Analytical gradient of restricted second-order Møller–Plesset correlation energy with the resolution of the identity approximation, applied to the TCNE dimer anion complex

The evaluation of the analytical gradient of restricted open shell second-order Møller–Plesset (RMP2) correlation energy for restricted open-shell systems is discussed within the framework of the resolution of the identity (RI) approximation. The theory can be feasibly implemented on the basis of an existing unrestricted MP2 (UMP2) algorithm. The method is applied to characterize the structure of a dimer formed by tetracyanoethylene and its anion. It is shown that the optimized dimer structure in RMP2 theory (twisted) is markedly different compared to the UMP2 structure (parallel). This difference is explained as a consequence of spin-contamination in the UMP2 model.