Stilbene and stiff-stilbene represent prototypical examples for carbon-carbon double bond photoisomerization (Fig. 2). The steric hindrance between the phenyl groups prevents cis-stilbene and cis-stiff-stilbene from being completely planar in the ground electronic state (S0), resulting in a reduction in symmetry from C2v to C2, with the C2 rotational axis perpendicular to the ethylene bond. The C2 axis represents the chirality axis for the molecule, and two helically twisted enantiomers arise for both cis-stilbene and cis-stiff-stilbene showing right-hand and left-hand axial chirality (P and M respectively, Fig. 2).
Although the photoisomerization of stilbene and stiff-stilbene has been the topic of numerous theoretical and experimental studies over the past century,10-15 to our knowledge the cis-trans photoisomerization dynamics has never been explored from the perspective of its rotational directionality. Here, we explore the rotational directionality in the non-adiabatic dynamics of the P and M enantiomers of cis-stilbene and cis-stiff-stilbene in the gas-phase using graphical processing unit (GPU)-accelerated multiconfigurational electronic structure theory in TeraChem16-18 coupled to ab initio multiple spawning (AIMS).19-21
To simulate the unidirectional photoisomerization in both cis-stilbene and cis-stiff-stilbene, AIMS trajectories for both P and M enantiomers are initiated from thirty initial conditions (positions and momenta) sampled from a 0K harmonic Wigner distribution around their respective ground state minimum. Fig. 3 shows the time-evolution of the central ethylenic twist angle (τ in Fig. 2) around the photoisomerizing carbon-carbon bond for the two enantiomers (P and M) of cis-stilbene and cis-stiff-stilbene on the first singlet excited state PES, S1. We observe that the photoisomerization dynamics for each isomer are unidirectional: the evolution of the P enantiomer shows an increasing value of the τ angle until the P S1/S0 conical intersection (CI) region is reached at 90o (CW rotation), whereas the excitation of the M isomer leads to ACW rotation of t to -90o at the M S1/S0 CI.
In addition to the photoisomerization around t, cis-stilbene may also relax back to the ground state via photocyclization leading to 4a,4b-dihydrophenanthrene (DHP). As a consequence of the unidirectional dynamics, an enantioselective photocyclization is observed. Indeed, the CW rotation in (P)-cis-stilbene leads to (4aS,4bS)-4a,4b-dihydrophenanthrene (S,S-DHP), while (4aR,4bR)-4a,4b-dihydrophenanthrene (R,R-DHP) is formed from the ACW motion in (M)-cis-stilbene.
No P-M helical inversion is observed on S1 for both cis-stilbene and cis-stiff-stilbene indicating the occurrence of excited state axial chirality that leads to unidirectional photoisomerization. Hence, in spite of being formally achiral at thermal equilibrium on S0 due to the fast helical inversion process (inversion barriers are 1.6 and 4.9 kcal/mol for stilbene and stiff-stilbene, respectively), cis-stilbene and cis-stiff-stilbene behave as chiral molecules during their short life on S1. This behavior can be easily rationalized by inspecting the frontier molecular orbitals involved in the electronic excitation (Fig. S1). Indeed, the S0 ® S1 transition corresponds to a HOMO ® LUMO p-p* one electron excitation characterized by a transfer of electron density from the central ethylenic bond to the p orbitals of the adjacent carbon pairs. The new electronic arrangement reached on S1 lowers the barrier for the rotation around the central carbon-carbon double bond and hinders the rotation of the phenyl groups necessary for the P-M inversion. As a result, unidirectional photoisomerization is observed.
Nevertheless, in order to achieve photo-induced net unidirectional motion, the preferential excitation of a specific enantiomer is required. Photoexcitation with nonpolarized or linearly polarized light is unsuitable for this purpose because it would lead to a racemate on the excited state. In contrast, the differential absorption of circularly polarized light (CPL) results in bands with opposite sign in the electronic circular dichroism (ECD) spectrum for both enantiomers, meaning that an excess of one enantiomer is excited over the other. In Fig. S2, we present the simulated relative absorption spectra for right circularly polarized light (r-CPL) of the (M)- and (P)-conformers of cis-stilbene. We use the quantum mechanically determined optical anisotropy Kuhn factor, g, (ratio of the dipole strength and the rotatory strength)22 for the S0 ® S1 excitation to evaluate the enantiomeric excess of excited chiral species following r-CPL absorption (a more detailed discussion is reported in the SI). In the optical window 230-350 nm, the M enantiomer preferentially absorbs the r-CPL, while the l-CPL is preferentially absorbed by the P conformer. As a consequence, the excitation of the ground state sample of cis-stilbene with r-CPL will preferentially excite the left-handed helical twisted M-enantiomer, whereas the P enantiomer can be preferentially excited with l-CPL.
To supplement our findings for the unidirectional photoisomerization of cis-stilbene, we simulated a rather straightforward experiment based on the enantioselective photocyclization leading to S,S-DHP and R,R-DHP. Indeed, the excitation of cis-stilbene (existing as a racemic mixture of the P and M enantiomers at thermal equilibrium) with non-polarized UV light will lead to a racemic mixture of the chiral DHP photoproduct, whereas an excess of one enantiomer over the other is expected with the CPL excitation. Due to the fact that DHP can absorb CPL in the same optical window as cis-stilbene, the enantiomeric excess (ee) of DHP reached at the photo-stationary state can be predicted considering the kinetic model reported in Fig. 4a. In agreement with the results of the AIMS simulations, we assume that the cis-trans isomerization and the DHP cyclization happen on the excited state whereas the helical inversion process takes place only on S0. At the photo-stationary state, the enantiomeric excess of DHP can be expressed as follows (the complete derivation is discussed in the SI):
![](data:image/png;base64,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)
where gstil and gDHP are the g factors of cis-stilbene and DHP, respectively (Fig. S2), while kcis®trans and krac represent the kinetic constants of the cis-trans photoisomerization reaction, and the ground state helical inversion process, respectively. The above expression demonstrates how the ee depends on the asymmetry of the electronic excitations (via the g factors), the cis-trans photoisomerization and the ground state helical inversion processes.
For a given set of g factors, three limiting cases arise: the cis-trans photoisomerization is faster than the ground state helical inversion (kcis®trans >> krac), S0 racemization is faster than the cis-trans isomerization (krac >> kcis®trans) or these processes take place on comparable time scale (kcis®trans ~ krac). The wavelength-dependent enantiomeric excess of DHP is reported for the three cases in Fig. 4b. According to our simulation, the maximum enantiomeric excess reached around 250 nm is ~0.23% when the photoisomerization is faster than the helical inversion process (which is the case for cis-stilbene due to its sub-picosecond cis-trans photoisomerization10-15), whereas it is ~0.25% in the other two limit cases. The predicted ee is comparable with what Butchardt and co-workers reported for the asymmetric synthesis of chiral helicenes with CPL.23-25 In these early experiments, the different CPL absorption of the enantiomeric conformations of the diarylethylene substrate led to an optical yield of about 0.2%.24,25 More recently, Feringa and co-workers were able to induce asymmetric photoisomerization in sterically overcrowded alkenes where they reached an ee of 0.07%26-28 by enantioselectively exciting a racemic mixture of thermally stable enantiomers (free enthalpy of racemization larger than 20 kcal/mol) with CPL leading to unidirectional photo-isomerization.
Our kinetic model shows that the expected enantiomeric excess is strongly dependent on the g factors. Considering that the anisotropy factors are typically quite small (less than 0.01) a low ee should be expected.23 Future improvements may include the excitation to states with larger g factors as well as shifting of the photo-stationary equilibrium, e.g., by selective removal of one of the enantiomeric photoproducts. Indeed, the optimal condition to maximize the ee is reached when one enantiomer is preferentially formed and the other destroyed by the same monochromatic CPL irradiation (corresponding to g factors with opposite sign, see Fig. S3 for a generic A ® B photoreaction). Since the anisotropy factors are wavelength-dependent, the aim is to find the optical window that maximizes the excitation asymmetry.
In conclusion, our non-adiabatic simulations of stilbene and stiff-stilbene suggest that electronic excitation can change the inherent chiral behavior of molecules. We coin the term electronically prochiral to describe molecules whose enantiomer interconversion can be hindered on the excited electronic state, opening up the possibility for asymmetric photochemistry from an effectively nonchiral starting point. Exploiting such asymmetric photochemistry and its connection with unidirectional motion will represent the next step toward designing new generations of responsive smart materials.