The change box keyword

Purpose

• This keyword is used to change the simulation box. The box variables and the atom positions are changed according to the following equations:

$$ \left( \begin{array}{ccc} a_x^{\rm new} & b_x^{\rm new} & c_x^{\rm new} \\ a_y^{\rm new} & b_y^{\rm new} & c_y^{\rm new} \\ a_z^{\rm new} & b_z^{\rm new} & c_z^{\rm new} \end{array} \right) = \left( \begin{array}{ccc} \mu_{xx} & \mu_{xy} & \mu_{xz} \\ \mu_{yx} & \mu_{yy} & \mu_{yz} \\ \mu_{zx} & \mu_{zy} & \mu_{zz} \\ \end{array} \right) \left( \begin{array}{ccc} a_x^{\rm old} & b_x^{\rm old} & c_x^{\rm old} \\ a_y^{\rm old} & b_y^{\rm old} & c_y^{\rm old} \\ a_z^{\rm old} & b_z^{\rm old} & c_z^{\rm old} \end{array} \right); $$ $$ \left( \begin{array}{c} x^{\rm new}_i \\ y^{\rm new}_i \\ z^{\rm new}_i \end{array} \right) = \left( \begin{array}{ccc} \mu_{xx} & \mu_{xy} & \mu_{xz} \\ \mu_{yx} & \mu_{yy} & \mu_{yz} \\ \mu_{zx} & \mu_{zy} & \mu_{zz} \\ \end{array} \right) \left( \begin{array}{c} x_i^{\rm old} \\ y_i^{\rm old} \\ z_i^{\rm old} \end{array} \right). $$

• The deformation matrix [math]\mu_{\alpha\beta}[/math] will be specified by the parameters of this keyword, as we detail below.

Grammar

• This keyword accepts 1 or 3 or 6 parameters.

• In the case of 1 parameter [math]\delta[/math] (in units of Angstrom),

change_box delta

we have $$ \left( \begin{array}{ccc} \mu_{xx} & \mu_{xy} & \mu_{xz} \\ \mu_{yx} & \mu_{yy} & \mu_{yz} \\ \mu_{zx} & \mu_{zy} & \mu_{zz} \\ \end{array} \right) = \left( \begin{array}{ccc} \frac{a_x^{\rm old} + \delta}{a_x^{\rm old}} & 0 & 0 \\ 0 & \frac{b_y^{\rm old} + \delta}{b_y^{\rm old}} & 0 \\ 0 & 0 & \frac{c_z^{\rm old} + \delta}{c_z^{\rm old}} \\ \end{array} \right) $$

• In the case of 3 parameters, [math]\delta_{xx}[/math] (in units of Angstrom), [math]\delta_{yy}[/math] (in units of Angstrom), and [math]\delta_{zz}[/math] (in units of Angstrom),

change_box delta_xx delta_yy delta_zz

we have $$ \left( \begin{array}{ccc} \mu_{xx} & \mu_{xy} & \mu_{xz} \\ \mu_{yx} & \mu_{yy} & \mu_{yz} \\ \mu_{zx} & \mu_{zy} & \mu_{zz} \\ \end{array} \right) = \left( \begin{array}{ccc} \frac{a_x^{\rm old} + \delta_{xx}}{a_x^{\rm old}} & 0 & 0 \\ 0 & \frac{b_y^{\rm old} + \delta_{yy}}{b_y^{\rm old}} & 0 \\ 0 & 0 & \frac{c_z^{\rm old} + \delta_{zz}}{c_z^{\rm old}} \\ \end{array} \right) $$

• In the case of 6 parameters (the box type must be triclinic), [math]\delta_{xx}[/math] (in units of Angstrom), [math]\delta_{yy}[/math] (in units of Angstrom), [math]\delta_{zz}[/math] (in units of Angstrom), [math]\epsilon_{yz}[/math] (dimensionless strain), [math]\epsilon_{xz}[/math] (dimensionless strain), and [math]\epsilon_{xy}[/math] (dimensionless strain),

change_box delta_xx delta_yy delta_zz epsilon_yz epsilon_xz epsilon_xy

we have $$ \left( \begin{array}{ccc} \mu_{xx} & \mu_{xy} & \mu_{xz} \\ \mu_{yx} & \mu_{yy} & \mu_{yz} \\ \mu_{zx} & \mu_{zy} & \mu_{zz} \\ \end{array} \right) = \left( \begin{array}{ccc} \frac{a_x^{\rm old} + \delta_{xx}}{a_x^{\rm old}} & \epsilon_{xy} & \epsilon_{xz} \\ \epsilon_{yx} & \frac{b_y^{\rm old} + \delta_{yy}}{b_y^{\rm old}} & \epsilon_{yz} \\ \epsilon_{zx} & \epsilon_{zy} & \frac{c_z^{\rm old} + \delta_{zz}}{c_z^{\rm old}} \\ \end{array} \right) $$