finite value, thereby allowing each component of the first-order wave function to contribute to the correlation energy. On the other hand, the case with p = 2 is very similar to the imaginary level shift, where the amplitudes associated to small denominators are completely suppressed. In fact, it is instructive to directly compare f (∆ i ; ε) for the imaginary shift and the σ 2 regularizer, as shown in Figure . For matching values of the input parameter, the behavior at ∆ i → 0 is the same for both techniques. However, the σ 2 regularizer follows more closely the unmodified 1/∆ i function for larger values of ∆ i . We thus expect the σ 2regularized energy to be less sensitive to the input parameter ε than the imaginary level shift, which is supported by the Taylor expansion of f (∆ i ; ε) around ∆ i → 0 and ε → 0 (see section 1.3 in the Supporting Information for details). Moreover, the energy obtained with σ 1 -regularized amplitudes is expected to be even less affected by the value of ε, because no contributions to the energy are suppressed, rather they are just damped to a finite value.