where the underbar indicates quantities expressed in the crystalline orbital (CO) basis with coefficients C, the tilde indicates symmetrization with respect to forward and backward replication of the unit cell along the translation vectors, p is the momentum operator, and U is the vector of matrices that transforms the CO coefficients C to their gradient with respect to k, ∇ k C = CU . Although formulated for the OR, these expressions can be used to compute the transition moments between electronic states used in Eq. 3.