Singularity-free static lattice energy minimization

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Abstract
Comparative analyses are made of static lattice energy minimization procedures based on Newton or quasi‐Newton algorithms with rigid body orientations being parametrized in terms of Euler angles or quaternion parameters. It is shown that potential functions in terms of Euler angles can have artificial saddle points and artificial minima in the plane where the azimuthal angle ϑ (the angle between the body and laboratory z axes) is zero. Quaternions are found to form the only numerically acceptable parametrization of orientations in less than five variables and lead to a singularity‐free energy function which can be minimized efficiently by any routine for unconstrained optimization.