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

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 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.

Strongly Red-Emissive Molecular Ruby [Cr(bpmp)2]3+ Surpasses [Ru(bpy)3]2+

“…83−86 Complete active space self-consistent field (CASSCF) calculations combined with N-electron valence state perturbation theory (NEVPT2) to account for dynamic electron correlation based on a fully internally contracted (FIC) wave function have been successfully used for open-shell metal complexes. [83][84][85][86]58,44 This method was employed in the following for the complexes selected.…”

“…A clear-cut correlation with ligand types for chromium(III) spin-flip emitters 49 remains elusive beyond the classical ligand field parameters of the covalently reduced d−d interelectronic repulsion (B and C ligand field parameters), that is, the nephelauxetic series of simple classical ligands such as halides. 76−78 The accurate description 79−82 of the relevant excited quartet and doublet states [83][84][85][86]58 is challenging due to the required consideration of interelectronic repulsion. 81 The localized spin-flip character instead of the charge transfer nature of the classical CT luminophores with separately addressable spatially distinct wave functions has furthermore precluded reliable predictions for spin-flip levels so far.…”

“…Unlike the straightforward and well-founded correlations elucidated for charge transfer complexes with MLCT, LMCT, or LL′CT excited states and organic emitters with donor–acceptor character, shifting of the excited doublet state levels of such spin-flip emitters and hence the emission color by chemical measures, such as donor atom variation or substitution patterns of the ligands, is extremely difficult to predict. A clear-cut correlation with ligand types for chromium­(III) spin-flip emitters remains elusive beyond the classical ligand field parameters of the covalently reduced d–d interelectronic repulsion ( B and C ligand field parameters), that is, the nephelauxetic series of simple classical ligands such as halides. − The accurate description − of the relevant excited quartet and doublet states − , is challenging due to the required consideration of interelectronic repulsion . The localized spin-flip character instead of the charge transfer nature of the classical CT luminophores with separately addressable spatially distinct wave functions has furthermore precluded reliable predictions for spin-flip levels so far.…”

Revealing the nature of electron correlation in transition metal complexes with symmetry breaking and chemical intuition

“…[55][56][57] We note that these models have recently been connected with sophisticated ab initio quantum-chemical methods, and successfully applied to a variety of experimental observations. 58,59 We take one step further now, and seek to explore how ligand-field theoretical arguments can be used to understand and predict MR character, in conjunction with the quantitative use of SSB in SR theories that include some electron correlations. Thus, one main goal of this work is to provide, through a series of illustrative and chemically relevant examples, a link between chemical intuition and the occurrence of a MR wavefunction.…”

Virtual Issue on New Tools and Methods in Physical Chemistry Research

“…Not surprisingly, there have been a number of articles that describe new theoretical and computational approaches. These include advances in surface hopping algorithms, descriptions of thermostat schemes, and the development of an ab initio ligand field theory, which is based on multireference perturbation theory calculations . Other contributions describe a protocol for evaluating rate constants using multiconformer transition state theory and an approach for configuration sampling of aqueous clusters of atmospheric interest .…”