# Setting tags¶

Most of the setting tags have respective command-line options (Command options). When both of equivalent command-line option and setting tag are set simultaneously, the command-line option supersedes the setting tag. The configuration file is recommended to place at the first position for the mixed use of setting tags and command-line options, i.e.,

phonopy setting.conf [command-line-options]


For specifying real and reciprocal points, fractional values (e.g. 1/3) are accepted. However fractional values must not have space among characters (e.g. 1 / 3) are not allowed.

## Basic tags¶

### DIM¶

The supercell is created from the input unit cell. When three integers are specified, a supercell elongated along axes of unit cell is created.

DIM = 2 2 3


In this case, a 2x2x3 supercell is created.

When nine integers are specified, the supercell is created by multiplying the supercell matrix $$M_\mathrm{s}$$ with the unit cell. For example,

DIM = 0 1 1  1 0 1  1 1 0


the supercell matrix is

$\begin{split}M_\mathrm{s} = \begin{pmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{pmatrix}\end{split}$

where the rows correspond to the first three, second three, and third three sets of numbers, respectively. When lattice parameters of unit cell are the column vectors of $$\mathbf{a}_\mathrm{u}$$, $$\mathbf{b}_\mathrm{u}$$, and $$\mathbf{c}_\mathrm{u}$$, those of supercell, $$\mathbf{a}_\mathrm{s}$$, $$\mathbf{b}_\mathrm{s}$$, $$\mathbf{c}_\mathrm{s}$$, are determined by,

$( \mathbf{a}_\mathrm{s} \; \mathbf{b}_\mathrm{s} \; \mathbf{c}_\mathrm{s} ) = ( \mathbf{a}_\mathrm{u} \; \mathbf{b}_\mathrm{u} \; \mathbf{c}_\mathrm{u} ) M_\mathrm{s}$

Be careful that the axes in POSCAR is defined by three row vectors, i.e., $$( \mathbf{a}_\mathrm{u} \; \mathbf{b}_\mathrm{u} \; \mathbf{c}_\mathrm{u} )^T$$.

### PRIMITIVE_AXES or PRIMITIVE_AXIS¶

When specified, transformation from the input unit cell to the primitive cell is performed. With this, the primitive cell basis vectors are used as the coordinate system for the phonon calculation. The transformation matrix is specified by nine values. The first, second, and third three values give the rows of the 3x3 matrix as follows:

PRIMITIVE_AXES = 0.0 0.5 0.5  0.5 0.0 0.5  0.5 0.5 0.0


Likewise,

PRIMITIVE_AXES = 0 1/2 1/2  1/2 0 1/2  1/2 1/2 0


The primitive cell for building the dynamical matrix is created by multiplying primitive-axis matrix $$\mathrm{M}_\mathrm{p}$$. Let the matrix as,

$\begin{split}\mathrm{M}_\mathrm{p} = \begin{pmatrix} 0.0 & 0.5 & 0.5 \\ 0.5 & 0.0 & 0.5 \\ 0.5 & 0.5 & 0.0 \end{pmatrix}\end{split}$

where the rows correspond to the first three, second three, and third three sets of numbers, respectively.

When lattice parameters of unit cell (set by POSCAR) are the column vectors of $$\mathbf{a}_\mathrm{u}$$, $$\mathbf{b}_\mathrm{u}$$, and $$\mathbf{c}_\mathrm{u}$$, those of supercell, $$\mathbf{a}_\mathrm{p}$$, $$\mathbf{b}_\mathrm{p}$$, $$\mathbf{c}_\mathrm{p}$$, are determined by,

$( \mathbf{a}_\mathrm{p} \; \mathbf{b}_\mathrm{p} \; \mathbf{c}_\mathrm{p} ) = ( \mathbf{a}_\mathrm{u} \; \mathbf{b}_\mathrm{u} \; \mathbf{c}_\mathrm{u} ) \mathrm{M}_\mathrm{p}.$

$$\mathrm{M}_\mathrm{p}$$ is a change of basis matrix and so $$\mathrm{M}_\mathrm{p}^{-1}$$ must be an integer matrix. Be careful that :math:the axes in POSCAR is defined by three row vectors, i.e., $$( \mathbf{a}_\mathrm{u} \; \mathbf{b}_\mathrm{u} \; \mathbf{c}_\mathrm{u} )^T$$.

New in v1.14.0 PRIMITIVE_AXES = AUTO is supported. This enables to choose the transformation matrix automatically. Since the choice of the primitive cell is arbitrary, it is recommended to use PRIMITIVE_AXES = AUTO to check if a possible transformation matrix exists or not.

### ATOM_NAME¶

Chemical symbols

ATOM_NAME = Si O


The number of chemical symbols have to be same as that of the numbers in the sixth line of POSCAR.

Chemical symbols read by phonopy are overwritten by those written in POSCAR. See POSCAR examples. In WIEN2k mode, you don’t need to set this tag, i.e., chemical symbols are read from the structure file.

### EIGENVECTORS¶

When this tag is ‘.TRUE.’, eigenvectors are calculated. With -p option, partial density of states are calculated.

### MASS¶

This tag is not necessary to use usually, because atomic masses are automatically set from the chemical symbols.

Atomic masses of a primitive cell are overwritten by the values specified. The order of atoms in the primitive cell that is defined by PRIMITIVE_AXIS tag can be shown using -v option. It must be noted that this tag does not affect to the symmetry search.

For example, when there are six atoms in a primitive cell, MASS is set as follows

MASS =   28.085 28.085 16.000 16.000 16.000 16.000


### MAGMOM¶

Symmetry of spin such as collinear magnetic moments is considered using this tag. The number of values has to be equal to the number of atoms in the unit cell, not the primitive cell or supercell. If this tag is used with -d option (CREATE_DISPLACEMENTS tag), MAGMOM file is created. This file contains the MAGMOM information of the supercell used for VASP. Unlike MAGMOM in VASP, * can not be used, i.e., all the values (the same number of times to the number of atoms in unit cell) have to be explicitly written.

MAGMOM = 1.0 1.0 -1.0 -1.0


### CELL_FILENAME¶

CELL_FILENAME = POSCAR-unitcell


See Input cell.

### FREQUENCY_CONVERSION_FACTOR¶

Unit conversion factor of frequency from input values to your favorite unit can be specified, but the use should be limited and it is recommended to use this tag to convert the frequency unit to THz in some exceptional case, for example, a special force calculator whose physical unit system is different from the default setting of phonopy is used. If the frequency unit is different from THz, though it works just for seeing results of frequencies, e.g., band structure or DOS, it doesn’t work for derived values like thermal properties and mean square displacements.

The default values for calculators are those to convert frequency units to THz. The default conversion factors are shown at Default unit conversion factor of phonon frequency to THz. These are determined following the physical unit systems of the calculators. How to calcualte these conversion factors is explained at Physical unit conversion.

## Displacement creation tags¶

### CREATE_DISPLACEMENTS¶

Supercells with displacements are created. This tag is used as the post process of phonon calculation.

CREATE_DISPLACEMENTS = .TRUE.
DIM = 2 2 2


### DISPLACEMENT_DISTANCE¶

Finite atomic displacement distance is set as specified value when creating supercells with displacements. The default displacement amplitude is 0.01 Angstrom, but when the wien2k, abinit, Fleur or turbomole option is specified, the default value is 0.02 Bohr.

### DIAG¶

When this tag is set .FALSE., displacements in diagonal directions are not searched, i.e. all the displacements are along the lattice vectors. DIAG = .FALSE. is recommended if one of the lattice parameter of your supercell is much longer or much shorter than the other lattice parameters.

### PM¶

This tag specified how displacements are found. When PM = .FALSE., least displacements that can calculate force constants are found. This may cause less accurate result. When PM = .TRUE., all the displacements that are opposite directions to the least displacements are also found, which is called plus-minus displacements here. The default setting is PM = AUTO. Plus-minus displacements are considered with this tag. If the plus and minus displacements are symmetrically equivalent, only the plus displacement is found. This may be in between .FALSE. and .TRUE.. You can check how it works to see the file DISP where displacement directions on atoms are written.

### RANDOM_DISPLACEMENTS¶

The number of random displacement supercells are created by the specified positive integer values. In each supercell, all atoms are displaced in random direction with a constant displacement distance specified by DISPLACEMENT_DISTANCE tag. The random seed can be specified by RANDOM_SEED tag.

To obtain force constants with random displacements and respective forces, external force constants calculator is necessary.

CREATE_DISPLACEMENTS = .TRUE.
DIM = 2 2 2
RANDOM_DISPLACEMENTS = 20
DISPLACEMENT_DISTANCE = 0.03


### RANDOM_SEED¶

The random seed used for creating random displacements by RANDOM_DISPLACEMENTS tag. The value has to be 32bit unsigned int. The random seed is useful for crating the same random displacements with using the same number.

## Band structure tags¶

### BAND and BAND_POINTS¶

BAND gives sampling band paths. The reciprocal points are specified in reduced coordinates. The given points are connected for defining band paths. When comma , is inserted between the points, the paths are disconnected.

BAND_POINTS gives the number of sampling points including the path ends. The default value is BAND_POINTS = 51.

An example of three paths, (0,0,0) to (1/2,0,1/2), (1/2,1/2,1) to (0,0,0), and (0,0,0) to (1/2,1/2,1/2), with 101 sampling points of each path are as follows:

BAND = 0 0 0  1/2 0 1/2,  1/2 1/2 1  0 0 0   1/2 1/2 1/2
BAND_POINTS = 101


### BAND_LABELS¶

Labels specified are depicted in band structure plot at the points of band segments. The number of labels has to correspond to the number of band paths specified by BAND plus one. When LaTeX math style expression such as $$\Gamma$$ (\Gamma) is expected, it is probably necessary to place it between two $characters. BAND = 1/2 0 1/2 0 0 0 1/2 1/2 1/2 BAND_LABELS = X$\Gamma\$ L


The colors of curves are automatically determined by matplotlib. The same color in a band segment shows the same kind of band. Between different band segments, the correspondence of colors doesn’t mean anything.

### BAND_CONNECTION¶

With this option, band connections are estimated from eigenvectors and band structure is drawn considering band crossings. In sensitive cases, to obtain better band connections, it requires to increase number of points calculated in band segments by the BAND_POINTS tag.

BAND = 1/2 0 1/2   0 0 0   1/2 1/2 1/2
BAND_POINTS = 101
BAND_CONNECTION = .TRUE.


## Mesh sampling tags¶

Mesh sampling tags are used commonly for calculations of thermal properties and density of states.

### MESH, MP, or MESH_NUMBERS¶

MESH numbers give uniform meshes in each axis. As the default behavior, the center of mesh is determined by the Monkhorst-Pack scheme, i.e., for odd number, a point comes to the center, and for even number, the center is shifted half in the distance between neighboring mesh points.

Examples of an even mesh with $$\Gamma$$ center in two ways,

MESH = 8 8 8
GAMMA_CENTER = .TRUE.

MESH = 8 8 8
MP_SHIFT = 1/2 1/2 1/2


If only one float value is given, e.g., MESH = 100.0, $$\Gamma$$ centred sampling mesh is generated with the mesh numbers $$(N_{\mathbf{a}^*}, N_{\mathbf{b}^*}, N_{\mathbf{c}^*})$$ computed following the convention of the VASP automatic k-point generation, which is

$N_{\mathbf{a}^*} = \max[1, \mathrm{nint}(l|\mathbf{a}^*|)], \; N_{\mathbf{b}^*} = \max[1, \mathrm{nint}(l|\mathbf{b}^*|)], \; N_{\mathbf{c}^*} = \max[1, \mathrm{nint}(l|\mathbf{c}^*|)],$

where $$l$$ is the value to be specified. With this, GAMMA_CENTER becomes simply ignored, but MP_SHIFT works on top of the $$\Gamma$$ centred sampling mesh.

MESh = 100


### MP_SHIFT¶

MP_SHIFT gives the shifts in direction along the corresponding reciprocal axes ($$a^*$$, $$b^*$$, $$c^*$$). 0 or 1/2 (0.5) can be used as these values. 1/2 means the half mesh shift with respect to neighboring grid points in each direction.

### GAMMA_CENTER¶

Instead of employing the Monkhorst-Pack scheme for the mesh sampling, $$\Gamma$$ center mesh is used. The default value is .FALSE..

GAMMA_CENTER = .TRUE.


### WRITE_MESH¶

With a dense mesh, with eigenvectors, without mesh symmetry, sometimes its output file mesh.yaml or mesh.hdf5 can be huge. However when those files are not needed, e.g., in (P)DOS calculation, WRITE_MESH = .FALSE. can disable to write out those files. With (P)DOS calculation, DOS output files are obtained even with WRITE_MESH = .FALSE.. The default setting is .TRUE..

WRITE_MESH = .FALSE.


## Phonon density of states (DOS) tags¶

Phonon density of states (DOS) is calcualted either with a linear tetrahedron method (default) or smearing method. Phonons are calculated on a sampling mesh, therefore these tags must be used with Mesh sampling tags. The physical unit of horizontal axis is that of frequency that the user employs, e.g., THz, and that of vertical axis is {no. of states}/({unit cell} x {unit of the horizontal axis}). If the DOS is integrated over the frequency range, it will be $$3N_\mathrm{a}$$ states, where $$N_\mathrm{a}$$ is the number of atoms in the unit cell.

Phonon-DOS is formally defined as

$g(\omega) = \frac{1}{N} \sum_\lambda \delta(\omega - \omega_\lambda)$

where $$N$$ is the number of unit cells and $$\lambda = (\nu, \mathbf{q})$$ with $$\nu$$ as the band index and $$\mathbf{q}$$ as the q-point. This is computed on a set of descritized sampling frequency points for which $$\omega$$ is specified arbitrary using DOS_RANGE. The phonon frequencies $$\omega_\lambda$$ are obtained on a sampling mesh whose the number of grid points being $$N$$. In the smearing method, the delta function is replaced by normal distribution (Gaussian function) with the standard deviation specified by SIGMA. In the tetrahedron method, the Brillouin integration is made analytically within tetrahedra in reciprocal space.

### DOS¶

This tag enables to calculate DOS. This tag is automatically set when PDOS tag or -p option.

DOS = .TRUE.


### DOS_RANGE¶

DOS_RANGE = 0 40 0.1


Total and partial density of states are drawn with some parameters. The example makes DOS be calculated from frequency=0 to 40 with 0.1 pitch.

FMIN, FMAX, and FPITCH can be alternatively used to specify the minimum and maximum frequencies (the first and second values).

### FMIN, FMAX, and FPITCH¶

The uniform frequency sampling points for phonon-DOS calculation are specified. FMIN and FMAX give the minimum, maximum frequencies of the range, respectively, and FPITCH gives the frequency pitch to be sampled. These three values are the same as those that can be specified by DOS_RANGE.

### PDOS¶

Projected DOS is calculated using this tag. The formal definition is written as

$g^j(\omega, \hat{\mathbf{n}}) = \frac{1}{N} \sum_\lambda \delta(\omega - \omega_\lambda) |\hat{\mathbf{n}} \cdot \mathbf{e}^j_\lambda|^2,$

where $$j$$ is the atom indices and $$\hat{\mathbf{n}}$$ is the unit projection direction vector. Without specifying PROJECTION_DIRECTION or XYZ_PROJECTION, PDOS is computed as sum of $$g^j(\omega, \hat{\mathbf{n}})$$ projected onto Cartesian axes $$x,y,z$$, i.e.,

$g^j(\omega) = \sum_{\hat{\mathbf{n}} = \{x, y, z\}} g^j(\omega, \hat{\mathbf{n}}).$

The atom indices $$j$$ are specified by

PDOS = 1 2, 3 4 5 6


These numbers are those in the primitive cell. , separates the atom sets. In this example, atom 1 and 2 are summarized as one curve and atom 3, 4, 5, and, 6 are summarized as another curve.

PDOS = AUTO is supported To group symmetrically equivalent atoms automatically.

PDOS = AUTO


EIGENVECTORS = .TRUE. and MESH_SYMMETRY = .FALSE. are automatically set, therefore the calculation takes much more time than usual DOS calculation. With a very dense sampling mesh, writing data into mesh.yaml or mesh.hdf5 can be unexpectedly huge. If only PDOS is necessary but these output files are unnecessary, then it is good to consider using WRITE_MESH = .FALSE. (WRITE_MESH).

### PROJECTION_DIRECTION¶

Eigenvectors are projected along the direction specified by this tag. Projection direction is specified in reduced coordinates, i.e., with respect to a, b, c axes.

PDOS = 1, 2
PROJECTION_DIRECTION = -1 1 1


### XYZ_PROJECTION¶

PDOS is calculated using eigenvectors projected along x, y, and z Cartesian coordinates. The format of output file projected_dos.dat becomes different when using this tag, where phonon-mode-frequency and x, y, and z components of PDOS are written out in the order:

frequency atom1_x atom1_y atom1_z atom2_x atom2_y atom2_z ...


With -p option, three curves are drawn. These correspond to sums of all projections to x, sums of all projections to y, and sums of all projections to z composents of eigenvectors, respectively.

XYZ_PROJECTION = .TRUE.


### SIGMA¶

A smearing method is used instead of a linear tetrahedron method. This tag also specifies the smearing width. The unit is same as that used for phonon frequency. The default value is the value given by the difference of maximum and minimum frequencies divided by 100.

SIGMA = 0.1


### DEBYE_MODEL¶

By setting .TRUE., DOS at lower phonon frequencies are fit to a Debye model. By default, the DOS from 0 to 1/4 of the maximum phonon frequencies are used for the fitting. The function used to the fitting is $$D(\omega)=a\omega^2$$ where $$a$$ is the parameter and the Debye frequency is $$(9N/a)^{1/3}$$ where $$N$$ is the number of atoms in unit cell. Users have to unserstand that this is not a unique way to determine Debye frequency. Debye frequency is dependent on how to parameterize it.

DEBYE_MODEL = .TRUE.


### MOMEMT and MOMENT_ORDER¶

Phonon moments for DOS and PDOS defined below are calculated using these tags up to arbitrary order. The order is specified with MOMENT_ORDER ($$n$$ in the formula). Unless MOMENT_ORDER specified, the first and second moments are calculated.

The moments for DOS are given as

$M_n(\omega_\text{min}, \omega_\text{max}) =\frac{\int_{\omega_\text{min}}^{\omega_\text{max}} \omega^n g(\omega) d\omega} {\int_{\omega_\text{min}}^{\omega_\text{max}} g(\omega) d\omega}.$

The moments for PDOS are given as

$M_n^j(\omega_\text{min}, \omega_\text{max}) =\frac{\int_{\omega_\text{min}}^{\omega_\text{max}} \omega^n g^j(\omega) d\omega} {\int_{\omega_\text{min}}^{\omega_\text{max}} g^j(\omega) d\omega}.$

$$\omega_\text{min}$$ and $$\omega_\text{max}$$ are specified :using ref:dos_fmin_fmax_tags tags. When these are not specified, the moments are computed with the range of $$\epsilon < \omega < \infty$$, where $$\epsilon$$ is a small positive value. Imaginary frequencies are treated as negative real values in this computation, therefore it is not a good idea to set negative $$\omega_\text{min}$$.

MOMENT = .TRUE.
MOMENT_ORDER = 3


## Thermal displacements¶

### TDISP, TMAX, TMIN, and TSTEP¶

Mean square displacements projected to Cartesian axes as a function of temperature are calculated from the number of phonon excitations. The usages of TMAX, TMIN, TSTEP tags are same as those in thermal properties tags. Phonon frequencies in THz, which is the default setting of phonopy, are used to obtain the mean square displacements, therefore physical units have to be set properly for it (see Interfaces to calculators.) The result is given in $$\text{Angstrom}^2$$ and writen into thermal_displacements.yaml. See the detail of the method, Thermal displacement. These tags must be used with Mesh sampling tags

Optionally, FMIN tag (--fmin option) with a small value is recommened to be set when q-points at $$\Gamma$$ point or near $$\Gamma$$ point (e.g. using very dense sampling mesh) are sampled to avoid divergence. FMAX tag (--fmax option) can be used to specify an upper bound of phonon frequencies where the phonons are considered in the summation. The projection is applied along arbitrary direction using PROJECTION_DIRECTION tag (PROJECTION_DIRECTION).

mesh.yaml or mesh.hdf5 is not written out from phonopy-1.11.14.

TDISP = .TRUE.
PROJECTION_DIRECTION = 1 1 0


### TDISPMAT, TMAX, TMIN, and TSTEP¶

Mean square displacement matricies are calculated. The definition is shown at Thermal displacement. Phonon frequencies in THz, which is the default setting of phonopy, are used to obtain the mean square displacement matricies, therefore physical units have to be set properly for it (see Interfaces to calculators.) The result is given in $$\text{Angstrom}^2$$ and writen into thermal_displacement_matrices.yaml where six matrix elements are given in the order of xx, yy, zz, yz, xz, xy. In this yaml file, displacement_matrices and displacement_matrices_cif correspond to $$\mathrm{U}_\text{cart}$$ and $$\mathrm{U}_\text{cif}$$ defined at Mean square displacement matrix, respectively.

Optionally, FMIN tag (--fmin option) with a small value is recommened to be set when q-points at $$\Gamma$$ point or near $$\Gamma$$ point (e.g. using very dense sampling mesh) are sampled to avoid divergence. FMAX tag (--fmax option) can be used to specify an upper bound of phonon frequencies where the phonons are considered in the summation.

The 3x3 matrix restricts distribution of each atom around the equilibrium position to be ellipsoid. But the distribution is not necessarily to be so.

mesh.yaml or mesh.hdf5 is not written out from phonopy-1.11.14.

TDISPMAT = .TRUE.


### TDISPMAT_CIF¶

This tag specifis a temperature (K) at which thermal displacement is calculated and the mean square displacement matrix is written to the cif file tdispmat.cif with the dictionary item aniso_U. Phonon frequencies in THz, which is the default setting of phonopy, are used to obtain the mean square displacement matricies, therefore physical units have to be set properly for it (see Interfaces to calculators.) The result is given in $$\textrm{Angstrom}^2$$.

mesh.yaml or mesh.hdf5 is not written out from phonopy-1.11.14.

TDISPMAT_CIF = 1273.0


## Specific q-points¶

### QPOINTS¶

When q-points are supplied, those phonons are calculated. Q-points are specified successive values separated by spaces and collected by every three values as vectors in reciprocal reduced coordinates.

QPOINTS = 0 0 0  1/2 1/2 1/2  1/2 0 1/2


With QPOINTS = .TRUE., q-points are read from QPOITNS file (see the file format at QPOINTS) in curret directory phonons at the q-points are calculated.

QPOINTS = .TRUE.


### WRITEDM¶

WRITEDM = .TRUE.


Dynamical matrices $$D$$ are written into qpoints.yaml in the following $$6N\times3N$$ format, where N is the number of atoms in the primitive cell.

The physical unit of dynamical matrix is [unit of force] / ([unit of displacement] * [unit of mass]), i.e., square of the unit of phonon frequency before multiplying the unit conversion factor (see FREQUENCY_CONVERSION_FACTOR).

$\begin{split}D = \begin{pmatrix} D_{11} & D_{12} & D_{13} & \\ D_{21} & D_{22} & D_{23} & \cdots \\ D_{31} & D_{32} & D_{33} & \\ & \vdots & & \\ \end{pmatrix},\end{split}$

and $$D_{jj'}$$ is

$\begin{split}D_{jj'} = \begin{pmatrix} Re(D_{jj'}^{xx}) & Im(D_{jj'}^{xx}) & Re(D_{jj'}^{xy}) & Im(D_{jj'}^{xy}) & Re(D_{jj'}^{xz}) & Im(D_{jj'}^{xz}) \\ Re(D_{jj'}^{yx}) & Im(D_{jj'}^{yx}) & Re(D_{jj'}^{yy}) & Im(D_{jj'}^{yy}) & Re(D_{jj'}^{yz}) & Im(D_{jj'}^{yz}) \\ Re(D_{jj'}^{zx}) & Im(D_{jj'}^{zx}) & Re(D_{jj'}^{zy}) & Im(D_{jj'}^{zy}) & Re(D_{jj'}^{zz}) & Im(D_{jj'}^{zz}) \\ \end{pmatrix},\end{split}$

where j and j’ are the atomic indices in the primitive cell. The phonon frequencies may be recovered from qpoints.yaml by writing a simple python script. For example, qpoints.yaml is obtained for NaCl at $$q=(0, 0.5, 0.5)$$ by

phonopy --dim="2 2 2" --pa="0 1/2 1/2  1/2 0 1/2  1/2 1/2 0" --qpoints="0 1/2 1/2" --writedm


and the dynamical matrix may be used as

#!/usr/bin/env python

import yaml
import numpy as np

dynmat = []
dynmat_data = data['phonon'][0]['dynamical_matrix']
for row in dynmat_data:
vals = np.reshape(row, (-1, 2))
dynmat.append(vals[:, 0] + vals[:, 1] * 1j)
dynmat = np.array(dynmat)

eigvals, eigvecs, = np.linalg.eigh(dynmat)
frequencies = np.sqrt(np.abs(eigvals.real)) * np.sign(eigvals.real)
conversion_factor_to_THz = 15.633302
print frequencies * conversion_factor_to_THz


## Non-analytical term correction¶

### NAC¶

Non-analytical term correction is applied to dynamical matrix. BORN file has to be prepared in the current directory. See BORN (optional) and Non-analytical term correction. The default method is NAC_METHOD = GONZE after v1.13.0.

NAC = .TRUE.


### NAC_METHOD¶

The method of non-analytical term correction is chosen by this tag between two, NAC_METHOD = GONZE (Correction by dipole-dipole interaction) and NAC_METHOD = WANG (Interpolation scheme at general q-points with non-analytical term correction), and the default is the former after v1.13.0.

### Q_DIRECTION¶

This tag is used to activate non-analytical term correction (NAC) at $$\mathbf{q}\rightarrow\mathbf{0}$$, i.e. practically $$\Gamma$$-point, because NAC is direction dependent. With this tag, $$\mathbf{q}$$ is specified in the fractional coordinates of the reciprocal basis vectors. Only the direction has the meaning. Therefore Q_DIRECTION = 1 1 1 and Q_DIRECTION = 2 2 2 give the same result. This tag is valid for QPOINTS, IRREPS, and MODULATION tags.

Away from $$\Gamma$$-point, this setting is ignored and the specified q-point is used as the q-direction.

QPOINTS = 0 0 0
NAC = .TRUE.
Q_DIRECTION = 1 0 0


## Group velocity¶

### GROUP_VELOCITY¶

Group velocities at q-points are calculated by using this tag. The group velocities are written into a yaml file corresponding to the run mode in Cartesian coordinates. The physical unit depends on physical units of input files and frequency conversion factor, but if VASP and the default settings (e.g., THz for phonon frequency) are simply used, then the physical unit will be Angstrom THz.

GROUP_VELOCITY = .TRUE.


Technical details are shown at Group velocity.

### GV_DELTA_Q¶

The reciprocal distance used for finite difference method is specified. The default value is 1e-5 for the method of non-analytical term correction by Gonze et al.. In other case, unless this tag is specified, analytical derivative is used instead of the finite difference method.

GV_DELTA_Q = 0.01


## Symmetry¶

### SYMMETRY_TOLERANCE¶

This is used to set geometric tolerance to find symmetry of crystal structure. The default value is 1e-5. In general, it is not a good idea to loosen the tolerance. It is recommended to symmetrize crystal structure before starting phonon calculation, e.g., using --symmetry option.

SYMMETRY_TOLERANCE = 1e-3


### SYMMETRY¶

P1 symmetry is enforced to the input unit cell by setting SYMMETRY = .FALSE.

### MESH_SYMMETRY¶

Symmetry search on the reciprocal sampling mesh is disabled by setting MESH_SYMMETRY = .FALSE.. In some case such as hexagonal systems or primitive cells of cubic systems having F and I-centrings, the results with and without mesh symmetry give slightly different values for those proprerties that can employ mesh symmetry. This happens when the uniform sampling mesh made along basis vectors desn’t have the same crystallographic point group as the crystal itself. This symmetry breaking may be also seen by the fact that weight written in mesh.yaml can be different from possible order of product group of site-symmetry group and time revesal symmetry. Generally the difference becomes smaller when increasing the sampling mesh numbers.

### FC_SYMMETRY¶

Changed at v1.12.3

Previously this tag required a number for the iteration. From version 1.12.3, the way of symmetrization for translation invariance is modified and this number became unnecessary.

This tag is used to symmetrize force constants by translational symmetry and permutation symmetry with .TRUE. or .FALSE..

FC_SYMMETRY = .TRUE.


From the translation invariance condition,

$\sum_i \Phi_{ij}^{\alpha\beta} = 0, \;\;\text{for all j, \alpha, \beta},$

where i and j are the atom indices, and $$\alpha$$ and $$\beta$$ are the Catesian indices for atoms i and j, respectively. When this condition is broken, the sum gives non-zero value. This value is subtracted from the diagonal blocks. Force constants are symmetric in each pair as

$\Phi_{ij}^{\alpha\beta} = \frac{\partial^2 U}{\partial u_i^\alpha \partial u_j^\beta} = \frac{\partial^2 U}{\partial u_j^\beta \partial u_i^\alpha} = \Phi_{ji}^{\beta\alpha}$

Mind that the other symmetries of force constants, i.e., the symmetry from crystal symmetry or rotational symmetry, are broken to use FC_SYMMETRY.

## Force constants¶

### FORCE_CONSTANTS¶

FORCE_CONSTANTS = READ


There are three values to be set, which are READ and WRITE, and .FALSE.. The default is .FALSE.. When FORCE_CONSTANTS = READ, force constants are read from FORCE_CONSTANTS file. With FORCE_CONSTANTS = WRITE, force constants calculated from FORCE_SETS are written to FORCE_CONSTANTS file.

The file format of FORCE_CONSTANTS is shown here.

### FULL_FORCE_CONSTANTS¶

FULL_FORCE_CONSTANTS = .TRUE. is used to compute full supercell constants matrix. The default setting is .FALSE.. By .TRUE. or .FALSE., the array shape becomes (n_patom, n_satom, 3, 3) or (n_satom, n_satom, 3, 3), respectively. The detail is found at FORCE_CONSTANTS and force_constants.hdf5.

### READ_FORCE_CONSTANTS¶

READ_FORCE_CONSTANTS = .TRUE. is equivalent to FORCE_CONSTANTS = READ.

### WRITE_FORCE_CONSTANTS¶

WRITE_FORCE_CONSTANTS = .TRUE. is equivalent to FORCE_CONSTANTS = WRITE.

### FC_CALCULATOR¶

External force constants calculator can be used using this tag. Currently ALM is supported. The phonopy’s default force constants calculator is based on finite difference method, for which atomic displacements are made systematically. The following is the list of the force constants calculator currently possible to be invoked from phonopy.

#### ALM¶

New in v2.3 ALM (https://github.com/ttadano/ALM) is based on fitting approach and any displacements set of atoms in supercell can be handled. For example, random displacements generated by RANDOM_DISPLACEMENTS can be used to compute force constants. To use ALM, its python module has to be installed. The installation instruction is found here.

When ALM is used, please cite the paper: T. Tadano and S. Tsuneyuki, J. Phys. Soc. Jpn. 87, 041015 (2018).

FC_CALCULATOR = ALM


## Create animation file¶

### ANIME_TYPE¶

ANIME_TYPE = JMOL


There are V_SIM, ARC, XYZ, JMOL, and POSCAR settings. Those may be viewed by v_sim, gdis, jmol (animation), jmol (vibration), respectively. For POSCAR, a set of POSCAR format structure files corresponding to respective animation images are created such as APOSCAR-000, APOSCAR-001,….

There are several parameters to be set in the ANIME tag.

### ANIME¶

The format of ANIME tag was modified after ver. 0.9.3.3.

#### For v_sim¶

ANIME = 0.5 0.5 0


The values are the q-point to be calculated. An animation file of anime.ascii is generated.

#### For the other animation formats¶

Phonon is only calculated at $$\Gamma$$ point. So q-point is not necessary to be set.

anime.arc, anime.xyz, anime.xyz_jmol, or APOSCAR-* are generated according to the ANIME_TYPE setting.

ANIME = 4 5 20  0.5 0.5 0


The values are as follows from left:

1. Band index given by ascending order in phonon frequency.

2. Magnitude to be multiplied. In the harmonic phonon calculation, there is no amplitude information obtained directly. The relative amplitude among atoms in primitive cell can be obtained from eigenvectors with the constraint of the norm or the eigenvectors equals one, i.e., number of atoms in the primitive is large, the displacements become small. Therefore this has to be adjusted to make the animation good looking.

3. Number of images in one phonon period.

4. (4-6) Shift of atomic points in reduced coordinate in real space. These values can be omitted and the default values are 0 0 0.

For anime.xyz_jmol, the first and third values are not used, however dummy values, e.g. 0, are required.

## Create modulated structure¶

### MODULATION¶

The MODULATION tag is used to create a crystal structure with displacements along normal modes at q-point in the specified supercell dimension.

Atomic displacement of the j-th atom is created from the real part of the eigenvectors with amplitudes and phase factors as

$\frac{A} { \sqrt{N_\mathrm{a}m_j} } \operatorname{Re} \left[ \exp(i\phi) \mathbf{e}_j \exp( \mathbf{q} \cdot \mathbf{r}_{jl} ) \right],$

where $$A$$ is the amplitude, $$\phi$$ is the phase, $$N_\mathrm{a}$$ is the number of atoms in the supercell specified in this tag and $$m_j$$ is the mass of the j-th atom, $$\mathbf{q}$$ is the q-point specified, $$\mathbf{r}_{jl}$$ is the position of the j-th atom in the l-th unit cell, and $$\mathbf{e}_j$$ is the j-th atom part of eigenvector. Convention of eigenvector or dynamical matrix employed in phonopy is shown in Dynamical matrix.

If several modes are specified as shown in the example above, they are overlapped on the structure. The output filenames are MPOSCAR.... Each modulated structure of a normal mode is written in MPOSCAR-<number> where the numbers correspond to the order of specified sets of modulations. MPOSCAR is the structure where all the modulations are summed. MPOSCAR-orig is the structure without containing modulation, but the dimension is the one that is specified. Some information is written into modulation.yaml.

#### Usage¶

The first three (nine) values correspond to supercell dimension (supercell matrix) like the DIM tag. The following values are used to describe how the atoms are modulated. Multiple sets of modulations can be specified by separating by comma ,. In each set, the first three values give a Q-point in the reduced coordinates in reciprocal space. Then the next three values are the band index from the bottom with ascending order, amplitude, and phase factor in degrees. The phase factor is optional. If it is not specified, 0 is used.

Before multiplying user specified phase factor, the phase of the modulation vector is adjusted as the largest absolute value, $$\left|\mathbf{e}_j\right|/\sqrt{m_j}$$, of element of 3N dimensional modulation vector to be real. The complex modulation vector is shown in modulation.yaml.

MODULATION = 3 3 1, 1/3 1/3 0 1 2, 1/3 1/3 0 2 3.5

MODULATION = 3 3 1, 1/3 1/3 0 1 2, 1/3 0 0 2 2

MODULATION = 3 3 1, 1/3 1/3 0 1 1 0, 1/3 1/3 0 1 1 90

MODULATION = -1 1 1 1 -1 1 1 1 -1, 1/2 1/2 0 1 2


## Characters of irreducible representations¶

### IRREPS¶

Characters of irreducible representations (Irreps) of phonon modes are shown. For this calculation, a primitive cell has to be used. If the input unit cell is a non-primitive cell, it has to be transformed to a primitive cell using PRIMITIVE_AXES tag.

The first three values gives a q-point in reduced coordinates to be calculated. The degenerated modes are searched only by the closeness of frequencies. The frequency difference to be tolerated is specified by the fourth value in the frequency unit that the user specified.

IRREPS = 0 0 0 1e-3


Symbols of Irreps for the 32 point group types at the $$\Gamma$$ point are shown but not at non-$$\Gamma$$ point.

### SHOW_IRREPS¶

Irreducible representations are shown along with character table.

IRREPS = 1/3 1/3 0
SHOW_IRREPS = .TRUE.


### LITTLE_COGROUP¶

Show irreps of little co-group (point-group of wavevector) instead of little group.

IRREPS = 0 0 1/8
LITTLE_COGROUP = .TRUE.


## Input/Output file control¶

### FC_FORMAT, READFC_FORMAT, WRITEFC_FORMAT¶

There are two file-formats to store force constants. Currently text style (TEXT) and hdf5 (HDF5) formats are supported. The default file format is the text style. Reading and writing force constants are invoked by FORCE_CONSTANTS tag. Using these tags, the input/output formats are switched.

FC_FORMAT affects to both input and output, e.g.:

FORCE_CONSTANTS = WRITE
FC_FORMAT = HDF5


READFC_FORMAT and WRITEFC_FORMAT can be used to control input and output formats separately, i.e., the following setting to convert force constants format is possible:

READ_FORCE_CONSTANTS = .TRUE.
WRITE_FORCE_CONSTANTS = .TRUE.
WRITEFC_FORMAT = HDF5


### BAND_FORMAT, MESH_FORMAT, QPOINTS_FORMAT¶

There are two file-formats to write the results of band structure, mesh, and q-points calculations. Currently YAML (YAML) and hdf5 (HDF5) formats are supported. The default file format is the YAML format. The file format is changed as follows:

BAND_FORMAT = HDF5

MESH_FORMAT = HDF5

QPOINTS_FORMAT = HDF5


### HDF5¶

The following output files are written in hdf5 format instead of their original formats (in parenthesis) by HDF5 = .TRUE.. In addition, force_constants.hdf5 is read with this tag.

• force_constants.hdf5 (FORCE_CONSTANTS)

• mesh.hdf5 (mesh.yaml)

• band.hdf5 (band.yaml)

• qpoints.hdf5 (qpoints.yaml)

HDF5 = .TRUE.


#### force_constants.hdf5¶

With --hdf5 option and FORCE_CONSTANTS = WRITE (--writefc), force_constants.hdf5 is written. With --hdf5 option and FORCE_CONSTANTS = READ (--readfc), force_constants.hdf5 is read.

#### mesh.hdf5¶

In the mesh sampling calculations (see Mesh sampling tags), calculation results are written into mesh.hdf5 but not into mesh.yaml. Using this option may reduce the data output size and thus writing time when mesh.yaml is huge, e.g., eigenvectors are written on a dense sampling mesh.

#### qpoints.hdf5¶

In the specific q-points calculations (QPOINTS), calculation results are written into qpoints.hdf5 but not into qpoints.yaml. With WRITEDM, dynamical matrices are also stored in qpoints.hdf5. Using this option may be useful with large set of q-points with including eigenvector or dynamical matrix output.

#### band.hdf5¶

In the band structure calculations (Band structure tags), calculation results are written into band.hdf5 but not into band.yaml.

### summary¶

The following data may be optionally included in the summary yaml file called phonopy_disp.yaml/phonopy.yaml in addition to other file output settings. This happens at the end of the pre/post-process (after running the phonopy script):

• force constants

• force sets

• dielectric constant

• born effective charge

• displacements

• [all]

Including all relevant data in a single output file allows for a human readable convenient file format.

#### force constants¶

The --include-fc flag or setting INCLUDE_FC = .TRUE. will cause the force constants (if available) to be written as an entry in the yaml summary file. The written force constants will reflect the required/available format used during processing. So if --full-fc is set the entire matrix will be written.

#### force sets¶

The --include-fs flag or setting INCLUDE_FS = .TRUE. will cause the force sets (if available) to be written as an entry in the yaml summary file.

#### dielectric constant and born effective charge¶

The --include-born flag or setting INCLUDE_BORN = .TRUE. will cause the born effective charges and dielectric tensor (if available) to be written as an entry in the yaml summary file. The values will only be written if non-analytical term correction is set with the --nac flag or by setting NAC = .TRUE..

This is more convenient than keeping track of the BORN file created by the user.

#### displacements¶

The --include-disp flag or setting INCLUDE_DISP = .TRUE. will cause displacements data (if available) to be written as an entry in the yaml summary file.

This is set by default when the phonopy script is run in displacements mode.

#### all¶

All available data covered by the other include flags can be written to the yaml summary file using the --include-all flag or by setting INCLUDE_ALL = .TRUE.. Force constants are not stored when force sets are stored.