirements for preceding response-function DDB generation run: Same as for piezoflag=2'.

More detailed explanation : ANADDB can use the formalism described in Na Sai et al, PRB 66, 104108 (2002), to perform structural relaxations under the constraint that the polarization is equal to a value specified by the input variable targetpol. The user starts from a given configurationof a crystal and performs a ground-state calculation of the Hellman-Feynman forces and stresses and the Berry phase polarization as well as a linear response calculation of the whole matrix of second-order energy derivatives with respect to atomic displacement, strains and electric field.
In case polflag=1, ANADDB solves the linear system of equations (13) of the Na Sai paper, and computes new atomic positions (if relaxat=1) and lattice constant (if relaxstr=1). Then, the user uses these parameters to perform a new ground-state and linear-response calculation. This must be repeated until convergence is reached. THe user can also fix some atomic positions, or strains, thanks to the input variables natfix, nstrfix, iatfix, istrfix.
In case both relaxat and relaxstr are 0, while polflag=1, ANADDB only computes the polarization in cartesian coordinates.

• 0 => do not write the mode-by-mode decomposition of the electrooptic tensor;
• 1 => write out the contribution of the individual zone-center phonon modes to the electrooptic tensor.

Note that if the three first numbers are zero, then the code will do a calculation at Gamma without non-analyticities.

a) Case nqshft=1 In general, 0.5 0.5 0.5 with the ngqpt's even will give very economical grids. On the other hand, is it sometimes better for phonons to have the Gamma point in the grid. In that case, 0.0 0.0 0.0 should be OK. For the hexagonal lattice, the above mentioned quantities become 0.0 0.0 0.5 and 0.0 0.0 0.0 .

b) Case nqshft=2 The two q1shft vectors must form a BCC lattice. For example, use 0.0 0.0 0.0 and 0.5 0.5 0.5

c) Case nqshft=4 The four q1shft vectors must form a FCC lattice. For example, use 0.0 0.0 0.0 , 0.0 0.5 0.5 , 0.5 0.0 0.5 , 0.5 0.5 0.0 or 0.5 0.5 0.5 , 0.0 0.0 0.5 , 0.0 0.5 0.0 , 0.5 0.0 0.0 (the latter is referred to as shifted)

Further comments : by using this technique, it is possible to increase smoothly the number of q-points, at least less abruptly than relying on series of grids like (for the full cubic symmetry) 1x1x1 => (0 0 0) 2x2x2 (shifted) => (.25 .25 .25) 2x2x2 => 1x1x1 + (.5 0 0) (.5 .5 0) (.5 .5 0) 4x4x4 => 2x2x2 + (.25 0 0) (.25 .25 0) (.25 .5 0) (.25 .25 .25) (.25 .25 .5) (.25 .5 .5) ... with respectively 1, 1, 4 and 10 q-points, corresponding to a number of points in the full BZ of 1, 8, 8 and 64. Indeed, the following grids are made available : 1x1x1 with nqshft=2 => (0 0 0) (.5 .5 .5) 1x1x1 with nqshft=4 => (0 0 0) (.5 .5 0) 1x1x1 with nqshft=4 (shifted) => (.5 0 0) (.5 .5 .5) 2x2x2 with nqshft=2 => 2x2x2 + (.25 .25 .25) 2x2x2 with nqshft=4 => 2x2x2 + (.25 .25 0) (.25 .25 .5) 2x2x2 with nqshft=4 (shifted) => (.25 0 0) (.25 .25 .25) (.5 .5 .25) (.25 .5 0) ... with respectively 2, 2, 2, 5, 6 and 4 q-points, corresponding to a number of points in the full BZ of 2, 4, 4, 16, 32 and 32. For a FCC lattice, it is possible to sample only the Gamma point by using a 1x1x1 BCC sampling (nqshft=2).

• 0 => no sum rule is imposed;
• 1 => impose the sum rule on the Raman tensors, giving each atom an equal part of the discrepancy;
• 2 => impose the sum rule on the Raman tensors, giving each atom a part of the discrepancy proportional to the magnitude of its contribution to the Raman tensor.

• 1 => Blocks obtained by a non-stationary formulation.
• 2 => Blocks obtained by a stationary formulation.

• 0 => The effective charge tensor is left as it is.
• 1 => For each atom, the effective charge tensor is made isotropic, by calculating the trace of the matrix, dividing it by 3, and using this number in a diagonal effective charge tensor.
• 2 => For each atom, the effective charge tensor is made symmetric, by simply averaging on symmetrical elements.

• the normalized phonon DOS
• the phonon internal energy, free energy, entropy, constant volume heat capacity as a function of the temperature
• the Debye-Waller factors (tensors) for each atom, as a function of the temperature