1. Introduction

Recently, methods have been discussed for the computation of correlation energy estimators based on Møller-Plesset (MP) perturbation theory that may also be regarded as accelerating the convergence of the MP series [1],[2],[3],[4],[5],[6],[7],[8],[9],[10]. In [8], some methods were discussed that are based on MP calculations of fourth order (MP4)¹:

• The Feenberg energy of fourth order F4 [11],[12],[10],[8],
• The Padé approximant [2/2] ² [13],[14]
• The $\Pi$2 approximation that is computed as the zero of an effective characteristic polynomial [15],[16],[17],[18],[19],[20],[21],[22] of degree 2.

All these approximations are calculated from the terms of the MP series with negligible extra effort. Explicit formulas for these methods are given in Section 2. All the methods are size-extensive [8],[9]. Also, test calculations were reported in [8] for a rather large number of small molecules (BH, HF, CH₂, H₂O, NH₂, NH₃, CO, C₂H₂, O₃, CN) for which Full Configuration Interaction (FCI) or Coupled-Cluster (CC) including Single (S), Double (D) and Triple (T) excitations, i.e., CCSDT results are available, mainly for basis sets of double zeta (DZ) or DZ plus polarization (DZP) quality. It was shown that (for the treated cases) the $\Pi$2 method yields very good approximations for the energy if the values of F4, [2/2] and $\Pi$2 are sufficiently close together. If the latter criterion is satisfied, all three methods improve the MP4 values considerably. The above criterion to accept the result of the perturbation calculation is especially important since it is well-known that the quality of the MP results deteriorates for greater distances from the equilibrium geometry. Thus, the criterion allows to judge the quality of the MP series. The criterion will be further discussed in Section 2.

In the present contribution, we report further studies of the performance of the $\Pi$2 and also the F4 and [2/2] methods. In particular, the dependence on the choice of the basis sets is important for the application of the methods. We limit attention to diatomic systems. Also, we report some results concerning the quality of potential energy surfaces and the calculation of spectroscopic constants.