The generation of crystal coordinates

For the calculation of the interaction energies within a cluster of molecules with a specified geometry, the nuclear positions and the whole array of e-pixels are repeated in space by a rigid rotation-translation procedure (see Fig. 12.6). Let xlg be the coordinates of atomic nuclei and e-pixels in the standard reference frame (for example as defined in the electron density calculation by GAUSSIAN), and xlo the same for any of the surrounding molecules. Then the following transformation applies  

Let Ms, ts now be a matrix-vector pair representing a given symmetry operation within the crystal space group (Section 5.2). Then  

The expression for the orthogonal coordinates of the 5-th molecule in the molecular cluster that represents the crystal, x, in terms of the coordinates in the standard 

Many molecules surrounding the reference one in the crystal are generated by adding integer cell translations to the components of the ts vectors, within a specified value of the distance between centers of mass. In this way, any molecular object specified by Xlg coordinates, with location and orientation in the unit cell specified by vector t2 and matrix M2, respectively, can be packed into a crystal specified by the cell dimensions appearing in matrix P and by space group specified by Ms, ts pairs. 

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