In CASPT2, the functions Φ i are (linear combinations of) internally contracted configurations generated by the application of excitation operators to the CASSCF reference wave function (Equations (1a) to (1h) in Ref. 2), while in uncontracted theories such as MRMP2, they are configuration state functions or Slater determinants. In either case, ϵ i represents the zeroth-order energy associated to the perturber function Φ i . For the remainder of this article we will assume that the eigenfunctions Φ i and eigenvalues ϵ i are known, unless otherwise stated. This is in practice the case for the diagonal CASPT2 method (named CASPT2D in the original publication), but not for the (more conventional) full CASPT2 approach (referred to as CASPT2N by Andersson et al. ). In principle, it is possible to obtain the eigenpairs (Φ i , ϵ i ) in CASPT2 as well, but this would require the diagonalization of Ĥ(0) expressed in the FOIS basis, which is impractical from a computational perspective. Regardless of the particular implementation of RSPT2, the first-order correction to the wave function is expanded as follows