The energy of the SCF (zeroth-order wavefunction) part is included in L PT2 αβ , because it is dependent on the rotation matrix R αβ (see Eq. ( )). κ pq and P ⊥ γΓ are the orbital rotation and state rotation (out of the P space) parameters, respectively. κ αβ pq and P αβ⊥ γΓ are the Lagrange multipliers, determined by solving Z-vector equations, as described later. Following the formulation in Ref. 64, the orthonormalization conditions of MOs are not explicitly written in the Lagrangian, but the so-called connection term, which is a contraction between the overlap derivative and effective Fock matrices, is evaluated when taking the partial derivative with respect to nuclear displacements.