Photoinduced bond oscillations in ironpentacarbonyl give delayed synchronous bursts of carbonmonoxide release

Early excited state dynamics in the photodissociation of transition metal carbonyls determines the chemical nature of short-lived catalytically active reaction intermediates. However, time-resolved experiments have not yet revealed mechanistic details in the sub-picosecond regime. Hence, in this study the photoexcitation of ironpentacarbonyl Fe(CO)5 is simulated with semi-classical excited state molecular dynamics. We find that the bright metal-to-ligand charge-transfer (MLCT) transition induces synchronous Fe-C oscillations in the trigonal bipyramidal complex leading to periodically reoccurring release of predominantly axial CO. Metaphorically the photoactivated Fe(CO)5 acts as a CO geyser, as a result of dynamics in the potential energy landscape of the axial Fe-C distances and non-adiabatic transitions between manifolds of bound MLCT and dissociative metal-centered (MC) excited states. The predominant release of axial CO ligands and delayed release of equatorial CO ligands are explained in a unified mechanism based on the σ*(Fe-C) anti-bonding character of the receiving orbital in the dissociative MC states.


State
TDDFT/ CAM-B3LYP    Figure 2. UV-vis of gas phase Fe(CO)5. We show here computed UV-vis absorption spectra of gas phase Fe(CO)5 at TDDFT/CAM-B3LYP (blue) and NEVPT2 (green) level of theory, obtained from the transitions in Supplementary  Table 1 by convolution with a 0.8 eV full-width half-maximum Gaussian function. (They are calculated at the equilibrium geometry and the TDDFT curve in this graph is reproduced from Figure 1 in the main text.) The convoluted spectra are compared to the experimental Fe(CO)5 UV-vis spectra in gas phase (black) as given in the Ref.
[32]. The gray dashed line depicts the wave length corresponding to a 267 nm excitation, which is near the position of the peak at 250 nm in the experimental spectrum. Bright discrete states in the TDDFT calculation are included and denoted by state number and symmetry labels. Computational details are stated in Methods Section in the main text.
Supplementary Figure 3. Adiabatic potential energy surfaces for rigid scan corresponding to the dissociation of axial Fe-CO bond a) TDDFT/CAM-B3LYP adiabatic potential energy surfaces of the 10 lowest lying electronic singlet states plotted against varying an axial Fe-C distance starting from the equilibrium D 3h geometry (see Methods Section in main text), and distorted within C3v symmetry in a rigid scan displacing a CO ligand. These one dimensional cuts correspond to the two dimensional cuts presented in Supplementary Figure 10. b) The corresponding NEVPT2 data. The ground state potential is black and the dissociative states are presented in various shades of red, whereas the non-dissociative state are shown in different shades of blue. The vertical gray line represents the equilibrium distance.  Fe−C distance (Å) Supplementary Figure 5. Plot of 1-C 2 0 vs Fe-C distance along axial Fe-CO bond dissociation. The plot 1-C 2 0 vs Fe-C distance for taken from CASSCF(10e,10o) computation done for geometries from a excited state MD trajectory taken every 5 fs apart (left) and along a Fe-C scan (right) corresponding to Supplementary Figure 3

SUPPLEMENTARY NOTES 2
The problem about break down of TDDFT framework as the S 1 and S 0 potential energy surface approaches each other is very well known. We performed a CASSCF(10e,10o)/NEVPT2 along the Fe-C bond distance and plotted the energies in Supplementary Figure 3(b). Here we present a measure of the multireference character, i.e. plot of (1-C 2 0 ) vs the Fe-CO bond distance. The C 2 0 is taken as the co-efficient of the closed shell CSF contribution in the ground state wavefunction, i.e. |2222200000 . As seen from Supplementary Figure 5 (right panel) the development of multi-reference character in rather limited as the bond elongates and TDDFT can be applicable as far as single/multideterminant description is concerned. However, since the scans are rigid, we have conducted the same computation along one of the trajectories as mentioned earlier when we compare energetics, and plotted (1-C 2 0 ) vs Fe-C distance in Supplementary Figure 5 (left panel). We clearly see that even though the (1-C 2 0 ) remain nearly constant and below 0.2 mark most of the region and when Fe-C distance only goes beyond 2.55Å the system becomes multi-reference. This is also evident from the energies plot with respect to the distance where we see that S 1 and S 0 cross at a distance larger than 2.5 A. Thus we see that Fe(CO) 5 can be described as a single reference system and Fe(CO) 4 cannot. Our study focuses on dissociation of Fe(CO) 5 to Fe(CO) 4 and based on Supplementary Figure 5 we can safely describe the region in between. Based on this limitation of TDDFT we have refrained ourselves of involving S 1 or S 0 dynamics, as based on this diagnostic we see that any description of S 1 state is flawed as S 0 and S 1 energies become quasi-degenerate once the bond breaks. One serious limitation of this piece of work is that we cannot describe the dynamics of the S 1 /S 0 state of Fe(CO) 4 .

Exclusion of Triplets from the ESMD Simulations:
The exclusion of triplets from the excited state MD simulation has been motivated primarily from overwhelming evidence from multiple experiments. Three independent articles, based on three different spectroscopic techniques, have ruled out the presence of inter-system crossing (ISC) and triplet pathway in the photodissociation of Fe(CO) 5 in the gas phase. Trushin and co-workers [8] have shown in their work that singlet pathway to be operative with no ISC. They have, based on computation of time-constants for the dissociation process, excluded the possibility of ISC happening, arguing that the photodissociation happens much faster than the ISC. Additionally, Wernet and co-workers [10] have corroborated the above claim based on the high-temporal resolution gas phase TR-XPS studies. XPS is very sensitive to the electronic structure of the species, not least to the multiplicity due to strong spin-orbit coupling in the final states of the XPS probe, and would in principle have picked up the formation of triplet species or if the triplet pathway had a major involvement. They have confirmed the absence of any triplet involvement up to 6ps which is beyond the temporal regime of our present studies. Recently using time resolved IR experiments Ramasesha and co-workers have shown that the ISC channels are only operative in the Fe(CO) 4 moiety after 15 ps timescale [11]. Thus, gathering from three independent experimental studies that triplet pathways are not operative it is pragmatic for us to exclude the triplet states in the study, and investigation of possible involvement of triplet states for less probable/minor pathways will have to await further investigations and improvements in simulations capabilities.
Also, our study inherently deals with the photo-dissociation, we are already running the risk of breakdown of DFT/TDDFT as the Fe-CO bond dissociates, which we have tried to state clearly in our work. As we know that Fe(CO) 4 has a triplet ground state, the inclusion of triplets would furthermore amplify the problem that the DFT/TDDFT already has in dealing with bond dissociation.
Ultrafast ISC has been simulated for other 3d transition metal (TM) complexes which deal with well-known iron based photo-sensitizers and hence have experimentally well-established evidence for the role of triplet states [35,36]. However, for the system we deal with here ample experimental evidence as discussed earlier tells us not to primarily consider it here for the dissociation dynamics. Nevertheless, in an attempt to find a justification for the singlet pathway and the absence of triplet states in the excited state dynamics following photo-excitation of iron pentacarbonyl in gas phase, we have made Fe-CO scans for both singlets and triplets involved at the NEVPT2 level of theory which is robust in its treatment of triplet and computation of SOC elements. The triplet manifold is an analogue of the singlet manifold, i.e., it comprises of four 3 MC states which are dissociative in nature and followed by these are the 3 MLCT bound states. In the figure below we show the NEVPT2 PES of the triplet (black lines) and singlet (blue lines). The systems where fast sub 100fs ISC happens, the ISC process happens between bound states having similar shapes (non-dissociative and hence described by LVC model) shown in Ref. [35,36]). The crossing between the 3 MLCT (bound) and 1 MLCT (bound) states (denoted by green circle in Supplementary Figure 6) are energetically much higher as compared to the crossing between 1 MLCT (bound) states and the 1 MC (dissociative) states. Thus the rate for transition from the 1 MLCT (bound) states to the 1 MC (dissociative) state will be much faster as compared to the ISC rate for the present system. The black circle in the left side figure denotes the crossing between the 1 MC (dissociative) state and the 3 MLCT (bound) states. The 3 MC states which are also dissociative in nature are well separated from the singlet manifold. Now the process involves excitation to a MLCT state followed by decay to dissociative 1 MC states followed by fast dissociation, as depicted by the curved arrow in Supplementary Figure 6. The internal conversion within the singlet manifold to the dissociative 1 MC state happens before the region where ISC could occur and by the time the system encounters the ISC region (highlighted by the black circle), the system is already in the process of a fast dissociation. Thus, the system likely spends too little time in that region for ISC to effectuate, or in other words the system has too large a nuclear velocity, which is an important factor in ISC rate, for ISC pathway to be competitive. Though the spin-orbit coupling (SOC) between a 1 MC and 3 MLCT states is expected to be low, when computed we found it to the order of 220 cm −1 , at NEVPT2 level of theory. Considering the timescale associated to the SOC is ∼75 fs under ideal conditions, and given the system only spends much less time in the resonant region due to the fact that singlet states are dissociative and triplet states are bound, we would assume that the branching ratio to the triplet state is rather low. This provides a justification for the experimentally observed singlet pathway. Alternatively nuclear wavepacket overlap, which is an important aspect in the ISC process, can also assumed to be low given the different shapes of the crossing dissociative singlet 1 MC PES and bound triplet 3 MLCT PES. This is again in stark difference to the two cases where fast ISC happens [35,36]. The scan at the TDDFT/CAM-B3LYP level in Supplementary Figure 6 also gives the same overall behavior for the singlet and triplet manifolds although the 3 MLCT states are less dispersed than the 1 MLCT states. Notice also that the crossings between the 1 MC and 3 MLCT states occur in a region where the dissociation has already been initiated. POPULATION DYNAMICS AND NON-ADIABATIC DYNAMICS:The time spent in a state averaged over the trajectories can be thought of as a measure of the lifetime of the state and they are listed in Supplementary  Table 2. Furthermore, looking at the number of jumps in the surface hopping matrix in Supplementary Table 3, we notice that hops predominantly occur to adjacent adiabatic states i.e. from S n to S n±1 , even though the surfacehopping algorithm is not restricted to these transitions. Based on this we did kinetic modeling (see the schematic Supplementary Figure 14) for the population dynamics. It is noticeable here from Supplementary Tables 2 and 3 that we also take into account that the system can hop up from S 6 state to S 7−9 states, which can be due to the fact that states can relax along different degrees of freedom and become lower in energy than the initial energy of the system. The fitted curves, of electronic population are overlayed with the simulated data as shown in Supplementary  Figure 13. The area under fitted curves were taken as a measure of lifetime of different states (since due to the presence of back reactions exponential fits were not an option) and was found to match well with the lifetime data from the simulation (see Supplementary Table 2). This also establishes that the dynamics can be accurately described in a simple model, in which hopping from one state predominantly happens to the adjacent adiabatic states.  The kinetic model was set up as a series of rate equations of the form where i + 1 = j = k − 1, 2 ≤ j ≤ 6, and N j is the population of the state j. For the special cases of j = 1 and j = 7, 8, 9, the equations reduce to and respectively (the 7, 8, 9 states are considered together). The initial population N j (t), t ≤ 0 was set to 0 for all states except j = 6. The rate equations were numerically integrated using the solve ivp ODE solver of Scipy Dissociative Supplementary Figure 14. The scheme employed for the kinetic modeling. The scheme is based on the hopping matrix data as shown in Supplementary Table 3. The forward and backward rate constant used in the modeling are shown below and above the arrows. The adiabatic TDDFT potential energy surfaces of all the states plotted against varying Fe-C distance starting from D 3h geometry (left side) and near C4v geometry (middle and right). The middle and right panel represent the dissociation of CO which was axial and equatorial respectively in the D 3h geometry and distorted (angular) to near C4v geometry. The dissociative and non-dissociative states are shown with shades of red and blue respectively which matches with the plot of the potential energy surfaces in Supplementary Figure 3. Figure 16. The correspondence between the potential energy surface of a S N 2 reaction and that of photodissociation of the Fe(CO)5. The right hand panel shows the well known energy profile of the SN2 reaction and the orbital overlap symmetry of the frontier molecular orbital. The left hand figure shown the similarity from symmetry and overlap symmetry point of view for Fe(CO)5. The highest occupied molecular orbital (HOMO -doubly filled) for SN2 transition state has been shown here. This orbital has the same anti-bonding overlap symmetry that we see in the metal centered 3d z 2 orbital shown in the left, which is singly occupied in the dissociative MC excited states. π* CO dz 2 (major)+ σ*  Figure 17. Frontier molecular orbitals involved in the photodissociation of ironpentacarbonyl at a geometry with one increased axial Fe-C distance (2.5Å), relative to the ground state geometry. Relevant connection between the electronic states and subsequent dissociation dynamics are summarized in the right part of this figure. The figure serves the purpose of connection between the orbital (one electron) picture with the electronic state (many electron) picture. As depicted here in the orbital picture, and in Supplementary Figure 11 in a state picture, as the Fe-C(axial) bond is stretched the lowest four (dissociative) states possess the MC character where as the higher lying bound states have MLCT character.