Anti-Stokes resonant x-ray Raman scattering for atom specific and excited state selective dynamics

Ultrafast electronic and structural dynamics of matter govern rate and selectivity of chemical reactions, as well as phase transitions and efficient switching in functional materials. Since x-rays determine electronic and structural properties with elemental, chemical, orbital and magnetic selectivity, short pulse x-ray sources have become central enablers of ultrafast science. Despite of these strengths, ultrafast x-rays have been poor at picking up excited state moieties from the unexcited ones. With time-resolved anti-Stokes resonant x-ray Raman scattering (AS-RXRS) performed at the LCLS, and ab initio theory we establish background free excited state selectivity in addition to the elemental, chemical, orbital and magnetic selectivity of x-rays. This unparalleled selectivity extracts low concentration excited state species along the pathway of photo induced ligand exchange of Fe(CO)5 in ethanol. Conceptually a full theoretical treatment of all accessible insights to excited state dynamics with AS-RXRS with transform-limited x-ray pulses is given—which will be covered experimentally by upcoming transform-limited x-ray sources.

To establish AS-RXRS we use the photochemical pathway of the photoinduced ligand exchange reaction of Fe(CO) 5 in ethanol solution (figure 1(A)) and conduct AS-RXRS at the Fe L 3 -edge of the electronically excited Fe(CO) 5 and Fe(CO) 4 species transiently present along the reaction pathway toward the ligand substituted Fe(CO) 4 EtOH (figure 1(B)) [28,29]. This dynamic pathway has been introduced for the gas phase by Trushin et al in [30] and modified for ethanol solution by the mechanism of ultrafast ligand addition and spin crossover by previous work of the authors [28,29]. Cascading dynamics of electronically excited states in Fe(CO) 5 is initiated by resonant absorption of a 266 nm (4.66 eV) photon. The initial photo-absorption creates a metal-toligand charge-transfer (MLCT) 1 E′ state which due to Jahn-Teller-like nuclear dynamics converts through possibly multiple internal conversions to a ligand field (LF) 1 E′ state with a time constant of 21 fs [30]. The conversion therefore includes a relaxation of an electron from delocalized 2π * orbital to localized d * s orbital (electron back-transfer). Since d * s is strongly σ-antibonding with respect to the Fe-CO bond, a Jahn-Teller-like motion on the 1 E′(LF) surface leads to a transition state (15 fs) which is followed by a dissociation of a single CO ligand and the creation of Fe(CO) 4 in an excited 1 B 2 (LF) state (30 fs) [30]. This electronically excited state evolution we summarize as 1 E′(MLCT)→ 1 E′(LF) and 1 E′(LF)→ 1 B 2 (LF), with 20 fs and 45 fs time constants, respectively ( figure 1(B)). Later, ultrafast ligand addition, spin crossover and geminate recombination finally leads to a branching from the vibrationally hot Fe(CO) 4 1 A 1 that is in the electronic ground state to the ground state ligand substituted complex Fe(CO) 4 EtOH and the picosecond lived high spin Fe(CO) 4 3 B 2 state [30]. The electronically excited states involved ( 1 E′(MLCT), 1 E′(LF) and 1 B 2 (LF)) can lead in resonant x-ray Raman Scattering to the emission of x-ray photons with an energy higher than the incident x-ray photon energy (hυ X, out >hυ X,in ), which is the anti-Stokes Raman signature in this x-ray analog to optical time-resolved resonant Raman spectroscopy. As depicted in figure 1(C) this AS-RXRS energy transfer/anti-Stokes shift corresponds to the valence electronic excitation energies.

Results
In figure 2 we show on the left side panels the electronic orbital structure of ground state Fe(CO) 5 (figure 2(A)) and how the Stokes resonant x-ray Raman scattering (also commonly denoted as resonant inelastic x-ray scattering, RIXS) leads in the schematic representation of the inelastic x-ray scattering plane (figure 2(C)) to a participator channel with zero energy transfer, and to Stokes energy transfer (loss) due to the creation of final state electron-hole pairs. In figure 2(E) the RIXS map of the Fe(CO) 5 ground state calculated with ab initio restricted active space self-consistent field (RASSCF) method [31] is shown (see methods for further details). On the right-hand side panels (B) and (D) of figure 2, we describe how in an one-electron orbital picture the creation of an initial electronic MLCT excitation through optical absorption leads to the opening of a lower energy scattering resonance and the occurrence of fully separated AS-RXRS spectral signatures. Different from the ground state, the optically excited Fe(CO) 5 1 E′(MLCT) state has a valence vacancy in the d π orbital. Thus a new energetically lower x-ray scattering resonance is opened up, depicted in figure 2(D). Resonant x-ray Raman Scattering through this excited state resonance occurs at a hv exc -red-shifted core-level resonance energy and leads for all electron-hole pair final states to the appearance of inelastic scattering features with hv exc -blueshifted emission energies in relation to the ground state situation. This is the signature of AS-RXRS. The Resonant x-ray Raman Scattering planes calculated using the RASSCF method in the ground state and in the 1 E′ (MLCT) excited state in figures 2(E) and (F) confirm the conceptual reasoning based on the simplified oneelectron orbitals. Therefore the AS-RXRS spectral features are a result of excitation to the d π vacancy that is followed by a decay of the excited electrons at the 2π * orbital. The most intense AS-RXRS peak in figure 2(F) is at −5 eV energy transfer which corresponds to scattering to the A 1 1 ¢ ground state. Dipole selection rules apply to all the involved transitions (pump and probe) and we note that in case of molecules with inversion symmetry, anti-Stokes scattering from optically populated state to the ground state is dipole forbidden. This is not the case for Fe(CO) 5 which belongs to the D 3h point group symmetry and thus has no inversion center.
In figure 3 we show all AS-RXRS maps of the excited states along the Fe(CO) 5 figure 4(B)). The 1 B 2 (LF) Fe(CO) 4 state correlates with the 1 E′(LF) Fe(CO) 5 state, however it has significantly lower energy due to strong structural relaxation which has taken place (i.e. CO dissociation): based on the RASSCF calculation, the 1 E′(LF) state is 4.6 eV above the Fe(CO) 5 ground state, whereas the relaxed 1 B 2 (LF) state has only ∼1 eV higher energy compared to the Fe(CO) 4 1 A 1 state. Thus this energy relaxation leads to the AS-RXRS feature with a smaller blue shift in comparison to the initial optical excitation energy of hv exc =4.66 eV. Simulation of the AS-RXRS feature at 706-707 eV incident photon energy region in figure 4(B) reproduces remarkably well the experimental spectral shape (note that RASSCF calculations at the 2π * core resonance at 710-714 eV are less accurate). The lifetime of 1 B 2 (LF) state is ∼100 fs and it relaxes via two parallel process to the 3 B 2 (LF) ground state of fourcoordinated Fe(CO) 4 or to the 1 A 1 ground state of five-coordinated Fe(CO) 4 L (L=EtOH, CO) [21]. This results in disappearance of the anti-Stokes scattering feature (region R3), whereas considerably intensity close to elastic peak at 706-707 eV (region R4) remains due to the 3 B 2 (LF) Fe(CO) 4 state ( figure 3(D)).

Discussion
We can now demonstrate in figure 5 the full potential of AS-RXRS with transform-limited Gaussian x-ray pulses (ΔEΔt=0.44 h) from upcoming x-ray lasers [34,35]. Three prototypical scenarios focusing on the initial electron back-transfer between the Fe(CO) 5 1 E′(MLCT) and 1E′(LF) states and subsequent CO removal during 1 E′(LF) to 1 B 2 (LF) inter conversion are presented. As defined in figure 3, anti-Stokes features of the 1 E′(MLCT), 1E′(LF) and 1 B 2 (LF) states are picked up within R1, R2 and R3, located at −5 eV, −4.6 eV and −1 eV energy transfer, respectively. AS-RXRS preserves the bandwidth ΔE of the scattered radiation at linear dispersion with an upper limit given by the natural core-hole lifetime broadening Γ (0.3 eV at the Fe L 3 -edge) reflecting the Fe L 3 -edge 2.2 fs natural core-hole lifetime. We give the overall temporal resolution in the simulation as the convolution of probe and pump pulses at delay t (assumed equal in duration). With different pulse length Δt, both the temporal resolution and the chemical selectivity can be varied and finest details of the dynamics and potential energy surfaces of excited states can be extracted background free. Column A of figure 5 shows highest temporal selectivity with a pulse duration of Δt=1 fs that separates the 1 E′(MLCT) and 1 E′(LF) states in time, but with ΔE=2.0 eV incident bandwidth at the cost of no spectral selectivity. However, the features from the 1 E′(MLCT) and 1 E′(LF) states can still be well distinguished since increasing the bandwidth beyond the core-hole lifetime broadening does not result in further broadening of the spectra. Column B of figure 5 shows optimized chemical selectivity and temporal resolution through a transform limited pulse with ΔE=0.2 eV and a pulse duration of Δt=10 fs. This yields distinction both energetically and temporally and separates AS-RXRS features of the 1 E′(MLCT), 1 E′(LF) and 1 B 2 (LF) states. Column C of figure 5 shows how sub-natural linewidth resolution maps out the potential energy surfaces [22,25,36] of the 1 E′(MLCT), 1 E′(LF) excited states individually for transform limited pulses with ΔE=0.02 eV and pulse duration of Δt=100 fs. Although no direct temporal separation occurs, the chemical shift between the x-ray scattering resonances of the different 1 E′ (MLCT), 1 E′(LF) excited states separates them, thus allowing to map the potential energy surface of the excited states undergoing rapid photochemical dynamics.

Methods
Computational details Theoretical x-ray spectra were derived from RASSCF calculations [37] using the MOLCAS-7 software [38]. For further details see [28,29]. The geometries were optimized with the CASPT2 method [39] and the TZVP basis set [40] for all atoms. The active space contained 12 electrons in 12 orbitals. Some of the geometries were optimized with density functional theory using the PBE functional [41] and the TZVP basis set.
Following experimental factors contribute to the spectral linewidth in the experiment and are taken into account in the simulation of the experiment: the 0.3 eV core-hole lifetime broadening, 0.5 eV incident x-ray bandwidth, 1 eV spectrometer resolution and the 0.5 eV due to inhomogeneous broadening from solvent environment and vibrational effects (all values FWHM). RIXS spectra were simulated using the Kramers- Heisenberg formula. Spectra were calculated for an ensemble of randomly oriented molecules excited by linearly polarized light and detected in the plane of polarization. Interference effects were excluded.

Experimental details
Experiment was performed at the linac coherent light source (LCLS) soft x-ray materials science (SXR) instrument [42,43] with the liquid jet endsation [44]. The 1 mol l −1 Fe(CO) 5 ethanol solution was photo-excited at 266 nm (4.66 eV). The pump-laser pulse duration amounted to 100 fs (FWHM) and the pulse energy was estimated to ∼5 μJ. With a pump-laser spot size of 100×400 μm 2 , this corresponded to a peak fluence of ∼1.25 × 10 11 W cm −2 . We found no evidence for multi-photon processes at this fluence of the pump laser.
Fe L 3 -RIXS intensities were measured by scanning the incident photon energy from 703 to 715 eV. The resolution in the RIXS measurements along the incident-photon energy axis is defined by the excitation bandwidth. This amounted here to 0.5 eV (FWHM) and was determined by the slit size of 150 μm of the SXR monochromator. Incident flux was measured on a shot-by-shot basis using intensity monitor installed after the monochromator [45].