  We present a new approach to real-space multiple-scattering theory for
molecules and clusters, based on the two-potential (distorted-wave)
Lippmann-Schwinger equation formalism. Our approach uses a recently developed
form [D. L. Foulis, Phys. Rev. A70, 022706 (2004)], for the partial-wave
expansions of the exact time-independent single-particle Green function for a
general potential, to solve exactly the scattering problem for the distorting
potential. The multiple-scattering problem for the full multicenter molecular
potential is then developed along familiar lines, within a partition of space
consisting of non-overlapping atomic spheres, but relative to the distorting
potential. To achieve this some new general Green-function re-expansion
formulas are derived, as well as further developments of our earlier
partial-wave expansions. Based on the division of the multicenter molecular
potential into the non-singular distorting potential and a remaining singular
part we develop explicitly the secular equations of our approach and prove a
result concerning the symmetry of the atomic matrices. The new secular
equations are similar in overall form to those of related methods, requiring
coupled radial Schr\"odinger-equation solutions for each atomic center,
together with atomic-sphere surface integrals, but no volume integrals. We
treat both continuum (scattering) states and bound states within the same
framework, and consider also the case of an outer sphere.
