where D and C are the vectors of the diabatic and adiabatic coefficients, respectively. The diabatic basis, in the LD scheme, is redefined at each time step. At the beginning of the time step (t = 0), the transformation matrix is chosen to be the identity matrix, thus η(0) ≡ ψ(0). By choosing the diabatic states to be as invariant as possible within the time step considered, the dynamic couplings ⟨η i | ∂ ∂t |η j ⟩ can be neglected. However, the coupling vector vanishes only along the advancement coordinate identified by the velocity vector v: in this sense the η are "locally" diabatic for the given trajectory.