We have developed an improvement formalism for carrying out electronic structure calculations for surfaces, interfaces, and organic solids using muffin-tin-orbital (MTO) basis sets. We will first show how the variational flexibility of MTO tail functions can be improved by introducing generalized MTO tail functions composed of modified spherical Bessel functions K l(κ, r) and their derivatives with respect to κ. Next, we will show how energy dependent MTOs can be constructed by using double basis sets, the first partners being keyed to the radial solutions of the wave equation inside the MT spheres, and the second partners to the energy derivatives of these radial solutions. The energy dependence of these double MTO basis sets introduces additional variational flexibility. Since the first partners will normally be considerably larger than the second partners, the double-dimension secular equations can be solved economically by using the Löwdin partitioning scheme. Finally, we will indicate how the calculation of the interstitial matrix elements, which is usually the time-limiting step for open structures, can be approximated rather nicely by calculating these matrix elements inside a suitably chosen set of overlapping atomic spheres, and then extrapolating to a set of larger overlapping atomic spheres which enclose the most important portion of the interstitial region. With these improvements, it should be possible to carry out accurate calculations for open structures having large numbers of atoms per unit cell considerably more rapidly and economically than by existing MTO-type methods. © 1983 American Institute of Physics.