6. Making input files for alm

6.1. Format of input files

Each input file should consist of entry fields. Available entry fields are

&general, &interaction, &cutoff, &cell, &position, and &fitting.

Each entry field starts from the key label &field and ends at the terminate character “/”. (This is equivalent to Fortran namelist.)

For example, &general entry field of program alm should be given like

&general
  # Comment line
  PREFIX = prefix
  MODE = fitting
/

Multiple entries can be put in a single line. Also, characters put on the right of sharp (“#”) will be neglected. Therefore, the above example is equivalent to the following:

&general
  PREFIX = prefix; MODE = fitting  # Comment line
/

Each variable should be written inside the appropriate entry field.

6.2. List of input variables

“&general”-field

  • PREFIX-tag : Job prefix to be used for names of output files
Default:None
Type:String

  • MODE-tag = fitting | suggest
fitting
Perform fittings to estimate harmonic and anharmonic IFCs.
This mode requires appropriate DFILE and FFILE.
suggest
This mode suggests the displacement patterns necessary
to estimate harmonic and anharmonic IFCS.
Default:None
Type:String

  • NAT-tag : Number of atoms in the supercell
Default:None
Type:Integer

  • NKD-tag : Number of atomic species
Default:None
Type:Integer

  • KD-tag = Name[1], ... , Name[NKD]
Default:None
Type:Array of strings
Example:In the case of GaAs with NKD = 2, it should be KD = Ga As.

  • NSYM-tag = 0 | 1 | nsym
0
The program automatically generates the crystal symmetry
operations (rotational and translational parts).
When PRINTSYM = 1, symmetry operations will be saved
in the file “SYMM_INFO”.
1
Only the identity operation will be considered.
nsym
“nsym” symmetry operations will be read from “SYMM_INFO”
file.
Default:0
Type:Integer

  • TOLERANCE-tag : Tolerance for finding symmetry operations
Default:1.0e-6
Type:Double

  • PRINTSYM-tag = 0 | 1
0 Symmetry operations won’t be saved in “SYMM_INFO”
1 Symmetry operations will be saved in “SYMM_INFO”
Default:0
type:Integer

  • PERIODIC-tag = PERIODIC[1], PERIODIC[2], PERIODIC[3]
0
Do not consider periodic boundary conditions when
searching for interacting atoms.
1
Consider periodic boundary conditions when
searching for interacting atoms.
Default:1 1 1
type:Array of integers
Description:This tag is useful for generating interacting atoms in low dimensional systems. When PERIODIC[i] is zero, periodic boundary condition is turned off along the direction of the lattice vector \(\boldsymbol{a}_{i}\).

  • HESSIAN-tag = 0 | 1
0 Do not save the Hessian matrix
1 Save the entire Hessian matrix of the supercell as PREFIX.hessian.
Default:0
type:Integer

“&interaction”-field

  • NORDER-tag : The order of force constants to be calculated. Anharmonic terms up to \((m+1)\)th order will be considered with NORDER = \(m\).
Default:None
Type:Integer
Example:NORDER should be 1 for harmonic calculations, and 2 to include cubic terms.

  • NBODY-tag : Entry for excluding multiple-body interactions from anharmonic force constants
Default:NBODY = [2, 3, 4, ..., NORDER + 1]
Type:Array of integers
Example:If one wants to exclude three-body interactions from cubic force constants, one should explicitly give NBODY = 2 2.

“&cutoff”-field

In this entry field, one needs to specify cutoff radii of interaction for each order in units of Bohr. In the current implementation, cutoff radii should be defined for every possible pair of atomic elements. For example, the cutoff entry for a harmonic calculation (NORDER = 1) of Si (NKD = 1) should be like

&cutoff
 Si-Si 10.0
/

This means that the cutoff radii of 10 \(a_{0}\) will be used for harmonic Si-Si terms. Please note that the first column should be two character strings, which are contained in the KD-tag, connected by a hyphen (’-’).

When one wants to consider cubic terms (NORDER = 2), please specify the cutoff radius for cubic terms in the third column as the following:

&cutoff
 Si-Si 10.0 5.6 # Pair r_{2} r_{3}
/

Instead of giving specific cutoff radii, one can write “None” as follows:

&cutoff
 Si-Si None 5.6
/

which means that all possible harmonic terms between Si-Si atoms will be included.

Caution

Setting ‘None’ for anharmonic terms can greatly increase the number of parameters and thereby increase the computational cost.

When there are more than two atomic elements, please specify the cutoff radii between every possible pair of atomic elements. In the case of MgO (NKD = 2), the cutoff entry should be like

&cutoff
 Mg-Mg 8.0
 O-O 8.0
 Mg-O 10.0
/

which can equivalently be written by using the wild card (’*’) as

&cutoff
 *-* 8.0
 Mg-O 10.0 # Overwrite the cutoff radius for Mg-O harmonic interactions
/

Important

Cutoff radii specified by an earlier entry will be overwritten by a new entry that comes later.

Once the cutoff radii are properly given, harmonic force constants \(\Phi_{i,j}^{\mu,\nu}\) satisfying \(r_{ij} \le r_{c}^{\mathrm{KD}[i]-\mathrm{KD}[j]}\) will be searched.

In the case of cubic terms, force constants \(\Phi_{ijk}^{\mu\nu\lambda}\) satisfying \(r_{ij} \le r_{c}^{\mathrm{KD}[i]-\mathrm{KD}[j]}\), \(r_{ik} \le r_{c}^{\mathrm{KD}[i]-\mathrm{KD}[k]}\), and \(r_{jk} \le r_{c}^{\mathrm{KD}[j]-\mathrm{KD}[k]}\) will be searched and determined by fitting.


“&cell”-field

Please give the cell parameters in this entry in units of Bohr as the following:

&cell
 a
 a11 a12 a13
 a21 a22 a23
 a31 a32 a33
/

The cell parameters are then given by \(\vec{a}_{1} = a \times (a_{11}, a_{12}, a_{13})\), \(\vec{a}_{2} = a \times (a_{21}, a_{22}, a_{23})\), and \(\vec{a}_{3} = a \times (a_{31}, a_{32}, a_{33})\).


“&position”-field

In this field, one needs to specify the atomic element and fractional coordinate of atoms in the supercell. Each line should be

ikd xf[1] xf[2] xf[3]

where ikd is an integer specifying the atomic element (ikd = 1, ..., NKD) and xf[i] is the fractional coordinate of an atom. There should be NAT such lines in the &position entry field.


“&fitting”-field

This field is necessary when MODE = fitting.

  • DFILE-tag : File name containing atomic displacements in Cartesian coordinate
Default:None
Type:String
Description:The format of DFILE can be found here

  • FFILE-tag : File name containing atomic forces in Cartesian coordinate
Default:None
Type:String
Description:The format of FFILE can be found here

  • NDATA-tag : Number of displacement-force data sets
Default:None
Type:Integer
Description:DFILE and FFILE should contain at least NDATA\(\times\) NAT lines.

  • NSTART, NEND-tags : Specifies the range of data to be used for fitting
Default:NSTART = 1, NEND = NDATA
Type:Integer
Example:To use the data in the range of [20:30] out of 50 entries, the tags should be NSTART = 20 and NEND = 30.

  • ICONST-tag = 0 | 1 | 2 | 3
0 No constraints
1 Constraints for translational invariance will be imposed between IFCs.
2
In addition to ICONST = 1, constraints for rotational invariance
will be imposed up to (NORDER + 1)th order.
3
In addition to ICONST = 2, constraints for rotational invariance
between (NORDER + 1)th order and (NORDER + 2)th order, which
are zero, will be considered.
11
Same as ICONST = 1 but the constraint is imposed algebraically
rather than numerically.
Default:1
Type:Integer
Description:See this page for the numerical formulae.

  • ROTAXIS-tag : Rotation axis used to estimate constraints for rotational invariance. This entry is necessary when ICONST = 2, 3.
Default:None
Type:String
Example:When one wants to consider the rotational invariance around the \(x\)-axis, one should give ROTAXIS = x. If one needs additional constraints for the rotation around the \(y\)-axis, ROTAXIS should be ROTAXIS = xy.

  • FC2XML-tag : XML file to which the harmonic terms will be fixed upon fitting
Default:None
Type:String
Description:When FC2XML-tag is given, harmonic force constants will be fixed to the values stored in the FC2XML file. This may be useful for optimizing cubic and higher-order terms without changing the harmonic terms. Please make sure that the number of harmonic terms in the new computational condition is the same as that in the FC2XML file.

  • FC3XML-tag : XML file to which the cubic terms will be fixed upon fitting
Default:None
Type:String
Description:Same as the FC2XML-tag, but FC3XML is to fix cubic force constants.

6.3. Format of DFILE and FFILE

The displacement-force data sets obtained by first-principles (or classical force-field) calculations have to be saved to DFILE and FFILE to estimate IFCs with MODE = fitting. In DFILE, please explicitly specify the atomic displacements \(u_{\alpha}(\ell\kappa)\) in units of Bohr as follows:

\begin{eqnarray*} u_{x}(1) & u_{y}(1) & u_{z}(1) \\ u_{x}(2) & u_{y}(2) & u_{z}(2) \\ & \vdots & \\ u_{x}(\mathrm{NAT}) & u_{y}(\mathrm{NAT}) & u_{z}(\mathrm{NAT}) \end{eqnarray*}

When there are NAT atoms in the supercell and NDATA data sets, there should be NAT \(\times\) NDATA lines in the DFILE without blank lines. In FFILE, please specify the corresponding atomic forces in units of Ryd/Bohr.