For ∆ i → 0, (1 -e -σ|∆ i | p ) goes to zero faster than 1/∆ i diverges, such that the singularity is effectively suppressed. Similarly to the imaginary shift, the regularized amplitudes depend on the energy denominator appearing in the exponential factor, which in CASPT2 we approximate with the diagonal one as done for the imaginary shift. The integer value p changes the functional form of the regularizer and the way in which the the singularity at ∆ i = 0 is avoided. In this work we consider the values p = 1 and p = 2, as these were found to be the most promising in regularized MP2. Interestingly, inserting Equation ( ) into Equation ( ) results in the same energy expression as in the driven similarity renormalization group approach. The parameter σ is the counterpart of ε in the real and imaginary shifts, and the two can be conveniently related by the following expression (see Section 1.2 in the Supporting Information for more details)