Gradients are the derivative of the energy with respect to nuclear displacements. Based on the chain rule of the derivative, we may think that the derivatives of the wavefunction parameters (such as MO coefficients) have to be evaluated. This can be done by solving coupledperturbed SCF equations; however, the evaluation is usually as complex as solving the corresponding SCF equation, so doing this for all nuclear displacements would be prohibitively expensive even for medium-sized systems. By employing the Lagrangian 62 or Z-vector methods, we can avoid explicitly evaluating the dependence of the wavefunction parameters on the displacement. Similar to previous analytic derivative theories for MRPT methods, we use the Lagrangian technique. The total Lagrangian L CASPT2 αβ is defined as the sum of the SA-CASSCF and PT2 Lagrangians,