Real-time tracking of the entangled pathways in the multichannel photodissociation of acetaldehyde†

The roaming mechanism, an unconventional reaction path, was discovered more than a decade ago in the studies of formaldehyde photodissociation, H2CO → H2 + CO. Since then, observations of roaming have been claimed in numerous photochemical processes. A closer examination of the presented data, however, revealed that evidence for roaming is not always unequivocal, and some of the conclusions could be misleading. We report here an in-depth, joint experimental and theoretical study of the title reaction. By tracking the time-evolution of the pair-correlated product state distributions, we decipher the competing, interwoven reaction pathways that lead to the radical (CH3 + HCO) and molecular (CH4 + CO) products. Possible roaming pathways are then elucidated and a more precise descriptor of the phenomenon is delineated.


Introduction
The concept of the transition state (TS) is central to the understanding of chemical reactivity. 1 An activated reaction is oen envisioned to proceed from reactants to products along the minimum energy path (MEP) through a tight TS that serves as the bottleneck in breaking and forming bonds. Recent experimental and theoretical studies, however, documented a growing body of evidence that in some cases signicant reactivity can also be derived from those trajectories bypassing the conventional saddle-point TS. [2][3][4] A notable example, which sparked a surge of interest in non-TS dynamics, is the UV (ultraviolet) photodissociation of formaldehyde (H 2 CO). 5,6 The formation of H 2 + CO was experimentally observed and theoretically veried to proceed via two distinct pathways. In addition to the conventional TS mechanism that yields the product pair of a rotationally hot CO with a vibrationally cold H 2 , the socalled roaming mechanism leads instead to a highly vibrationally excited H 2 together with a rotationally cold CO coproduct accompanied by a low total kinetic energy release (TKER). Theoretical analysis of the trajectory revealed that roaming arises from the incipient H/HCO radical channel where the two fragments do not have sufficient kinetic energy along the reaction coordinate to dissociate, but instead orbit each other (i.e., roaming with signicant kinetic energy tied to the centrifugal motion) and eventually undergo a radical recombination reaction by direct abstraction of the H atom from HCO at a long range to form H 2 + CO, thereby emerging with distinct pair-correlated product distributions.
Since then, roaming has been claimed in numerous unimolecular dissociation processes, 7 including the closely related acetaldehyde (CH 3 CHO) photodissociation. [8][9][10][11][12][13][14] In those studies, experimental evidence for roaming is almost universally, with a few exceptions, 8,14 based on the observation of a bimodal rotational state distribution (or sometimes a distribution with two Boltzmann rotational temperatures) for one of the molecular fragments. However, it is known that a bimodal rotational distribution of a reaction product can have several different mechanistic origins. 15 Merely sighting a bimodal distribution, therefore, does not provide convincing evidence for roaming and such a claim is susceptible to controversy. For example, in the photodissociation of CH 3 CHO at 308 nm, [8][9][10][11][12][13] the assigned roaming fraction varied from 15% of total CO yields in the initial report 8 to a predominant 76-84% in more recent ones. 11,12 A large disparity was also found at shorter wavelengths. 9,13,14,16 Theoretical investigations so far did not help settle the dispute because of the complexity of the much higher dimensionality (15 degrees of freedom) and the involvement of nonadiabatic couplings of multiple potential energy surfaces (PESs).
The rst absorption band of acetaldehyde (S 0 / S 1 ) spans from 340 nm to 230 nm and arises from excitation of an electron from the oxygen lone pair to the lowest p* orbital localized on the C-O bond. Upon excitation, several dissociation channels are possible, among which the CH 3 + HCO and CH 4 + CO channels dominate. Here, we report a joint experimental and theoretical study of the photodissociation of CH 3 CHO at 267 nm, focusing on these two channels, 17 to clarify some of the confusing issues. Experimentally, a picosecond (ps) pumpprobe approach (Fig. S1 †) was employed to track the time evolution of product pair-correlated distributions 19 (see the Methods section). With the aid of concurrent theoretical calculations [Methods], this set of two-dimensionaltime and pair-correlationresults enable us to disentangle the multiple, interwoven dissociation pathways.
2. Two-dimensional perspective: time and pair-correlation Fig. 1a presents the temporal proles of the three products, CH 3 (0 0 ), CO(v ¼ 0, j $ 0), and CO(v ¼ 0, j pk $ 43), probed by the resonance-enhanced multiphoton ionization (REMPI) spectroscopic technique [ Fig. S2 †]. Both low-and high-j states of CO(v ¼ 0) products display similar proles, which can be tted by the apparent, rst-order kinetics with comparable time constants (s) of 340 ps and 310 ps, respectively. On the other hand, the growth of CH 3 (0 0 ) is clearly bi-exponential, strongly suggestive of complicated, multiple dissociation pathways. For the off-resonance probes (Fig. 1b), all time-dependent ion signals exhibit single-exponential decay with the same s d $ 190 ps. Those off-resonance ion signals were ascribed to the two-color, dissociative ionization processes from the pumplaser excited CH 3 CHO(S 1 ). The observed proles then correspond to the non-radiative decay of the S 1 state to the T 1 state by intersystem crossing (ISC) processes and/or to the ground S 0 state via internal conversion (IC). The contaminations from those non-resonant backgrounds (Fig. 1b) were subtracted accordingly from the on-resonance data to unveil the proles presented in Fig. 1a. For clarity, all formation s herein refer to the overall time constant encompassing both this initial S 1decay (s d ) and the ensuing dissociation on the S 0 or the T 1 surfaces. Fig. 2 illustrates how to unravel the multiple reaction pathways for a given product from the time-of-ight (TOF) mass and the image data. Here, we dene a pathway by its unique rate of formation and/or the distinct product paircorrelated distribution. Exemplied in Fig. 2b are two raw difference-images (with the pump-and probe-only backgrounds subtracted from the image with both lasers on) for each of the three products. The resultant product speed distribution P(u; Dt) and the partitioned components are shown in Fig. 2c Fig. 2c) displays a clear bimodal structure in accord with previous ns-laser studies, reecting the internal energy distribution of the HCO coproduct. Signicantly, adding the temporal evolution information unveils three distinct pathways. This product channel adiabatically correlates with both T 1 and S 0 surfaces. All three distributions peak substantially away from zero TKER, suggesting

Tracking the CH 3 + HCO radical channel
in red, and CH 3 (0 0 ) in black. While the rates of formation for low-and high-j states of CO are single-exponential and nearly identical (s $ 340 ps and 310 ps, respectively), that for CH 3 is distinct and clearly bi-exponential with s 1 $ 210 ps and s 2 $ 1650 ps. Note that the raw profiles (with the one-color backgrounds subtracted) actually show finite values at zero and negative time delays, which arise from the two-color dissociative ionization processes. Such backgrounds were accounted for with the aid of the non-resonant results shown in (b). (b) The temporal dependency of fragment-ions observed with the probe laser off-resonance from the respective REMPI bands: CH 3 + and CH 3 CO + at 230 nm, HCO + at 333 nm. All profiles consistently display a single exponential decay of s d $ 190 ps. Three curves are vertically offset for clarity. dissociations over exit-channel barriers and thus ruling out the barrierless pathway from the S 0 equilibrium minimum.
The low energy component (red) accounts for about 19% of the branching fraction and has a long s of 800 ps. The blue and green components are translationally hotter and exhibit remarkably similar P(E)-distributions. What differentiates the last two is the vastly different rates of formation. The blue path (36%) is fast and its formation time (190 ps) is essentially the time for S 1 -decay, indicating that once the S 1 state is deactivated, CH 3 + HCO is produced within a few ps. In marked contrast, the green pathway (45%) proceeds substantially slower (s $ 1.8 ns), signifying possible isomerization during the course of dissociation (vide infra). Intriguingly, it ends up with a similar energy disposal to the fast-forming blue-component.

Tracking the CH 4 + CO molecular channel
As for the CH 4 + CO channel, three distinct paths are identied for the low-j states of CO(v ¼ 0). The intense red-path (30%) with s $ 480 ps yields low kinetic energy, f TKER $ 0.05. By virtue of energy conservation, the CH 4 coproducts must be highly internally excited. As is seen, a large fraction of the red component falls within the energy range for triple fragmentations to H + CO + CH 3 . This possibility, however, can be discarded from two previous reports. 21 Therefore, we conclude that those highly excited CH 4 co-fragments must be metastable to secondary dissociation, at least up to 40-70 ns of the pump-probe delay of the previous ns-laser experiments. 18,22 The remaining two pathways, blue (46%) and green (24%), have similar s $ 300 ps, but differ in TKER with f TKER $ 0.28 and 0.13, respectively. Hence, the corresponding CH 4 coproducts from these two paths are also highly excited. Taken together, all three paths yield internally hot CH 4 coproducts with energy content far exceeding half of the C-H bond dissociation energy (Fig. 3).
When imaging the high-j states of CO(v ¼ 0), only two features are notable and both proceed at about the same rates, s $ 300 ps. The dominant blue feature (86%) is nearly the sameboth in rate and TKERas the blue component for j $ 0. The  Table 1. All components exhibit single-exponential growths (shown by the lines) and the fitted time constants (s) are given in Table 1 distributions of both j CO states peak at the same recoil energy of 28.6 kcal mol À1 ; then, by conservation of energy, the difference in the probed CO rotational energy is entirely compensated for by the corresponding CH 4 internal energy. A similar behavior was reported in a previous study at 248 nm. 14 The weaker, lowerenergy feature (green) encompasses an energy range over the green and red components for j $ 0. The peak prole and the overall s of 310 ps suggest that its main contribution proceeds via the same path as that of the green component for j $ 0. Remarkably, a casual inspection of the P(E) distribution of either low or high j CO indicates that none of the CH 4 coproducts are born with internal energy less than $50 kcal mol À1 , in sharp contrast to the result deduced from the IR emission of CH 4 products photolyzed at 308 nm (ref. 10 and 12) or 248 nm. 16 Table 1 summarizes the characteristics of the partitioned components of the three products. To unravel their reaction pathways, we rst noted that a previous calculation 23 predicted a conical intersection (CI) between S 1 and S 0 at a fairly elongated C-C bond conguration, which provides a facile pathway to dissociation. This CI is preceded by a barrier, TS cc (S 1 ), located at $103 kcal mol À1 above S 0 ; 23 an additional image of CH 3 was then acquired with photolysis at 286 nm (photon energy of $100 kcal mol À1 ). As evidenced in Fig. S6, † the resultant P(E) distribution features a single Gaussian-like peak near  a The color-codes correspond to those depicted in Fig. 2-4. b The growth of each partitioned component can be tted by an apparent, rst-order kinetics of B(1 À exp(Àt/s)). The quoted error represents AE (one standard deviation) from the tting. c The sum of branching fractions for a given product is set to unity. The typical error of each entry is AE2%.

CH 3 + HCO channel
11 kcal mol À1 and the lower-energy structure observed at 267 nm is entirely absent. Hence, the red feature (near 5 kcal mol À1 ) of the radical channel in Fig. 3 is assigned to the CI(S 1 /S 0 ) pathway. This pathway is mediated by the gradient difference vector at the CI and asymptotically correlates with CH 3 ( 2 A 2 00 ) + HCO*( 2 A 00 ). At 267 nm, however, this electronically excited product pair is energetically inaccessible. Recalling that CI(S 1 / S 0 ) occurs at a large C-C distance, the observed CH 3 ( 2 A 2 00 ) + HCO( 2 A 0 ) ground-state pair is therefore ascribed to the result of inter-fragment quenching of the excited radical paira nonreactive event akin to the roaming reaction. The long formation time of 800 ps may reect the additional time needed for this roaming-mediated quenching process. The blue component in the CH 3 + HCO channel is produced at about the same rate as that of S 1 -decay, which can readily be ascribed to a rapid, direct dissociation on T 1 aer ISC. This pathway must surmount a late exit-barrier of TS cc (T 1 ), thereby causing a substantial TKER; the observed f TKER $ 0.51 supports this assignment. The green component, on the other hand, takes an order-of-magnitude longer to form, yet with a very similar energy release (f TKER $ 0.45) to that of the blue one.
Previous studies indicated that the ISC of S 1 / T 1 is a facile process and competes favorably with the direct IC in the Frank-Condon region, with the preference increasing with increasing photolysis energy. 13,18,[24][25][26][27] Thus, the dominant pathway for relaxing S 1 to S 0 at 267 nm is most likely a cascade of ISC pathways of S 1 / T 1 / S 0 in the acetaldehyde (AA) conguration space. A number of feasible isomerization pathways on the S 0 surface have recently been identied near the T 1 -dissociation threshold. 28 Present theoretical calculations further suggest that the isomerization of vibrationally hot acetaldehyde to vinyl alcohol (CH 2 CHOH, VA) could become even more competitive at higher energies. More importantly, the S 0 and T 1 states are nearly degenerate in the structural landscape of the T 1 minimum of VAfrom an internal rotation of the terminal CH 2 group, thus facilitating the S 0 / T 1 transition, (ISC) VA . Once on the (T 1 ) VA surface, a facile enol-keto isomerization can occur aer surpassing a barrier TS(T 1 ) VA located at 105 kcal mol À1 , taking the system back to the AA conguration, (T 1 ) AA . Apparently, the last step must take place before reaching TS cc (T 1 ) so that the ensuing dissociation will leave a similar dynamical imprint to that of the direct T 1 -dissociation pathway of the blue component. This complex, winding interconversionfrom (AA / VA) S 0 to (T 1 ) VA via (ISC) VA , followed by (VA / AA) T 1over the S 0 and T 1 surfaces delays the formation of CH 3 + HCO (green). 29 It should be noted that these isomerization and ISC processes are likely reversible, meaning that they could undergo multiple interconversions rather than a single step, thus further delaying the formation of nal products. For clarity, Fig. 4 depicts the three pathways that lead to the radical channel, as well as those to the molecular channel as discussed below.

CH 4 + CO channel
As for the CO + CH 4 molecular channel, the lowest energy feature (red in Fig. 3) is ascribed to the CI(S 1 /S 0 ) pathsimilar to the radical case. This bifurcated CI-path is now governed by the derivative coupling vector at the S 1 /S 0 intersection point and yields either a hot CH 3 CHO(S 0 ) or the ground-state pair of CH 3 and HCO. Either way, the subsequent formation of CO + CH 4 could be attributed to the roaming reaction. Its P(E) distribution peaks around 5.7 kcal mol À1 , similar to that of the red component (also via the CI(S 1 /S 0 )-path) in the radical channel.
The molecular products CH 4 + CO are exclusively formed on the S 0 surface. Three possible ways can deactivate S 1 at 267 nm: IC of S 1 / S 0 , CI(S 1 /S 0 ), and ISC of S 1 / T 1 . The red component has been assigned above to the CI(S 1 /S 0 ) path. As mentioned earlier, the relaxation of S 1 to S 0 is dominated by a cascade of ISC pathways of S 1 / T 1 / S 0 . Yet, two distinct components, blue and green, are retrieved from these time-resolved, paircorrelated data. We ascribed the blue component to the TSpath, and the green to the one bypassing the TS.
Assigning the major blue-feature ($76%, accounting for both low and high j CO data) to the TS-path may sound provocative in view of the current perception that roaming dominates the acetaldehyde photodissociation with a minor contribution from the TS mechanism. [9][10][11][12]16,31 The key argument for roaming was based on the comparison of the experimental CH 4 internal energy and j CO distributions with the quasiclassical trajectory (QCT) results. A huge discrepancy was found when the directdynamics trajectories were initiated at the TS cc (S 0 ) saddle point, while a closer accordancealbeit notable discrepancies Fig. 4 The roadmap of CH 3 CHO photodissociation at 267 nm (hv ¼ 107 kcal mol À1 ). Six distinct, color-coded pathways are identified and elucidated for the formation of the CH 3 + HCO and CH 4 + CO channels. The labeled numbers refer to those in Table 1 and the black wavy arrows denote the ISC transitions. For clarity, detailed characterization of the key stationary points and the relevant energetics is presented in Fig. S8. † This journal is © The Royal Society of Chemistry 2020 Chem. Sci., 2020, 11, 6423-6430 | 6427 still remained 31was obtained for trajectories starting from the acetaldehyde equilibrium minimum. A similar disagreement between the experiment and an estimated QCT-TS was found in this work on the CH 4 internal energy distribution (Fig. S7 †).
On the other hand, assigning the dominant blue-component as the result of the CH 3 /HCO roaming reaction appears at odds with such high j-states of CO(j $ 43) products and large recoil energy ($29 kcal mol À1 or f TKER $ 0.30). Particularly worth noting from Fig. 3 is the striking variation of the relative intensities of the three partitioned components with the probed j CO -states, which is obvious for the lower energy (red/green) components, but not so for the high energy (blue) feature. Recall that the correlated distribution of two concomitant products is the key experimental hallmark to differentiate roaming from the TS mechanism in the H 2 CO benchmark. 5,6 Then, how do we reconcile the dilemma? As mentioned earlier and clearly demonstrated in Fig. 3, upon photolysis of CH 3 CHO at 267 nm all CH 4 products are born extremely hot, and a majority of them possess internal energy contents very close to the C-H dissociation limit. Due to the multi-reference nature, the CCSD(T) or any other single-reference based methods may fail to provide an accurate description of the dynamical properties of such highly excited CH 4 products. 32 Yet, almost all the QCT dynamical simulations 9,10,16,31,33 have been performed on the basis of the CCSD(T) calculated S 0 -PES. It is also known that the QCT results suffer from zero-point energy leakage, 34,35 where a part of the energy of the high-frequency modes is transferred to the low-frequency ones, thus resulting in an unrealistic energy distribution. Obviously, this deciency becomes more problematic for acetaldehyde than formaldehyde.
In addition, a number of new pathways may open up and produce CO + CH 4 upon photolysis at 267 nm. Previous ab initio calculations, 36 also conrmed in this study, indicated three TS structures for the C-C bond cleavage on the S 0 surface. The lowest energy one, as shown in Fig. 3, with a C-H-C three-center structure has been assumed to be the only TS cc (S 0 ) in all previous QCT calculations. Nonetheless, the presence of multiple transition states and presumably the associated valleyridge inection regions 37,38 underscore the complexity of this multi-dimensional PES and the challenge in accurate dynamical simulations. At present, as to the origin of the discrepancy between the experimental assignment and the QCT-TS result, it is not yet totally clear. Further theoretical investigations are warranted.
The rate of formation of the green component in the CO + CH 4 channel is comparable to that of the blue component of the same product channel, which differs from all other pathways (Table 1). Its yield is sensitive to the probed j CO state (Fig. 3) similar to the roaming-mediated red component, yet with a signicantly larger TKER than the latter (f TKER ¼ 0.13 versus 0.05). These distinct characteristics (or properties) of the green component strongly suggest a different pathway from the red and blue paths. On intuitive ground, we posit that the formation of this green component (path ⑤) could be the result of the bifurcation of the trajectories from the valley-ridge inection point on the S 0 surfacea dynamically driven pathway or non-TS mechanism. 2,37-39

Implications and outlook
As clearly elucidated in the formaldehyde case, a roaming event arises from the self-reaction of a frustrated radical dissociation at a long distance, resulting in an anomalous product paircorrelated distribution. The undisputable roaming signature for acetaldehyde should, by analogy, be manifested in the correlated behavior of CO(j) + CH 4 (v). As demonstrated here by the time-and state-resolved P(E) measurements, the twodimensional viewtime and pair-correlationis particularly illuminating to unravel the complexities and permits new physical insight that is otherwise inaccessible by merely probing the nal product distributions. Because of the high dimensionality of a polyatomic molecule, numerous isomeric structures are ubiquitous in the (conceivably rugged) potential landscape of a typical medium-to-large molecule. Many of them, despite being situated at higher internal energies, can readily be accessible upon visible/UV excitation. We surmise that isomerization of energized molecules prior to dissociation might well be the rule rather than the exception in many polyatomic unimolecular processes.
One may address a deeper and more intriguing question: "what are the deciding factors that guide a trajectory towards the roaming region or to follow the tight TS path"? We conjecture that the answer might be traced back to how the system behaves in the vicinity of a TS: the response to the topographical energy landscape (e.g., the presence of a valley-ridge inection point or a second-order saddle point 40 ) and/or the dynamical behaviors of a highly energized molecule as it traverses the barrier. 39 Some trajectories, instead of climbing over the barrier through a narrow window, may stray far from the MEP and skirt around the barrier by the entropic advantage of diverse, alternative paths because of the rugged, high-dimensional PES. As inferred above for path ⑤, those non-TS trajectories on S 0 experience very different forces and could, in principle, proceed further by a dynamically driven migration of the aldehyde-H atom to produce CH 4 + CO, leaving distinct non-MEP imprints in product attributes. Hence, the barrier-skirting route may or may not lead to a roaming event, which usually refers to an orbiting self-reaction of failed radical dissociation near the asymptote. In other words, roaming seems to require both non-MEP paths at a short range and orbiting radicalrecombination at a long distance in a at region of the PES.
Clearly, a conceptual framework of the roaming phenomenon is far from complete: one needs to comprehend not only the dynamical description near the asymptote, which has been amply investigated theoretically, but also how and why the trajectories get there. A promising theoretical approach based on the geodesic paths (not classical trajectories) has recently been formulated and applied to the formaldehyde benchmark. 41 That study scrutinized the onset of the paths that will eventually roam and suggested that their stochastic character in the early stage sets the destination. A nonlinear dynamics theory from the phase space perspective, albeit with reduced dimensionality, has also been developed to frame and to analyze the roaming phenomenon and dynamical characteristics. 42 Extending these new approaches to acetaldehyde can not only further sharpen our understanding of the nature of the non-MEP paths and roaming events proposed here, but can also pave the road for systems of higher dimensions in general.

Experiment
The experiment employed the typical pump-probe spectroscopic technique with a picosecond (ps, 10 À12 s) resolution [see Fig. S1 † for the experimental setup]. A 267 nm laser pulse initiated the photochemical process by exciting CH 3 CHO to the S 1 state. The probe laser, using a (2 + 1) REMPI scheme via the 3p z transition at 333 nm to probe the CH 3 radical or via the Bstate at $230 nm for either the low-j (j $ 0) or the high-j (j $ 43 at peak) of CO(v ¼ 0) (Fig. S2 †), was red at variable delays to track the formation of the targeted products. Both pump and probe lasers were derived from a kHz 100 fs (femtosecond, 10 À15 s) laser system, modied to ps in this study with a pulse duration of $1.7 ps and a $2 times transform-limited frequency bandwidth. The reactant CH 3 CHO was delivered to a vacuum chamber from a pulsed molecular beam running at 500 Hz. Two modes of data acquisition were adopted: the time-of-ight (TOF) mass spectrometry registered the temporal evolution of all correlated fragments and the time-sliced, velocity-mapped image 43-45 for a given product at a preset pump-probe delay informed the time-dependent, pair-correlated state distribution.
Partitioning the time-dependent P(u; Dt) distributions In order to decompose the entangled multicomponent contributions from the observed, time-dependent P(u; Dt) distributions in a least unbiased manner, we posited that each component will correspond to a single reaction pathway, which can be characterized by a unique rate of formation and/or the distinct product pair-correlated distribution. With this assumption, in conjunction with the TOF-normalized image results, we partitioned each time-dependent P(u; Dt) distribution at a given Dt into 20 or more segments in the velocity space and then examined the temporal evolution of each segment. We found that the proles in the fast and slow recoil velocity regions can indeed be respectively tted by a single exponential growth prole with unique time constants. For the intermediate or overlapped speed region, a double-or triple-exponential growth form was invoked, and their relative magnitudes were varied in the t under the constraint of a consistent growth rate for each individual component (or reaction pathway).

Theory
The stationary and intersection structures, which are relevant to the radical (CH 3 + HCO) and molecular (CH 4 + CO) channels that occur on the S 0 , T 1 , and S 1 surfaces of CH 3 CHO, were rstly optimized by using a three-state averaged complete active space self-consistent eld method (SA3-CASSCF), together with the 6-311G** basis set. The optimized structures were conrmed to be minimum-energy or rst-order saddle points by harmonic frequency calculations. The active space for the SA3-CASSCF calculation is composed of 14 electrons in 13 orbitals, referred to as SA3-CAS (14,13), which include all the valence orbitals of CH 3 CHO, except for the s and s* orbitals of the C-O bond. In order to account for dynamical electron correlation, the single-point energies were calculated with multi-state second-order perturbation theory on the basis of the SA3-CAS(14,13)/6-311G** optimized structures and calculated electronic wave functions, referred to as MS-SA3-CASPT2(14,13)/6-311G**. Further calculations were performed for the S 0 and T 1 states with the B3LYP functional and MP2 methods, along with the cc-pVTZ basis set. The B3LYP/cc-pVTZ and MP2/cc-pVTZ calculated results are well consistent with those from the MS-SA3-CASPT2(14,13)/6-311G** calculations, which justies the reliability of the present theoretical calculation. In comparison with the experimental ndings where available, the B3LYP/cc-pVTZ calculations provide a slightly better estimation for the S 0 and T 1 states. Therefore, the relative energies shown in Fig. S8 † come from the MS-SA3-CASPT2(14,13)/6-311G** calculation for the S 1 state and the B3LYP/cc-pVTZ calculation for the S 0 and T 1 states.

Data availability
The data that support the ndings of this study are available from the corresponding author upon request.

Conflicts of interest
The authors declare no competing nancial interests.