Unraveling the photoredox chemistry of a molecular ruby

Abstract

In contrast to well-studied 4d⁶ and 5d⁶ transition metal complexes such as the modern-day drosophila of photochemistry, Ru(ii)-tris(bipyridine), which often feature a typical triplet metal-to-ligand charge transfer emission in the nanosecond timescale, the photophysics of Cr(iii) complexes are drastically different. The 3d³ configuration of the chromium(iii) allows for an unusual spin-flip emission from the low-lying metal-centered (MC; ²T₁ and ²E) states, exhibiting lifetimes up to the milliseconds to seconds timescale. In this fully computational contribution, the photophysical properties as well as the application of such long-lived excited states in the context of photoredox chemical transformations are investigated for the recently introduced [Cr(dqp)₂]³⁺ [Cr(iii)-(2,6-bis(8'-quinolinyl)pyridine)₂]³⁺, otherwise known as a type of molecular ruby. Our in-depth theoretical characterization of the complicated electronic structure of this 3d³ system relies on state-of-the-art multiconfigurational methods, i.e. the restricted active space self-consistent field (RASSCF) method followed by second-order perturbation theory (RASPT2). This way, the light-driven processes associated with the initial absorption from the quartet ground state, intersystem crossing to the doublet manifold as well as the spin-flip emission were elucidated. Furthermore, the applicability of the long-lived excited state in [Cr(dqp)₂]³⁺ in photoredox chemistry, i.e. reductive quenching by N,N-dimethylaniline, was investigated by ab initio molecular dynamics (AIMD). Finally, the thermodynamics and kinetics of these underlying intermolecular electron transfer processes were analyzed in the context of semiclassical Marcus theory.

Fig. 1. (A) Tanabe–Sugano diagram of d³ octahedral ligand field and, (B) structure of [Cr(dqp)₂]³⁺.

Fig. 2. (A) Simulated UV-vis absorption spectrum of [Cr(dqp)₂]³⁺ as predicted at the TDDFT level of theory in acetonitrile (AcN). Simulated transitions are broadened by Lorentzian functions with a full width at half maximum of 0.1 eV; state labels according to color scheme of Fig. 1. (B) and (C) Contribution of quartet metal-centered (⁴MC) transitions, i.e., associated with low-energy ⁴T₂ and high-energy ⁴T₁ states at the TDDFT and MS-RASPT2 levels of theory, respectively. (D) Spin density of the quartet ground state (⁴A₂) as well as charge density difference plots for selected ⁴LMCT and ⁴MC (⁴T₂ and ⁴T₁) transitions; charge transfer occurs from red to blue.

Fig. 3. Molecular orbitals for the RAS (15,2,2;4,11,5) used in the state average procedure covering the lowest eight quartet and the lowest eight doublet roots of [Cr(dqp)₂]³⁺; two in each irreducible representation. The partitioning with respect to the RAS1, RAS2 and RAS3 subspaces is indicated as well as the orbital occupation within the Hartree–Fock (HF) reference wavefunction with each t_2g orbital being singly occupied within the quartet ground state. The active space spans over 9 125 459 configuration state functions (CSFs).

Fig. 4. Jablonski scheme visualizing excited state processes in [Cr(dqp)₂]³⁺ associated with intersystem crossing (ISC) from the quartet to the doublet manifold and radiative phosphorescence lifetimes as obtained based on the multiconfigurational results.

Fig. 5. Simulated emission spectrum of [Cr(dqp)₂]³⁺ based on the MS-RASPT2 data.

Fig. 6. (A) AIMD setup with one [Cr(dqp)₂]³⁺ complex, one DMA molecule, three chloride ions and 31 AcN solvent molecules in the QM box (30 × 22 × 22 ų), embedded in a MM box (59.7 × 47.7 × 52.1 ų), which contains further 729 solvent molecules. (B) and (C) Spin density of QM region within the donor and the acceptor state respectively; blue and red represents α and β-spin, respectively. (D) Probability (dots) of the various energy gaps ΔE of the donor (red) and the acceptor state (blue) states along the trajectory as well as ideal Gaussian distributions; bin size is 1 kJ mol⁻¹. (E) Fitted Marcus parabolas of the donor and acceptor states using the Warshel histogram approach; driving force and reorganization energies are indicated. (F) Intersection region of the diabatic potential energy curves along the trajectory and electronic coupling obtained by the minimum energy splitting method.