Interestingly, this is essentially equivalent to the intruder state avoidance technique developed for MRMP2 and to Tikhonov regularization in linearized coupled cluster. In contrast to Equation (11), Equation ( ) does not contain any singularity, hence the imaginary level shift effectively removes the ISP. This happens by suppressing the contributions associated to small energy denominators: the smaller ∆ i , the greater the reduction of T i . Vice-versa, when ∆ i ≫ 0, we have that ε 2 /∆ i → 0 and the amplitudes remain unmodified. Crucially, the ability of the imaginary shift to quench the contributions only when the energy denominators are small comes from its dependence on ∆ i . As long as the zeroth-order Hamiltonian is diagonal, such as in CASPT2D and MRMP2, the values of these energy denominators are known. However, this is not the case for a non-diagonal Ĥ(0) , preventing the use of the true denominators in ε 2 /∆ i . In CASPT2, the imaginary shift is approximated by using only the diagonal entries of the zeroth-order Hamiltonian matrix, which typically yields a reasonable estimate of the exact ∆ i as long as the off-diagonal couplings are small. It is important to note that the imaginary shift is in practice a real shift too, as can be seen from Equation (14).