Assessing Excited State Energy Gaps with Time-Dependent Density Functional Theory on Ru(II) Complexes

Abstract

A set of density functionals coming from different rungs on Jacob's ladder are employed to evaluate the electronic excited states of three Ru(II) complexes. While most studies on the performance of density functionals compare the vertical excitation energies, in this work we focus on the energy gaps between the electronic excited states, of the same and different multiplicity. Excited state energy gaps are important for example to determine radiationless transition probabilities. Besides energies, a functional should deliver the correct state character and state ordering. Therefore, wavefunction overlaps are introduced to systematically evaluate the effect of different functionals on the character of the excited states. As a reference, the energies and state characters from multi-state second-order perturbation theory complete active space (MS-CASPT2) are used. In comparison to MS-CASPT2, it is found that while hybrid functionals provide better vertical excitation energies, pure functionals typically give more accurate excited state energy gaps. Pure functionals are also found to reproduce the state character and ordering in closer agreement to MS-CASPT2 than the hybrid functionals.

Quantitative wave function analysis for excited states of transition metal complexes

“…More than often, it is necessary to assess the quality of the results of some excited-state calculation against another excited-state calculation using a di erent-possibly more reliable-electronic structure method. A simple comparison of the excitation energies is in most cases not su cient, because the order of the states (in terms of state character) might change [184]. Hence, wave function analysis techniques can be very useful, especially in TMCs with their very high density of states.…”

Early Relaxation Dynamics in the Photoswitchable Complex trans‐[RuCl(NO)(py)4]2+

“…[24] The choice of this functional is based on the realization that pure functionals, such as BP86, best describe the singlet-triplet gaps of Ru complexes. [25] Hybrid functionals such as B3LYP deliver better excitation energies;h owever,f or surface-hopping small errors in state crossings are preferable over small errors in excitations energies that only lead to as hift in the absorption spectrum. Moreover,t he character and ordering of the states at the equilibrium geometry predicted by BP86 agree with Figure 1.…”

Following the evolution of excited states along photochemical reaction pathways

“…Computing the overlap between full electronic wave functions is a common practice to compare ESs at the same or different molecular geometries . On the other hand, the nature of the ESs can also be described by inspecting only the nature of the “hole” and the “particle” entities.…”

“…Computing the overlap between full electronic wave functions is a common practice to compare ESs at the same or different molecular geometries. [38][39][40]45] On the other hand, the nature of the ESs can also be described by inspecting only the nature of the "hole" and the "particle" entities. Indeed, computing the mono-electronic wave function overlap between NTOs has proven to be a robust procedure to compare ESs.…”