Tuning Stilbene Photochemistry by Fluorination - ACS Publications

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Cite This: J. Am. Chem. Soc. 2017, 139, 15265-15274

Tuning Stilbene Photochemistry by Fluorination: State Reordering Leads to Sudden Polarization near the Franck−Condon Region Ilya N. Ioffe,*,† Martin Quick,‡ Michael T. Quick,‡ Alexander L. Dobryakov,‡ Celin Richter,‡ Alex A. Granovsky,§ Falko Berndt,‡ Rainer Mahrwald,‡ Nikolaus P. Ernsting,‡ and Sergey A. Kovalenko*,‡ †

Department of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia Department of Chemistry, Humboldt-Universität zu Berlin, Brook-Taylor-Str. 2, D-12489 Berlin, Germany § Firefly Project, Moscow 117593, Russia ‡

S Supporting Information *

ABSTRACT: Spontaneous polarization of a nonpolar molecule upon photoexcitation (the sudden polarization effect) earlier discussed for 90°-twisted alkenes is observed and calculated for planar ring-fluorinated stilbenes, trans2,3,5,6,2′,3′,5′,6′-octofluorostilbene (tF2356) and trans2,3,4,5,6,2′,3′,4′,5′,6′-decafluorostilbene (tF23456). Due to the fluorination, Franck−Condon states SFC and SFC are 1 2 dominated by the quasi-degenerate HOMO−1 → LUMO and HOMO−2 → LUMO excitations, while their interaction gives rise to a symmetry-broken zwitterionic S1 state. After optical excitation of tF2356, one observes an ultrafast (∼0.06 ps) evolution that reflects relaxation from initial nonpolar SFC 3 to long-lived (1.3 ns in n-hexane and 3.4 ns in acetonitrile) polar S1. The polarity of S1 is evidenced by a solvatochromic shift of its fluorescence band. The experimental results provide a sensitive test for quantum-chemical calculations. In particular, our calculations agree with the experiment, and raise concerns about the applicability of the common TDDFT approach to relatively simple stilbenic systems.

1. INTRODUCTION The sudden polarization of alkenes in the 90°-twisted molecular geometry, a manifestation of the pseudo-Jahn− Teller effect,1 was theoretically predicted2 in 1970s and thoroughly discussed3−8 because of its crucial role in photochemical reactions.7 An experimental verification of the effect came decades later, with the progress in ultrafast spectroscopy and owing to suitable probes, such as stilbene.9−13 The photochemistry of stilbene is now well understood.14−32 Upon optical excitation to the Franck−Condon SFC 1 state, the isomerization proceeds on the S1 surface, by torsion about the ethylenic bond toward the perpendicular conformation P, where a conical intersection S1/S0 gives rise to cis and trans products. P is sometimes called the phantom state14,15 as it long escaped experimental characterization. Only recently has it been detected16 and spectroscopically identified.17−20 Similarly to alkenes, the P state in stilbenes is a symmetrybroken zwitterionic product of sudden polarization.21,26,27 Upon perpendicular twisting, the ethylenic bond breaks, and (assuming C2 symmetry) the HOMO and LUMO become quasi-degenerate A- and B-symmetric combinations of the decoupled halves. This gives rise to quasi-degeneracy of the Asymmetric S0 and the B-symmetric S1 states, also expressible as symmetric and antisymmetric combinations of two ionic © 2017 American Chemical Society

configurations. With the symmetry breaking, the degeneracy is removed, and the molecule becomes zwitterionic. Experimentally, the polar character of P can be derived from the isomerization kinetics. Thus, in polar acetonitrile the isomerization of trans-stilbene takes 40 ps, twice faster than in nonpolar n-hexane, 84 ps.17 As the SFC 1 state is nonpolar, this indicates barrier lowering in acetonitrile, due to the stabilization of the polar P. Hence, the sudden polarization of the perpendicular state in stilbene has been qualitatively justified. Taking this as a starting point, one may ask if similar polarization effects may be observable in the Franck−Condon region, for planar untwisted molecules. Obviously, such effects would require the S1 state (the only long-lived excited singlet state according to Kasha’s rule) to efficiently interact with closely located singlet states of different symmetry. In parent stilbene that is clearly not the case. The available MCSCF, MSPT2 and TDDFT data22−29 suggest that photoexcitation should result in the states with appreciable contribution of the HOMO1LUMO1 electronic configuration, since the lowerenergy excitations other than the HOMO → LUMO one are of negligible oscillator strength. Initially, the HOMO1LUMO1 Received: September 8, 2017 Published: October 6, 2017 15265

DOI: 10.1021/jacs.7b09611 J. Am. Chem. Soc. 2017, 139, 15265−15274

Article

Journal of the American Chemical Society

Figure 1. Transient absorption (TA) spectra ΔA(λ,t) of t-stilbene and 5 fluoro-stilbenes in n-hexane upon excitation at about 320 nm. Here the HOMO → LUMO excitation corresponds to the S0 → SFC 1 transition as in most stilbene derivatives. Bleach and stimulated emission (SE) enter the signal with negative sign, while excited-state absorption (ESA) is positive. Vertical arrows indicate the signal evolution. Pump−probe delays t in ps are shown as inserts. The intramolecular twist SFC 1 → P, from planar to the perpendicular conformation P, proceeds on the S1 surface. The twist results in the concomitant decay of SE, ESA and bleach bands. The residual bleach at late time originates from cis and trans products. The P → S0 step is ultrafast, ∼ 0.3 ps,17 and therefore not directly visible. Note that the ESA decays are very well fitted by single exponentials (denoted as “1 exp” in the graphs; see also Table 1 and Figure S1).

correlation functionals within the TDDFT approach do not pass that test.

electronic configuration may be distributed between two closely FC FC 22,27 located singlet states, SFC but rapid 1 and either S2 or S3 , relaxation of stretching coordinates invariably gather it in the symmetric nonpolar S1, just as one would normally presume.27 Experimental data perfectly corroborate the theoretical suggestions, revealing no transient spectral signatures of any intermediate states or processes between the initial excitation and subsequent emergence of the P state, or recovery of the ground state.17−20 However, in the present paper, we demonstrate that derivatization of stilbene can introduce some surprising changes. Deep symmetric fluorination results in a HOMO → LUMO transition shifted above the quasi-degenerate pair of HOMO−1 → LUMO and HOMO−2 → LUMO excitations that belong to different symmetry representations. Interaction of the two electronic configurations constitutes an example of sudden polarization near the Franck−Condon absorption region, giving rise to a symmetry-broken zwitterionic S1 state. This effect is expressed most pronouncedly in trans2,3,5,6,2′,3′,5′,6′-octofluorostilbene (tF2356), and is also observed in trans-2,3,4,5,6,2′,3′,4′,5′,6′-decafluorostilbene (tF23456). In addition, the sudden polarization in fluorostilbenes is a test for quantum-chemical computations of their excited states, and we find that many popular exchange-

2. EXPERIMENTAL RESULTS We begin with the common case, when optical excitation S0 → SFC 1 directly populates the S1 potential energy surface. This is valid for parent stilbene and for almost all of the derivatives studied so far. Figure 1 illustrates the case by transient absorption (TA) spectra33−35 of trans-stilbene (t-stilbene) and of 5 fluorostilbenes in n-hexane, upon optical excitation at 320 nm. The spectra reveal three bands: negative bleach in the range 280−320 nm, negative stimulated emission (SE) between 320 and 390 nm, and positive excited-state absorption (ESA) peaked at 550−590 nm. The signal evolution is quite simple: the bands decay concomitantly, reflecting the twist SFC 1 → P from planar to perpendicular conformation. The final P → S0 isomerization step is not visible as the P lifetime is in the subpicosecond range,17 much faster than its buildup. The residual bleach at late time corresponds to cis and trans groundstate products. Note that the ESA decays can be accurately fitted by single exponentials (see Figure S1 in Supporting Information). The fitted times τS1→P in n-hexane (he), perfluoro-n-hexane (pfh) and acetonitrile (ac) are collected in Table 1. 15266


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the signal decays slowly, with 1.3 ns in n-hexane and 3.4 ns in acetonitrile (middle), with an incomplete bleach recovery indicating cis and trans photoisomerization products. We shall see from the calculation section that the nanosecond decay is associated with the S1 → P twist from the zwitterionic S1 state, while the earlier ultrafast evolution corresponds to the SFC 3 → S1 relaxation. The long-living S1 state formed after the initial ultrafast decay reveals intense quasistationary fluorescence, as shown at the bottom of Figure 2, with fluorescence quantum yield Y = 0.053 in n-hexane and 0.095 in acetonitrile. This quasistationary fluorescence is not directly recognized in the late TA spectra of Figure 2 because it is overlapped with more intense ESA. The yields allow one to calculate the radiative lifetimes τrad = 24 ns in n-hexane and 36 ns in acetonitrile, the difference between the two being probably due experimental inaccuracy. Taking the average value, τrad = 30 ns, one can estimate the corresponding S1 → S0 oscillator strength f S1 = 0.026, that is 20 times lower than the oscillator strength of the HOMO → LUMO transition for t-stilbene.36 Furthermore, the quasistationary SE band (at the bottom of Figure 2) is solvatochromic; it shifts by 1700 cm−1 when going from n-hexane to acetonitrile. Hence the state is a singlet and located on the S1 potential energy surface. But unlike in other

Table 1. Isomerization and Relaxation Time Constants at 21 °C τS1→P (ps)a optical excitation t-stilbene tF4 tF35 tF345 tF26 tF246 tF2356 tF23456

S0 → S1

S0 → S3

τS3→S1 (ps)a

heb

acb

pfhb

he

ac

pfh

85 174 58 50 17 9 1300 13

39 88 24 23.5 6.0 5.5 3400 15

51 147 37 38 12 3.9 2270 14

− − − − − − 0.06 0.16

− − − − − − 0.03 0.15

− − − − − − 0.05 0.03

Derived from fits of Figure S1 in Supporting Information. bn-hexane (he), perfluoro-n-hexane (pfh), acetonitrile (ac). a

Figure 2 shows TA spectra of heavily fluorinated stilbenes, tF2356 and tF2345 in n-hexane. In this case the excited-state evolution is very different from that shown in Figure 1. Consider first tF2356 (at left). The earliest spectrum at t = 0.06 ps (in black, top) reveals an SE band around 340 nm and an ESA band at 540 nm. The both decay ultrafast, within 0.06 ps, and simultaneously a new band at 395 nm develops. Afterward

Figure 2. TA spectra of tF2356 and tF23456 upon optical excitation at 310 nm. Contrary to the common case (Figure 1), here S1 is not based on the initially excited HOMO → LUMO transition. In tF2356 (at left), the early spectrum at t = 0.06 ps (in black, top left) is associated with the initial nonpolar state (SFC 3 ) which reveals an SE band about 340 nm and an ESA band at 540 nm. The bands decay within 0.06 ps, reflecting sudden polarization that gives zwitterionic S1 with a new ESA peak at 395 nm. The subsequent S1 → P twist is much slower, with 1.3 ns in n-hexane and 3.4 ps in acetonitrile. The long lifetime is due to deep stabilization of S1. Absorption and quasistationary SE spectra are displayed at the bottom, with negative sign as in the TA spectra. The SE spectra, λ4F(λ), are calculated from the measured fluorescence distribution F(λ). Dashed lines are for −1 between n-hexane (he) and acetonitrile comparison of the late SE (from S1) with the early SE (from SFC 3 ). The solvatochromic SE shift, 1700 cm (ac), proves the polarity of S1. In tF23456 (at right), one also observes an ultrafast decay (0.3 ps), and a solvatochromic shift of SE. The measured fluorescence yields are for tF2356 Yhe = 0.053, Yac = 0.095, and for tF23456 Yhe = 0.005, Yac = 0.004. 15267


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Figure 3. TA spectra and kinetics of cF2356 in n-hexane upon optical excitation at 285 nm. The ESA peak at 570 nm (top left) is ascribed to nonpolar HOMO → LUMO excitation. During t = 0.1−1 ps the signal in the red decays, while the perpendicular state P rises at about 335 nm. The subsequent P → S0 relaxation with 3 ps is well resolved (unlike for trans-F2356 in Figure 2). The sudden polarization is not directly resolved, but its 34,20 They decay involvement is suggested by the kinetics (at right). The kinetics are given by band integrals I(λ1,λ2) ∼ ∫ λ2 λ1ΔA(t,λ) dλ/λ. biexponentially, a1 exp(−t/τ1) + a2 exp(−t/τ2) where (a1 + a2) = 1. In the graph, the time constants are in ps and a1 is in percentages. Note that I(540,600) reflects the S1 → P relaxation, and it decays with 1.1 ps in acetonitrile, slower than in n-hexane (0.4 ps). This may be due to extrastabilization of the zwitterionic S1 in polar acetonitrile (similar as observed for tF2356 in Figure 2). Next, I(320,370) reflects the P → S0 relaxation, and decays with 3 ps in n-hexane, slower than in acetonitrile (1 ps), in agreement with the polar character of the P state (see Figure 7).

position and evolution is very similar to that observed with parent cis-stilbene and other stilbenes. In the case of cF2356, the P band decays with 3 ps resulting in trans and cis isomers in the ground state (bottom left). Thus, the P → S0 relaxation is well resolved in the cis-to-trans path, unlike for tF2356 in the opposite trans-to-cis path in Figure 2. The sudden polarization effects are not directly seen in the TA spectra of Figure 3. Yet decay kinetics (at right) indicate the involvement of a zwitterionic S1 state. Indeed, the band integral I(540,600), related to the S1 → P relaxation, decays with 1.1 ps in acetonitrile, slower than in n-hexane (0.4 ps). Such behavior agrees with the stabilization of the zwitterionic S1 in polar acetonitrile, similar to tF2356. The other band integral, I(320,370), reflects the P → S0 relaxation; it decays with 3 ps in n-hexane, slower than in acetonitrile (1 ps), that is consistent with the polar character of the P state.

stilbenes, it is polar (zwitterionic) and not associated with the HOMO → LUMO excitation. Furthermore, this zwitterionic S1 is obviously planar or nearly planar, i.e., its geometry is similar to that in the Franck−Condon region, since any considerable twisting would shift the SE band far more to the red due to a steep rise of the S0 energy. The dipole moment μ1 in the S1 state of the probe molecule can be estimated35 from the solvatochromic SE shift, Δν = 1700 cm−1, using the relation hcΔν = gμ21/r3. Here g = [2(ε − 1)/(2ε + 1) − 2(n2 − 1)/(2n2 + 1)] is solvent polarity parameter calculated via dielectric constant ε and refractive index n. With g = 0.6 for acetonitrile and g = 0 for n-hexane, and with r = 4 Å for the probe radius, this gives μ1 ≈ 6 D. Switching to tF23456 (Figure 2 at right) one notices similar (but less pronounced) features as observed for tF2356. A smaller solvatochromic shift of the SE band suggests that the relaxed S1 state is less polar than in tF2356, or that there is some equilibrium between the polar and nonpolar domains in S1 which contribute jointly to the fluorescence band. The latter interpretation is supported by that the fluorescence quantum yield, Y = 0.005 in n-hexane and 0.004 in acetonitrile, is only 1 order of magnitude lower than in tF2356 while the lifetime of S1 is 2 orders of magnitude shorter. In addition, the initial ESA bands are preserved during the evolution, in contrast to drastic spectral changes observed for tF2356. The SFC 3 → S1 and S1 → P relaxation times of tF2356 and tF23456 are collected in Table 1. We have also measured the cis isomer, cF2356. Figure 3 shows its TA spectra and kinetics in n-hexane. At early delays (t = 0.1 ps, top left) the signal in the red is peaked at 570 nm. It decays with 0.3 ps and a new band about 335 nm develops. This band is ascribed to the perpendicular P state as its spectral

3. QUANTUM-CHEMICAL CALCULATIONS AND DISCUSSION Quantum chemical calculations are performed using mainly Firefly QC package, version 8.237 partially based on the GAMESS (US) source code.38 Also, Gaussian0939 is used for additional calculations with range-separated and meta-GGA exchange-correlation functionals. Excited state potential energy surfaces are studied at the TDDFT level with frozen chemical core using various exchange-correlation functionals and the Def2-TZVPP basis set. Higher level single-point calculations are carried out with XMCQDPT2 multistate multireference perturbation theory at second order,40 also with frozen chemical core, using the geometries optimized with TDO3LYP (with VWN functional 5 for local correlation; the unusual choice of the exchange-correlation functional is 15268


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exchange-correlation functionals and as semicanonical CASSCF orbitals. In Table 2 we summarize the PBE0 orbital energies for symmetric ring fluorinated stilbenes computed at the S0

explained below). The XMCQDPT2/cc-pVTZ treatment is based on CASSCF(14,14), i.e., complete π-orbital active space, with density averaging over the six lowest singlet roots, in order to properly cover the relevant excited states. 27 The XMCQDPT2 space included 12 singlet states, and the intruder state avoidance (ISA) shift was set to 0.02 au. Fluorination Effects on the Frontier Orbitals of Stilbene and Symmetry Breaking. One starts with an assumption that candidates for the zwitterionic S1 state near the Franck−Condon region should be dominated by singleelectron excitations. It is instructive to consider the trends in frontier orbital energies over the whole series of symmetrically fluorinated trans-stilbenes. We find that in tF2356 and tF23456 the LUMO+1 and higher unoccupied orbitals are shifted farther above the LUMO than in unsubstituted stilbene. On the contrary, the gap between the HOMO−1 and the HOMO shrinks, indicative of lower relative energy of excitation from the orbitals below the HOMO. Therefore, we limit here our consideration to the HOMO−2 and HOMO−1 that are found to form a nearly degenerate pair, HOMO, and LUMO. Their shapes for tF2356 are presented in Figure 4; in addition to symmetrized or antisymmetrized orbitals that exist at the planar C2h or nearly planar C2-symmetric geometries, we also show nonsymmetric orbitals that can form upon symmetry breaking within the HOMO−2/HOMO−1 pair, as discussed later. The present orbitals are largely independent of the fluorination pattern, and are consistently reproduced with different

Table 2. PBE0/Def2-TZVPP Energies of Selected Frontier Orbitals in Fluorinated trans-Stilbenes at the C2h-Symmetric Ground State Geometry orbital energy, eV

compound F0a F2 F3 F4b F23 F24 F25 F26 F34 F35 F234 F235 F236 F245 F246 F345 F2345 F2346 F2356 F23456

HOMO−2 HOMO−1 HOMO −7.38 −7.38 −7.42 −7.77 −7.40 −7.75 −7.46 −7.35 −7.76 −7.52 −7.73 −7.50 −7.38 −7.79 −7.71 −7.83 −7.81 −7.71 −7.43 −7.74

−7.37 −7.34 −7.38 −7.76 −7.40 −7.68 −7.33 −7.35 −7.65 −7.51 −7.73 −7.47 −7.36 −7.60 −7.71 −7.83 −7.78 −7.67 −7.43 −7.74

−6.03 −6.20 −6.35 −6.07 −6.51 −6.24 −6.47 −6.35 −6.35 −6.67 −6.53 −6.79 −6.64 −6.49 −6.40 −6.64 −6.78 −6.66 −6.93 −6.93

LUMO

E(HOMO) − E(HOMO−1), eV

−1.60 −1.85 −1.94 −1.66 −2.12 −1.90 −2.20 −1.89 −1.98 −2.23 −2.16 −2.44 −2.19 −2.23 −1.92 −2.26 −2.47 −2.20 −2.48 −2.49

1.34 1.14 1.03 1.69 0.89 1.44 0.86 1.00 1.30 0.84 1.20 0.68 0.72 1.11 1.31 1.19 1.00 1.01 0.50 0.81

a

Unsubstituted stilbene. bHOMO−1 in F4 rather correlates with the HOMO−3 in the rest of the molecules; listed are the HOMO−3 and HOMO−2 of F4.

equilibrium geometry (given with minor exceptions as C2hsymmetric by most of the common exchange-correlation functionals). The fluorination-induced trends in the orbital energies are also reproduced with other functionals and are verifiable via the corresponding TDDFT excitation energies. The tendencies in Table 2 can be summarized as follows. Any symmetric fluorination pattern stabilizes the HOMO, except fluorination at site 4, and contributions from multiple fluorination sites are approximately additive. In contrast, the quasi-degenerate HOMO−1 and HOMO−2 are stabilized by fluorination at position 4, and remain mainly unaffected by fluorination at the other sites. This can be rationalized as interplay of two effects: (a) the general stabilizing effect of any fluorination pattern due to the electron-withdrawing properties of fluorine, and (b) the site-specific destabilizing repulsion between the respective π-orbitals and the out-of-plane lone pairs of the fluorine atoms. Indeed, one can see from Figure 4 and Table 2 that the extent of orbital stabilization by fluorination of any particular site anticorrelates with the degree of orbital localization at that site. Thus, the HOMO is more stabilized upon fluorination at sites 3 and 5 (coupled via phenyl rotation), less stabilized upon fluorination at sites 2 and 6, and almost unaffected by fluorination at position 4 (as a sign that the stabilization and destabilization effect cancel out). In case of HOMO−1 and HOMO−2, the orbitals are evenly distributed over sites 2, 3, 5, 6, and have a nodal surface that

Figure 4. Key frontier molecular orbitals in tF2356 (representations under C2 symmetry are in parentheses). The HOMO−2sym and HOMO−1sym orbitals (top) are quasi-degenerate, but breakdown of symmetry between the two phenyl rings can remove orbital degeneracy producing a pair of nonsymmetric orbitals, each localized on one of the rings (middle). In contrast, the HOMO and the LUMO (bottom) mostly retain their shape irrespective of geometry distortions. 15269


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Journal of the American Chemical Society runs through site 4. Accordingly, the fluorination effect is opposite: only 4-fluorination is markedly stabilizing. Small deviations from the above simplistic model are associated with minor variations in the shape of the HOMO−1 and HOMO−2 that depend on the fluorination pattern. In some structures, the two orbitals become slightly dissimilar, as reflected in increased splitting between their energy. Thus, the gap between the HOMO and the HOMO−1/ HOMO−2 becomes the lowest in F2356, followed by F235 and F236, and then by F23456. That points to the excitations HOMO−1/HOMO−2 to the LUMO as the main source of the experimentally discovered zwitterionic S1 in tF2356 and tF23456. Previously, any low-lying excited states of stilbenes, other than the conventional S1 based on the HOMO → LUMO excitation, escaped from direct experimental observation, and indications regarding them were rather suggestive than firm.41 Therefore, quantitative discrepancies between various levels of theory in modeling the spectrum of excited states resulted in inconclusive discussions.25,27 Now, the zwitterionic S1 state in tF2356 and tF23456 provides a solid benchmark for critical testing of various levels of theory. Applicability of TDDFT to Excited States in Stilbenes. Initially we intended to carry out the geometry optimization across S1 directly at the XMCQDPT2 level, however that proved to be impossible. Currently, optimizations with the full π-electron (14e,14o) active space are still prohibitively expensive. Reduction of the active space to (10e,10o) by excluding the least important outermost π and π* orbitals makes the task technically feasible but introduces instabilities that persist irrespective of variations in state averaging scheme or size of the model space. Therefore, we restrict ourselves to single point XMCQDPT2 recalculations at TDDFT-optimized geometries. A formal TDDFT search of stationary points on the S1 potential energy surface in tF2356, to assess the performance of different exchange-correlation functionals, has led us to the following findings: (1) Two kinds of stationary points in the near-Franck− Condon region of S1 are identified at the TDDFT level, though only particular functionals locate the both kinds. Geometry predictions are consistent between the functionals. The stationary points of the first kind are due to the conventional HOMO → LUMO excitation. They are nonpolar and C2-symmetric, with twisting angle of around 165 degrees. Those of the second kind are planar, zwitterionic and without C2 symmetry (hence Cssymmetric), i.e., are characterized by inequivalence of the phenyl rings. They are dominated by the excitation from the nonsymmetric HOMO−1 asym to the LUMO (hereinafter orbital designations refer to Figure 4). Their formation is a result of sudden polarization that involves the two initially quasi-degenerate singly excited states belonging to different representations of the C 2 (C 2h ) point group: the A(A g )-symmetric state dominated by the (HOMO−2sym)1(LUMO)1 configuration, and the B(Bu)-symmetric state dominated by the (HOMO−1sym)1(LUMO)1 one. Similar to sudden polarization that gives rise to the P state of stilbene, those two states can be represented as linear combinations of the nonsymmetric zwitterionic (HOMO−2asym)1(LUMO)1 and (HOMO−1asym)1(LUMO)1 configurations, each

characterized by 0.5e formal charge transfer between the halves of the molecule. Upon the symmetry breaking the degeneracy is removed, and the (HOMO−1asym)1(LUMO)1 state emerges as the zwitterionic S 1 (here HOMO−1 asym becomes almost isoenergetic to the HOMO). The nature of this zwitterionic S 1 is further corroborated at the XMCQDPT2 level. (2) Hybrid functionals with high fraction of exact exchange added either in a range-independent (M06-2X), or a range-separated manner (CAM-B3LYP, ωB97X) do not locate any zwitterionic stationary points in the nearFranck−Condon region of S1 in tF2356 and therefore prove completely incorrect already on a qualitative level. Furthermore, M06-2X and ωB97X predict barrierless twisting toward the phantom state. (3) Popular hybrid functionals with 20−30% of exact exchange (PBE0, X3LYP, M06) locate both zwitterionic and nonpolar stationary points on the S1 surface of tF2356, yet the nonpolar one appears to be more stable by 0.03 eV (TD-X3LYP) to 0.13 eV (TD-M06). Also, they give strongly underestimated twisting barrier in S1, below 0.1 eV. These results are still qualitatively incorrect, yet they show a promising trend. (4) The functionals τHCTHhyb (15% of exact exchange) and O3LYP (11.61%) also identify both zwitterionic and nonpolar stationary points in S1, and they correctly place the zwitterionic point below the nonpolar one by, respectively, 0.12 and 0.23 eV. In view of better agreement with single point XMCQDPT2 recalculations and with experimental barriers, our further geometry optimizations in S1 are based on TD-O3LYP. We think that the TPSSh functional (10%) would be also applicable, but lack of excited state derivatives in the available software prevented us from its use. (5) Finally, pure GGA functional PBE, and pure mGGA functional τHCTH locate zwitterionic stationary points only, and predict considerably overestimated twisting barrier of 0.4 eV in S1. Compared to the XMCQDPT2 results, the pure functionals shift the HOMO → LUMO excitation too far above the HOMO−1asym → LUMO excitation. It turns out that most of the exchange-correlation functionals cannot correctly describe the relative energy of the polar and nonpolar states in tF2356. Although the functionals with higher fraction of exact exchange are expected to increase the relative energy of charge-transfer states, one may be surprised that the best results are produced by a functional like O3LYP rather than PBE0 or range-separated ones. Furthermore, as shown in Table 4, the incorrect estimate of the relative energy refers not only to the zwitterionic state. The functionals with higher amount of exact exchange show similar problems with the relative position of the nonpolar HOMO−1sym/HOMO−2sym → LUMO excitations at the C2h-symmetric S0 geometry. A similar dependence on the amount of exact exchange has been reported for trans-stilbene,25 and we observed the same tendency for the other fluorinated molecules in Table 2. To summarize, there are serious indications of general TDDFT deficiencies in the description of excited stilbenes. These may become critical whenever other states, different from the products of the HOMO → LUMO transition, come into play. The doubt on the performance of the popular 15270


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Journal of the American Chemical Society Table 3. Lowest Vertical Excitations in tF2356 and cF2356 (XMCQDPT2(14,14)/cc-pVTZ//PBE0/Def2-TZVPP) tF2356 (C2h) state/symmetry SFC 1 /Ag SFC 2 /Bu SFC 3 /Bu

E01, eV 4.19 4.19 4.47

cF2356 (C2)

f 0i

principal excitation

state/symmetry

E01, eV

f 0i

principal excitation

0 0.04 1.04

HOMO−2sym → LUMO HOMO−1sym → LUMO HOMO → LUMO

SFC 1 /A SFC 2 /B SFC 3 /B

4.33 4.39 4.79

0.01 0.02 0.66

HOMO−2sym → LUMO HOMO−1sym → LUMO HOMO → LUMO

of exact exchange, the effect being less for the HOMO → LUMO than for the HOMO−1sym/HOMO−2sym → LUMO. As a result, a more correct order of excited states comes at a cost of stronger underestimated excitation energy. The proper HOMO → LUMO transition energy is approached only by the range-separated functionals and by M06-2X, but they all place the two rivalling states irrelevantly high. Thus, there is no satisfactory option to correctly reproduce the absolute positions of full set of lowest excitations by means of the TDDFT. S1 Potential Energy Surface and Zwitterionic State in tF2356. In Figure 5 we show TD-O3LYP relaxed scans of the

exchange-correlation functionals also touches the QD-NEVPT2 multistate perturbation theory, both in strongly and partially contracted variants. Indeed its predictions for trans-stilbene,25 of a large separation between the S1 based on the HOMO → LUMO and the next B-symmetric singlet state, disagree with MS-CASPT222 and XMCQDPT227 calculations but are close to CAM-B3LYP results which are drastically incorrect in the present tF2356 case. Vertical Excitations in F2356. Table 3 reports the XMCQDPT2 data on the three lowest vertical excitations in tF2356 and cF2356. Note that in addition to the principal transition from the HOMO−2sym/HOMO−1sym to the LUMO, FC SFC 1 and S2 include admixtures of other excitations, mainly HOMO → LUMO+2/LUMO+3, the latter two orbitals being the antibonding analogs of HOMO−1sym and HOMO−2sym. SFC 3 is a purer product of the HOMO → LUMO excitation, in contrast to XMCQDPT2 and MS-CASPT2 findings for unsubstituted stilbene, where the HOMO → LUMO and HOMO−1sym → LUMO transitions of the same symmetry demonstrate a tendency to mix.22,27 Note that the calculated vertical S0 → S3 transition agrees with the measured absorption maximum in n-hexane (see Figure 2). Setting TDDFT vertical transitions in tF2356 (see Table 4) against the XMCQDPT2 results, one can see that the Table 4. Three Lowest Vertical Excitations in tF2356 (TDDFT/Def2-TZVPP) with Different Exchange Correlation Functionals at the PBE0/Def2-TZVPP GroundState Geometry (C2h) xc functional PBE TPSS τHCTH O3LYP TPSSh τHCTHhyb X3LYP B98 PBE0 M06 M06-2X CAM-B3LYP ωB97X XMCQDPT2

E(HOMO → LUMO)/no. of excited state 3.72 3.80 3.73 3.90 3.93 3.92 3.99 4.00 4.06 3.96 4.29 4.25 4.39 4.47

(S3) (S3) (S3) (S3) (S3) (S3) (S1) (S1) (S1) (S1) (S1) (S1) (S1) (S3)

E(HOMO− 1sym → LUMO)

E(HOMO− 2sym → LUMO)

3.35 3.48 3.43 3.79 3.81 3.88 4.08 4.09 4.16 4.14 4.65 4.60 4.79 4.19

3.35 3.48 3.43 3.79 3.81 3.88 4.08 4.09 4.17 4.14 4.65 4.60 4.79 4.19

Figure 5. Relaxed scans of the zwitterionic and nonpolar domains of S1 along the twisting coordinate (TD-O3LYP/Def2-TZVPP). The energy is given with respect to the zwitterionic stationary point. The domains are connected by a virtually barrierless path that runs at nearly planar trans-geometry and involves mostly the stretching coordinates. TS marks the transition state for S1 → P relaxation.

potential energy surface of S1 in its zwitterionic and nonpolar domains along the twisting coordinate. TD-O3LYP data suggest that the higher-lying nonpolar domain is locally stable in a broad range of twisting angles, being separated with a barrier from the zwitterionic one. The exact transition state between the two domains is difficult to establish: in agreement with ultrafast relaxation of the photoexcited state, it is found to be within negligible 3 meV above the nonpolar stationary point. Furthermore, XMCQDPT2 recalculations suggest completely barrierless path to the zwitterionic domain at nearly planar geometries. In any case, the XMCQDPT2 data confirm that the S1 points along the nonpolar scan path indeed correspond to the HOMO → LUMO excited state.

qualitatively correct order of excitations is given by the same functionals that identify the zwitterionic minimum in S1 as the more stable or even the only one. They include PBE, TPSS, τHCTH, O3LYP, TPSSh, and τHCTHhyb, i.e., either the pure functionals or the hybrids with lower fraction of exact exchange. However, they all considerably underestimate the absolute excitation energies. In general, the calculated energies of the three lowest excitations considerably increase with the amount 15271


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However, different levels of theory do not provide consistent quantitative predictions in this regard. Thus, relaxed TDO3LYP density yields dipole moment of as much as 10.2 D, and TD-PBE0 gives only slightly lower 9.5 D. In TDDFT calculations with state-specific solvation, this translates into more than 4-fold overestimated solvatochromic shift of the fluorescence band between hexane and acetonitrile. On the other hand, zero order XMCQDPT2 density analysis provides a likely underestimated result of 3.6 D. In any case, the associated geometric asymmetry between the halves of the molecule is quite pronounced, as shown in Figure 6. Note the shortened

TD-O3LYP scans reveal that twisting in the zwitterionic domain of S1 is unfavorable. Indeed, if the S1 state is nonpolar (i.e., based on the HOMO−LUMO excitation), it combines population of the LUMO that is antibonding with respect to the central bond with depopulation of the bonding HOMO, resulting in relatively low or even zero twisting barrier.18,19 In the zwitterionic domain, however, depopulated is asymmetric HOMO−1 which does not directly affect the central bond. Therefore the zwitterionic scan path shows pronounced elevation along the twisting coordinate and ultimately rises above the flat nonpolar domain, yet the zwitterionic state remains stable against spontaneous relaxation to the P state. This is because the zwitterionic state, unlike the nonpolar one, does not develop quasi-degeneracy with S0. As a result, the S1 → P transition state (denoted “TS” in Figure 5) is found, similarly to the other stilbenes, in the nonpolar domain of S1. The transition state geometry is C2-symmetric, with the twisting angle of 137 degrees. In Table 5, we present the relative energy of three lowest excited states of tF2356 taken at the TD-O3LYP optimized key Table 5. Relative Energy of the S1−S3 States in tF2356 at Three TD-O3LYP Optimized Key Points of the Potential Energy Surface of S1a

Figure 6. Bond lengths in the asymmetric minimum of S1 (TDO3LYP/Def2-TZVPP). The charge-depleted ring is at right.

relative energy, meV, and principal contribution point of the PES (twisting angle) Zwitterionic minimum (180°)

state

TD-O3LYP

XMCQDPT2

S1

0 (HOMO−1asym → LUMO) 579 (HOMO → LUMO) 598 (HOMO−2asym → LUMO) 227 (HOMO → LUMO) 377 (HOMO−2sym → LUMO) 386 (HOMO−1sym → LUMO) 247 (HOMO → LUMO) 747 (HOMO−2sym → LUMO) 753 (HOMO−1sym → LUMO)

0 (HOMO−1asym → LUMO) 454 (HOMO−2asym → LUMO) 623 (HOMO → LUMO) 256 (HOMO → LUMO) 282 (HOMO−1sym → LUMO) 284 (HOMO−2sym → LUMO) 264 (HOMO → LUMO) 612 (HOMO−2sym → LUMO) 616 (HOMO−1sym → LUMO)

S2 S3 Nonpolar minimum (167°)

S1 S2 S3

Twisting barrier (137°)

S1 S2 S3

a

C−F bonds on the right, cationic, side, possibly due to reduced repulsion and increased conjugation between the fluorine lone pairs and the depleted π-density. Lastly, Figure 7 helps to qualitatively rationalize the effect of a polar solvent on the isomerization barriers and on the corresponding reaction rate. The top frame refers to the common case of S0 → SFC optical excitation, when S1 is 1 nonpolar and P polar. The barrier S1 → P in acetonitrile decreases relative to that in n-hexane, and the isomerization proceeds faster. Table 1 shows that this is true for the commonly behaving molecules represented by Figure 1. However, it is just opposite for the uncommon case of zwitterionic S1: in tF2356, the S1 → P twist in acetonitrile is slower than in n-hexane. The reason is that the energy of polar solvation of the initial state, i.e., zwitterionic S1, directly adds to the barrier height, while stabilization of the final state P in polar solvents lowers the transition state only by a fraction of the solvation energy. The bottom frame of Figure 7 illustrates this case. Also, the diagram in Figure 7 correctly reflects the polarity dependence of the P → S0 relaxation revealed by the evolution of cF2356 in Figure 3. Zwitterionic States in tF23456 and cF2356. Let us now consider tF23456 that also shows an early subpicosecond evolution indicative of sudden polarization, but with a much shorter S1 lifetime of 13 ps in n-hexane. TD-O3LYP locates the zwitterionic minimum in S1, but predicts it to be virtually isoenergetic to the nonpolar one, their electronic structure being similar to the respective states of tF2356. This suggests comparable abundance of the zwitterionic and nonpolar states in the excited wavepacket in S1 upon early ultrafast evolution, seemingly consistent with rapid ca. 2-fold drop of the ESA band at 514 nm (Figure 2 at right) and with lesser decrease in the fluorescence quantum yield compared to tF2356 than their S1 lifetime ratio would suggest. On the other hand, the contribution of the zwitterionic state to the fluorescence band would then be negligible due to large difference in oscillator strengths, so one would not have detected the solvatochromic

All values are given with respect to the zwitterionic minimum in S1.

points of S1 and recalculated at the XMCQDPT2 level. As seen, the two levels of theory yield very similar energies of different points in S1, though TD-O3LYP systematically up-shifts the states associated with HOMO−2sym/HOMO−1sym → LUMO excitations, as also evidenced by Table 4. Importantly, the twisting barrier agrees with the experimental 1.3 ns lifetime in hexane, that gives ca. 0.23 eV free energy of activation at room temperature. XMCQDPT2 data for the zwitterionic state show it to be relaxed by 0.55 eV with respect to the initially vertically excited SFC 3 . The S0−S1 gap becomes 3.55 eV, in good agreement with the emission data measured in hexane, as well as the oscillator strength of 0.014. For the inter-ring distance of 6 Å, a simplistic model of transferring half an electron from one ring to the other (HOMO−1asym → LUMO excitation) would give ca. 14 D, well above the 6 D experimental estimate. Thence, the actual amount of charge transfer is damped by the π-electron density. 15272


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with constraints on the twisting angle, the nonpolar region in S1 is locally stable only in a narrow range of dihedral angles of 45− 50 degrees, showing a descending trend toward the P state. According to XMCQDPT2, the zwitterionic S1 is located 0.74 eV below SFC 3 (see Table 2), the S0−S1 gap becoming 3.61 eV with the oscillator strength of 0.017. TD-O3LYP and XMCQDPT2 dipole moment estimates for the S1 state are 9.6 and 5.5 D, respectively. As discussed above, the experiment provides only indirect indications of the zwitterionic state in cF2356. Perhaps, its photoinduced evolution should be viewed as a dynamic process where the forces that act on the atoms steer the molecule aside from the nearest stationary points. Recall that the HOMO → LUMO excitation in cis-stilbenes creates a considerable gradient along the twisting coordinate toward the phantom state.24,26,27 That is in stark contrast to tF2356 where the twisting forces are very weak or even vanishing. Low, or even zero, photochemical yields of DHP despite its closest geometric proximity to cis-stilbene is a common phenomenon12,13,17,20,32 reproducible, e.g., in the molecular dynamics simulations with spin-flip TDDFT potentials.30,31 Likewise, the excited cF2356 can also miss the zwitterionic domain in S1 (or pass it without complete relaxation of internal energy) on a way to the P state.

4. CONCLUSION AND OUTLOOK We have observed and calculated the sudden polarization in the S1 state in planar ring-fluorinated stilbenes. Until now the phenomenon has been known and discussed for 90°-twisted alkenes, in the perpendicular phantom state P. However, the latter is dark in fluorescence and usually short-lived, so it may only be observable by ultrafast transient absorption. On the contrary, the sudden polarization of S1, when it is allowed and long-lived, can be easily studied even via routine fluorescence spectro scopy, as demonstrated here with trans2,3,5,6,2′,3′,5′,6′-octofluorostilbene. We believe that the sudden polarization near the Franck− Condon region is likely a phenomenon common to other stilbenes, not specifically F2356 or F23456. Indeed, one would expect the quasi-degenerate pair of electronic states due to the HOMO−1sym/HOMO−2sym → LUMO excitations to enter symmetry-breaking interactions in many different stilbenes. In most of them, however, that interaction would not leave detectable consequences since the interacting states remain higher than photoexcited nonpolar S1. The uniqueness of F2356 (and to a lesser extent of F23456) is that the substitution strongly shifts the HOMO closer to the HOMO−1sym/HOMO−2sym, and by reordering of the exited states brings the HOMO → LUMO transition above the others. As a result, the sudden polarization occurs in S1 near the Franck−Condon domain and significantly alters the subsequent evolution. Possibly, one can suggest other substituents and/or substitution patterns that would promote deviations from presupposed excited state ordering and consequent alterations of photochemical behavior. Identification and rationalization of such cases will require an educated selection of computational schemes to cope with the shortcomings of TDDFT discovered in the present study, the incorrect order of excited states given by widely used hybrid exchange-correlation functionals with above 20% of exact exchange and poor absolute excitation energies with most of the functionals. In this regard, accurate MS-PT2 benchmarks will be of crucial importance.

Figure 7. Diabatic potential energy surfaces for the common case of nonpolar S1 (a) and for the uncommon case of zwitterionic S1 (b). The polar terms are stabilized in polar acetonitrile (red) relative to nhexane (blue). In the top frame, isomerization barriers are indicated for S1 → P and P → S0 relaxation. Stabilization of the P state in polar solvents partly translates into lowering of both barriers. In the bottom frame, the S1 → P transition state is still defined by the intersection of P with nonpolar domain of S1, but the barrier is measured with respect to the new zwitterionic S1 whose stabilization outweighs the effects due to the P state.

shift. Or, if the shift were due to a pronouncedly increased zwitterionic contribution in acetonitrile compared to n-hexane, the fluorescence quantum yield in acetonitrile would have become noticeably lower. Also, the 22 meV TD-O3LYP twisting barrier in tF23456 is strongly underestimated. XMCQDPT2 recalculations, however, shift the zwitterionic minimum in S1 0.1 eV below the nonpolar one, and predict the twisting barrier of 113 meV, consistent with the experimental lifetime. The 0.1 eV separation between the two minima corresponds to ca. 40:1 population ratio at room temperature, close to the inverted ratio of the respective oscillator strengths for emission. Then the contributions to the emission spectra from S1 and S3 should be comparable, resulting in a moderate solvatochromic shift as observed in the experiment. Thus, both TD-O3LYP and XMCQDPT2 predictions have certain points of agreement with the experimental results, and the problem of more precise assessment of the relative contributions of the nonpolar and zwitterionic states in tF2356 is, perhaps, slightly beyond the current experimental and computational accuracy. For cF2356, TD-O3LYP predicts no nonpolar stationary point in S1. Two types of local minima are found: a zwitterionic one like in tF2356 and a DHP-like ring-cooperated domain,12,17,24,26−28,32 where TDDFT breaks down because of static electronic correlation and low separation from S0. Even 15273


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(21) Quenneville, J.; Martínez, T. J. J. Phys. Chem. A 2003, 107, 829− 37. (22) Gagliardi, L.; Orlandi, G.; Molina, V.; Malmqvist, P.-Å.; Roos, B. O. J. Phys. Chem. A 2002, 106, 7355−61. (23) Improta, R.; Santoro, F.; Dietl, C.; Papastathopoulos, E.; Gerber, G. Chem. Phys. Lett. 2004, 387, 509−16. (24) Improta, R.; Santoro, F. J. Phys. Chem. A 2005, 109, 10058− 10067. (25) Angeli, C.; Improta, R.; Santoro, F. J. Chem. Phys. 2009, 130, 174307. (26) Minezawa, N.; Gordon, M. S. J. Phys. Chem. A 2011, 115, 7901− 7911. (27) Ioffe, I. N.; Granovsky, A. A. J. Chem. Theory Comput. 2013, 9, 4973−90. (28) Chaudhuri, R. K.; Freed, K. F.; Chattopadhyay, S.; Mahapatra, U. S. J. Phys. Chem. A 2013, 117, 9424−34. (29) Tomasello, G.; Garavelli, M.; Orlandi, G. Phys. Chem. Chem. Phys. 2013, 15, 19763−73. (30) Harabuchi, Y.; Keipert, K.; Zahariev, F.; Taketsugu, T.; Gordon, M. S. J. Phys. Chem. A 2014, 118, 11987−98. (31) Harabuchi, Y.; Yamamoto, R.; Maeda, S.; Takeuchi, S.; Tahara, T.; Taketsugu, T. J. Phys. Chem. A 2016, 120, 8804−12. (32) Quick, M.; Berndt, F.; Dobryakov, A. L.; Ioffe, I. N.; Granovsky, A. A.; Knie, C.; Mahrwald, R.; Lenoir, D.; Ernsting, N. P.; Kovalenko, S. A. J. Phys. Chem. B 2014, 118, 1389−1402. (33) Kovalenko, S. A.; Dobryakov, A. L.; Ruthmann, J.; Ernsting, N. P. Phys. Rev. A: At., Mol., Opt. Phys. 1999, 59, 2369−84. (34) Kovalenko, S. A.; Schanz, R.; Hennig, H.; Ernsting, N. P. J. Chem. Phys. 2001, 115, 3256−73. (35) Moreno, J.; Gerecke, M.; Dobryakov, A. L.; Ioffe, I. N.; Granovsky, A. A.; Bleger, D.; Hecht, S.; Kovalenko, S. A. J. Phys. Chem. B 2015, 119, 12281−88. (36) Sajadi, M.; Dobryakov, A. L.; Garbin, E.; Ernsting, N. P.; Kovalenko, S. A. Chem. Phys. Lett. 2010, 489, 44−47. (37) Granovsky, A. A. Firefly v. 8.2; http://classic.chem.msu.su/gran/ firefly/index.html. (38) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. J. Comput. Chem. 1993, 14, 1347−1363. (39) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö .; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, Revision A.02; Gaussian, Inc.: Wallingford, CT, 2009. (40) Granovsky, A. A. J. Chem. Phys. 2011, 134, 214113. (41) Dietl, C.; Papastathopoulos, E.; Niklaus, P.; Improta, R.; Santoro, F.; Gerber, G. Chem. Phys. 2005, 310, 201−211. (42) Sadovnichy, V.; Tikhonravov, A.; Voevodin, V.; Opanasenko, A. “Lomonosov”: Supercomputing at Moscow State University, In Contemporary High Performance Computing; CRC Press: Boca Raton, 2013; pp 283−307.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b09611. Decay kinetics, photochemical conversion of tF2356, oxygen effects on the decay kinetics, femtosecond stimulated Raman spectra, and computed coordinates in the S1 state (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*ioff[email protected] *[email protected] ORCID

Nikolaus P. Ernsting: 0000-0002-0731-8244 Sergey A. Kovalenko: 0000-0003-4278-9305 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The contributors from HU Berlin are grateful to the Deutsche Forschungsgemeinschaft for financial support. I.N.I. and A.A.G. thank the Supercomputer center of the Moscow State University (Lomonosov supercomputer)42 for computational support, and Dr. A. Ya. Freidzon (Photochemistry Center of RAS) for stimulating discussions. A.A.G. acknowledges support from the Russian Science Foundation (grant no. 17-13-01276).

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REFERENCES

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Tuning Stilbene Photochemistry by Fluorination - ACS Publications

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