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X-ray emission transients

In previous ultrafast22,23 or quasi-static42 Kβ XES studies, the assignment of spin states relied on the comparison with reference spectra of model compounds. Supplementary Fig. 3 shows the steady-state Kβ emission spectra of hexacoordinated MbNO and pentacoordinated deoxyMb and compares them with those of reference Fe-based molecular complexes in Supplementary Fig. 3b22, and reference Fe(II) LS and HS porphyrin compounds42. While the trends are similar as a function of increasing the spin in all three panels, with the intensity increase of the Kβ’ line around 7045 eV and a blue shift and intensity decrease of the Kβ1,3 line near 7058 eV, some differences also show up in that the blue shift of the Kβ1,3 line in Supplementary Fig. 3a and its energy splitting with respect to the Kβ’ line are smaller than in Supplementary Fig. 3b and c. These differences may point to a covalency change43,44,45,46 in addition to the spin change, as will be discussed later. Supplementary Fig. 4a shows the steady-state Kα lines of MbNO and deoxyMb. There is an intensity decrease and slight blue shift and broadening of the Kα1 line with increasing spin, as reported for other compounds24, while the Kα2 line undergoes an intensity decrease and a slight broadening. Because Kα XES spectra of reference compounds are lacking, we resorted to DFT to simulate them (see Supplementary Note 4), as discussed later. In summary, the above XES spectra for the Mb LS hexacoordinated and the HS pentacoordinated forms provide the two extreme cases before and after photodissociation of the ligand, expected in time-resolved experiments, which allow us to identify the intermediate steps.

The laser-off and laser-on Kβ spectra are shown in Fig. 3 for time delays up to ~1.4 ps, while the inset zooms into the region of the maximum of the Kβ1,3 line. These spectra show an intensity decrease and blue shift of the latter, an intensity decrease in the 7050–7055 eV region and a slight increase of the Kβ´ line in the 7045–7050 eV region, all of which reflect the trends predicted for a change from LS to HS Mb (Supplementary Fig. 3a) and qualitatively agree with reference Fe(II) complexes (Supplementary Fig. 3b and c)22. Laser-on spectra at later times are shown in Supplementary Fig. 5, and they exhibit a return to the laser-off spectra on tens to hundreds of ps. Further insight into these changes is obtained from the normalized transient Kβ XES spectra (excited minus ground state signal) shown in Supplementary Fig. 6a for time delays up to 1.36 ps, and Supplementary Fig. 6b for time delays up to 100 ps. These transients exhibit a derivative-like shape near 7058 keV, a negative signal that extends down to 7050 eV and a positive one below in the region of the Kβ´ line. Beyond ~1 ps, the normalized transient spectra no longer change but before, the 7050–7057 eV region shows a gradual increase of negative amplitude, while the peak near 7060–7062 eV is most blue shifted at 0.26 ps, and then shifts slightly to the red and stabilizes at 7060 eV for times >1 ps. The evolution of the 7050–7057 eV region qualitatively reproduces the static difference spectra of reference Fe-complexes of different spins (Supplementary Figs. 7 and 19), that revealed the transient population of a triplet state in the photoinduced SCO of [Fe(bpy)3]2+22. From Fig. 3 and Supplementary Fig. 6a, we conclude that reaching the final HS deoxyMb state requires ~1 ps and proceeds via an intermediate state.

Fig. 3: Kβ XES spectra of MbNO at various time delays after visible photoexcitation.
figure3

Laser-off (−0.09 ps) and Laser-on Kβ XES spectra of MbNO at different time delays between 0.026 and 1.36 ps (from blue to red) showing a blue shift of the Kβ1,3 line and an intensity decrease. The inset zooms into the region of the maximum of (K_{beta _{1,3}}{mathrm{{XES}}}) line at different time delays between −0.09 and 1.36 ps (from blue to red) showing peak shifts smaller than the energy resolution (~0.5 eV) of our experiment.

Figure 4 shows the laser-off and laser-on Kα1 and Kα2 XES lines at different time delays, while the insets zoom into the region of their maxima. One notices a clear gradual weakening and a slight broadening (and for Kα1, a slight blue shift) of the bands within the first ps. The trends in energy, width and intensity of these lines are consistent with the differences we observe between MbNO and deoxyMb (Supplementary Fig. 4), but in Fig. 4, the evolution is gradual and on a similar time scale as for the Kβ lines. Supplementary Fig. 8 shows the laser-on spectra at later times, and just as in Supplementary Fig. 6, they exhibit a return to the laser-off spectra on tens to hundreds of ps. In order to highlight the changes, Supplementary Fig. 9 shows the experimental Kα XES transients at 0.26 and 1.36 ps time delay, while those at intermediate and at later times are shown in Supplementary Fig. 10. The normalized transient line shapes reflect the broadening, shift and intensity changes of the asymmetric emission lines, which do not change beyond ~1 ps, by which time the system is in the HS state, as confirmed by the difference of the experimental steady-state spectra deoxyMb minus MbNO (Supplementary Fig. 9b). In summary, both the Kα and Kβ XES transients point to an intermediate state being populated prior to the HS deoxyMb state that is fully formed by ~1 ps.

Fig. 4: Kα XES spectra of MbNO at various time delays after visible photoexcitation.
figure4

Laser-on (−0.09 ps) and laser-om (K_alpha) XES spectra of MbNO at different time delays between 0.26 and 1.36 ps (from blue to red) showing an intensity decrease for Kα2 over the first 1.2 ps after excitation and an intensity decrease and change in peak width for Kα1. Also, the visibility of changes in peak width (σ) smaller than the energy resolution (~0.6 eV) can be well observed. The insets zoom into the peaks of the Kα2 and Kα1 laser-on (pumped) XES spectra of MbNO at different time delays between −0.09 and 1.36 ps (from blue to red) showing an intensity decrease for Kα2 over the first 1.2 ps after excitation and an intensity decrease and change in peak width for Kα1. The changes in peak width (σ) smaller than the energy resolution (~0.6 eV) can be well observed.

X-ray emission kinetics

The signal around 7053 eV in Fig. 3 and Supplementary Fig. 6 best differentiates the intermediate state from the initial excited LUMO state to the quintet state. As already mentioned, this is where the signature of an intermediate spin state was most pronounced in the previous study on [Fe(bpy)3]2+22. By plotting its amplitude as a function of time for the transients available up to 3.6 ps, we can get an estimate of the lifetime of the intermediate state, using a three-level kinetic model (Supplementary Note 10 and Supplementary Fig. 11), assuming 100% Q-state population at t = 0 that decays to the triplet state in ~100 fs, as concluded from ultrafast fluorescence up-conversion studies47. The fit yields a lifetime of 500 ± 250 fs for the intermediate state (Supplementary Figs. 12 and 13).

Further details into the ultrafast kinetics comes from the peak position of the laser-on (K_{beta _{1,3}}) line (Fig. 3 and Supplementary Fig. 5) and the full width at half maximum (FWHM) of the laser-on Kα1 line (Fig. 4 and Supplementary Fig. 8), both of which are sensitive to spin. During the first ps, these spectra reflect a mixture of doublet, short-lived intermediate state and of the final quintet state, before the entire excited population settles in the latter. The Kβ1,3 peak energy shift and the FWHM of the Kα1 line are plotted in Fig. 5 for times up to 750 ps, while the inset zooms into the first 10 ps. The red trace is a fit of the experimental data using a function consisting of a rising component and a biexponential decay. The former corresponds to a risetime of 800 ± 150 fs (see Supplementary Note 6), significantly longer than our cross-correlation (~150 fs), while the decay components have time constants (pre-exponential factors) of τ1 = 30 ± 9 ps (A1 = 0.6) and τ2 = 1.5 ± 0.9 ns (A2 = 0.4). Interestingly, while the UV–visible and IR TA results are characterized by a prompt risetime and decay times of 5–20, 110–290 ps, and a weak ns component7,11,13,30,31,32,33,34,35,36,37, the present XES observables exhibit different kinetics with a rise of ~800 fs and decays of ~30 ps and ns’s. As mentioned previously, the ~30 ps decay had been reported in the time-resolved resonance Raman studies by Kruglik et al.13, who attributed it to the relaxation from the domed HS deoxyMb–NO species to the LS planar MbNO. Given the spin sensitivity of XES our observation of the ~30 ps decay is fully consistent with this interpretation as it reflects the return of the system to the LS ground state. Since the trigger to this process is the binding of the NO ligand to deoxyMb, in principle the geminate recombination (in 5–20 and 110–250 ps) and the non-geminate recombination (ns component) should feed the 30 ps component. In this scenario, the 5–20 ps component would appear as a rise time, while the 110–250 ps and the ns components would show up as decay because they are rate-determining to the 30 ps component. However, due to the scatter of data points at early times in Fig. 5, we refrained from extracting such times from the fits, preferring the above phenomenological function, which captures the important features using a single rise time and a biexponential decay. In this respect, the relatively large pre-exponential factor of the ns decay component, compared to previous reports (see ref. 37 and references therein), most likely reflects the fact that it includes both geminate (110–250 ps) and non-geminate (ns) recombination of NO ligands.

Fig. 5: Kinetic traces.
figure5

Temporal evolution of the relative (K_{beta _{1,3}}) shift for MbNO (blue triangles, centroid obtained from Gaussian fit, max shift is ~0.45 eV, see Supplementary Note 6) and of the (K_{alpha _1}) peak width changes for MbNO (black squares, normalized σ obtained from a Gaussian fit, maximum change in σ is ~0.3). The red line is a fit of the experimental data using a function consisting of a rising component and a biexponential decay. The former corresponds to a risetime of 800 ± 150 fs (see Supplementary Note 6 and Supplementary Fig. 18), significantly longer than our cross-correlation (~150 fs), while the decay components have time constants (pre-exponential factors) of τ1 = 30 ± 9 ps (A1 = 0.6) and τ2 = 1.5 ± 0.9 ns (A2 = 0.4). The inset shows the temporal evolution during the first 10 ps of both signals. The error bars represent the 1-sigma uncertainty of the Gaussian fit for the spectra at each time-point. Details are given in Supplementary Note 6 and Supplementary Fig. 18.

Coming back to the short time dynamics, we have yet to identify the intermediate state between the initial MbNO excited state and the HS deoxyMb. The changes occurring at early times (Fig. 3 and Supplementary Fig. 5) reflect the transient population of an intermediate, most likely an S = 1 spin state, if we parallel the present results with those on photoexcited [Fe(bpy)3]2+22. We further support the assignment of the intermediate state as having S = 1 using DFT calculations, presented in Supplementary Note 4 and Supplementary Figs. 14, 15 and 20. However, in addition to its spin sensitivity, Kβ XES is also sensitive to metal–ligand covalency43,44,45,46, which represents the charge donation from the ligands to the metal and therefore, it has a significant influence on the nature of metal–ligand bonds. The degree of covalency is connected via the effective number of unpaired 3d electrons to the magnitude of the exchange splitting. In Kβ XES, it manifests itself in, among others, the splitting between the Kβ1,3 and Kβ’ lines. Thus, covalency could also affect the transient spectra as a result of dissociating the NO ligand and of the relaxation to the HS state, which involves an elongation of the Fe–Np bonds (Np are the pyrrole nitrogens). We hold it however unlikely that covalency effects affect our results: (a) Given the recombination times of NO to deoxyMb (5–20 and 110–290 ps), it seems surprising that the Kβ transient XES no longer changes beyond 1 ps (Supplementary Fig. 5). This is consistent with the Kβ XES predominantly reporting on the spin state of the metal, i.e. since it does not distinguish between the HS deoxyMb and HS deoxyMb–NO species; (b) Also, the invariance of spectra in the relaxation from NO–deoxyMb to planar MbNO in ~30 ps is to note, as this corresponds to a contraction of the Fe–Np bonds; (c) Thus, neither NO rebinding nor the ensuing relaxation from domed to planar seem to affect the Kβ XES. A fortiori, we would also exclude a contribution of covalency at early times (<1 ps), since the reverse processes occur therein (ligand detachment, Fe–Np bond elongation); (d) It should also be noted that the Kβ XES changes reported in the case of photoexcited [Fe(bpy)3]2+, where a significant bond elongation occurs48 towards the HS state, were fully interpreted in terms of transient population via an intermediate spin state based on reference spectra22; (f) Last but not least, covalency effects have not been reported on Kα XES and the very close correspondence between the temporal evolutions of the Kα and Kβ XES (Fig. 5) suggests that signature of covalency is negligible in the latter.

To summarize our results, Fig. 6 shows the complete photocycle of MbNO: Upon photoexcitation into the Q-bands, prompt (<100 fs) photodissociation of NO occurs leaving an excited pentacoordinated haem that undergoes doming by first relaxing to an intermediate spin state (S = 1), followed by a second relaxation step to the HS S = 2 state forming deoxyMb. The entire cascade occurs in ~800 fs. The relaxation back from the domed HS haem to the planar ground state occurs in ~30 ps upon NO recombination. The latter takes place over several time scales due to geminate (5–20, 110–200 ps) and non-geminate recombination (ns’s). These results also show that the relaxation from domed NO–deoxyMb to the planar MbNO is a genuine HS to LS relaxation, as theoretically predicted by Franzen38, although constraints due to the F-helix (Fig. 1)13 cannot be fully excluded. Thus, the entire cycle of detachment and rebinding of NO to deoxyMb is accounted for by a SCO followed by a reverse SCO (Fig. 6). There are many parameters that affect the rates of forward-SCO and back-SCO but in the context of our interpretation, it is clear that the former is a stepwise process by jumps of ΔS = 1, which are ultrafast in metal complexes49, while the reverse SCO is a ΔS = 2 process occurring on a much slower time scale.

Fig. 6: Scheme of the spin cross-over (SCO) and reverse SCO characterizing the photocycle of MbNO.
figure6

The low-spin ground state MbNO (S = 1/2) haem (lower left panel) undergoes prompt dissociation of NO upon π−π* excitation. The porphyrin Q-state decays to a triplet state (S = 1, upper left panel) of the pentacoordinated deoxyMb haem in <100 fs47. Further relaxation to the quintet state of the pentacoordinated haem occurs in ~500 ± 250 fs (right “High-Spin” panel). The entire process (NO dissociation and relaxation from the Q-state to the high-spin quintet state) occurs in ~800 fs. Upon recombination of NO to deoxyMb leading to a hexacoordinated HS-domed haem (right “ligated high-spin” panel), relaxation back to the LS planar ground state occurs in ~30 ps. The initial low spin structure is PDB entry 2FRJ (Fe = orange, N = blue, O = red and C = grey), the sizes of the Fe atom, the NO molecule and the doming are exaggerated in order to highlight the key changes in the photocycle. The actual structural differences between MbNO and deoxyMb are shown in Supplementary Fig. 1.

The above results have several implications on the description of the energy flow in haem proteins: (a) upon ligand detachment, the formation of the fully domed deoxyMb requires ~800 fs, as it proceeds via an intermediate triplet state, which decays in 500 ± 250 fs; (b) The ligand detachment is here mimicked by a photodissociation, which is prompt (<50 fs), implying that the ensuing dynamics is taking place in the pentacoordinated haem and should therefore be the same for all ferrous haems involved in ligand release. This was already suggested by Ye et al. 8 based on UV–visible TA studies, but they concluded that the ensuing evolution within the deoxyMb product is due to relaxation of a vibrationally hot species, while we conclude that it is an electronic relaxation cascade. The debate to determine the initial pathways for ultrafast energy flow in haem proteins, has been going one for over 30 years now, with the interpretation about formation of deoxyMb going from an electronic cascade via spin states5,6, to a vibrational energy redistribution8,16. Here by using element-specific and spin-specific observables (XES), that are not sensitive to thermal and vibrational effects, we show that the initial scenario of a cascade among spin states is operative. Nevertheless, the cascade is non-radiative and energy gaps between spin states are dissipated in the form of heat to the environment. We believe that this behaviour is not limited to ferrous haems (that undergo distal ligand dissociation) but it also includes ferric haems (that remain hexacoordinated) as suggested by the conclusions of UV–visible studies on metMb50 and MbCN51. Finally, doming has been suggested to trigger large-scale conformational changes of the protein, the so-called “protein quake”, that opens a channel for ligand escape from the protein52. Our results show this is unlikely to be a very fast process, contrary to earlier claims that assumed it to occur on the time scale of the Fe–ligand bond breaking53.

The present work identifies the transition from the planar ligated haem involved in ligand release to the domed deoxy form as a SCO, which we believe is identical in all ferrous haem proteins. However, the ensuing events following ligand recombination are specific to the NO ligand and are characterized by a reverse SCO. This work also shows the power of ultrafast XES at unravelling exquisite details of the haem transformations upon ligand release and uptake in haem proteins.

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