Improvement of Ab Initio Ligand Field Theory by Means of Multistate Perturbation Theory

[Image: see text] Over the last few years, ab initio ligand field theory (AILFT) has evolved into an important tool for the extraction of ligand field models from ab initio calculations. The inclusion of dynamic correlation on top of complete active space self-consistent field (CASSCF) reference functions, which is important for accurate results, was so far realized at the level of second-order N-electron valence state perturbation theory (NEVPT2). In this work, we introduce two alternative methods for the inclusion of dynamic correlation into AILFT calculations, the second-order dynamic correlation dressed complete active space method (DCD-CAS(2)) and the Hermitian quasi-degenerate NEVPT2 (HQD-NEVPT2). These methods belong to the class of multistate perturbation theory approaches, which allow for the mixing of CASSCF states under the effect of dynamic correlation (state-mixing). The two new versions of AILFT were tested for a diverse set of transition-metal complexes. It was found that the multistate methods have, compared to NEVPT2, an AILFT fit with smaller root mean square deviations (rmsds) between ab initio and AILFT energies. A comparison of AILFT excitation energies with the experiment shows that for some systems, the agreement gets better at the multistate level because of the smaller rmsds. However, for some systems, the agreement gets worse, which could be attributed to a cancellation of errors at the NEVPT2 level that is partly removed at the multistate level. An investigation of trends in the extracted ligand field parameters shows that at the multistate level, the ligand field splitting Δ gets larger, whereas the Racah parameters B and C get smaller and larger, respectively. An investigation of the reasons for the observed improvement for octahedral Cr(III) halide complexes shows that the possibility of state-mixing relaxes constraints that are present at the NEVPT2 level and that keep Δ and B from following their individual preferences.