Recent improvements in the muffin‐tin method

Three different approaches to the attempts to improve the muffin‐tin method used in X α calculations on molecules and solids are described. These are the method of Danese and Connolly, who start with the orbitals and charge density given by the conventional muffin‐tin method and use these to compute the expectation value of the X α many‐electron energy EX α; the overlapping‐sphere method used by Johnson and coworkers; and the exact cellular method used by Williams. They bear out the impression that it is the errors arising from the muffin‐tin method, rather than those coming from the X α exchange‐correlation potential, which are largely responsible for the shortcomings of the multiple‐scattering X α method as it has been used. They indicate that the overlapping‐sphere method has good theoretical justification and suggest that it may furnish a good way of making the required corrections to the muffin‐tin method.