Regularized CASPT2: an intruder-state-free approach

In this work we present a new approach to fix the intruder state problem (ISP) in CASPT2 based on σp regularization. The resulting $σ^p$-CASPT2 method is compared to previous techniques, namely the real and imaginary level shifts, on a theoretical basis and by performing a series of systematic calculations. The analysis is focused on two aspects, the effectiveness of $σ^p$-CASPT2 in removing the ISP and the sensitivity of the approach with respect to the input parameter. We found that σp-CASPT2 compares favorably with respect to previous approaches, and that different versions, $σ^1$-CASPT2 and $σ^2$-CASPT2, have different potential application domains. This analysis also reveals the unsuitability of the real level shift technique as a general way to avoid the intruder state problem.