Accessing metal-specific orbital interactions in C-H activation with resonant inelastic X-ray scattering

Abstract

Photochemically prepared transition-metal complexes are known to be effective at cleaving the strong C-H bonds of organic molecules in room temperature solutions. There is also ample theoretical evidence that the two-way, metal to ligand (MLCT) and ligand to metal (LMCT), charge-transfer between an incoming alkane C-H group and the transition metal is the decisive interaction in the C-H activation reaction. What is missing, however, are experimental methods to directly probe these interactions in order to reveal what determines reactivity of intermediates and the rate of the reaction. Here, using quantum chemical simulations we predict and propose future time-resolved valence-to-core resonant inelastic X-ray scattering (VtC-RIXS) experiments at the transition metal L-edge as a method to provide a full account of the evolution of metal-alkane interactions during transition-metal mediated C-H activation reactions. For the model system cyclopentadienyl rhodium dicarbonyl (CpRh(CO)₂), we demonstrate, by simulating the VtC-RIXS signatures of key intermediates in the C-H activation pathway, how the Rh-centered valence-excited states accessible through VtC-RIXS directly reflect changes in donation and back-donation between the alkane C-H group and the transition metal as the reaction proceeds via those intermediates. We benchmark and validate our quantum chemical simulations against experimental steady-state measurements of CpRh(CO)₂ and Rh(acac)(CO)₂ (where acac is acetylacetonate). Our study constitutes the first step towards establishing VtC-RIXS as a new experimental observable for probing reactivity of C-H activation reactions. More generally, the study further motivates the use of time-resolved VtC-RIXS to follow the valence electronic structure evolution along photochemical, photoinitiated and photocatalytic reactions with transition metal complexes.

Fig. 1. Metal–ligand orbital interactions in photoinitiated C–H bond activation by CpRh(CO)₂ probed using VtC-RIXS. (a) Schematic depiction of the key intermediates and reaction steps in photo-initiated C–H activation by CpRh(CO)₂. (b) Conceptual depiction of charge donation and back-donation interactions between the metal (M) and one ligand in the original M–CO configuration, in the M–alkane σ-complex configuration and in the final M–C–H metal hydride product (arrows denote the direction of charge transfer interaction, their thicknesses indicate the proposed relative strengths of the charge transfer). (c) State picture of the RIXS process (total energy many-electron picture), with excitation from the initial ground state (GS) to the intermediate core-excited state (CES) with incident photon energy X-ray_in and inelastic scattering to the final valence-excited state (VES) with the measured scattered photon energy X-ray_out and the resulting energy transfer ΔE. (d) Corresponding orbital picture (orbital energy one-electron picture) where a Rh 2p electron is promoted to a vacant molecular orbital (here of Rh 4d character) via a 2p → 4d transitions, followed by transition of an electron from an occupied 4d orbital to fill the hole on the 2p orbital (via 4d → 2p transitions), creating the metal-centered (MC) d–d valence-excited final states.

Fig. 2. VtC-RIXS of CpRh(CO)₂ as a probe of MC d–d final states. (a) Experimental Rh L-edge X-ray absorption spectrum (top) and Rh L-edge RIXS map (bottom) for CpRh(CO)₂. (b) Simulated Rh L-edge X-ray absorption spectra and RIXS map at the TD-DFT level of theory. X-ray absorption spectra result from integration of RIXS intensities in a given incident-energy range along the energy-transfer axis. Vertical dashed lines in (a) and (b) indicate the energy of 3005.8 eV at which cuts were obtained to target the valence-excited MC states or, alternatively, HOMO, HOMO−1, to LUMO transitions. (c) Cuts from the experimental and simulated RIXS maps at 3005.8 eV. The dominant peaks correspond to transitions from the ground to MC states or, alternatively, to the HOMO, HOMO−1, HOMO−2, HOMO−3 (4d_yz, 4d_z², 4d_xz, and 4d_x²–y², respectively) to 4d_xy LUMO orbital transitions.

Fig. 3. Simulated VtC-RIXS for key intermediates upon C–H activation in octane by CpRh(CO)₂. Simulated Rh L₃-edge RIXS maps for (a) CpRh(CO)₂, (b) free fragment CpRhCO, (c) sigma-complex CpRhCO–octane (abbreviated as CpRhCO-oct) and (d) final activated product complex CpRhCO–R–H (along with the Rh L₃-edge X-ray absorption spectra on top of the panels). (e) Cuts through the RIXS maps for the four intermediates in (a–d) at incidence energies of pre-edge excitation (indicated by the vertical lines in panels (a–d)). As in Fig. 2(c), the RIXS transitions are labeled according to the involvement of the four occupied Rh 4d orbitals (gray lines connect the corresponding transitions and the evolution of their energies and intensities along the reaction pathway).

Fig. 4. Simulated VtC-RIXS difference signatures for the oxidation addition step vs. the orbital correlation diagram. (a) and (b) RIXS difference maps of CpRhCO–octane and CpRhCO–R–H, respectively, obtained by subtracting the RIXS map of CpRh(CO)₂ shown in Fig. 3(a) from the RIXS maps shown in Fig. 3(c) and (d). Red regions denote positive intensity, blue regions denote depletion. Vertical lines indicate incidence energies where RIXS cuts were obtained. (c) Cuts in the difference RIXS maps for CpRhCO–octane (red) and CpRhCO–R–H (blue). Individual peaks are labeled by the occupied 4d orbitals as in Fig. 2 and 3. Gray lines illustrate the evolution of RIXS peaks upon oxidative addition. (d) Correlation diagram as motivated and derived from interpreting the RIXS spectra for CpRhCO–octane and CpRhCO–R–H from panel (c).

Fig. 5. Simulated VtC-RIXS difference signatures as fingerprints of σ-complex reactivity. (a) Difference RIXS map of Rh(acac)(CO)–octane obtained by subtracting the calculated RIXS map of Rh(acac)(CO)₂, as shown in Fig. S4 in the ESI, from the calculated RIXS map of Rh(acac)(CO)–octane. (b) Difference RIXS map of CpRhCO–octane (same as in Fig. 4(a)). (c) Cuts through the difference RIXS maps in (a) and (b) at the X-ray absorption pre-edge at 3004.4 eV (dashed lines in (a) and (b)) for Rh(acac)(CO)–octane (top) and CpRhCO–octane (bottom).