A T-matrix method for determining the effective potential appropriate to the correlated Gaussian functions employed in lattice dynamics is developed. The method is similar to those discussed by Guyer and Horner for single particle functions. The T matrix and the correlated functions are then computed iteratively, much as suggested for the Brueckner–Hartree–Fock method for nuclear matter, to obtain an internally consistent result. Employing the T matrix, phonon dispersion curves, elastic constants, and Debye temperatures which include the cubic anharmonic term are calculated. The cubic contribution is larger for the T matrix than for the Nosanow effective potential and this leads to upward curvature of the T2[110] phonon branch, as noted by Horner, and thus a possible explanation of the anomalous Debye temperature observed at low temperatures. No resolvable second peaks in the scattering response functions were found.