Felix Bloch himself had noted in his 1928 thesis that there exists a limit opposite to that of nearly free electrons: when electrons are strongly bound to their parent atoms and only occasionally "hop" to neighboring atoms, the crystal's wave function can be approximated as a linear combination of atomic orbitals centered at each lattice site — the so-called tight-binding or LCAO (linear combination of atomic orbitals) method, also commonly used in molecular quantum chemistry. For more than two decades, however, tight-binding remained mostly a qualitative conceptual framework: calculating real energy bands for a specific material with it required evaluating overlap integrals between neighboring atomic orbitals that were, in practice, extremely costly to calculate from first principles. John C. Slater, already author of the 1937 APW method, solved this problem in 1954 together with George F. Koster, a member of his solid-state and molecular theory group at MIT, with a pragmatic proposal: instead of calculating the tight-binding integrals from scratch for each material, treat them as a reduced set of adjustable parameters, determined so that the interpolation method exactly matches higher-precision calculations (obtained via the cellular method or OPW) at high-symmetry points of the Brillouin zone, and then use those same parameters to interpolate the complete energy band at any other point. The paper includes the famous "Slater-Koster table", which systematically tabulates the Hamiltonian matrix elements for all combinations of atomic orbitals (s, p, d) and all common crystal structures, turning tight-binding for the first time into a practical, reproducible computational tool. The method is still used today, especially in the study of nanostructures and two-dimensional materials such as graphene, where its low computational cost relative to first-principles methods is especially valuable.