5.1. ALM: Input files
Format of input files
Each input file should consist of entry fields. Available entry fields are
&general, &interaction, &cutoff, &cell, &position, and &optimize.
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 = optimize
/
Multiple entries can be put in a single line. Also, characters put on the right of sharp (“#”) are neglected. Therefore, the above example is equivalent to the following:
&general
PREFIX = prefix; MODE = optimize # Comment line
/
Each variable must be given inside the appropriate entry field.
List of supported input variables
&general |
|||
&interaction |
|||
&optimize |
|||
Description of input variables
“&general”-field
PREFIX-tag : Job prefix to be used for names of output files
- Default:
None
- Type:
String
MODE-tag = optimize | suggest
optimize (>= 1.1.0)
Estimate harmonic and anharmonic IFCs.This mode requires an appropriate &optimize field.suggest
Suggests the displacement patterns necessaryto 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 beKD = Ga As
.
TOLERANCE-tag : Tolerance for finding symmetry operations
- Default:
1.0e-3
- 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
FCSYM_BASIS-tag = Cartesian | Lattice
Cartesian, C
Symmetry reduction of force constant is performed in the Cartesian basis
Lattice, L
Symmetry reduction of force constant is performed in the \(\boldsymbol{a}_1, \boldsymbol{a}_2, \boldsymbol{a}_3\) basis
- Default:
Lattice
- type:
String
- Description:
The calculation results should not depend on the choice of
FCSYM_BASIS
whenLMODEL = ols
. For other regression methods (enet, adaptive LASSO), an optimal value of theL1_ALPHA
changes when you change theFCSYM_BASIS
option.In some cases,
FCSYM_BASIS = Lattice
is more stable and efficient. In particular, we recommend settingFCSYM_BASIS = Lattice
for hexagonal systems. If a calculation withFCSYM_BASIS = Lattice
is slow, please switch toFCSYM_BASIS = Cartesian
.For more details about the symmetry reduction of force constants, please see here.
Important
When
FCSYM_BASIS = Lattice
, the basis of force constants saved inPREFIX
.fcs becomes the \(\boldsymbol{a}_1, \boldsymbol{a}_2, \boldsymbol{a}_3\) basis. Hence, to compare the values of force constants saved inPREFIX
.fcs, you will have to change their basis to the Cartesian basis manually. The basis of force constants saved inPREFIX
.xml is Cartesian irrespective of theFCSYM_BASIS
value.Also, imposing the constraints for rotational invariance with
FCSYM_BASIS = Lattice
is not supported. Therefore, if you want to apply the constraints for rotational invariance, please useFCSYM_BASIS = Cartesian
.
MAGMOM-tag : List of magnetic moments
- Default:
0 … 0 (
NAT
entries whenNONCOLLINEAR = 0
, 3xNAT
entries whenNONCOLLINEAR = 1
.)- type:
Array of double
- Example:
When a supercell containts 64 atoms and the local magnetic moments of the first 32 atoms are up and those of the last 32 atoms are down, please set the
MAGMOM
tag asMAGMOM = 32*1 32*-1
. The wildcard (*
) is available whenNONCOLLINEAR = 0
. For the noncollinear case (NONCOLLINEAR = 1
), the wildcard is not supported. So, please give the magnetic moment explicitly asMAGMOM = 0 0 1 0 0 1 0 0 1 ... 0 0 -1 0 0 -1 ...
(3\(\times\)NAT
entries in one line).Note
MAGMOM
information is used only for generating space group operations. So, the values of the magnetic moment are somewhat arbitrary. For the 4\(\times\) 4\(\times\) 4 supercell of ferromagnetic bcc Fe (64 atoms), for instance,MAGMOM = 64*1
andMAGMOM = 64*2
give the same results. By contrast,MAGMOM = 32*1 32*2
of course gives a different result because it breaks the symmetry of the original lattice.
NONCOLLINEAR-tag = 0 | 1
- Default:
0
- type:
Integer
- Description:
When
NONCOLLINEAR = 1
, the code accepts a noncollinear magnetic structure as an input to theMAGMOM
tag and uses it for generating space group operations. The spin quantization axis is fixed to the (0,0,1) direction of the Cartesian axis.Caution
Still experimental. Please use with care.
PERIODIC-tag = PERIODIC[1], PERIODIC[2], PERIODIC[3]
0
Do not consider periodic boundary conditions whensearching for interacting atoms.1
Consider periodic boundary conditions whensearching 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 \(\boldsymbol{a}_{i}\).
NMAXSAVE-tag : The maximum order of anharmonic force constants printed out in
PREFIX
.xml
- Default:
min(5,
NORDER
)- Type:
Integer
- Example:
If your model includes anharmonic terms up to the sixth-order (
NORDER = 5
), but you want to avoid printing out the fifth-order and sixth-order IFCs inPREFIX
.xml, please setNMAXSAVE = 3
.
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
FC3_SHENGBTE-tag = 0 | 1
0
Do not save the third-order force constants for ShengBTE code1
Save the third-order force constants for the ShengBTE code in PREFIX.FORCE_CONSTANT_3RD.
- Default:
0
- type:
Integer
FC_ZERO_THR-tag : Threshold value used when trimming force constants when creating PREFIX.xml
- Default:
1.0e-12
- Type:
Double
- Description:
FC_ZERO_THR
defines the threshold of force constants to be saved in an XML file. If the absolute value of force constant is smaller thanFC_ZERO_THR
, it will NOT be printed out.Note
If the harmonic force constants are calculated using a model potential (e.g., classical FF) where the interaction becomes zero beyond a certain cutoff raius, the default value of
FC_ZERO_THR
may raise a warning when creating a renormalize harmonic FCSXML usingtools/dfc2
. This issue may be resolved by using a smallerFC_ZERO_THR
, sayFC_ZERO_THR = 1.0e-15
. The force constants that become exactly zero due to symmetry and acoustic sum rule constraints will not be printed even when settingFC_ZERO_THR = 0
.
“&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 = 1
for calculate harmonic terms only,NORDER = 2
to include cubic terms as well, and so on.
NBODY-tag : Entry for excluding multiple-body interactions from anharmonic force constants
- Default:
NBODY
= [2, 3, 4, …,NORDER
+ 1]- Type:
Array of integers
- Description:
This tag may be useful for excluding multi-body clusters which are supposedly less important. For example, a set of fourth-order IFCs \(\{\Phi_{ijkl}\}\), where \(i, j, k\), and \(l\) label atoms in the supercell, can be categorized into four different subsets; on-site, two-body, three-body, and four-body terms. Neglecting the Cartesian coordinates of IFCs for simplicity, each subset contains the IFC elements shown as follows:
on-site
\(\{\Phi_{iiii}\}\)two-body
\(\{\Phi_{iijj}\}\), \(\{\Phi_{iiij}\}\) (\(i\neq j\))three-body
\(\{\Phi_{iijk}\}\) (\(i\neq j, i\neq k, j \neq k\))four-body
\(\{\Phi_{ijkl}\}\) (all subscripts are different from each other)Since the four-body clusters are expected to be less important than the three-body and less-body clusters, you may want to exclude the four-body terms from the Taylor expansion potential because the number of such terms is huge. This can be done by setting the
NBODY
tag asNBODY = 2 3 3
together withNORDER = 3
.- More examples:
NORDER = 2; NBODY = 2 2
includes harmonic and cubic IFCs but excludes three-body clusters from the cubic terms.
NORDER = 5; NBODY = 2 3 3 2 2
includes anharmonic terms up to the sixth-order, where the four-body clusters are excluded from the fourth-order IFCs, and the multi (\(\geq 3\))-body clusters are excluded from the fifth- and sixth-order IFCs.
“&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 radius of 10 \(a_{0}\) is 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 are 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.
“&optimize”-field
This field is necessary when MODE = optimize
.
LMODEL-tag : Choice of the linear model used for estimating force constants
“least-squares”, “LS”, “OLS”, 1
Ordinary least square
“elastic-net”, “enet”, 2
Elastic net
“adaptive-lasso”, 3
Adaptive LASSO
- Default:
least-squares
- Type:
String
- Description:
When
LMODEL = ols
, the force constants are estimated from the displacement-force datasets via the ordinary least-squares (OLS), which is usually sufficient to calculate harmonic and third-order force constants.The elastic net (
LMODEL = enet
) or adaptive LASSO (LMODEL = adaptive-lasso
) are useful for calculating fourth-order (and higher-order) force constants. When the elastic net or adaptive LASSO is selected, the users have to set the following related tags:CV
,L1_RATIO
,L1_ALPHA
,CV_MAXALPHA
,CV_MINALPHA
,CV_NALPHA
,STANDARDIZE
,ENET_DNORM
,MAXITER
,CONV_TOL
,NWRITE
,SOLUTION_PATH
,DEBIAS_OLS
,STOP_CRITERION
. Please be noted thatSTANDARDIZE
will be effective only for the elastic net.
DFSET-tag: File name containing displacement-force datasets for training
New in version 1.1.0.
- Default:
None
- Type:
String
- Description:
The format of
DFSET
can be found here
NDATA-tag : Number of displacement-force data sets
- Default:
None
- Type:
Integer
- Description:
If
NDATA
is not given, the code reads all lines ofDFSET
(excluding comment lines) and estimatesNDATA
by dividing the line number byNAT
. If the number of lines is not divisible byNAT
, an error is raised.DFSET
should contain at leastNDATA
\(\times\)NAT
lines.
NSTART, NEND-tags : Specifies the range of data to be used for training
- 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
andNEND = 30
.
SKIP-tag : Specifies the range of data to be skipped for training
- Default:
None
- Type:
Two integers connected by a hyphen
- Description:
SKIP
=\(i\)-\(j\) skips the data in the range of [\(i\):\(j\)]. The \(i\) and \(j\) must satisfy \(1\leq i \leq j \leq\)NDATA
. This option may be useful when doing cross-validation manually (CV=-1
).
ICONST-tag = 0 | 1 | 2 | 3 | 11
0
No constraints
1
Constraint for translational invariance is imposed between IFCs.Available only whenLMODEL = ols
.11
Same asICONST = 1
but the constraint is imposed algebraically rather than numerically.Select this option whenLMODEL = enet
.2
In addition toICONST = 1
, constraints for rotational invariance will beimposed up to (NORDER
+ 1)th order. Available only whenLMODEL = ols
.3
In addition toICONST = 2
, constraints for rotational invariance between (NORDER
+ 1)th orderand (NORDER
+ 2)th order, which are zero, will be considered.Available only whenLMODEL = ols
.
- Default:
11
- Type:
Integer
- Description:
See this page for the numerical formulae.
PERIODIC_IMAGE_CONV-tag = 0 | 1
0
Impose the constraints on IFCs (acoustic sum rule) in the considering supercell.
1
Consider the periodic images when generating the constraints.The resultant IFCs simultaneously satisfy the permutation symmetry, ASR,and the space group symmetry in the infinite space.For more details, please see Appendix D of the original paper.(Note that we use the term “mirror image” instead of “periodic image” in the paper.)
- Default:
1
- Type:
Integer
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 beROTAXIS = xy
.
FC2XML-tag : XML file to which the harmonic terms are fixed upon training
- Default:
None
- Type:
String
- Description:
When
FC2XML
-tag is given, harmonic force constants are fixed to the values stored in theFC2XML
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 theFC2XML
file.Important
The
FCSYM_BASIS
option must be the same as the one used when creating the reference harmonic force constant file (FC2XML
). The code raises an error when they are inconsistent.
FC3XML-tag : XML file to which the cubic terms are fixed upon training
- Default:
None
- Type:
String
- Description:
Same as the
FC2XML
-tag, butFC3XML
is to fix cubic force constants.Important
The
FCSYM_BASIS
option must be the same as the one used when creating the reference cubic force constant file (FC3XML
). The code raises an error when they are inconsistent.
SPARSE-tag = 0 | 1
0
Use a direct solver (SVD or QRD) to estimate force constants
1
Use a sparse solver to estimate force constants
- Default:
0
- Type:
Integer
- Description:
When you want to calculate force constants of a large system and generate training datasets by displacing only a few atoms from equilibrium positions, the resulting sensing matrix becomes large but sparse. For such matrices, a sparse solver is expected to be more efficient than SVD or QRD in terms of both memory usage and computational time. When
SPARSE = 1
is set, the code uses a sparse solver implemented in Eigen3 library. You can change the solver type viaSPARSESOLVER
. Effective whenLMODEL = ols
.
SPARSESOLVER-tag : Type of the sparse solver to use
- Default:
SimplicialLDLT
- Type:
String
- Description:
Currently, only the sparse solvers of Eigen3 library can be used. Available options are SimplicialLDLT, SparseQR, ConjugateGradient, LeastSquaresConjugateGradient, and BiCGSTAB. When an iterative algorithm (conjugate gradient) is selected, a stopping criterion can be specified by the
CONV_TOL
andMAXITER
tags. Effective whenLMODEL = ols
andSPARSE = 1
.See also
Eigen documentation page: Solving Sparse Linear Systems
MAXITER-tag : Number of maximum iterations in iterative algorithms
- Default:
10,000
- Type:
Integer
- Description:
Effective when an iterative solver is selected via
SPARSESOLVER
(whenLMODEL = ols
) or whenLMODEL = enet | adaptive-lasso
.
CONV_TOL-tag : Convergence criterion of iterative algorithms
- Default:
1.0e-8
- Type:
Double
- Description:
When
LMODEL = ols
and an iterative solver is selected viaSPARSESOLVER
,CONV_TOL
value is passed to the Eigen3 function via setTolerance(). WhenLMODEL = enet | adaptive-lasso
, the coordinate descent iteration stops at \(i\)th iteration if \(\sqrt{\frac{1}{N}|\boldsymbol{\Phi}_{i} - \boldsymbol{\Phi}_{i-1}|_{2}^{2}} <\)CONV_TOL
is satisfied, where \(N\) is the length of the vector \(\boldsymbol{\Phi}\).See also
Eigen documentation page: IterativeSolverBase
L1_RATIO-tag : The ratio of the L1 regularization term
- Default:
1.0 (LASSO)
- Type:
Double
- Description:
The
L1_RATIO
changes the regularization term asL1_ALPHA
\(\times\) [L1_RATIO
\(|\boldsymbol{\Phi}|_{1}\) + \(\frac{1}{2}\) (1-L1_RATIO
) \(|\boldsymbol{\Phi}|_{2}^{2}\)]. Therefore,L1_RATIO = 1
corresponds to LASSO.L1_RATIO
must be0 < L1_ratio <= 1
. Effective whenLMODEL = enet
. See also here.
L1_ALPHA-tag : The coefficient of the L1 regularization term
- Default:
0.0
- Type:
Double
- Description:
This tag is used when
LMODEL = enet | adaptive-lasso
andCV = 0
. See also here.
CV-tag : Cross-validation mode for elastic net
0
Cross-validation mode is off.The elastic net optimization is solved with the givenL1_ALPHA
value.The force constants are written toPREFIX
.fcs andPREFIX
.xml.>= 2
CV
-fold cross-validation is performed automatically.NDATA
training datasets are divided intoCV
subsets, andCV
different combinations oftraining-validation datasets are created internally. For each combination, the elastic netoptimization is solved with the variousL1_ALPHA
values defined by theCV_MINALPHA
,CV_MAXALPHA
, andCV_NALPHA
tags. The result of each cross-validation is stored inPREFIX
.cvset[1, …,CV
], and their average and deviation are stored inPREFIX
.cvscore.-1
The cross-validation is performed manually.The Taylor expansion potential is trained by using the training datasets inDFSET
, andthe validation score is calculated by using the data inDFSET_CV
for variousL1_ALPHA
valuesdefined theCV_MINALPHA
,CV_MAXALPHA
, andCV_NALPHA
tags.After the calculation, the fitting and validation errors are stored inPREFIX
.cvset.This option may be convenient for a large-scale problem since multiple optimization tasks withdifferent training-validation datasets can be done in parallel.
- Default:
0
- Type:
Integer
- Description:
This tag is used when
LMODEL = enet | adaptive-lasso
.
DFSET_CV-tag : File name containing displacement-force datasets used for manual cross-validation
- Default:
DFSET_CV = DFSET
- Type:
String
- Description:
This tag is used when
LMODEL = enet | adaptive-lasso
andCV = -1
.
NDATA_CV-tag : Number of displacement-force validation datasets
- Default:
None
- Type:
Integer
- Description:
This tag is used when
LMODEL = enet | adaptive-lasso
andCV = -1
.
NSTART_CV, NEND_CV-tags : Specifies the range of data to be used for validation
- Default:
NSTART_CV = 1
,NEND_CV = NDATA_CV
- Type:
Integer
- Example:
This tag is used when
LMODEL = enet | adaptive-lasso
andCV = -1
.
CV_MINALPHA, CV_MAXALPHA, CV_NALPHA-tags : Options to specify the
L1_ALPHA
values used in cross-validation
- Default:
CV_MAXALPHA
is set automatically
CV_MINALPHA = CV_MAXALPHA * 1.0e-6
CV_NALPHA = 50
- Type:
Double, Double, Integer
- Description:
CV_NALPHA
values ofL1_ALPHA
are generated fromCV_MINALPHA
toCV_MAXALPHA
in logarithmic scale. WhenCV_MAXALPHA
is not specified by user, the code automatically setsCV_MAXALPHA
so that the maximumL1_ALPHA
makes all coefficients zero. The default value ofCV_MINALPHA
isCV_MAXALPHA * 1.0e-6
, which is reasonable in many cases. If the minimum value of the validation score is found atCV_MINALPHA
, you may need to use a smaller value ofCV_MINALPHA
. This tag is used whenLMODEL = enet | adaptive-lasso
and the cross-validation mode is on (CV > 0
orCV = -1
).
STANDARDIZE-tag = 0 | 1
0
Do not standardize the sensing matrix
1
Each column of the sensing matrix is standardized in such a way that its mean valuebecomes 0 and standard deviation becomes 1.
- Default:
1
- Type:
Integer
- Description:
This option influences the optimal
L1_ALPHA
value. So, if you change theSTANDARDIZE
option, you have to rerun the cross-validation. Effective only whenLMODEL = enet
.
ENET_DNORM-tag : Normalization factor of atomic displacements
- Default:
1.0
- Type:
Double
- Description:
The normalization factor of atomic displacement \(u_{0}\) in units of bohr. When \(u_{0} (\neq 1)\) is given, the displacement data are scaled as \(u_{i} \rightarrow u_{i}/u_{0}\) before constructing the sensing matrix. This option influences the optimal
L1_ALPHA
value. So, if you change theENET_DNORM
value, you will have to rerun the cross-validation. Effective only whenLMODEL = enet
andSTANDARDIZE = 0
.
SOLUTION_PATH-tag = 0 | 1
0
Do not save the solution path.
1
Save the solution path of each cross-validation combination in
PREFIX
.solution_path.
- Default:
0
- Type:
Integer
- Description:
Effective when
LMODEL = enet | adaptive-lasso
and the cross-validation mode is on.
DEBIAS_OLS-tag = 0 | 1
0
Save the solution of the elastic net problem to
PREFIX
.fcs andPREFIX
.xml.1
After the solution of the elastic net optimization problem is obtained,only non-zero coefficients are collected, and the ordinary least-squares fitting issolved again with the non-zero coefficients before saving the results toPREFIX
.fcs andPREFIX
.xml. This might be useful to reduce the bias of the elastic net solution.
- Default:
0
- Type:
Integer
- Description:
Effective when
LMODEL = enet
andCV = 0
.
STOP_CRITERION-tag : The scan over
L1_ALPHA
stops when the cross-validation score keeps increasing inSTOP_CRITERION
consecutive steps
- Default:
5
- Type:
Integer
- Description:
Effective when
LMODEL = enet | adaptive-lasso
and the cross-validation mode is turned on (CV > 0
orCV = -1
).
How to make a DFSET file
Format of DFSET
The displacement-force data sets obtained by first-principles (or classical force-field) calculations
have to be saved to a file, say DFSET. Then, the force constants are estimated by setting DFSET =
DFSET and with MODE = optimize
.
The DFSET file must contain the atomic displacements and corresponding forces in Cartesian coordinate for at least NDATA
structures (displacement patterns)
in the following format:
Here, NAT
is the number of atoms in the supercell.
The unit of displacements and forces must be bohr and Ryd/bohr, respectively.