Assigning symmetry terms to molecular orbitals in asymmetric Fischer carbenes using FALDI in a theoretical study

Abstract

Molecular orbitals (MOs) are one of the most useful tools available for explaining and describing the electronic structure of a chemical system. These MOs are obtainable through different means, which falls under two approaches; the conceptual and computational approach. The conceptual approach is mostly limited to symmetric systems but provides a qualitative and interpretable result, this is obtainable through methods like Symmetry Adapted Linear Combinations (SALCs) of atomic orbitals. While the computational approach applies to any system, irrespective of the symmetry and provides quantitative results but is limited by the interpretability. In this study, a Fragment, Atomic, Localized, Delocalized, Interatomic (FALDI) electron density decomposition scheme-based approach is investigated that aims to bridge the conceptual and computational approach of MOs. Multiple distinct theoretical chemistry techniques have been used to produce a consistent and accurate model which labels MOs in asymmetric octahedral metal complexes. These techniques include the Quantum Theory of Atoms in Molecules (QTAIM) to obtain the atomic overlap matrix (AOM) which is used in FALDI to obtain electron density (ED). FALDI recovers the localized ED (loc-ED) and the delocalized ED (deloc-ED) which is needed for the FALDI MO analysis and FALDI fragments. The work illustrates how an asymmetric complex is manipulated into a symmetric function, which is used to obtain the symmetry terms. The symmetric functions are known as Natural Density Functions (NDFs) and is derived using the loc-ED of the metal centre. The relationship between the loc-ED and the deloc-ED can be correlated to recover the delocalized indices (DI) between two atoms interacting whilst assigning symmetry labels. The development of the model was tried and tested on a symmetric model system and a simple octahedral metal centred asymmetric system (Fischer carbene) to ensure consistency and validity. This study then took the FALDI MO analysis further and considered fragments. Fragments are a summation of diatomic interactions which allow multiple atoms interacting with each other to be considered. Linking the symmetry terms to the metal centre provides the delocalized interactions of the fragments, resulting in a quantitative tool that is also interpretable at a classical level. The result is a method that allows for bonding modes such as - and -character to be recovered while assigning contributions which can be traced back to each molecular orbital origin. The FALDI fragments were applied to multiple asymmetric Fischer carbene systems to not only further verify the robustness of the method but also to test the limits. Finally, experimental (with available data) Fischer carbene systems were considered for which novel interpretations and approaches were suggested, which promises a potential future in tuning Fischer carbene systems to achieve the desired chemical traits using the FALDI MO analysis technique.