Letter pubs.acs.org/JPCL
Evidence for Dominant Role of Tunneling in Condensed Phases and at High Temperatures: Double Hydrogen Transfer in Porphycenes Piotr Ciąćka,† Piotr Fita,*,† Arkadiusz Listkowski,‡,§ Czesław Radzewicz,† and Jacek Waluk*,‡,§ †
Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland § Faculty of Mathematics and Natural Sciences, College of Science, Cardinal Stefan Wyszyński University, Dewajtis 5, 01-815 Warsaw, Poland ‡
S Supporting Information *
ABSTRACT: Investigation of the double hydrogen transfer in porphycene, its 2,7,12,17tetra-tert-butyl derivative, and their N-deuterated isotopologues revealed the dominant role of tunneling, even at room temperature in condensed phase. Ultrafast optical spectroscopy with polarized light employed in a wide range of temperatures allowed the identification and evaluation of contributions of two tunneling modes: vibrational ground-state tunneling, occurring from the zero vibrational level, and vibrationally activated, via a large amplitude, low-frequency mode. Good correspondence was found between the rates of incoherent tunneling occurring in condensed phase and the values estimated on the basis of tunneling splittings observed in molecules isolated in supersonic jets or helium nanodroplets. The results provide solid experimental insight into widely proposed quantum facets of ubiquitous hydrogen-transfer phenomena.
A
tunneling mechanisms and estimate their contributions to reaction rates in a wide range of temperatures. Porphycene found large interest among theoreticians as a good model for intramolecular double hydrogen transfer.12−22 Various NMR techniques have been used to obtain the rate of this reaction in the ground electronic state for porphycene in a crystalline state23,24 and in solution.25 Tautomerization in this case is a self-exchange process, involving conversion between two chemically equivalent trans tautomers (Scheme 1).26 For an isolated molecule, coherent delocalization of two inner hydrogen atoms leads to tunneling splittings. Studies of this phenomenon for porphycene isolated in supersonic jets27−30 and helium nanodroplets31 revealed that the splittings are vibrational mode dependent. In parallel, the reaction was investigated in condensed phases,32−38 where it occurs as a rate
ccepted to occur under nonroutine conditions, i.e., in isolated molecules at low temperatures,1 hydrogen tunneling in room-temperature, condensed phase reactions continues to be a subject of intense research.2 The ubiquitousness as well as chemical and biological importance of hydrogen transfer lead scientists to seek tunneling contributions in such processes as spontaneous DNA damage3,4 or various enzymecatalyzed reactions.5−8 Most of the experiments, especially in enzymes, infer tunneling exclusively by measuring isotope effects on product formation.5−8 Attempting to elucidate inherently fast phenomena by observing slow processes, such experiments require an additional assumption on hydrogen transfer being the rate-limiting step in a series of reactions. Dynamical NMR experiments9 offer time scales down to picoseconds, and time domain techniques of ultrafast spectroscopy10,11 are required to reach femtosecond temporal resolution. The latter methods usually rely on spectral changes between substrates and products and are typically applied to light-induced reactions and excited-state hydrogen transfers. However, using polarized light, it is possible to measure also the rates of self-exchange reactions, where the substrate and product are formally identical. In this work, we present data which demonstrate a dominant role of tunneling in spontaneous tautomerization of porphycenes observed in condensed phase in a wide temperature range, even above 293 K. The combination of a direct time domain technique of polarized pump−probe spectroscopy and a suitable model molecule, porphycene, allows us to not only present compelling evidence of tunneling but also discriminate between different © XXXX American Chemical Society
Scheme 1. Tautomerization in Porphycene, Accompanied by a Change in the Direction of the S0−S1 Transition Moment (Represented by the Double Arrow)
Received: November 6, 2015 Accepted: January 4, 2016
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Figure 1. Arrhenius plots for tautomerization of 1 (a, b) and 2 (c, d) and their doubly deuterated isotopologues 1-d2 and 2-d2 in the electronic ground (a, c) and excited states (b, d). Tautomerization rates are also presented in Figure 1S and Tables 1S and 2S in the Supporting Information.
Table 1. Kinetic Parameters Extracted from Time-Resolved Measurements Performed at Different Temperatures k0 [s−1]
compound/state 1/S0 1/S1 1-d2/S0 1-d2/S1 2/S0 2/S1 2-d2/S0 2-d2/S1 a
(6.0 (3.0 (2.8 (1.8 b (7.0 (3.8 (7.0 (3.7 (2.8 (5.8 (4.2
k1 [s−1]
E1 [kcal/mol]
± ± ± ±
0.2)·10 1.6)·108 0.3)·109 1.2)·109
± ± ± ± ± ± ±
1.2)·108 0.2)·1011 1.0)·109 0.2)·1010 0.5)·1010 0.4)·109 0.2)·109
10
(5.4 ± 0.2)·10 (7.7 ± 0.4)·1010 − (9 ± 12)·109 − (0 ± 10)·109 (2.3 ± 0.2)·1012 (1.5 ± 0.5)·1011 − (8 ± 4)·1010 − (1.5 ± 1.2)·1010
a
11
0.52 0.52a − 0.5a − 0.5a 0.5a 0.5a − 0.5a − 0.5a
E2 [kcal/mol]
k2 [s−1]
± ± ± ± ± ± ± ± ± ± ± ±
(2.3 ± 0.5)·1013 (7.5 ± 1.4)·1012 (6.8 ± 1.1)·1012 (6.8 ± 1.7)·1012 (1.5 ± 0.2)·1012 (1.4 ± 0.4)·1012 (3.2 ± 3.0)·1014 (3.0 ± 1.0)·1012 (2.1 ± 0.3)·1012 (3.1 ± 0.8)·1012 (4.9 ± 1.0)·1011 (7 ± 4)·1011
2.5 2.7 2.1 2.1 2.1 2.1 3.9 1.5 1.7 2.0 1.6 2.0
0.2 0.2 0.1 0.2 0.1 0.2 0.7 0.2 0.1 0.3 0.1 0.4
Fixed value. bValue too small to be measured.
lifetime of the chromophore are much longer than that of the reaction. Investigations of a large number of differently substituted porphycenes33,38 revealed that tautomerization is always slower in S1 than in S0, because of a larger NH···N distance in S1, which leads to weaker intramolecular hydrogen bonds. These studies also provided several observations suggesting that tautomerization may be governed by tunneling. First, in differently substituted porphycenes, the reaction rates are strongly correlated with the NH···N donor−acceptor distance38 and vary over 3 orders of magnitude upon the relative change of the distance not exceeding 10%. Second, the activation energy determined for the reaction in S1 in the parent porphycene is several times smaller than the calculated reaction barrier.36 On the other hand, its value corresponds to the energy of a low-frequency mode (180 cm−1) that reveals the largest tunneling splitting under conditions of molecular isolation.29 Finally, in meso-alkylated porphycenes, for which both trans and cis tautomers are present (the latter correspond to the protons located on the same bipyrrole unit), the trans−
process. Tautomerization in porphycenes can now be monitored even on a single-molecule level.39−44 The reactant and product of a self-exchange process are formally identical. However, they differ in the direction of transition moments (Scheme 1). Taking advantage of this property, we have developed techniques based on using polarized light that enable determination of the reaction rate in both ground (S 0 ) and excited (S 1 ) electronic states.32,33,36,38,45 The most general procedure exploits the analysis of anisotropy of transient absorption signals obtained for parallel (ΔApar) and perpendicular (ΔAperp) pump and probe polarizations: r(t) = (ΔA(t)par − ΔA(t)perp)/(ΔA(t)par+2ΔA(t)perp). A judicious choice of pump and probe wavelengths allows the separation of the contributions to anisotropy caused by tautomerization in S0 and S1 and thus the determination of the values of k0PT and k1PT, the rates of double hydrogen transfer in the two states. The experiment is carried out under conditions when the rotational relaxation time and excited-state 284
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The Journal of Physical Chemistry Letters trans tautomerization, involving the transfer of two hydrogens, was found to be faster than a single hydrogen-transfer cis−trans conversion, even though the calculations predicted a lower barrier for the latter process.37 Thus, efficient tunneling between equivalent, isoenergetic configurations may be involved in the simultaneous double hydrogen transfer and account for the faster rate of the trans−trans reaction. Tunneling would be the only reaction channel probed by transient absorption anisotropy measurements if they were performed near 0 K. At higher temperatures classical channels may also contribute to the overall reaction rate. Thus, in order to assess the role of temperature-independent and thermally activated channels, the transient absorption setup was equipped for measurements in the temperature range of 20−400 K. Parent porphycene (1) and its 2,7,12,17-tetra-tert-butyl derivative (2) were investigated. The two molecules have very similar electronic spectra; the geometries of the inner cavity, composed of four nitrogen atoms, differ only slightly, but the double hydrogen-transfer time at 293 K is about three times shorter in 2 than in 1, both in S0 (0.6 vs 1.8 ps) and S1 (2.9 vs 9.4 ps).38 Figures 1 and 1S show the Arrhenius plots for the groundand excited-state tautomerization rates obtained for 1, 2, and their N-deuterated isotopologues in a wide temperature range. Better solubility of 2 allowed for measurements down to a lower temperature limit than with the parent molecule 1, and plateaus of the Arrhenius plots were reached. The plateaus correspond to regions where tunneling from the vibrational ground state becomes the only reaction channel. Its rate is controlled by two factors: (i) N-deuteration and (ii) increase of the barrier upon electronic excitation. Therefore, the highest vibrational ground-state tunneling rate (k0 in Table 1) is obtained for tautomerization in the electronic ground state of an undeuterated molecule, and the lowest is obtained for the excited deuterated isotopologue. The shape of the Arrhenius plots clearly indicates that in addition to vibrational ground-state tunneling also thermally activated channels (such as vibrationally activated tunneling or over the barrier crossing) are involved in tautomerization. Therefore, the data obtained in the temperature range accessible in our experiments should be simulated using the general equation ⎧ k + ln k(T ) = ln⎨ ⎪ 0 ⎩ ⎪
N
⎛
⎛ −En ⎞⎞⎫ ⎟⎟⎬ RT ⎠⎠⎪ ⎭
∑ ⎜⎝kn exp⎝⎜ n=1
In contrast, the Arrhenius plots for deuterated 1 and 2 (1-d2 and 2-d2) can be well-reproduced with only one thermally activated channel whose activation energy is in the 1.6−2.1 kcal/mol range. One can also fit them with biexponential functions with fixed value of E1 ≈ 0.5 kcal/mol to test for the effect of the 180 cm−1 mode excitation. The obtained values of k1 are similar to those of k0 (Table 1), and no large tautomerization enhancement occurs after excitation of this mode. Therefore, in this case the hydrogen−deuterium exchange efficiently suppresses the mechanism of vibrationally activated tunneling. This observation is rather surprising because one could in principle expect the opposite result, larger enhancement of tunneling by vibrational excitation for deuterated molecules. The 180 cm−1 vibration promotes tunneling because it shortens the donor−acceptor N−N distance and effectively lowers the barrier; thus, its influence should be more pronounced for larger barriers and heavier atoms.46 The former dependence is observed for undeuterated 1 and 2 in both S0 and S1, where the k1/k0 ratio is greater the lower k0 is. In principle, the unexpected behavior of the vibrational enhancement of tunneling via the 180 cm−1 mode after the proton−deuteron exchange could result from the change of the character of this mode. We recently observed a similar effect in supersonic jet studies of 1 and its isotopologue with all 12 peripheral hydrogen atoms replaced by deuterons.30 For just one specific vibration, 4Ag, deuteration resulted in doubling of the tunneling splitting, changing the mode character from neutral to tautomerization-promoting. The character of the 180 cm−1 vibration, however, does not change to the extent which could explain the reduced enhancement of tunneling in 1-d2 and 2-d2 compared to 1 and 2 (Figure 2S in the Supporting Information).47 Thus, it may be necessary to invoke dynamical effects of periodic perturbations of the potential by molecular vibrations. It has been shown theoretically48−50 and confirmed experimentally51 that the tunneling rate of a particle in a symmetrical double-well can be controlled (reduced or increased) by small periodic perturbations of the potential. Analysis of a particle in a simplified model of a double-well potential modulated by the 180 cm−1 vibration shows that tunneling is accelerated and the degree of acceleration very strongly depends on the mass of the particle: increase of the particle’s mass by a factor of 2 may reduce the tunneling enhancement effect by more than an order of magnitude. This result agrees very well with our observations; nevertheless, further theoretical studies are required to provide an unequivocal explanation of the effect of N-deuteration on the vibrationally enhanced tunneling. The temperature dependence of the isotope effect in the electronic ground state of 1 and 2 is shown in Figure 2. The curves go through maxima arising because of the smaller contribution of vibrationally enhanced tunneling in deuterated molecules. Inspection of Figure 2 shows values of the isotope effect that are larger than the classical limit, in particular for 2 at room temperature. This becomes understood upon analyzing the temperature dependence of contributions from different reaction channels, presented in Figures 3, 3S, and 4S. Two channels, tunneling from the vibrational ground state and vibrationally activated via the 180 cm−1 mode, dominate for temperatures below 270 K for 1 and even up to 370 K in the case of 2. In the latter, all other channels contribute no more than 20% at room temperature. Actually, these minor channels also can contribute via vibrationally assisted tunneling: for 1, a
⎪
where k0 is the vibrational ground-state tunneling rate and kn describes a relative contribution of nth channel with activation energy En. Consistent fitting of the Arrhenius data for nondeuterated 1 and 2 in both S0 and S1 with the same number N of thermally activated channels requires N = 2. Actually, it is possible to fit all the four curves with functions which share one of the activation energies E1 ≈ 0.5 kcal/mol (Table 1). This value coincides with energy of the 180 cm−1 vibrational mode which exhibits the largest tunneling splitting in isolated 1.29 Equality of these energies under conditions in which different shapes and heights of the tautomerization barrier are expected strongly supports the model assuming a significant acceleration of the trans−trans tunneling through excitation of this vibration. For the above-discussed molecules, the ratio k1/k0 of the vibrationally activated (k1) and vibrational ground-state (k0) reaction rates ranges from approximately 6 to more than 100. 285
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which experiments in helium nanodroplets31 allowed estimation of Δ as 0.02 cm−1, corresponding to 0.83 ns, whereas for S1, 1/k0 = (3.3 ± 1.8) ns. Analogously, for 2, the observed value of Δ in S0 is 9 cm−1,54 which gives τ = 1.9 ps, to be compared with 1/k0 = (2.6 ± 0.2) ps. Because k1 can be identified as the rate of tautomerization originating from the v = 1 level of the 2Ag vibration, one can compare the k1/k0 ratio with the expected value based on tunneling splittings. For 2Ag vibrationally excited electronic ground state (S0) of 1, Δ = 12 cm−1.29 In the incoherent tunneling regime the rate is proportional to Δ2, the square of the tunneling splitting.1,52 We obtain (12/4.4)2 = 7.4, in excellent agreement with k1/k0 = 7.0 ± 0.9. In summary, we demonstrated that tautomerization in porphycenes can be governed by tunneling, not only in the low-temperature regime but also under “normal” experimental conditions. It is important to note that the calculated tautomerization barrier is of the order of a few kilocalories per mole, so one could naturally expect an “over the barrier” path to be dominant. A general conclusion is that one should not neglect tunneling while studying hydrogen/proton-transfer reactions. At higher temperatures, vibrationally activated tunneling channels will usually be more important, but even vibrational ground-state tunneling can contribute significantly.
Figure 2. Temperature dependence of the kHH/kDD ratio obtained for ground-state tautomerization in 1 (a) and 2 (b). The solid curves were obtained using the parameters from Table 1.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.5b02482. Experimental procedures, additional figures, and tautomerization rates (PDF) Experimental data (ZIP)
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AUTHOR INFORMATION
Corresponding Authors
*E-mail: fi
[email protected]. *E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
Figure 3. Contributions of different reaction channels to the electronic ground-state tautomerization rates in 1 (top panel) and 2 (bottom panel) at various temperatures: (a) vibrational ground-state tunneling; (b) vibrationally activated (E1 = 0.5 kcal/mol) tunneling; and (c) other channels.
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ACKNOWLEDGMENTS This work has been supported by the Polish National Science Centre Grants DEC-2011/01/B/ST2/02053, DEC-2011/02/ A/ST5/00043, and DEC-2013/10/M/ST4/00069. The authors thank Tomasz Sowiński for valuable discussions on the influence of periodic perturbations on tunneling in a doublewell potential.
mode calculated at 947 cm−1 (= 2.7 kcal/mol, very close to E2; cf. Table 1) was suggested as reaction-promoting.19 We are now ready to correlate the reaction rates in the condensed phase with the data obtained for isolated molecules from the values of tunneling splittings.52,53 The inverse of k0 can be compared with residence time, τ, in the coherent process defined as τ = h/(2Δ), where h is the Planck’s constant and Δ is the tunneling splitting. For the vibrational ground state of porphycene in S0, Δ= 4.4 cm−1,27,29,31 yielding τ = 3.8 ps. This residence time sets the lower limit on the hydrogen tunneling time under incoherent conditions, the latter determined to be 1/k0 = (15 ± 1) ps. As expected, the reaction is slower in the condensed phase than in an isolated molecule because of asymmetrical perturbations of the potential well induced by interactions with the solvent. Lingering time of a proton in a double-well potential is extremely sensitive to such perturbations because they strongly hinder the tunneling.53 Similar comparison can be made for the singlet excited-state S1 of 1, for
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DOI: 10.1021/acs.jpclett.5b02482 J. Phys. Chem. Lett. 2016, 7, 283−288
