Abstract
In this work, we provide a nuanced view of electron correlation in the context of transition metal complexes, reconciling computational characterization via spin and spatial symmetry breaking in single-reference methods with qualitative concepts from ligand-field and molecular orbital theories. These insights provide the tools to reliably diagnose the multi-reference character, and our analysis reveals that while strong (i.e., static) correlation can be found in linear molecules (e.g., diatomics) and weakly bound and antiferromagnetically coupled (monometal-noninnocent ligand or multi-metal) complexes, it is rarely found in the ground-states of mono-transition-metal complexes. This leads to a picture of static correlation that is no more complex for transition metals than it is, e.g., for organic biradicaloids. In contrast, the ability of organometallic species to form more complex interactions, involving both ligand-to-metal σ-donation and metal-to-ligand π-backdonation, places a larger burden on a theory's treatment of dynamic correlation. We hypothesize that chemical bonds in which inter-electron pair correlation is non-negligible cannot be adequately described by theories using MP2 correlation energies and indeed find large errors vs experiment for carbonyl-dissociation energies from double-hybrid density functionals. A theory's description of dynamic correlation (and to a less important extent, delocalization error), which affects relative spin-state energetics and thus spin symmetry breaking, is found to govern the efficacy of its use to diagnose static correlation.
Highlights
While it can be agreed that the ab initio modeling of transition metal chemistry is a long-sought goal, the field is marked by stark differences of assumptions and approach
In this work we provide a nuanced view of electron correlation in the context of transition metal complexes, reconciling theoretical concepts such as spin and spatial symmetry breaking in single-reference methods with physically-transparent intuition from ligand-field and molecular orbital theories
While all methods provide a satisfactory description of H2 in the dissociation limit, we note that in the region beyond ∼1.5 ̊A, nLUNO as approximated using Density Functional Theory (DFT) orbitals appears to be closer to the exact value than when derived from HF and κ-UOOMP2 theories
Summary
While it can be agreed that the ab initio modeling of transition metal chemistry is a long-sought goal, the field is marked by stark differences of assumptions and approach. Despite the evident complexity of systems with multiple spin centers such as oxygen-bridged multi-metal clusters,[6,7] some groups, perhaps due to the absence of another feasible methodological option and/or some encouraging benchmarks[8], have chosen to use DFT to study multi-metal clusters such as the oxygen evolving complex in Photosystem II.[9] Amid this backdrop, this work aims to provide an intuitive way of understanding the nature of electron correlation in various types of transition metal compounds, which can serve to inform the choice of a suitable quantum chemical method in computing properties of such systems. Variational optimization of a single-determinant wavefunction, here, can only yield one of at times multiple configurations which when superposed yield the correct symmetry, and spatial SB occurs.[16] Simple examples can be found in HF calculations of stretched diatomics such as F+2 .17. Simple examples can be found in HF calculations of stretched diatomics such as F+2 .17 While we note that independentparticle theories can break other intrinsic symmetries of the electronic Hamiltonian,[18,19] e.g. those related to complex conjugation and time-reversal, in this work we will focus on spin and, to a lesser extent, spatial symmetry breaking and their relationship to MR character
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