Abstract
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 CrIII 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.
Highlights
Ligand field theory (LFT) is a powerful tool for the rationalization of the properties of transition-metal (TM) complexes
Already in our initial work on that method,[27] we observed for one specific complex, [CrF6]3−, that this new method might provide a better starting point for the ab initio ligand field theory (AILFT) parametrization than the NEVPT2 method that is predominantly used so far to include dynamic correlation. We investigate if this finding is part of a more general trend by comparing the performance of DCD-CAS(2) and another recently introduced MS-MRPT29 when they are combined with AILFT
Equations 9−11 represent the different choices for ab initio effective Hamiltonians including the effect of dynamic correlation that we investigate in this work
Summary
Ligand field theory (LFT) is a powerful tool for the rationalization of the properties of transition-metal (TM) complexes. In general and in particular for low-symmetry situations fits of the LFT model to experimental data are often severely underdetermined. Given the severity of the parameterization problem, it seems logical to turn to quantum chemistry in the hope that it can provide first-principles predictions of ligand field parameters. Indirect procedures are necessary and have been proposed in the literature.[4−6] These approaches typically suffer either from a lack of generality or a lack of uniqueness in the reconstruction of the ligand field parameters from actual quantum chemical calculations. One of the early successful and general procedures is the ligand field density functional theory (LFDFT) developed by Atanasov, Daul, and Rauzy.[7,8]
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