The proposed nuclear energy in an atomic lattice (NEAL) mechanism for nuclear fusion in a cathode during electrolysis of D2O is examined. In this mechanism, coupled harmonic motion of deuterons is supposed to lead to a reduction in the width of the Coulomb barrier for proton-deuteron (p-d) fusion in palladium, thereby substantially increasing the fusion rate. Instead, it is argued that deuteron-deutron coupling does not have an important effect and that interaction with phonons does not enhance the p-d fusion rate.