Quantitative wave function analysis for excited states of transition metal complexes

TL;DR

This paper reviews a quantitative, automated method using charge transfer numbers to analyze excited states in transition metal complexes, improving objectivity and reproducibility over traditional visual inspection.

Contribution

It introduces a formalism for spin-orbit-mixed states and a statistical analysis method for charge transfer numbers, demonstrating their application to various transition metal complexes.

Findings

Charge transfer numbers effectively characterize excited states.

The method reveals trends in orbital delocalization and nonradiative decay.

Application to Ir, Ru, and Re complexes shows broad utility.

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 different 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 identified by considering the most important wave function excitation coefficients 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-defined 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, effect of spin-orbit couplings on state character, and comparison among results obtained from different electronic structure methods.