the lowest excited state of singlet oxygen , o2 ( g ) , has become 
 in the last few years 
 a precious chemical .
its versatility and physical and chemical characteristics 
 have opened the door to a wide range of application fields .
for instance , properties such as its stereoselectivity 
 are exploited for the synthesis of oxygen - containing fine organic 
 chemicals , whereas its extreme reactivity 
 and oxidation power are key to its use 
 in the decontamination of waters or in medical and environmental 
 photodynamic processes including the sterilization of blood or plasma 
 samples and cancer therapy . moreover ,
the particularly long radiative lifetime 
 of this excited state and its excess of energy relative to the ground 
 state ( gs ) , resonant to iodine atoms , allows its use in laser technology 
 for the production of excited iodine atoms via energy transfer .
this great heterogeneity of scenarios has 
 motivated the quest for 
 the search of new methods for its synthesis , specifically adapted 
 to the conditions and requirements of the different contexts where 
 this species needs to be produced .
attending to the nature of 
 the force that drives the o2 generation mechanism , 
 these protocols can be classified 
 into physical or chemical .
physical processes produce o2 from the direct excitation of molecular oxygen with 
 photons of different wavelengths ( i.e. , radiofrequency or ir ) .
chemical methods that can be mediated or not by light , however , 
 involve the participation of other reagents that chemically evolve 
 to o2 or that alternatively act as intermediates 
 for the storage of energy that is then transferred to molecular oxygen 
 in its gs , leading to the desired excited product .
decomposition 
 of polyoxygenated species such as ozonides , endoperoxides , 
 peroxyacetyl nitrate , or superoxide ions stand out as important chemical 
 sources of o2 in the absence of light .
the following reactions of hydrogen peroxide : i(ref ( 11))ii(ref ( 12))iii(ref ( 13))iv(haber - weiss reaction)or the self - reaction of alkylhydroperoxidesv(russell 
 reaction ) have been also reported as 
 efficient chemical methods for producing o2 in the dark .
interestingly , some of these reactions have been 
 as well proposed 
 to be responsible for the generation of o2 in 
 biological systems . in fact
, reactions ( i ) 
 and ( iv ) have been postulated as part of the 
 defense strategy occurring during phagocytosis , and lipid hydroperoxides generated along oxidative stress 
 processes connected to diseases such as atherosclerosis were found to decompose with the participation 
 of a metal cation catalyst or enzymes following reaction ( v ) , leading to o2 .
conventional o2 reactions initiated by light require the excitation 
 of a sensitizer , showing preferably an important yield for intersystem 
 crossing ( isc ) and characterized by long - lived triplets .
once the 
 triplet state of the photosensitizer has been populated , an energy - transfer 
 process occurs during the collision of this species with surrounding 
 gs molecular oxygen molecules that leads to the generation of o2 and the recovery of the sensitizer in its initial 
 gs ( type ii mechanism of photosensitization ) .
obviously , keeping the 
 concentration of environmental oxygen molecules constant and high 
 is a key factor for the success of these techniques but can , however , 
 pose problems for particular applications where the oxidant needs 
 to be generated in oxygen depleted conditions .
this is for instance the case of solid or vascular damaged 
 tumors where oxygen is not able to reach their interior . in these 
 cases ,
the efficacy of conventional photosensitizing reactions is 
 expected to be low and thus alternative photosensitive oxygen carriers , 
 able to release singlet oxygen upon their activation with the correct 
 wavelength , have been specifically designed for this purpose .
an example 
 of a prototype of oxygen carrier photosensitizer is the tetraantraporphyrazine 
 proposed by freyer and leupold , which 
 combines the virtues of tetrapyrrole standard photosensitizers ( i.e. , 
 absorption maxima in the red / nir region of the electromagnetic spectrum , 
 etc . ) with the possibility to eject o2 regardless 
 the concentration of molecular oxygen in the tissues , thanks to the 
 four anthraceneendoperoxide ( apo ) moieties with which the porphyrazine 
 core is substituted .
a model to delve in the understanding of how o2 alone , without considering other reactive oxygen species , 
 participates in cell damaging in photodynamic processes .
the photochemistry of endoperoxides has 
 also been investigated 
 in detail from both theoretical and experimental standpoints .
it has been demonstrated that o2 is not the only photoproduct that results from 
 the interaction of endoperoxides with uv photons ( see scheme 1 ) .
in addition to cycloreversion or the breaking 
 of the pair of c  o bonds that leads to the aromatic hydrocarbon 
 + o2 , competing o  o homolysis ( recall 
 scheme 1 ) is responsible of diverse photoproducts , 
 such as quinones , acetals , or diepoxides .
although the aromatic moiety influences greatly the absorption 
 spectrum of endoperoxides , a common feature to this class of compounds 
 is the nature of the electronic states leading to the two main photochemical 
 decomposition pathways .
while  * states are responsible 
 for cycloreversion ,  * states can lead to o  o 
 homolysis .
this work presents the first full - dimensional dynamical study 
 of 
 a model endoperoxide , the cyclohexadieneendoperoxide ( chdepo , c6h6o2 ) system , which shows an eight - fold 
 degeneracy region ( 8ci ) in the potential energy surface ( pes ) , where 
 four singlets and four triplets are degenerate .
this time - resolved 
 picture , complemented with key frames extracted from quantum chemistry 
 calculations , sheds light on the two competing mechanisms that account 
 for o  o homolysis and the cleavage of c  o bonds , leading 
 to o2 .
particular key questions that will be 
 addressed are ( i ) the mechanism by which o2 is produced from endoperoxides , ( ii ) the degree of competition between o2 generation and o  o homolysis , and ( iii ) 
 the role played by the triplets in the photochemistry of these systems .
stationary points and conical 
 intersections ( ci ) were optimized at the casscf level of theory , employing an ano - s basis set , contracted for h as [ 2s1p ] and for c , o as [ 3s2p1d ] . 
 unless otherwise specified , the active space used throughout the calculations 
 includes the complete  valence space ( two pairs of cc/*cc and oo/*oo ) and the  orbitals sitting on the oxygens co/*co ( two pairs ) and oo/*oo , necessary to properly account for o 
o 
 homolysis and cycloreversion ; this comprises altogether a total of 
 14 electrons distributed into 12 orbitals , ( see figure s1 ) .
stationary points in the first singlet potential 
 were optimized using a single root , whereas in the case of cis2/s1 and cis1/s0 ( see below ) state average casscf 
 calculations over three and two roots were used , respectively .
condon 
 region was ensured by computing minimum energy paths ( meps ) at the 
 same level of theory as specified above with a 6 - 31 g * basis set and using the minimum number of roots necessary , 
 i.e. , equal to the root numbering of the gradient followed .
final 
 energies were calculated as state average over four singlet and four 
 triplet states at ms - caspt2//casscf(14,12)/ano - rcc on the optimized geometries .
the contraction 
 scheme for the ano - rcc is h [ 3s2p ] and for c , o as [ 4s3p2d ] .
unless 
 otherwise specified , all the calculations were performed with the 
 76 version of the molcas program . for 
 completeness and consistency , since the basis set and active spaces 
 used herein differ from previous studies , we have recomputed particular 
 regions of the o  o homolysis mep already discussed in other 
 works , following the casscf(14,12)/ano - rcc protocol and calculated 
 from the scratch others , necessary to interpret the dynamical results .
orbit 
 couplings ( soc ) were simulated using tully s fewest switches 
 surface hopping scheme ( see supporting information for further details ) , as described in the sharc method .
nuclei 
 are treated classically and follow newton s equations , whereas 
 electrons are treated quantum mechanically . for the integration of 
 newton s equations
the evolution 
 of the probability amplitudes determining the contribution of the 
 different adiabatic states to the total wave function was integrated 
 using the fourth order runge  kutta algorithm with a time step 
 of 10 fs .
a decoherence correction was applied , 
 as recommended by granucci and persico with the parameters c = 1 and  = 0.1 hartree . 
 these parameters ( c and  ) rescale the amplitudes 
 of the electronic wavepacket after each nuclear time step , accounting 
 for the evolution of hypothetical trajectories running in other electronic 
 states along other gradients different to that of the current electronic 
 state .
previous studies on three - dimensional atom - molecule systems 
 have highlighted the importance of accounting for decoherence effects 
 but have also demonstrated that the precise value of these parameters 
 has a small influence in the dynamics when comparing with quantum 
 approaches .
however , other larger systems 
 as polyconjugated organic molecules have been demonstrated to be much 
 more sensitive to their variation . for the simulation of the uv spectrum , a set of 1000 initial uncorrelated 
 geometries and velocities was generated according to a wigner harmonic 
 distribution of the lowest vibrational state of the ground electronic 
 state , taking as input an harmonic frequency calculation at the casscf(14,12)/6 - 31 g * 
 level of theory .
casscf / ano - rcc and caspt2 
 spectra , considering the first four singlet states , were constructed 
 from a superposition of gaussians with the maximum height modified 
 according to the oscillator strength of the transitions and sitting 
 at the position of the vertical excitation energies computed at these 
 two levels of theory ( width of the gaussian = 0.1 ev ) . for comparison
, 
 the casscf and ms - caspt2 vertical absorption spectra of chdepo were 
 calculated following the same protocol specified above , using the 
 casscf/6 - 31 g * optimized geometry as a reference . from the initial 
 ensemble of 1000 geometries ,
a subset of 78 initial conditions , concentrated 
 in an energy window of 0.15 ev centered around the absorption maximum 
 at 4.65 ev , were selected , based on their oscillator strengths . for 
 these trajectories , energies and gradients for the first four singlets 
 and triplets
were computed on - the - fly using the casscf(14,12)/ano - rcc 
 protocol as implemented in molcas package .
after the hop events the kinetic energy was adjusted with the goal 
 to conserve the total energy of the system , scaling the atom velocities 
 along their current direction . finally , and unless otherwise specified 
 to avoid the artificial elongation of the c 
h bonds due to 
 the failure of the harmonic approximation , dynamics simulations were 
 performed substituting hydrogen atoms for deuterium , as suggested 
 elsewhere . the vertical casscf and caspt2 
 absorption spectra of chdepo
the casscf method predicts the brightest transitions (  * ) 
 above 8 ev , not shown in table 1 .
the low - energy 
 region of the casscf spectrum is in turn dominated by two weaker absorptions 
 at 5.0 and 6.0 ev , showing a mixed oo*cc/*oo*oo character .
in contrast 
 to the casscf spectrum , the most intense bands (  * ) are 
 concentrated in the region around 5.5 ev , whereas two transitions 
 governing the lowest energy region of the spectrum are calculated 
 below 5 ev at 3.9 and 4.7 ev , the second four times more intense than 
 the first one . similarly to casscf , caspt2 predicts a strong *oo*cc/*oo*oo mixing for the s1 and s2 electronic states .
subtle 
 differences with previous works are 
 attributed to small changes in the reference geometry and the 
 basis set .
figure 1 displays the position 
 of the casscf 
 and caspt2 vertical excitations ( black and red vertical lines below 
 8 and 6 ev , respectively ) , superimposed to the casscf and caspt2 spectra 
 based on the 1000 geometries generated to mimic the nuclear wavepacket 
 ( solid black and red spectra ) .
both spectra consist of an intense 
 band , showing a shoulder at higher energies , preceded by a weaker 
 absorption .
consistently with what is observed for the vertical spectrum , 
 we find that casscf overestimates by a factor of 0.25 the absorption 
 energies , taking caspt2 as a reference ; compare the position of the 
 least ( 4.8 vs 3.8 ev ) and most energetic bands ( 6.2 vs 4.7 ev ) at 
 casscf and caspt2 .
a decomposition analysis of these bands in terms 
 of the contributing states ( see figures s6 and 
 s7 ) reveals that the weakest band mainly results from the first 
 excited state in both spectra , whereas the s2 and s3 states are the responsible for the principal band , increasing 
 the s3 its contribution to the main band after including 
 dynamic correlation .
the pathological 
 overestimation of excitation energies by casscf at the fc region , 
 as compared with caspt2 calculations , could be detrimental for the 
 dynamics , leading to undesired photoproducts due to the excess of 
 energy accumulated by the starting ensemble of initial geometries . 
 however , taking into account that caspt2 analytical gradients are 
 not available in molcas and that the use of caspt2 numerical gradients 
 is computationally unaffordable for a study as the one suggested here , 
 we opted for a common solution previously adopted by other authors 
 that consists in the scaling of the energies and gradients ( see supporting information for more details ) .
black solid line 
 corresponds 
 to the spectrum calculated using sa4-casscf(14,12)/ano - rcc level of 
 theory , while red solid line represents the results corrected using 
 the ms - caspt2 method .
black dotted line outlines the casscf scaled 
 spectrum ( casscf ) . to quantify the impact of such approximation , we have scaled 
 by 
 a factor of 0.75 the casscf spectrum and compare it with the caspt2 
 one .
the almost complete superposition of the red solid line and the 
 dotted black line in figure 1 denotes a very 
 good agreement between the scaled casscf and the caspt2 results at 
 the franck 
a similar assessment of the impact 
 of the scaling was performed along the mep , taking as a reference 
 the gs equilibrium geometry .
guide the interpretation of the dynamical 
 results and to assess the quality of the method used in the on - the - fly 
 electronic structure calculations , we have investigated the mep connected 
 to both o  o homolysis and cycloreversion with the casscf method . 

since the reaction paths are independent of the nuclear masses , all 
 the static calculations were performed on hydrogenated chdepo .
more 
 reliable caspt2 calculations were performed at the stationary , critical , 
 and intermediate points along the mep where the comparison with caspt2 
 benchmark values was found to be critical for the dynamics .
interestingly , 
 casscf and caspt2 provide pes in qualitatively good agreement , at 
 least for the regions relevant to the photochemistry of these systems . 

the scaling of the casscf energies along the two 
 meps was found to reduce the slope of the profiles mimicking the caspt2 
 result but also to decrease the energy barriers . however , since casscf 
 provides similar reaction barriers as caspt2 and the system has only 
 to face these barriers at the gs pes , the scaling of the energies 
 was suppressed once the trajectory deactivates to the gs .
thus , overall , 
 we expect the scaling to have a small effect on the time scales of 
 the two photochemical processes studied but not to influence the mechanism 
 or product distributions .
figure 2 shows 
 the scheme proposed for o  o 
 homolysis mechanism based on the casscf mep calculated following the 
 gradient of the second root ( i.e. , first excited state ) . similarly 
 to previous calculations for the same and other endoperoxides , the mep from 
 the franck 
condon region leads barrierlessly to an energetically 
 accessible high degeneracy point of four singlet states ( 4ci ) , among 
 which the gs is included . structurally speaking
, this corresponds 
 to a point of the pes where the system presents an internuclear o 
o 
 distance at which the distribution of six electrons into the oo , *oo , oo and *oo orbitals leads to four different configurations energetically 
 indistinguishable . extrapolating from other previous dynamics 
 works studying nonadiabatic 
 dynamics across more than two state degeneracy points , deactivation through this particular funnel 

is expected to be achieved on very short time scales due to the occurrence 
 of large regions of seams of three and two degenerate states that 
 would significantly enhance the population transfer toward the gs .
global 
 static picture of the o  o homolysis mechanism of 
 chdepo based on mep calculations ( from this work and ref ( 21e ) ) .
final energies relative 
 to the gs minimum ( in ev ) were calculated at ms - caspt2//sa4-casscf(14,12)/ano - rcc 
 level of theory .
this high - order degeneracy point of the pes was previously 
 shown 
 to be connected with four different 
 diradical minima in the gs pes approximately of the same stability . 

starting from the most stable , minbryy , we have estimated 
 in 0.7 ev the energy barrier , tsh2 , that requires 
 the breaking of the two ch bonds sitting at the endoperoxide carbons , 
 leading to the formation of the benzoquinone and molecular h2 photoproducts .
these photoproducts have been identified as the most 
 stable for chdepo and the only ones observed from our dynamics simulations 
 following o  o homolysis mechanism , see below .
condon region following the gradient of the 
 brighter second excited state ( third root ) .
similarly to the mep from 
 the first excited state in figure 2 , this path 
 proceeds showing neither minima nor energy barriers toward a ci with 
 the gs , see figure 3 . on the way to the gs
, 
 however , a ci s2/s1 with the second root is 
 also found that might deviate population to the lower lying state . 

the s1/s0 conical intersection is expected to 
 bifurcate population between two minima in the ground pes , i.e. , the 
 franck  condon minimum ( minfc ) and minsw . along the mep
coordinate , we observe the stretching of one 
 of the 
 two c  o bonds that increases from a 1.472  value at the 
 fc geometry to 3.901  at the position of the minsw , corresponding to the intermediate along the stepwise cleavage of 
 the endoperoxide bridge .
logically , the rupture of one of the two 
 c  o bonds is concomitant to the progressive recovery of the 
 planarity of the hydrocarbon moiety , due to the redistribution of 
 electronic density among all the c of the ring .
o 
 bond still separates the population reaching minsw from 
 the final cycloreversion photoproducts , benzene + o2 ( recall scheme 1 and figure 3 ) . starting from this minimum
, the breaking of the 
 second c  o bond involves overcoming an energy barrier of 0.3 
 ev to reach a predissociation minimum , mino2 , where the hydrocarbon and oxygen are weakly interacting through 
 van der waals forces .
the 
 height of the barrier ( 0.3 ev ) , much lower than the initial franck 
condon 
 energy ( 4.72 ev ) , is not expected to prevent the formation of the 
 cycloreversion products along the dynamics . the probability 
 to populate the triplets along both o 
o 
 homolysis and cycloreversion pathways was evaluated by computing the 
 soc at selected points of the pes . especially relevant
are the values 
 of the couplings calculated at the position of the 4ci that amount 
 to 70 cm or at the region of the pes corresponding 
 to minimum mino2 , where the soc increases up 
 to 180 cm . global static picture 
 of the cycloreversion mechanism of chdepo 
 based on mep calculations .
final energies relative to the gs minimum 
 ( in ev ) were calculated at ms - caspt2//sa4-casscf(14,12)/ano - rcc level 
 of theory . other information on the mep calculations can be found 
 in the supporting information .
although very mixed at the fc region , from the 
 inspection of the 
 fate of the meps constructed along the gradient of the two lowest 
 lying excited states , it could be inferred that the character of the 
 two first excited states is respectively *oo*oo and *oo*cc , which is 
 also consistent with the oscillator strengths computed vertically . in summary
, the static picture described above reveals that the 
 two proposed deactivation mechanisms for chdepo , o  o homolysis 
 and cycloreversion , are likely to take place simultaneously upon uv 
 excitation . in both scenarios ,
the system would reach barrierlessly 
 a gs minimum , minbryy / minsw , from which a small 
 energy barrier separates the final photoproducts .
the following dynamics 
 simulations will help elucidating additional details on the deactivation 
 mechanisms as well as the final ratio of different photoproducts .
figure 4 shows the time 
 evolution of the four singlet ( s0 , s1 , s2 , and s3 ) and four 
 triplet states ( t1 , t2 , t3 , and t4 ) population of the 78 trajectories propagated , created using 
 deuterated chdepo , along 100 fs . although the propagation was done 
 in 16 spin 
orbit states , arising from the diagonalization of 
 the total hamiltonian , for simplicity the analysis will be done on 
 the spin - free states , where the electronic wave function was projected 
 back into the initial singlet and triplet states .
initially , the trajectories 
 are distributed according to a 65:35 ratio between the s2 and s3 electronic states .
this translates into a mixture 
 of *oo*oo and *oo*cc states , where the *oo*cc states are dominant ( 85% vs 15% ) .
interestingly , 30 
 fs only after photoexcitation , the population of the initially populated 
 states ( s2 and s3 ) rapidly decays in favor of 
 the s1 and s0 states .
this fast decay is perfectly 
 consistent with the steep meps computed for o  o homolysis and 
 cycloreversion mechanisms , which do not predict any barrier on the 
 way to the population of lower lying electronic states . at t
= 50 fs , the population of the four singlets 
 becomes equal and oscillates for 10 fs around an average value of 
 0.2 , which is compatible with a situation of the wavepacket exploring 
 the region of the pes corresponding to the 4ci . from 60 fs onward , 

the population of the s0 grows momentarily slightly larger 
 than for the other singlets to decrease again at the final time of 
 the propagation . at the final time of the simulations ,
the total population 
 is distributed as 60% in the singlet and 40% in the triplet manifold , 
 with all the electronic states within each manifold carrying approximately 
 the same population .
a particularly interesting observation 
 is that the triplet character 
 of the trajectories shows up at very early times of the simulation , 
 i.e. , below 20 fs , and that the maximum total expected population 
 of the triplets is achieved already at a t = 50 fs . 

this observation is in line with the conclusions drawn in other works 
 that support that isc in organic molecules can be ultrafast even if no heavy elements are present . in order to determine the final distribution of photoproducts 
 derived 
 from o
 o homolysis and cycloreversion processes , we have followed 
 the evolution of the distance between the centers of mass of the benzene 
 and o2 moieties , dbenz 
this distance is expected 
 to oscillate around small values for the trajectories evolving via 
 the o  o homolysis mechanism , whereas for cycloreversion this 
 value is expected to increase gradually as the two co bonds are cleaved .
time evolution 
 of the average quantum probability of singlet ( s0 in red , 
 s1 in green , s2 dark blue , 
 s3 in pink ) and triplet ( t1 in light blue , t2 in yellow , t3 in black , t4 in gray ) 
 states .
trajectories 
 leading to o  o homolysis , in blue the ones producing b+o2 and other products in red and green . percentages 
 for the different products are specified .
according to this criterion , we have classified all the trajectories 
 into four main groups .
2  , which corresponds to the distance between o2 and benzene centers of mass at the optimized casscf gs geometry . 

the first group of trajectories , denoted in black in figure 5 , is characterized by a progressive diminishing 
 of the dbenz 
oo distance until 
 reaching the value of zero ; this corresponds to a structure where 
 the two oxygens , although still bonded to their adjacent c atoms , 
 lie at the largest possible distance , coplanar with the rest of the 
 atoms of the ring .
after t = 80 fs , this distance 
 again increases until reaching a slightly smaller value than the initial 
 one .
these trajectories , which represent a 63% of the total , have 
 been ascribed to the o  o homolysis mechanism and perfectly 
 describe the oscillating bending movement that the system experiences 
 as the endoperoxide bond is broken and the 8ci degeneracy point is 
 reached .
these trajectories will end up in any of the four theoretically 
 predicted minima , characterized by a dbenz 
next group of trajectories , distinguished 
 in blue in figure 5 , are characterized by a 
 linear increase in the dbenz 
oo distance with time , reaching a maximum value of 6  
 at the final time of the simulation .
these trajectories , which amount 
 to 10% , correspond to cycloreversion , leading to benzene and o2 as final products .
another 20% of the 
 trajectories , in green in figure 5 , evolve 
 to a structure in which both the endoperoxide and 
 a single c  o bonds are dissociated .
a similar situation is 
 observed for the remaining 4% of the trajectories , highlighted in 
 red in figure 5 , which show the simultaneous 
 increase of both the o  o and the two c  o distances . 
 from the very high energy expected for these processes
, we could infer 
 that the employed ab initio methodology is not able to correctly describe 
 this region of the pes and significantly underestimates the energy 
 barrier for the dissociation of two or more bonds simultaneously . in principle , the shape of the potential energy profiles for cycloreversion 
 depicted in figure 3 shows energy barriers 
 flanking minsw , that would favor the evolution of the system 
 toward the formation of cycloreversion products , rather than reverting 
 to the initial gs or o  o homolysis products , and the structural 
 evolution of the red and green trajectories in figure 5 parallel to the blue group of trajectories would justify 
 directly imputing these later trajectories to cycloreversion ( in blue ) . 
 with this more logical assumption , a final total yield for cycloreversion 
 of ca .
30% is obtained , in line with the experimental observations 
 for the larger endoperoxide , apo .
an analysis of the multiplicity at the final point of the propagation 
 for different groups of trajectories reveals that no cycloreversion 
 products are formed in the triplet manifold ( blue trajectories in 
 figure 5 ) .
however , ca . 50% of the trajectories 
 leading to o  o homolysis end up in a triplet state .
this is 
 compatible with the existence of the 8ci along the rupture of the 
 endoperoxide bridge .
also interesting is the fact that none of the 
 trajectories revert to the starting point of the simulation , leading 
 to a 100% yield of photoproducts , also in line with the experiments 
 in refs ( 22b and 22c ) .
although 
 we have evidence that birradical minima are formed from 
 the o  o homolysis mechanism along the dynamics , quite unexpectedly , 
 none of these trajectories was found to lead to the final products , 
 i.e. , benzoquinone + d2 during the 100 fs propagation time . 

we attribute these results to the combination of dynamic effects and 
 the use of a reduced active space . in principle , the correct and simultaneous 
 description of both o  o homolysis and cycloreversion processes 
 would require that the active space includes a pair of co , *co , ch , and *ch orbitals . after including the remaining  orbitals 
 from the ring and  and  orbitals of the endoperoxide
, 
 such an active space would necessarily increase its size to 16 orbitals , 
 which is computationally prohibitive for a dynamical study , such as 
 the one proposed here .
however , since the inclusion of the ch and *ch orbitals is decisive for a correct 
 description of the tsh2 structure , lacking these 
 orbitals most likely overestimates the energy barrier connected to 
 the loss of h2 , hindering the evolution of the trajectories 
 toward the final photoproducts .
further dynamical effects might also 
 influence the output of this product in the dynamics .
the formation 
 of h2 involves on the one hand the concerted cleavage of 
 the two ch bonds and , on the other , the in phase bending vibration 
 of the two oc1c2 angles , where c1 and c2 stand for the c atoms holding the endoperoxide 
 bridge .
this bending mode would allow the symmetric puckering of the 
 hydrocarbon ring and the h atoms to encounter .
in other words , the 
 momenta of the oxygen and h atoms should point in opposite directions 
 to direct the approach between the two h atoms . this precise alignment 
 of the momenta of o and h atoms might need longer time scales than 
 the ones allowed here , partially explaining the absence of trajectories 
 leading to the final products bq + h2 .
in fact , an exemplary 
 trajectory propagated during additional 80 fs demonstrates the formation 
 of h2 ( see next section ) .
o 
 homolysis and cycloreversion mechanisms will be provided in the next analysis of representative trajectories section . in this section , 

several trajectories representative for the o  o homolysis and 
 cycloreversion photoreactions will be discussed in detail .
figures 6 and 7a , respectively , exemplify 
 the generation of o2 and h2 from 
 excited chdepo . for the description of cycloreversion ( figure 6 ) ,
we have chosen two trajectories with chdepo initially 
 photoexcited to the s3 ( panel a ) and the s2 ( panel 
 b ) . the trajectory in panel a , illustrates the generation of o2 in the excited state followed by gs relaxation , 
 whereas the trajectory in panel b , is representative for the other 
 trajectories where the dissociation of o2 takes 
 place in two sequential stages : the first in the excited state and 
 the second in the gs , in agreement with the static picture described 
 in figure 3 .
time evolution of two representative trajectories 
 of deuterated 
 chdepo leading to b + o2 products .
singlet 
 states are represented by solid lines , ( s0 in red , s1 in green , s2 in blue , and s3 in pink ) , 
 while triplet states are denoted with dotted lines in light blue t1 , yellow t2 , black t3 , and gray t4 .
the trajectory of figure 6a relaxes 
 to the 
 s2 very fast after 10 fs .
the cleavage of one of the two 
 c  o bonds induces the degeneracy of the s3 and s2 electronic states , promoting the backward hop to the upper 
 electronic state 10 fs later . during the following 40
fs the system 
 evolves in the s3 , where it experiences the dissociation 
 of the second c  o bond . in this region of the pes
, we observe 
 the degeneracy between the s3 and the second triplet state 
 ( t2 in yellow ) .
however , no isc is observed at this point 
 of the propagation . for t
= 60 fs , the system hops 
 back to the s2 state , where it remains for 15 fs more and 
 then finally decays to the s0 .
this last stage of the mechanism 
 structurally translates into the distancing of the o2 molecule 
 from the hydrocarbon moiety . the second trajectory in figure 6b relaxes 
 as well via internal conversion within the first 10 fs to the immediately 
 below excited state , s1 , where it spends the following 
 10 fs , until it reaches a new internal conversion funnel to the s0 .
the former two interstate crossings can be readily identified 
 with the cis2/s1 and cis1/s0 conical intersections optimized along 
 the static calculations , see figure 3 . at t
= 20 fs , the oxygen moiety is bonded to the hydrocarbon 
 through a single c
 o bond , while the other has been dissociated 
 on the way to the gs .
an increase of the potential energy for the 
 s0 is observed upon the dissociation of the remaining c  o 
 bond .
finally , an additional barrier needs to be overcome for the 
 dissociation of the weak van der waals complex , in agreement again 
 with the topology of the potential energy profiles depicted in figure 3 . from the careful analysis of the electronic 
 structure of the final 
 benzene and oxygen moieties and the degeneracy ( double ) of the singlet 
 electronic states where the system is at the final time of the propagation 
 for all the trajectories leading to o2
, we 
 infer that the hydrocarbon and o2 are generated in their 
 ground and g electronic state , respectively . 

also interesting is the fact that the electronic state reached at 
 the end of the propagation does not correspond to the most stable , 
 since there is at least another triplet of lower energy ( t1 ) . in spite of the significant soc computed along this mechanism 
 and the occurrence of degeneracy regions between singlets and triplets , 
 no isc was observed along none of the trajectories evolving according 
 to the cycloreversion mechanism .
we ascribe this negligible role of 
 the triplets in the cycloreversion mechanism to the topology of the 
 singlet and triplet potentials along the global cycloreversion reaction 
 coordinate .
in fact , the only region of the pes where isc is likely 
 to occur , i.e. , where close lying triplet states ( see figure 6b ) and considerable spin - orbit coupling ( 60 cm ) exist , is at the position of the minsw minimum , where the system could be trapped .
however , the orientation 
 of the momentum of the trajectories undergoing cycloreversion in the 
 direction of the access to the transition state tso2 prevents the confinement of the trajectories in this region 
 of the pes long enough time for the system to reach the triplet manifold .
the trajectory selected for describing o  o homolysis ( figure 7 ) was created using hydrogenated chdepo .
this trajectory 
 starts from the second excited state , s2 , and evolves very 
 rapidly ( in 20 fs ) following a very steep potential to the 8ci region , 
 consistently with the static results discussed above , recall figure 2 . during this time , the system starts dissociating 
 the endoperoxide bridge . once in the high degeneracy region , the system 
 spends several tens of fs visiting different electronic states , including 
 triplets .
the gs is reached for the first time only 25 fs after the 
 trajectory is initiated , supporting the findings of previous work , stating that high order degeneracy points constitute 
 extremely efficient deactivation funnels to the gs . from a structural 
 viewpoint , during its journey along the 8ci
, 
 the endoperoxide bond continues dissociating at the same time that 
 the two d atoms sitting at the carbons holding the endoperoxide bridge 
 move closer . since for none of the trajectories computed ,
the two 
 d atoms succeeded in forming molecular h2 , the opposite 
 movement , restoring the endoperoxide bridge while separating the d 
 atoms , was observed .
for some trajectories , this oscillatory movement 
 was repeatedly observed until the final time of the simulations . in 
 order to study the last stages of the o  o homolysis mechanism , 
 an additional trajectory based on initial conditions generated using 
 h instead of d
was propagated for a longer time . since the short ch 
 distances of the structure for t = 100
fs did not 
 allow introducing the ch and *ch orbitals , we decided to propagate further the trajectory with the 
 smaller active space ( 10,8 ) excluding ch and co  orbitals and 
 the 6 - 31 g basis set .
this figure also presents the optimized geometry 
 for the tsh2 , accounting for the concerted dissociation 
 of the two ch bonds leading to h2 , that is similar to the 
 geometries recorded at t = 140 and 150 fs . as concluded 
 from the sequence of frames of this trajectory , the generation of 
 h2 from the preceding biradicals requires ca .
100 more 
 fs either to evolve the active space so as to exchange other less 
 important valence orbitals for the ch and *ch orbitals or to put in phase the momenta of h / o atoms to 
 correctly describe h2 dissociation .
( a ) time evolution of 
 a representative trajectory leading to bq 
 + h2 products .
singlet states are represented as solid 
 lines , ( s0 in red , s1 in green , s2 in blue , and s3 in pink ) , while triplet states are denoted 
 with dotted lines in light blue t1 , yellow t2 , black t3 , and gray t4 .
the vertical 
 dotted line in black in panel a indicates the point when the trajectory 
 reaches the s0 and the energy scaling is switched off . 

( b ) snapshots for longer propagation times and the optimized geometry 
 of the tsh2 for comparison . note that for this 
 trajectory deuterium atoms where replaced by hydrogens ( see text ) .
this 
 work presents the first complete analysis , from both static 
 and dynamic viewpoints , of the photophysics and photochemistry of 
 an endoperoxide . to this aim
o homolysis , leading to benzoquinone + 
 h2 , and cycloreversion , generating benzene and o2 as photoproducts .
the static and dynamic results 
 are consistent in describing both 
 pathways consisting of two steps .
the first step is a barrierless 
 deactivation to gs intermediates : minsw ( cycloreversion , 
 figure 3 ) or one of the four biradical minima , 
 for instance minbryy , ( o  o homolysis , figure 2 ) .
the second step to generate the final photoproducts 
 takes place in the gs , where the system needs to overcome an energy 
 barrier that corresponds to the cleavage of the second c  o 
 bond , tso2 , in cycloreversion ( figure 3 ) or to the concerted rupture of both ch bonds simultaneously , 
 tsh2 , in o  o homolysis ( figure 2 ) . a number of important mechanistic conclusions 
 with implications in several biological and technological applications 
 can be drawn from our study:(1)the generation of o2 takes place 
 through a stepwise mechanism .
the breaking of 
 the first c  o bond takes place barrierlessly on the way to 
 the gs after going through several conical intersections .
the second 
 c  o is , however , cleaved once the system is in the gs after 
 overcoming an energy barrier.(2)in agreement with the experimental 
 observations , our dynamics simulations 
 predict that o2 is generated in its lower electronic 
 excited state ( g).(3)according to the present simulations , 
 the triplets do not play a significant role in the o2 generation mechanism .
no isc was registered along any of 
 the cycloreversion trajectories in contrast to o  o homolysis , 
 where an important population transfer to the triplet manifold was 
 observed .
the breaking of 
 the first c  o bond takes place barrierlessly on the way to 
 the gs after going through several conical intersections .
the second 
 c  o is , however , cleaved once the system is in the gs after 
 overcoming an energy barrier . in agreement with the experimental 
 observations ,
our dynamics simulations 
 predict that o2 is generated in its lower electronic 
 excited state ( g ) . according to the present simulations
, 
 the triplets do not play a significant role in the o2 generation mechanism .
no isc was registered along any of 
 the cycloreversion trajectories in contrast to o  o homolysis , 
 where an important population transfer to the triplet manifold was 
 observed . despite the lack of experimental 
 information on chdepo , it is possible 
 to establish some links between our simulations and the recent femtosecond 
 uv pump probe experiments investigating 
 the dual photochemistry of the larger endoperoxide apo .
interestingly , 
 and similar to the experiments , our 
 simulations predict the full transformation of the endoperoxide into 
 its photoproducts ; that is , no trajectories were found to revert to 
 the original gs of chdepo .
excitation of apo at 270 or 282 nm , which 
 populates the high - lying spectroscopic state s4 (  * ) , 
 leads to a yield for the cycloreversion reaction oscillating between 
 25% and 29% , in line with our theoretical results ( 30% ) , starting 
 from the *oo*cc electronic state .
also consistent with the experiment , the leading photodeactivation 
 process is o  o homolysis with a final yield of 65% .
however , 
 and in contrast with the experiment , we do not detect any cycloreversion trajectory evolving along the 
 triplet manifold in chdepo .
the role of the triplets seems to be only 
 important along the o  o homolysis deactivation pathway .
the rationalization of the mechanism for o2 generation and its competition with side pathways leading to photoproducts 
 is expected to inspire the development of new photosensitizers to 
 be used in the many different areas where the production of this oxidant 
 has a leading role .
 a synergistic approach 
 combining high - level multiconfigurational 
 static calculations and full - dimensional ab initio surface hopping 
 dynamics has been employed to gain insight into the photochemistry 
 of endoperoxides . 
 electronic excitation of endoperoxides triggers 
 two competing pathways , cycloreversion and o  o homolysis , that 
 result in the generation of singlet oxygen and oxygen diradical rearrangement 
 products . 
 our results reveal that cycloreversion or the rupture of 
 the two c  o bonds occurs via an asynchronous mechanism that 
 can lead to the population of a ground - state intermediate showing 
 a single c  o bond . 
 furthermore , singlet oxygen is directly 
 generated in its most stable excited electronic state 1g . 
 the triplet states do not intervene in this 
 mechanism , as opposed to the o  o homolysis where the exchange 
 of population between the singlet and triplet manifolds is remarkable . 
 in line with recent experiments performed on the larger anthracene-9,10-endoperoxide , 
 upon excitation to the spectroscopic  * electronic states , 
 the primary photoreactive pathway that governs deactivation of endoperoxides 
 is o  o homolysis with a quantum yield of 65% . 
Introduction
Results and Discussion
Conclusions