where E j and E i are the upper and lower adiabatic energy surfaces, respectively, and |ϕ j ⟩ and |ϕ i ⟩ are the corresponding adiabatic states. H corresponds to the electronic Hamiltonian, and the gradient ∇ is taken with respect to the nuclear coordinates. The nascent branching vectors in Eq. 1 are in general not orthogonal, but can be orthogonalized by a rotation: