Mechanical Activation of Forbidden Photoreactivity in Oxa-di-π-methane Rearrangement

In this work, we demonstrate that the forbidden oxirane-type photoproduct (the cyclopropyl ketone photoproduct is the allowed one) of the oxa-di-π-methane photorearrangement can be obtained by mechanochemical control of the photoreactions. This control is achieved by the application of simple force pairs rationally chosen. By analyzing in detail the effect of the applied forces on this photoreaction, it comes to light that the mechanical action affects the diverse properties of the oxa-di-π-methane rearrangement, modifying all the steps of the reaction: (i) the initial ground-state conformers’ distribution becomes affected; (ii) the new conformational population makes the triplet excitation process to be changed, responding to the magnitude of the applied force; (iii) the stability of the different intermediates along the triplet pathway also becomes affected, changing the dynamical behavior of the system and the reaction kinetics; and (iv) the intersystem crossing also becomes strongly affected, making the forbidden oxirane-type photoproduct to decay more efficiently to the ground state. All these changes provide a complex scenario where a detailed study of the effect of applied forces is necessary in order to predict its overall effect on the photoreactivity.


Computational and Methodological Details: 1a. DFT Functional Benckmark
To validate the selected level of theory, we have performed a functional benchmark.
In particular, the B3LYP and M062X functionals have been considered. The results show similar energy barriers. For each sampling structure, the T 1 energy is computed, being possible to construct from this data a normalized gaussian distribution function for the triplet excitation energy for each conformer. Subsequently, by summing up the individual gaussian distribution functions of each isomer weighted by their equilibrium population at 300K, the final triplet excitation energy distribution is obtained for different forces (from 0nN to 2nN). Thus, the triplet energy distribution of the system at a given force in thermal equilibrium would be determined by Eq. S3.
where is the population of the conformer "i" at 300K, and is the normalized Gaussian function corresponding to the spectrum of this conformer: is the unitary vector pointing from "j" atom to "i" atom, being | | the magnitude of the applied force. The equations of motion are integrated with the new force field including the external forces.
In order to determine the initial sampling for the dynamics, a classical distribution (Boltzmann distribution) at 300K has been performed. The same approach has been employed when external forces are included. It has to be noted that the application of the external forces only changes the equilibrium structure, but does not actually affect the geometry distribution obtained, since the external forces do not alter the force constants (i.e. second derivatives of the energy).

S7
The equilibrium populations in the absence of external forces are indicated in Fig.   S2. These populations show that at 0nN force, the photochemistry is mainly governed by the isomer A. Nevertheless, the inclusion of an external force pair (as described in the main text) changes these equilibrium populations in a complex way.
To determine the population of each conformer for different external force magnitudes, we performed a sequence of restricted optimizations, lengthening the C1-C6 distance to each isomer, and determining the stationary points for each considered force (COGEF approximation).
The inclusion of the external force pair makes the topology of the potential energy surface to be affected, making some stationary points to be displaced in terms of coordinates, changing the relative energy among them and eventually even to disappear (i.e. being no longer minima on the potential energy surface). This behavior is at the origin of the changes in the population of each isomer as a function of the applied force. For the studied ODMP system, the potential energy surfaces become largely affect by the inclusion of external forces (see Fig. 4 in the main text).
Initially (F=0nN) all the 8 conformers are present with different stability, and therefore different equilibrium populations. Conformer A has the largest population (ca. 64%). For small force magnitude (0.5nN), most of the isomers do not correspond to any minimum on the potential energy surface as they are no longer stable, and therefore, their population is vanishing. In fact, only isomers "C", "D" and "E" are present. Finally, for larger force magnitudes (e.g. up to 1.5nN), only isomers "D" and "E" are stable (see Fig. S3). A minimum on the potential energy surface (associated with a stable isomer) disappears when the applied force exceeds a certain limit ( ).

S8
These results can be explained in terms of coupling between mechanical coordinates (i.e. the distance between methyl groups where the force pair is applied) and relevant torsions (i.e. 1 and 2 ). More specifically, the mechanical coordinate is strongly coupled with 2 , in such a way that applying stretching forces, makes the mechanical energy to largely change as the torsion approaches to zero, therefore, stabilizing conformers with 2 dihedrals close to this value. In this case, conformers D and E are the most favored (see Fig. S3) and therefore they tend to persist in the equilibrium as the forces grow up. S9

Spin densities in the triplet state after triplet energy excitation transfer.
The two triplet excited states of ODMP correspond to the local excitation in the C=C and C=O moieties. S2 In order to follow the type of triplet excitation (CC* or CO*), the spin density has been analysed (see Fig. S4).

Fig. S4. Representation of the spin density for BR1 localized on C=C moiety (left) and
C=O moiety (right).

Molecular dynamics simulation of triplet energy transfer between CC and CO moieties with inclusion of external forces.
In order to look for potential triplet energy migration, during molecular dynamics simulations the wavefunction has been determined on each point of the dynamics from the scratch, in order to correctly identify the lowest lying triplet state. In this way, when the two triplet states (corresponding to C=C and C=O triplet excitations) cross, the system remains in the lowest state, and therefore, a hop event is detected. Hoping between states is identified by analysing the spin density on the different moieties. To identify where the spin density is located to the greatest extent, the spin density of each chromophore (C=C and C=O respectively) is summed up. The difference between both spin densities (i.e. spin density of C=C minus that of C=O) provides an easy parameter to interpret, in such a way that for positive values the diradical character corresponds to the C-C bond, while for negative values the diradical can be assigned to the C-O bond. S10 Figure S5 shows the simulations made for the most abundant conformer at different applied strength forces.

Degeneracy between singlet and triplet states for BR3 and BR3B.
The singlet-triplet energy gap in BR3 and BR3B has been studied for different force magnitudes. For both BR3 and BR3B the stable conformation changes as indicated in Figure S6. In both cases, the energy degeneracy is basically fulfilled for all the force magnitudes considered.

Dynamics on T 1 at different forces from BR2 yielding BR3 and BR3B.
A series of 20 molecular dynamics trajectories has been simulated starting from BR2 (sampling obtained at 300K from a Boltzmann distribution and explicit inclusion of external forces as explained above) for each external force magnitude considered (i.e. 0nN, 1.5nN, 3.0nN and 4.2nN). The trajectories can be splited into two sets, the first one corresponding to q 1 (C 2 -C 3 distance) and the second one to q 2 (C 2 -C 5 distance).
The first path is related to C 2 -C 3 bond-breaking, and therefore with the formation of the classical photoproduct, while the second is related to C 2 -C 5 bond-breaking, leading to classically forbidden photoproducts. Large force magnitudes permit to identify the S12 formation of the classically forbidden product in the hundreds of femtosecond timescale (specifically 400fs).

Spin-orbit couplings in BR3 and BR3B
Determination of spin-orbit couplings (SOC) for different conformers as a function of the applied force magnitude (most stable conformers at a given force are displayed in Figure S8). The SOC is ca. 10 times larger in BR3B than in BR3, and therefore the corresponding intersystem crossing (ISC) rate constant is ca. 100 higher for BR3B than in BR3. SOC values have been determined with ORCA using B3LYP functional and the 6-31G(d) basis set. S6 Fig. S8. SOC values for BR3 and BR3B as a function of the applied force.

Kinetic model for predicting photoproducts formation.
Once the ODPM is excited to triplet state, the system evolves to yield BR2 independently on the applied forces. where is the Boltzmann's constant, ℎ the Planck's constant, and is the absolute temperature. The units of the ideal gas constant in the above expressions are = 1.989 · 10 −3 · −1 · −1 , therefore, the activation energies are expressed in kcal·mol -1 and F (i.e. the force magnitude) in nanonewtons (nN). The ratio of the intersystem rate constants 1 ( ) and 2 ( ) can be estimated by assuming that spin orbit coupling values for each reacting species (i.e. BR3 and BR3B respectively) is the S15 determining factor distinguishing between both rate constants. Since SOC is ca. 10 times for BR3B than for BR3 (see Figure S8), the ratio between ISC rate constants is: According to these values, the rate equations for the different species are the following (taking BR2 as the starting point): Numerically integrating this set of differential equations, the ratio of the photoproducts can be determined. This ratio for a wide range of force magnitudes and temperatures (ranging from 250K to 450K temperature and 0nN to 4nN force magnitudes) were performed in order to obtain the results summarized in Figure 9 of the main text. For each simulation, a total of 10 8 steps of integration were computed (time step of integration of 10fs), reaching the equilibrium in each case at the end of the