cell File

This is a detailed description of options for CASTEP's cell file. See the basic cell file page for an overview. This page has the most frequently-used cell file options, but for a full set use CASTEP's built-in help. There is also a concise table of cell keywords.

The cell file is one of CASTEP's two main input files. It contains all of the information about the crystal lattice and the atomic positions, as well as additional information such as Brillouin zone sampling ('k-points'), pseudopotentials, cell symmetry, external pressure, constraints on motion of the atoms or cell, and atomic properties such as the mass of each species.

The file itself is a free-format keyword-driven text file, consisting of keywords and blocks of information. These may be given in any order, with blocks indicated by the special %block and %endblock markers. Most of the keywords and blocks are optional, but CASTEP requires two block entries: a block to specify the lattice, and another to specify the atomic elements and positions within the cell.

At the very least, the cell lattice vectors and ionic positions must be specified. Reasonable defaults are chosen for anything else not specified.

For the purposes of the following definitions, all variables represented by $R$ are defined to be real numbers, those represented by $I$ are defined to be integers and those represented by $C$ are characters.

Cell Lattice Vectors

The cell lattice vectors may be specified in Cartesian coordinates or in terms of the lattice vector magnitudes and the angles between them ( $a, b, c, \alpha, \beta, \gamma$ ). Only one of LATTICE_CART and LATTICE_ABC may occur in a cell definition file.

The definitions of these keywords are as follows:

%BLOCK LATTICE_CART
[units]
a_x  a_y  a_z
b_x  b_y  b_z
c_x  c_y  c_z
%ENDBLOCK LATTICE_CART

Here a_x is the x-component of the first lattice vector, $\mathbf{a}$ , $b_y$ is the y-component of the second lattice vector, $\mathbf{b}$ , etc.

[units] specifies the units in which the lattice vectors are defined. If not present, the default is Å.

%BLOCK LATTICE_ABC
[units]
a b c
alpha beta gamma
%ENDBLOCK LATTICE_ABC

Here a is the value of the lattice constant $\vert\mathbf{a}\vert$ , gamma is the value of the cell angle $\gamma$ (in degrees) etc. If the lattice is specified in this manner, the absolute orientation is arbitrary. In this case the orientation is defined by applying the following constraints:

$\mathbf{a}$ lies along the x-axis
$\mathbf{b}$ lies in the xy plane
$\mathbf{c}$ forms a right-handed set with $\mathbf{a}$ and $\mathbf{b}$

[units] specifies the units in which the lattice vector magnitudes are defined. If not present, the default is Å. Angles should be specified in degrees.

Ionic Positions

The ionic positions may be specified in fractional coordinates relative to the lattice vectors of the unit cell, or in absolute coordinates. Only one of POSITIONS_FRAC and POSITIONS_ABS may occur in a cell definition file.

%BLOCK POSITIONS_FRAC
CCC_1  R_{1i}  R_{1j}  R_{1k}  [SPIN=s_1]
CCC_2  R_{2i}  R_{2j}  R_{2k}  [SPIN=s_2]
...
%ENDBLOCK END POSITIONS_FRAC

The first entry on a line is the symbol of the species (chemical element). Alternatively, the atomic number may be given instead, in which case CASTEP will be look up for chemical symbol. A symbol can have a maximum of three characters. The first alphabetical characters identify the element, from which default values for atomic mass etc.

The next three entries on a line in POSITIONS_FRAC are real numbers representing the position of the ion in fractions of the unit cell lattice vectors.

If the optional flag SPIN is present on a line, this sets the spin polarisation ( $N^\uparrow-N^\downarrow$ ) of the atom for initialisation of the spin density; for non-collinear spin calculations, the vector spin is specified as three numbers. If this flag is not present a non-spin polarised state will be assumed.

%BLOCK POSITIONS_ABS
[units]
CCC_1  R_{1i}  R_{1j}  R_{1k}  [SPIN=s_1]
CCC_2  R_{2i}  R_{2j}  R_{2k}  [SPIN=s_2]
...
%ENDBLOCK POSITIONS_ABS

The first entry on a line is the symbol or atomic number of the ionic species, as for POSITIONS_FRAC. The next three entries are real numbers representing the position of the ion in Cartesian coordinates.

[units] specifies the units in which the positions are defined. If not present, the default is Å.

The optional flag SPIN is defined above under POSITIONS_FRAC.

Brillouin Zone Sampling (k-points)

(N.B. in the following section the keywords with the prefixes KPOINT_ and KPOINTS_ are synonymous. KPOINT_ is the preferred usage.)

The k-points at which the Brillouin zone is to be sampled during a self consistent calculation to find the electronic ground state may be defined either by specifying a list of k-points or a Monkhorst-Pack grid in terms of the dimensions of the k-point mesh or a minimum k-point density. The origin of the Monkhorst-Pack grid may be offset by a vector from the origin of the Brillouin zone.

If no k-points are specified, the default will be a Monkhorst-Pack grid with a maximum spacing of 0.1Å $^{-1}$ and no offset of the origin.

The KPOINT_LIST, KPOINT_MP_GRID and KPOINT_MP_SPACING keywords are mutually exclusive. KPOINT_MP_OFFSET may be specified in combination with either KPOINT_MP_GRID or KPOINT_MP_SPACING.

%BLOCK KPOINT_LIST
\begin{array}{cccc}
R_{1i}  R_{1j}  R_{1k}  R_{1w}
R_{2i}  R_{2j}  R_{2k}  R_{2w}
...
%ENDBLOCK KPOINT_LIST

The first three entries on a line are the fractional positions of the k-point relative to the reciprocal space lattice vectors. The final entry on a line is the weight of the k-point relative to the others specified. The sum of the weights must be equal to 1.

KPOINT_MP_GRID I_i I_j I_k

This specifies the dimensions of the Monkhorst-Pack grid requested in the directions of the reciprocal space lattice vectors. The generated grid will be $I_i\times I_j\times I_k$ ; any symmetries generated (or supplied) will be used to reduce this number, when computing the irreducible wedge.

KPOINT_MP_SPACING R [units]

The single entry is the maximum distance between k-points on the Monkhorst-Pack grid. The dimensions of the grid will be chosen such that the maximum separation of k-points is less than this.

[units] specifies the units in which the k-point spacing is defined, although note that the actual units used are $2\pi$ units. If not present, the default is ang-1, such that the spacing is in $2\pi Å^{-1}$ .

KPOINT_MP_OFFSET R_i R_j R_k

This specifies the offset of the Monkhorst-Pack grid with respect to the origin of the Brillouin zone. The three entries are the offset in fractional coordinates relative to the reciprocal lattice vectors.

The k-point set for performing spectral calculations can be specified in the same manner, using version of the keywords above with SPECTRAL_ prepended. The same restrictions regarding mutually exclusive keywords apply.

For a non-self-consistent spectral calculation, the k-points may be defined along a path through reciprocal space or a list of k-points.

%BLOCK SPECTRAL_KPOINT_PATH
R_{1i} R_{1j} R_{1k}
R_{2i} R_{2j} R_{2k}
...
%ENDBLOCK SPECTRAL_KPOINT_PATH

The three numbers on each line are the fractional positions of the k-point relative to the reciprocal space lattice vectors. The k-points define a continuous sequence of straight line segments, unless the keyword BREAK appears on a separate line within the sequence of k-points. In this case the continuous path will end at the k-point immediately preceding the BREAK keyword and resume at the k-point immediately following. The path will be open unless the first and last point in the list are identical.

The maximum spacing of the points sampled along each line segment is defined by the keyword SPECTRAL_KPOINT_PATH_SPACING (default value $0.1 \times 2\pi$ Å $^{-1}$ ). If necessary, the actual spacing used may be smaller than this in order to ensure that the length of the line segment is an integer multiple of the spacing between points on that segment.

Alternatively, the k-point set for performing a band structure calculation can be specified in the same manner as the main k-point set, using version of the keywords above with BS_ prepended. The same restrictions regarding mutually exclusive keywords apply. In this case, the k-point weight in SPECTRAL_KPOINT_LIST is optional. If omitted, the weights for each k-point are assumed to be equal.

For a phonon spectrum calculation, the k-points may be defined along a path through reciprocal space or a list of k-points, in the same manner as for a spectral calculation. The corresponding keywords are identical to those for the band structure specification with the initial SPECTRAL_ replaced by PHONON_, e.g. PHONON_KPOINT_PATH, PHONON_KPOINT_PATH_SPACING and PHONON_KPOINT_LIST. The same restrictions regarding mutually exclusive keywords apply.

The block keyword PHONON_GAMMA_DIRECTIONS specifies the directions in which the gamma point will be approached when calculating the non-analytic terms of the LO/TO splitting. Each line in this block will consist of a 3-vector specifying a direction in the basis of reciprocal lattice vectors. If this keyword is not present, the default will be a single vector determined as follows:

If the gamma point is $q_i = 0$ and there is a successor kpoint $q_{i+1}$ in the list, then it is $q_{i+1}$ .
Otherwise if the gamma point is $q_i =0$ and there is a predecessor kpoint $q_{i-1}$ in the list then it is $q_{i-1}$ .
Otherwise (i.e. a Gamma point only calculation) the a-axis of the reciprocal cell.

For backwards compatibility the keywords beginning BS_ and OPTICS_ are synonyms for SPECTRAL_KPOINT_ and similarly those beginning.

Cell Symmetry

If no symmetry is specified in the cell definition file, the default is for no symmetry to be applied.

SYMMETRY_GENERATE

If this keyword is present in the cell, the highest symmetry group that applies to the structure of the cell will be found and the corresponding symmetry operations generated.

SYMMETRY_TOL R [units]

This parameter is the tolerance within which symmetry will be considered to be satisfied. If an ion is found within this distance of its symmetric position, the symmetry will be considered to be satisfied.

[units] specifies the units in which the tolerance is defined. If not present, the default is Å.

Alternatively, the symmetry operations may be provided directly in a SYMMETRY_OPS block. The symmetry of the cell is represented as a series of symmetry operations under which the unit cell is invariant. Each operation is represented as a $3\times 3$ array.

%BLOCK SYMMETRY_OPS
R_{11}   R_{21}   R_{31}
R_{12}   R_{22}   R_{32}
R_{13}   R_{23}   R_{33}
T_1      T_2      T_3

R_{11}   R_{21}   R_{31}
R_{12}   R_{22}   R_{32}
R_{13}   R_{23}   R_{33}
T_1      T_2      T_3
...
%ENDBLOCK SYMMETRY_OPS

Each of the first three lines contains 3 entries representing a row of a $3\times3$ array. These represent one symmetry rotation. The three entries on the following line contain the translation associated with this rotation.

Constraints

The movement of ions or the unit cell during a relaxation or molecular dynamics run may be constrained.

The constraints on the ionic motion may by specified as a set of linear constraints. Each constraint is specified as a series of coefficients $a_{ijk}$ such that: $$ \sum_{k=1}^{\tt N_\mathrm{species}} \quad \sum_{j=1}^{\mathrm{N_\mathrm{ions}}(k)} \quad \sum_{i=1}^{3} a_{ijk} \verb#ionic_positions(i,j,k)# = constant $$ where $\mathrm{N_\mathrm{ions}}(k)$ is the number of ions in species $k$ .

The change in the shape of the unit cell may also be constrained using the keyword CELL_CONSTRAINTS.

The special case of constraining the centre of mass of the ions to remain fixed is supported by a logical keyword FIX_COM. Also all ionic positions or cell parameters may be fixed by specifying the keywords FIX_ALL_IONS or FIX_ALL_CELL to be TRUE respectively.

If no ionic or cell constraints are specified in the cell definition file, the default is to fix the centre of mass.

%BLOCK IONIC_CONSTRAINTS
I_1  CCC_{1s}   I_{1s}   I_{n1}   R_{1i}   R_{1j}   R_{1k}
I_2  CCC_{2s}   I_{2s}   I_{n2}   R_{2i}   R_{2j}   R_{2k}
...
%ENDBLOCK IONIC_CONSTRAINTS

The first element on each line is an integer specifying the number of the constraint being specified. The second entry is either the symbol or atomic number of the species of the ion to which this constraint applies. The third element is the number of the ion within the species. The ordering of the ions in a species is the order in which they appear in the POSITIONS_FRAC or POSITIONS_ABS block in the cell definition file. The final three numbers are real numbers representing the coefficients of the Cartesian coordinates of the ionic position in the constraint sum. All coefficients in the sum not explicitly specified will be zero.

On reading this data, the matrix of ionic constraints will be orthogonalised.

%BLOCK CELL_CONSTRAINTS
I_a      I_b      I_c
I_alpha  I_beta   I_gamma
%ENDBLOCK CELL_CONSTRAINTS

The first three entries relate to the magnitude of the three lattice vectors $a,b,c$ and the second set of three entries to the angles $\alpha, \beta, \gamma$ .

If the value of the entry corresponding to a magnitude or angle is zero, this quantity will remain fixed. If two or three entries contain the same integer, the corresponding quantities will be constrained to have the same value. If a positive integer greater than 0 occurs in entries 1 through 3 the same integer cannot occur in entries 4 through 6 as this would imply that a vector length and angle must have the same value.

Species Characteristics

The mass of a species, the pseudopotential which represents the ion and the size of the LCAO basis set used for population anslsyis may be specified in the cell definition file.

%BLOCK SPECIES_MASS
[units]
CCC_1   I_1   R_1
CCC_2   I_2   R_2
...
%ENDBLOCK SPECIES_MASS

[units] specifies the units in which the masses are defined. If not present, the default is atomic mass units.

The first entry on a line is the symbol or atomic number of the species. This must correspond with the species symbol or atomic number of the species in the POSITIONS_FRAC or POSITIONS_ABS block. The second entry on each line is the mass of that species. Not all species need appear in the SPECIES_MASS block, any not present will assume the default mass for that species. If the initial alphabetical symbol specified for a species is not a standard element symbol in the periodic table, the mass of the species must be specified.

%BLOCK SPECIES_POT
CCC_1   I_1   <filename>
CCC_2   I_2   <filename>
...
%ENDBLOCK SPECIES_POT

The first entry on a line is the symbol or atomic number of the species. This must correspond with the species symbol or atomic number of the species in the POSITIONS_FRAC or POSITIONS_ABS block. The second entry on each line is the filename of the file containing the definition of the pseudopotential representing the ionic species. The file to which this refers may be a definition of the parameters of the pseudopotential which is to be generated at runtime, or an old-style pseudopotential definition containing the data for the pseudopotential.

Not all species need appear in the SPECIES_POT block. If a pseudopotential is not specified, the default pseudopotential parameters will be used to generate a pseudopotential for the element specified. If the initial alphabetical characters of a species label is not a standard element symbol in the periodic table, the potential for the species must be specified.

The charge on the ion for each species will be derived from the pseudopotential corresponding to that ion.

%BLOCK SPECIES_LCAO_STATES
CCC_1   I_1   I_{B1}
CCC_2   I_2   I_{B2}
...
%ENDBLOCK SPECIES_LCAO_STATES

The first entry on a line is the symbol or atomic number of the species. This must correspond with the species symbol or atomic number of the species in the POSITIONS_FRAC or POSITIONS_ABS block. The second number is the number of angular momentum channels to use in the LCAO basis set for the species when performing population analysis. For example, to use the 2s and 2p states for C (The 1s state is a core state) this should be 2. By default, the number of states will be the appropriate number to complete the valence shell to the next noble gas. If shallow core states are excluded from a pseudopotential, the value of SPECIES_LCAO_STATES for that species should be included in the cell file to ensure a meaningful basis set is used.

External Pressure

An external pressure may be applied to the unit cell by specifying a pressure tensor.

%BLOCK EXTERNAL_PRESSURE
[units]
R_{xx}   R_{xy}  R_{xz}
         R_{yy}  R_{yz}
                 R_{zz}
%ENDBLOCK EXTERNAL_PRESSURE

[units] specifies the units in which the pressure is defined. If not present, the default is GPa.

Entry $R_{xx}$ is the $xx$ -component of the pressure, $R_{xy}$ the $xy$ -component etc.

The default is to apply no external pressure.

Ionic Velocities

The initial ionic velocities may be specified in Cartesian coordinates in a cell definition file.

%BLOCK IONIC_VELOCITIES
[units]
CCC_1 V_{1x}  V_{1y}  V_{1z}
CCC_2 V_{2x}  V_{2y}  V_{2z}
...
%ENDBLOCK IONIC_VELOCITIES

The first entry on a line is the chemical symbol (or atomic number) of the ionic species. The correct symbol will be looked up for the atomic species if the atomic number is specified. A symbol can have a maximum of three characters. The next three entries are real numbers representing the velocity of the ion in Cartesian coordinates.

[units] specifies the units in which the positions are defined. If not present, the default is Å/ps.

If this keyword is not present and a molecular dynamics calculation is performed, the ionic velocities will be randomly initialised with the appropriate temperature.