Matrices large-small transformation, atomic

Thus, a small set of parameters can be used to describe the position and orientation of a large group of atoms. Equations (19-23) are used to form elements of the sparse matrix that transforms the set of atomic coordinate parameters into a smaller set of variables determined by the least squares refinement via Equations (17) and (18). 

In our work, we first constructed a large supercell from the primitive cell, then perturbed each atom in the original I = (0, 0, 0) cell by a small amount along the coordinate axes and calculated the forces on the atoms in the perturbed supercell. We obtained an approximate force constant matrix by the numerical differentiation of the forces, which we Fourier-transform to obtain the dynamical matrix. This procedure can be performed using any interatomic potential model, although using... 

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