Sensitivity of electronic band structure to changes in phase shifts

The linear response of an electronic energy level in crystal to small changes in the potential quantities for the $l\mathrm{th}$ partial wave (e.g., phase shifts or logarithmic derivatives) is studied within the framework of the Green's-function method (GFM). The expression obtained for the response function, which is called the sensitivity factor, is exact-within the GFM and is convenient to evaluate. A simple relationship between the sensitivity factors and the contribution of the $l\mathrm{th}$ partial wave to the normalization integral within the muffintin sphere is derived; and, as a corollary, it is shown that the first-order shift in the energy has the same sign as the change in $cot{\eta }_l$. It is also shown that the deformation potential for isotropic strains can be conveniently expressed in terms of the sensitivity factors. Numerical values of the sensitivities for some states of Al, Cu, and Ag at the symmetry points are presented and applications of these quantities, particularly in connection with the parametrization of band structures, are discussed.