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:

$$\sum_{k=1}^{\tt num\_species} \quad \sum_{j=1}^{\tt num\_ion... ...um_{i=1}^{3} a_{ijk}\ \verb ...$$

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

$$\begin{array}{cccccc} I_1 & CCC_{1s} \vert I_{1s} & I_{n1} &... ...{2s} & I_{n2} & R_{2i} & R_{2j} & R_{2k} \\ \vdots \end{array}$$

%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

$$\begin{array}{ccc} I_{a} & I_{b} & I_{c} \\ I_{\alpha} & I_{\beta} & I_{\gamma} \\ \end{array}$$

%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.