Calculation of the total energy in the multiple scattering-Xα method. I. General theory

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Abstract
The multiple scattering‐Xα method has been shown in previous work to be an accurate model for many properties of molecules and solids. However, in certain cases it has been found to be unreliable in determining total energies. This difficulty has been attributed mostly to the implementation of the multiple scattering part of the model rather than to the Xα approximation itself, since the multiple scattering equations are usually solved in the simplified ``muffin‐tin'' form. In this paper, it is shown, in general, how one can calculate the error involved in this approximation by means of a procedure which is analogous to first‐order perturbation theory and which establishes an upper bound to the exact Xα total energy. Expressions for the corresponding corrections to the one‐electron eigenvalues are also derived.