Quantitative wave function analysis for excited states of transition metal complexes

Abstract

The character of an electronically excited state is one of the most important descriptors employed to discuss the photophysics and photochemistry of transition metal complexes. In transition metal complexes, the interaction between the metal and the di erent ligands gives rise to a rich variety of excited states, including metal-centered, intra-ligand, metal-to-ligand charge transfer, ligand-to-metal charge transfer, and ligand-to-ligand charge transfer states. Most often, these excited states are identi ed by considering the most important wave function excitation coe cients and inspecting visually the involved orbitals. This procedure is tedious, subjective, and imprecise. Instead, automatic and quantitative techniques for excited-state characterization are desirable. In this contribution we review the concept of charge transfer numbers-as implemented in the TheoDORE package-and show its wide applicability to characterize the excited states of transition metal complexes. Charge transfer numbers are a formal way to analyze an excited state in terms of electron transitions between groups of atoms based only on the well-de ned transition density matrix. Its advantages are many: it can be fully automatized for many excited states, is objective and reproducible, and provides quantitative data useful for the discussion of trends or patterns. We also introduce a formalism for spin-orbit-mixed states and a method for statistical analysis of charge transfer numbers. The potential of this technique is demonstrated for a number of prototypical transition metal complexes containing Ir, Ru, and Re. Topics discussed include orbital delocalization between metal and carbonyl ligands, nonradiative decay through metal-centered states, e ect of spin-orbit couplings on state character, and comparison among results obtained from di erent electronic structure methods.

Green‐Light Activation of Push–Pull Ruthenium(II) Complexes

“…For the potential diagrams, the two Ru−N bonds that are elongated in the 3 MC states were constrained to the respective averaged elongated values. The assignment of the state characters has been done dividing the molecule into three fragments (metal center and two ligands) and calculating charge transfer numbers, as implemented in the TheoDore software package …”

Deactivation of Excited States in Transition‐Metal Complexes: Insight from Computational Chemistry

“…Moreover,p otential energy surfaces can be mapped out along (a selection of) the vibrational normalm odes [82,[96][97][98][99] to be used as input for explicit excited-state dynamics simulations as further described in Section4.3. Among the critical points on the PES of the different spin states, the minimal energy crossingpoints (MECPs) are of special relevance not only for luminescent properties [12,100] and photochemical reactions in transition-metal complexes, [101] but also to spin-forbidden reactions. [102] In the latter case, MECPs determine the lowest energy at which two electronic states of different spin are degenerate, and hence,take us to the lowest energybarrier in two-state reactivity.…”

“…However,i ti sn ot uncommon that the molecular orbitals are strongly delocalized over ligand and metal or that the wave function adopts ah igh multiconfigurational character andthat the character of the different electronic states is less evident. Among the different (semi-)automatic alternatives for the visual inspection, we mention here the orthogonal valence bond interpretation of the multiconfigurational wave function, [10,11] the analysis in terms of so-called charge-transfer numbers extracted from the one-electron transition density matrix recently presented by Mai et al, [12] and the density (difference) based indexes as descriptors for the character of the excited-state character by Ciofini and co-workers. [13] The photoinduced intramolecular electron transfer can be accompanied by important structural changes both in the molecular system and its nearest environment, which include cooperative effects, solvatione ffects or thermald istortions.T he extento ft he geometrical relaxation within the molecular complex as ar esult of the deactivation process relies on the particular system.…”

A comprehensive, self‐contained derivation of the one‐body density matrices from single‐reference excited‐state calculation methods using the equation‐of‐motion formalism

“…Depending on the method used for computing the electronic transitions, the objects derived from these calculations will not have the same structure and the same properties . As the analysis of the nature of the excited states generally relies on the use of these objects (in particular the transition and difference density matrices, that will both be at the center of this contribution), either from a qualitative point of view using exciton analysis or one‐particle charge density functions and their corresponding density matrices, or under a quantitative perspective using descriptors, a proper knowledge of their structure is required for selecting the right post‐processing strategy. Unfortunately, while the structure of the objects derived from the calculations are often known for the most common calculation methods, in most of the cases this structure is given without a demonstration.…”