Anomalous Rate of H+ and D+ Excited

Article Cite This: J. Phys. Chem. A XXXX, XXX, XXX−XXX

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Anomalous Rate of H+ and D+ Excited-State Proton Transfer (ESPT) in H2O/D2O Mixtures: Irreversible ESPT in 1‑Naphthol-4-sulfonate Oren Gajst,† Georgi Gary Rozenman,‡ and Dan Huppert*,† †

Raymond and Beverly Sackler Faculty of Exact Sciences, School of Chemistry and ‡Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics, Tel Aviv University, Tel Aviv 69978, Israel ABSTRACT: We employed steady-state and time-resolved fluorescence techniques to study the rates of excited-state proton and deuteron transfer (ESPT) from an irreversible photoacid, 1-naphthol-4-sulfonate, to solvent mixtures of H2O and D2O. We found that the overall ESPT rate to the solvent mixture does not follow a linear relation with the H2O mole ratio. We used a chemical kinetic model to explain the deviation of the ESPT rate constant from linear behavior with H2O mole ratio. There are three water species in the H2O−D2O mixtures, H2O, D2O, and HOD. There are six rate constants of H+ and D+ transfers to the three species. When the H2O mole ratio before mixing is 0.5, HOD mole ratio in the mixture is 0.5. The ESPT rate to HOD is much smaller than that of H+ transfer to neat H2O and hence the concave shape of the plot of ESPT rate constants versus the H2O molar ratio of the mixtures.

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In our recent experiment on excited-state H+/D+ proton/ deuteron transfer (ESPT) we obtained results similar to the conductance measurements of Weingärtner and Chatzidimttriou-Dreismann. The ESPT rate constant, kPT, did not follow linear dependence on the mole ratio, χD2O, but had a concave shape with increase in χH2O, and the relative deviation at χ°D2O = 0.5 was twice that of the conductance experiments.3 For the experiments, we employed a widely used photoacid, 8-hydroxy-1,3,6-pyrenetrisulfonate (HPTS), shown in Scheme 1a.

INTRODUCTION The proton conductance, λ°H+, in H2O is greater than the deuteron conductance, λD° +, in D2O and the ratio λ°D+/λ°H+ ≈ 2/3. Weingärtner and Chatzidimttriou-Dreismann1 reported in 1990 that the conductance of protons λ°H+ or λ°D+ in H2O and D2O mixtures does not follow a linear relation with the mole fraction of χD° 2O of the premix mixture. The conductance has a concave shape with χH2O and a maximum deviation from linearity at χH° 2O = 0.5. The relative deviation at χH° 2O = 0.5 is ∼13%. In H2O/D2O mixtures there are three constituents, H2O, D2O, and HOD. The equilibrium constant for the formation of HOD is ∼4.2

Scheme 1. Molecular Structure of (a) 8-Hydroxy-1,3,6pyrenetrisulfonate (HPTS) and (b) 1-Naphthol-4-sulfonate (1N4S)

K eq

H 2O + D2 O XoooY 2HOD

Calculation showed that at χH° 2O = 0.5, ∼50% of the constituents are HOD, and each of H2O and D2O is 25%. Recently we conducted an experiment similar to that of Dreismann et al. of measuring the excited-state proton-transfer (ESPT) rate constant from a reversible photoacid in H2O and D2O mixtures.3 Photoacids are weak electronic ground-state acids with pKa in the range of 5−10.4−20 In their first excited electronic singlet state they are much stronger acids, with pKa* in the range of −8 to 3.4. For a pKa* of 3.4, the predicted ESPT rate is on the order of kPT = 2 × 107 s−1, which is much smaller than the excited-singlet-state fluorescence rate constant, kF > 108 s−1. Therefore, photoacids with pKa* > 3.4 cannot be observed by transient and steady-state (time-integrated) optical techniques. Weak photoacids with pKa* > 0.4 have a large kinetic isotope effect (KIE) of ∼3, whereas stronger photoacids with pKa* < −2 have a KIE of 2 or smaller. © XXXX American Chemical Society

The deprotonated form of HPTS, RO−, has four negative charges, and so the attractive proton-RO− Coulomb potential is large. A gauge of the Coulomb potential between ionic species in solution is given by the Debye radius, RD Received: October 29, 2017 Revised: December 6, 2017 Published: December 7, 2017 A

DOI: 10.1021/acs.jpca.7b10684 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

Figure 1. Steady-state (time-integrated) fluorescence spectra of 1-naphthol-4-sulfonate (1N4S) photoacid in mixtures of H2O and D2O over the range of χH2O of 0 to 1. (a) Linear scale and (b) semilogarithmic scale.

RD =

2 1 |z1z 2|e 4πε0ε kBT

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EXPERIMENTAL SECTION We used fresh solutions of 1N4S (shown in Scheme 1b) in all measurements. HPLC-grade or analytical-grade solvents were used in this study. D2O and H2O were purchased from SigmaAldrich. 1N4S was purchased from TCI. For the time-correlated single-photon-counting (TCSPC) measurements, we used, for sample excitation, a cavity-dumped titanium/sapphire femtosecond laser (Mira, Coherent). The laser output consists of 120 fs pulses over the spectral range of 760−860 nm. The third harmonic of the laser was used to excite the samples at 280 nm. The cavity dumper operated at a rate of ∼800 kHz. The TCSPC detection system was based on a Hamamatsu 3809U multichannel plate photomultiplier and an Edinburgh Instruments TCC 900 integrated TCSPC system. The time response of the instrument was ∼35 ps (full width at half-maximum (fwhm)). The excitation pulse energy was reduced by neutral-density filters to ∼10 pJ. The steady-state emission spectra were recorded by a Horiba Jobin Yvon FluoroMax-3 spectrofluorometer.

(1)

where e is the electron charge, z is the number of electron charges of the ionic species, ε is the dielectric constant, and ε0 is the electrical permittivity. For z = 4 of the RO− species in water with ε ≈ 80 at room temperature, (298 K), RD ≈ 28 Å. This means that the Coulomb potential between the RO− and the proton is equal to the thermal energy, kBT, of the proton at 28 Å. At distances shorter than RD, the Coulomb potential is greater than the thermal energy and vice versa. HPTS is a reversible photoacid in which the excited-state proton-RO− diffusion-assisted geminate recombination takes place and reforms the RO−* in the excited state RO−* + H+ ⇄ ROH*

(2)

where the asterisk designates the excited-state species. The reversible geminate recombination process increases the time-dependent population of the ROH*(t) form of the photoacid and complicates the analysis of the time-resolved fluorescence. In the current experiment, we studied the excited-state proton and deuteron transfers in H2O and D2O mixtures and used an irreversible photoacid in which RO−* reacts with a proton and the reaction leads to a ground-electronic-state product, ROH(g). kPT

RO−* + H+ ⎯→ ⎯ ROH(g)

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RESULTS Steady State. Figure 1a,b shows, on linear and semilogarithmic scales, the steady-state (time-integrated) fluorescence spectra of 1N4S photoacid in mixtures of H2O and D2O over the range of χH2O (molar ratio of H2O) of 0 to 1. The sample was excited at 320 nm near the ROH maximum absorption wavelength at ∼335 nm. The pKa of 1N4S is ∼9 and the sample pH was ∼7. As we will show, the ESPT rate constant for 1N4S in neat H2O is 2.4 × 1010 s−1 and in D2O it is ∼0.8 × 1010 s−1. The deprotonated form of 1N4S has a fluorescence lifetime of ∼14 ns and therefore the intensity ratio of the steady-state fluorescence R = IFRO−/IFROH is ∼100. Figure 1b shows that the ratio R is ∼160 in neat H2O and 55 in neat D2O. Weller21 used a kinetic approach to estimate the ESPT rate constant, kPT, from the intensity-band ratio of the steady-state fluorescence spectrum, IFRO−/IFROH.

(3)

The irreversible photoacid we used is the 1-naphthol-4sulfonate (1N4S). In the Results section, we devote a subsection to show that the 1N4S photoacid is indeed an irreversible photoacid. We found that the ESPT rate constant, kPT, did not follow a linear relation with the mole fraction, χH2O. The curve of kPT versus χH2O has a concave shape with a maximum deviation from linearity at about χH2O = 0.5. We present a chemical-kinetic model that accounts for three solvent species, H2O, D2O, and HOD, in H2O and D2O mixtures. The model is based on six ESPT rate constants of H+ and D+ transfers to H2O, D2O, and HOD.

F F −1 −/ I kPT ≅ IRO ROH· τF

(4)

where IFRO− and IFROH are the steady-state fluorescence intensities of the RO− and ROH bands and τF is RO− fluorescence lifetime B


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The Journal of Physical Chemistry A of 1N4S, which is ∼14 ns. The kPT for H2O calculated from the steady-state ratio IFRO−/IFROH is ∼1.2 × 1010 s−1. Scheme 2 shows the photoprotolytic cycle of reversible and irreversible photoacids.

ROH signal is affected by small amounts of acid. The excess protons reform the RO−* species to the excited-state ROH* in ∼1 ns, and the population of the ROH* at long times (t > 0.5) forms an exponential tail that has the lifetime of the RO−* species of ∼5 ns. On a semilog scale the fluorescence tail shows approximately a straight line with a decay time of ∼5 ns. The amplitude of this line increases with increase in the acid concentration. Figure 2b shows, on a semilog scale, the time-resolved fluorescence of the ROH and RO− forms of 1N4S, an irreversible photoacid. The TCSPC ROH signal is not much affected by the acid concentration, whereas the RO− form is affected. The Figure shows five TCSPC signals of the RO− form. The longest decay time of ∼14 ns is in acid-free solution. When acid is introduced to solution the excess protons react with the RO−* and form the ground-state ROH(g) form. The reaction rate constant is about that of a diffusion-controlled reaction with an approximate second-order rate constant given by the following equation

Scheme 2. Photoprotolytic Cycle of Photoacids

Electronic excitation of the ROH form leads to an excitedstate-proton transfer to the solvent. The reversible route of the geminate proton in solution can cause recombination of the proton with the RO−* and reform the excited-state ROH* that can undergo a second cycle. For an irreversible photoacid, the geminate recombination leads to ground-state ROH, as in the case of 1-naphthol and its sulfonate derivatives. The irreversible route, which applies to the current study of the photoacid 1N4S, reforms the ground-state ROH(g) by a diffusion-assisted proton-recombination process. Because the RO− form is negatively charged by two electronic units in 1N4S, the proton geminate recombination is enhanced and contributes to the repopulation of the ROH(g). When we compare the fluorescence intensity of the ROH band in neat H2O and neat D2O, we note that the steady-state fluorescence intensity of the ROH in D2O is about three times that in H2O because the ESPT rate in D2O is smaller by a factor of ∼3 in 1N4S. To demonstrate the difference in the time-resolved fluorescence of reversible and irreversible photoacids we measured the acid effect on HPTS, a commonly used reversible photoacid, and on 1N4S, an irreversible photoacid. Figure 2a shows the time-resolved fluorescence of the ROH and RO− forms of HPTS in the absence of acid and in the presence of 10−2, 2 × 10−2, and 3 × 10−2 M HCl in aqueous solution. The TCSPC plots are shown on a semilog scale. For reversible photoacids, the RO− signal is not affected by the presence of low concentrations of acid. By contrast, the

kD = 4πN ′D H+RD

(5)

where kD is the diffusion-controlled second-order constant, DH+ is the proton diffusion coefficient of DH+ ≈ 10−4 cm2/sec, and N′ = NA/1000, where NA is Avogadro’s number. RD is the Debye radius given in eq 1. For RO− of 1N4S (two negative charges) kD is 1011 M−1 s−1. The acid concentrations in the experiment shown in Figure 2b are approximately 10, 20, 30, and 40 mM HCl. Figure 3a,b shows the time-resolved fluorescence (TRF) of 1N4S on a linear scale of the ROH form of the photoacid, in H2O and D2O mixtures, measured at 350 nm. Figure 3a shows the D2O-rich (0.5 ≤ χD2O ≤ 1) H2O/D2O mixtures, whereas Figure 3b shows H2O-rich (0.5 ≤ χH2O ≤ 1) H2O/D2O mixtures. Figure 3c,d displays the TRF of the ROH form in H2O/D2O mixtures on a semilogarithmic plot. We analyze the signals by a three-exponential fit function convoluted with the instrument-response function (IRF) of the TCSPC system. The IRF full width at half-maximum is ∼35 ps and is also shown in Figure 3.

Figure 2. (a) Normalized time-resolved fluorescence signal of the ROH and RO− forms of HPTS in acidified aqueous solutions. (b) RO− and ROH forms of 1-naphthol-4-sulfonate in acidified aqueous solutions. C


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Figure 3. Time-resolved fluorescence (TRF) of the ROH form of the photoacid 1N4S, measured at 350 nm. (a,b) Linear scale and (c,d) semilogarithmic scale.

Table 1 shows the amplitude and the time constants of the best-fit function of 1N4S solutions in various mixtures of H2O and D2O over the range of 0 ≤ χH2O ≤ 1. Because 1N4S is an irreversible acid and the charge of the RO− is only two electronic units, the diffusion-assisted geminate proton recombination has little effect on the fluorescence decay of the ROH. About 96% of the signal is exponential and provides the ESPT rate. About 4% of the ROH decay provides a reversible geminate recombination or it displays the fluorescence of the impurities in the powder provided by TCI Company (Japan). Figure 4a shows the ESPT rate constant, kPT, of 1N4S to a premix mixture of H2O and D2O (χH° 2O) as a function of χH2O in the range of 0 ≤ χ°H2O ≤ 1. There are 24 data points over the range of χH2O of 0 to 1. Over the range of 0.1 ≤ χH° 2O ≤ 0.8 we see a deviation of kPT from the linear relation of premix molar ratio of χ°H2O. The shape is concave and the maximum deviation from linearity is at about χH2O ≈ 0.5. The ESPT rate constant is determined from τ1 in the TRF analysis with amplitude of 0.96 of the total signal. Figure 4c shows the relative deviation of kPT of 1N4S from the linear molar ratio relation kL. The maximum deviation is ∼10% at χ°H2O ≈ 0.5.

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Table 1. Fit Parameters of Three-Exponent Fit for the TimeCorrelated Fluorescence Signal of 1N4S Solutions in Various Mixtures of H2O and D2Oa

MAIN FINDINGS a

(1) The ESPT rate constant, kPT, to the solvent from 1N4S in H2O/D2O mixtures does not follow a linear relation with the mole ratio of H2O. D

χwater

a1

τ1 (ps)

a2

τ2 (ns)

a3

τ3 (ns)

1 0.972 0.946 0.921 0.875 0.824 0.778 0.7 0.637 0.584 0.539 0.5 0.5 0.462 0.418 0.364 0.3 0.223 0.177 0.125 0.079 0.054 0.028 0

0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96

43 44 44 46 46.5 48.5 54.5 56 58.5 63 66.5 69 70.5 74 75.5 80 83.5 92 94 100 103 106 110 117

0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034

0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.24 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.30 0.30 0.32 0.32 0.32 0.32 0.32

0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0052 0.0055 0.0060 0.0072 0.0070 0.0070 0.0073 0.0073 0.0073 0.0073

1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8

Error in determination of ai is 3% and of τi is 5%.


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Figure 4. (a) ESPT rate constant of 1N4S to a premix mixture of H2O and D2O (χ°H2O) as a function of χH2O in the range of 0 ≤ χ°H2O ≤ 1. (b) Solid curve exponential fit f(χH2O) = a·exp(b·χH2O). (c) Relative deviation of kPT of 1N4S from linear molar-ratio relation kL. The estimated error for the (vertical) experimental values (panels a and b) is ±4%, and for (vertical) derived values (panel c) it is ±6%. The estimated error for the premix water molar ratio (X axis in all panels) is ±0.02.

therefore find ROH as well as ROD molecules in ground and excited states. The value of Keq of eq 6 was calculated by Wolfsberg2 with the use of statistical mechanics and studied experimentally by NMR methods.22 The Keq values determined in these studies are close to 4. Figure 5 shows a plot of the calculated mole fractions of HOD as a function of χH2O, for Keq = 4. The maximum mole ratio of HOD occurs when the mole ratios of H2O and D2O in the mixture are equal, χ°H2O = χ°D2O = 0.5. The mole ratio of HOD is ∼0.5 at χH° 2O = 0.5. It decreases symmetrically when the H2O and D2O mixtures deviate from χ°H2O = 0.5.

(2) The plot of kPT versus χH2O has a concave shape with a maximum deviation from linearity at χH2O = 0.5. (3) There are three chemical species in mixtures of H2O/ D2O, H2O, D2O, and HOD, that at χH2O = 0.5 is the main species χHOD = 0.5. (4) In the current study, on the basis of our calculations, we conclude that the rate constant of the ESPT to HOD, kHOD PT , of H+ or D+ is much lower than expected from linear relation of kPT versus χH2O and therefore the large deviation at χH2O = 0.5. (5) We found that kHOD = 1.17 ± 0.02 × 1010 s−1, kHOD = + DH H+ O DO 1.59 ± 0.02 × 1010 s−1, kH2+ = 2.4 × 1010 s−1, and kD2+ = 0.85 × 1010 s−1. The KIE of the ESPT rate constant in neat H2O and D2O is ∼2.85. The KIE of HOD is rather small, KIE = 1.36 ± 0.04.

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DISCUSSION Chemical Model for Anomalous H + and D + k PT Deviation from Linear Dependence from Premix Mole Ratio (χH° 2O). In a mixture of H2O and D2O, the solvent consists of three species, H2O, D2O, and HOD. Water rapidly exchanges the hydrogen or deuterium atoms. The chemical exchange reaction in an H2O/D2O mixture is given by K eq

H 2O + D2 O XoooY 2HOD

(6)

The irreversible photoacid 1N4S exchanges the hydroxyl hydrogen with deuterium, and in H2O and D2O mixtures, we

Figure 5. Calculated mole fractions of HOD as a function of χH2O. E


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Table 2. Calculated Values of the Prefactors a1, a2, a3, and a4 of the Four Unknown Rate Constants

Chemical Model assumptions: (1) The mole ratio of ROH to ROD in D2O-rich mixtures is determined by the equilibrium constant of the following process K ′eq

ROH + D2 O XoooY ROD + HOD

(7)

If the equilibrium constant k′eq is 4, then the ROH and ROD concentrations are the mole ratio values. (2) There are six ESPT rate equations kDHOD

ROD* + HOD ⎯⎯⎯⎯→ RO−* + D2 OH+

(8a)

kHHOD

ROH* + HOD ⎯⎯⎯⎯→ RO−* + H 2OD+

(8b)

kHD2O

ROH* + D2 O ⎯⎯⎯⎯→ RO−* + D2 OH+

(8c)

kDH2O

ROD* + H 2O ⎯⎯⎯→ RO−* + H 2OD+

(8d)

kDD2O

ROD* + D2 O ⎯⎯⎯⎯→ RO−* + D3O+

(8e)

kHH2O

ROH* + H 2O ⎯⎯⎯→ RO−* + H3O+

kDD2O,

kDH2O,

kHD2O,

kHH2O,

kHOD H ,

(8f)

kHOD D

where in and the superscript denotes the solvent molecule that accepts the proton or deuteron and the subscript denotes the proton or deuteron transferred from the excited ROH* or ROD* forms of the photoacid. The two rate constants kHH2O and kDD2O are determined from the experimental results of 1N4S in neat H2O and D2O, respectively. We tried to solve the following rate equation with four unknown rate constants 2

2

2

2

a1 (χHOD × χ°D2O)

a2 (χHOD × χ°H2O)

a3 (χD2O × χ°H2O)

a4 (χH2O × χ°D2O)

1 0.972 0.946 0.921 0.875 0.824 0.778 0.7 0.637 0.584 0.539 0.5 0.5 0.462 0.418 0.364 0.3 0.223 0.177 0.125 0.079 0.054 0.028 0

0 0.001524 0.005517 0.011496 0.027344 0.051048 0.076686 0.126 0.167874 0.202129 0.229098 0.25 0.25 0.267446 0.283173 0.294473 0.294 0.269263 0.239774 0.191406 0.134022 0.096651 0.052908 0

0 0.052907904 0.096650928 0.134022078 0.19140625 0.238999552 0.268746096 0.294 0.294588294 0.283758592 0.267860362 0.25 0.25 0.229665744 0.203378736 0.168534912 0.126 0.077278866 0.051567534 0.02734375 0.011495922 0.005517072 0.001524096 0

0 0.000762048 0.002758536 0.005747961 0.013671875 0.025524224 0.038342952 0.063 0.083936853 0.101064704 0.114548819 0.125 0.125 0.133723128 0.141586632 0.147236544 0.147 0.134631567 0.119887233 0.095703125 0.067011039 0.048325464 0.026453952 0

0 0.026454 0.048325 0.067011 0.095703 0.1195 0.134373 0.147 0.147294 0.141879 0.13393 0.125 0.125 0.114833 0.101689 0.084267 0.063 0.038639 0.025784 0.013672 0.005748 0.002759 0.000762 0

We assume that at χ°H2O = 0.5 two-thirds of the modified rate constant (the right-hand side of eq 9) is due to the proton and deuteron transfer to HOD and only one-third is the contribution of proton and deuteron transfer to D2O and H2O, kDH2O and kHD2O, respectively. We solved the two algebraic equations for kHOD and kHOD H D D2O and separately solved the two equations for kH and kHD2O. We found that the rates are

χD O χROH kHD2O + χH O χROD kDH2O + χHOD χROD kDHOD + χHOD χROH kHHOD = kd − (χH O χROH kHH2O + χD O χROD kDD2O)

χ°H2O

(9)

for four mixtures of H2O and D2O as we succeeded for HPTS.3 We failed to solve these four equations for 1N4S with D2O HOD reasonable values of the rate constants kHOD D , kH , kH , and H2O kD . Under the assumptions of the model, we failed to solve four kinetic equations at four different values of χ°H2O and get positive values for all four rate constants. We believe that the small, 10%, deviations of the maximum (at χ°H2O = 0.5) are not enough to solve eq 9. We therefore used a different strategy to obtain the four rate D2O H2O HOD constants kHOD H , kD , kH , and kD . Table 2 shows the calculated values of the prefactors a1, a2, a3, and a4 of the four unknown rate constants. At χH° 2O = 0.5 and χD° 2O = 0.5, the prefactors for kHOD and H DO HO HOD kD are each 0.25, whereas those of kH2 and kD2 are only 0.125 each, half that of kHOD and kHOD H D . We therefore solve two algebraic equations for two unknowns, kHOD and kHOD H D . The right-hand side of the equation is kESPT − (a5k5+a6k6). kESPT is the overall experimental rate constant of a certain H2O and D2O mixture, and k5 = kHH2O is the kPT in neat H2O, and k6 = kDD2O is the kPT in neat D2O. The prefactor a5 = χH2O × χH° 2O equals 1 for neat H2O and a6 = χD2O × χ°D2O equals 1 for neat D2O.

kHHOD = 1.59 ± 0.02 × 1010 s−1 kDHOD = 1.17 ± 0.02 × 1010 s−1

kHD2O = 1.02 ± 0.03 × 1010 s−1 kDH2O = 1.70 ± 0.03 × 1010 s−1

The KIE of H+/D+ transfer to HOD is very small, KIE = 1.36 ± 0.04. These values are compatible with the values we previously found for HPTS. χHOD is twice that of χH2O or χD2O at χ°H2O = 0.5. Therefore a1 is the prefactor for kHOD and we obtain a1 = D χHOD × χD° 2O = 2 × χH° 2O × χD° 2O × χD° 2O. a2 is the prefactor for kHOD and we obtain a2 = χHOD × χ°H2O = 2 × χ°D2O × χ°H2O × χ°H2O. H a3 is the prefactor for kDH2O and we obtain a3 = χD2O × χH° 2O = χ°D2O × χ°D2O × χ°H2O. a4 is the prefactor for kHD2O and we obtain a4 = χH2O × χD° 2O = χH° 2O × χH° 2O × χD° 2O. Thus we see that a2 = 2a4 and a1 = 2a3. Figure 6 shows the calculated rate constants of our model (red circles and blue solid line) as a function of the premix H2O molar ratio, χH° 2O. F


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two. The species are H2O, D2O, and HOD, which are formed rapidly in the solvent mixture. There are six ESPT rate constants for the transfer of H+ and D+ to the three solvent constituents. We solved four kinetic equations for four unknown rate constants. Similar anomalous behavior is found in the conductance of protons and deuterons in H2O and D2O mixtures.1 In the current study, we used an irreversible photoacid, 1N4S, and we found results similar to those found for the reversible photoacid, HPTS. The ESPT rate constant, kPT, of H+ and D+ to the three solvent constituents, H2O, D2O, and HOD, shows a milder deviation than that found for HPTS. We found a concave shape of the overall ESPT rate constant to the H2O and D2O mixtures. The deviation from linearity with χH2O is about half of that found for HPTS. The main conclusion of this research and the previous HPTS research is that the proton- and deuteron-transfer rate constants to HOD are smaller than the weight-average, χH2O × kHPT2O + DO χD2O × kDT2 . Thus the combined rate constant given in eq 9 is smaller than the straight line connecting the points of kDD2O and kHH2O in Figure 4.

Figure 6. Overall ESPT rate constant of 1N4S in mixtures of H2O and D2O. The red circles are the ones calculated with the use of eqs 8a−8f. The black squares are the experimental results deduced from the timeresolved fluorescence. The estimated error for the (vertical) experimental values is ±4%, and for premix water molar ratio (X axis) it is ±0.02.

We also added the experimental results (black squares). As seen in the Figure, the calculated results nicely fit the experimental k PT as analyzed from the time-resolved fluorescence of the ROH form of the irreversible photoacid 1N4S. The calculated ESPT rate constant, kPT, is

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Corresponding Author

6

kPT =

∑ aiki

*E-mail: [email protected]. Tel: 972-3-6407012. Fax: 972-3-6407491.

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i=1

ORCID

where ai are the prefactors given in Table 2 and ki are the rate constants given in eqs 8a−8f. Because maximum deviation from linear dependence of kPT on χH2O occurs at χH2O ≈ 0.5, we conclude that χD O kHD2O 2

+

χH O kDH2O 2

+

χHOD kDHOD

< χH◦ O kHH2O + χD◦ O kDD2O 2

2

+

Dan Huppert: 0000-0002-0292-4106 Notes

The authors declare no competing financial interest.

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χHOD kHHOD

ACKNOWLEDGMENTS This work was supported by a grant from the Israel Science Foundation 1587/16.

(11)

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where χ°H2O and χ°D2O are the premix mole fractions of H2O and D2O. We assume that in the χH2O = 0.5 mixture, the overall rate of all four kinds of reactions is smaller than the mean of the known rate constants,

kHH2O + kDD2O 2

AUTHOR INFORMATION

REFERENCES

(1) Weingärtner, H.; Chatzidimttriou-Dreismann, C. Anomalous H and D Conductance in H2O−D2O Mixtures. Nature 1990, 346, 548− 550. (2) Wolfsberg, M.; Massa, A. A.; Pyper, J. Effect of Vibrational Anharmonicity on the Isotopic Self-Exchange Equilibria H2X D2X= 2HDX. J. Chem. Phys. 1970, 53, 3138−3146. (3) Gajst, O.; Simkovitch, R.; Huppert, D. Anomalous H+ and D+ Excited-State Proton-Transfer Rate in H2O/D2O Mixtures. J. Phys. Chem. A 2017, 121, 6917−6924. (4) Martynov, Y.; Demyashkevich, A.; Uzhinov, B.; Kuz'min, M. Proton-Transfer Reactions in Excited States of Aromatic Molecules. Russ. Chem. Rev. 1977, 46, 1−15. (5) Ireland, J. F.; Wyatt, P. A. Acid-Base Properties of Electronically Excited States of Organic Molecules. Adv. Phys. Org. Chem. 1976, 12, 131−221. (6) Gutman, M.; Nachliel, E. The Dynamic Aspects of Proton Transfer Processes. Biochim. Biophys. Acta, Bioenerg. 1990, 1015, 391− 414. (7) Tolbert, L. M.; Solntsev, K. M Excited-State Proton Transfer: From Constrained Systems to “Super” Photoacids to Superfast Proton Transfer. Acc. Chem. Res. 2002, 35, 19−27. (8) Rini, M.; Magnes, B. Z.; Pines, E.; Nibbering, E. T. Real-Time Observation of Bimodal Proton Transfer in Acid-Base Pairs in Water. Science 2003, 301, 349−352. (9) Mohammed, O. F.; Pines, D.; Dreyer, J.; Pines, E.; Nibbering, E. T. Sequential Proton Transfer Through Water Bridges in Acid-Base Reactions. Science 2005, 310, 83−86.

. Under these assumptions, the

deviation of kPT from linear dependence on χH2O is expected. The overall ESPT rate constant, kPT, from ROD and ROH in H2O and D2O mixtures is smaller than expected from linear dependence on χH° 2O of the mixtures. The overall maximum deviation from linear dependence on χH2O for the ESPT reaction of the irreversible photoacid 1N4S is ∼10% at χH2O ≈ 0.5, where the solvent is HOD.

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SUMMARY AND CONCLUSIONS In a previous article,3 we employed the commonly used reversible photoacid HPTS, shown in Scheme 1a, to study the ESPT rate in mixtures of H2O and D2O over the range of χH2O of 0 to 1. We found that the ESPT rate constant, kPT, does not follow a linear relation with χH2O. The KIE of HPTS is ∼3. When we plot kPT as a function of χH2O of the H2O and D2O solvent mixture we obtain a concave shape and maximum deviation from the linear plot (see figure 4 of ref 3) at χH2O ≈ 0.5. We explained the deviation from linearity by pointing out that the solvent mixture contains three constituents rather than G


Article

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H


Anomalous Rate of H+ and D+ Excited

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