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Anomalous H and D Excited-State Proton-Transfer Rate in HO/DO Mixtures Oren Gajst, Ron Simkovitch, and Dan Huppert J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b04361 • Publication Date (Web): 21 Aug 2017 Downloaded from http://pubs.acs.org on August 27, 2017

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The Journal of Physical Chemistry

Anomalous H+ and D+ Excited-State Proton-Transfer Rate in H2O/D2O Mixtures Oren Gajst, Ron Simkovitch and Dan Huppert* Raymond and Beverly Sackler Faculty of Exact Sciences, School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel *Corresponding author: Dan Huppert E-mail: [email protected] Phone: 972-3-6407012 Fax: 972-3-6407491

Abstract We used the time-resolved fluorescence technique to measure the excited-state proton-transfer (ESPT) rates from 8-hydroxy-1,3,6-pyrenetrisulfonate (HPTS) to solvent mixtures of H2O and D2O. We found an anomalous deviation from linear mole-fraction behavior of the ESPT rate in H2O/D2O mixtures. We provide a chemical model based on equilibrium constant of the reaction H2O+D2O↔2HOD and rate constants of the ESPT process of H and D transfers from HPTS to the mixed solvent. Anomalous deviation from linear mole-fraction behavior was previously found for H+/D+ conductance in these mixtures.

1 Environment ACS Paragon Plus


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Introduction In 1990 Weingärtner and Dreismann1 reported that the electrical conductance Λ0 of protons and/or deuterons in H2O and D2O mixtures does not show a linear dependence on xD2O of the mixture. This anomalous conductance in H2O/D2O mixtures was not explained by a quantitative theory but by general comments that are related to fundamental quantum-mechanical phenomena such as quantum interference and correlation, because of the rather long thermal de Broglie wavelength of the proton of about 1Å. The conductance of D+ in D2O is about 2/3 of that of H+ in H2O. The kinetic isotope effect (KIE) is about 1.45 for the prototropic conductance i.e, the proton- and deuteron-transfer rates between H3O+ and H2O and D3O+ and D2O. The motivation for the current work was the findings of Weingärtner and Dreismann1 that the conductance of H+/D+ does not follow a linear relation with xD2O in H2O/D2O mixtures. The experimental values of Λ0 in the mixtures have smaller values than those calculated from a linear relation of Λ0 with xD2O . Photoacids are organic compounds that are weak acids in their ground electronic state but much stronger acids in their first excited electronic singlet state. Photoacids are usually hydroxyaryl compounds like naphthols and their derivatives. The ground-state pKa of photoacids range from 5-10 and their excited-state pKa* varies from -8 to about 3.4. The high photoacidity is followed by steady-state optical methods and by time-resolved fluorescence and other time-resolved optical techniques that monitor the excited-state population as a function of time of both the excited photoacid ROH* and of the conjugate base, RO-*.2-18 8-hydroxy-1,3,6pyrenetrisulfonate (HPTS), shown in Scheme 1, is a thoroughly studied photoacid.19-22 HO

-

SO3

-

SO3

-

SO3

Scheme 1 Molecular structure of 8-hydroxy-1,3,6-pyrenetrisulfonate (HPTS)


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The ground-state pKa is about 7.4 and the excited-state pKa* is ~1.3. The rate constant of the excited-state proton transfer (ESPT) to water, kPT, is ≈1010s-1 (τPT=100ps). When the HPTS is dissolved in D2O, the ESPT reaction rate constant is smaller by about a factor of three and thus the KIE is ~3. Kinetic isotope effects are measured for proton (hydrogen) and deuteron (deuterium) intramolecular and intermolecular transfer reactions. The KIEs of photoacids range from ≈5 in the biological environment of the green fluorescent protein GFP23 to about 1.7 for very strong photoacids with pKa*0.4, the ESPT rate constant, kPT, in H2O or D2O shows that KIE=3±0.2.

We conducted a study of the excited-state proton/deuteron-transfer rate of HPTS in H2O/D2O mixtures similar to the conductance measurements. We used timeresolved fluorescence to measure the ESPT rate constant, kPT, of HPTS in H2O/D2O mixtures. We found that the kPT values of H2O/D2O mixtures do not follow a linear relation with xH 2O as was found previously for the conductance of H+/D+ in H2O/D2O mixtures. We also found that the relative maximum deviation from linearity with xH 2O occurs at about xH 2O ≈0.4. The relative maximum deviation from linearity of the ESPT rate constant is about 27%, whereas that of Λ0 is only about 13%. Materials and Methods We used fresh solutions of HPTS (shown in Scheme 1) in all measurements. HPLC-grade or analytical-grade solvents were used in this study. D2O and H2O were purchased from Sigma-Aldrich. 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 120fs pulses over the spectral range of 760-860nm. The second harmonic of the laser was used to excite the samples at 395nm. The cavity dumper operated at a rate of ~800kHz. 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 approximately 40ps (full-width at half-maximum, FWHM). The excitation pulse energy was reduced by neutral-density filters to about 10pJ. The steady-state emission spectra were recorded by a Horiba Jobin Yvon FluoroMax-3 spectrofluorometer. Results Figure 1 shows the normalized steady-state fluorescence spectra of 8-hydroxy-1,3,6pyrene trisulfonate (HPTS) in 18 solutions of mixtures of slightly acidic (pH~6) H2O and D2O. a) 1.0

b) 1.0

xH O=0.499 2

xH O=0 2

xH O=0.539

xH O=0.091

2

xH O=0.637 2

xH O=0.700 2

0.6

xH O=0.770 2

xH O=0.834 2

xH O=0.909

0.4

xH O=0.167

0.8

2

Norm. Signal

Norm. Signal

2

xH O=0.584

0.8

2

xH O=1 2

2

xH O=0.231 2

xH O=0.293 2

0.6

xH O=0.352 2

xH O=0.408 2

xH O=0.454

0.4

2

xH O=0.501 2

0.2

0.2

0.0

0.0

450

500

550

600

650

450

Wavelength (nm)

c)

3x109

500

550

600

650

Wavelength (nm)

kHPTS PT

2x109

kHPTS PT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1x109

0 0.0

0.2

0.4

0.6

0.8

1.0

xH O 2

Figure 1: a. Normalized steady-state fluorescence spectra of HPTS in nine water-rich solutions of mixtures of slightly acidic (pH~6) H2O and D2O. b. normalized steady-state fluorescence spectra of HPTS in nine D2O-rich solutions of mixtures of slightly acidic (pH~6) H2O and D2O. c. kPT values deduced from Equation 1 versus the mole ratio of H2O in the H2O/D2O mixtures. The plot shows that the kPT values do not follow the mole-ratio dependence.


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The fluorescence spectra consist of two emission bands. The weaker emission band, with a maximum at about 440nm, is that of the protonated form of HPTS, the ROH, and the strong band, with a maximum at 512nm, is that of the RO- form. The samples were excited at 390nm, slightly blue-shifted from the ROH absorption-band maximum at ~405nm. The ground-state pKa is at 7.4 and the excited-state pKa*≈1.3. Figure 1a shows the fluorescence spectra of water-rich solutions, (0.5≤ x H 2O ≤1), whereas Figure 1b shows the spectra of D2O-rich mixtures, (0≤ x H 2O ≤0.50. As seen in the figures, the intensity ratio of the two bands, measured at the band maxima, depends on the mole ratio of the mixture. Scheme 2 shows the photoprotolytic cycle of photoacids.

Scheme 2: The photoprotolytic cycle of photoacids

Electronic excitation of the ROH form leads to an excited-state proton transfer to the solvent. The proton in solution can recombine with the RO-* and reform the ROH* that can undergo a second cycle. Because the RO- form is negatively charged by four electronic units, the proton geminate recombination is large and contributes to the repopulation of the ROH*. It is estimated that the intensity of the steady-state (timeintegrated) ROH HPTS fluorescence is more than twice that of an irreversible photoacid, where the geminate recombination leads to ground-state ROH, like 1naphthol and its sulfonate derivatives. When we compare the fluorescence intensity of the ROH band in neat H2O and D2O, we note that the fluorescence intensity of the ROH in D2O is about three times that in H2O. Weller24 used a kinetic approach to estimate the ESPT rate constant, kPT, from the steady-state fluorescence-spectrum F F intensity-band ratio, I RO - / I ROH .

F F -1 k PT ≅ I RO - / I ROH ⋅ τ F

1



F F where I RO - and I ROH are the steady-state fluorescence intensities of the RO and ROH

bands and τ F is RO- fluorescence lifetime of HPTS which is 5.4ns. The lifetime of the ROH form of HPTS in ethanol is about 5ns and in ethanol, the ESPT process does not take place. Figure 1c shows the kPT values deduced from the steady-state fluorescence spectra and Equation 1. The error in the determination of kPT values from the steadystate fluorescence spectra is estimated to be ±4%. The values of kPT are plotted versus the mole ratio of H2O in the H2O/D2O mixtures. The plot shows that the kPT values do not follow the mole-ratio dependence but are smaller than expected. A similar deviation from mole-ratio dependence was found for proton conductance λHo + in H2O/D2O mixtures by Weingärtner and Dreismann1. Figure 2 shows the time-resolved fluorescence of the ROH form of HPTS measured at 435nm, slightly blue-shifted from the steady-state fluorescence band peak at 445nm to avoid overlap with the RO- fluorescence. a)

1.0

b)

xH O=0

1

xH O=0

2

2

xH O=0.109

xH O=0.109

xH O=0.178

xH O=0.178

2

2

2

2

Norm. Signal

Norm. Signal

0.8

xH O=0.256 2

xH O=0.326

0.6

2

xH O=0.388 2

xH O=0.44 2

0.4

xH O=0.492 xH O=0.542 2

xH O=0.256

0.1

2

xH O=0.326 2

xH O=0.388 2

xH O=0.44 2

xH O=0.492 xH O=0.542 2

0.01

2

2

0.2 0.0

1E-3 0.0

0.5

1.0

1.5

0

2

Time (ns)

c)

4

6

8

10

Time (ns)

d)

1.0

xH O=0.50

1

xH O=0.50

2

2

xH O=0.545

xH O=0.545

xH O=0.60

xH O=0.60

2

0.8

2

2

Norm. Signal

2

Norm. Signal

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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xH O=0.66 2

xH O=0.73

0.6

2

xH O=0.805 xH O=0.896 2

2

0.4

xH O=1 2

xH O=0.66

0.1

2

xH O=0.73 2

xH O=0.805 xH O=0.896 2

2

xH O=1 2

0.01

0.2 0.0

1E-3 0.0

0.5

1.0

1.5

0

Time (ns)

2

4

6

8

Time (ns)

Figure 2: Time-resolved fluorescence decay curves of HPTS in H2O/D2O mixtures, showing the H2O mole fraction. a. mole fraction of water between 0-0.54, shown on a linear scale. b.


10

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mole fraction of water between 0-0.54, shown on a semilogarithmic scale. c. mole fraction of water between 0.5-1, shown on a linear scale. d. mole fraction of water between 0.5-1, shown on a semilogarithmic scale.

Figures 2a and 2b show, on linear and semilog scales, the signals of the ROH fluorescence decay of nine mixtures of H2O and D2O in the range of 0 < xH2O < 0.542 . As seen in Figure 2b, the fluorescence decay of the ROH form of HPTS in these solvent mixtures is nonexponential. The reason for this is the reversible diffusionassisted geminate recombination process. In the excited state, the HPTS is a stronger acid than in the ground state by about seven orders of magnitude. The ESPT rate constant, kPT, in H2O is 1010s-1 (τPT=100ps). The proton is transferred to the bulk water. The RO- form is negatively charged by four electronic units (z=4). The proton in solution is attracted to the RO- by a strong Coulomb potential. The Debye radius is a gauge for the Coulomb potential and is given by Equation 2.

RD =

z1z2 e2 4πε 0ε kBT 1

2

For z=4 at room temperature, (298K) RD≈28Å. This means that the thermal energy, kBT, of the proton at 28Å is equal to the Coulomb potential between the RO- and the proton. At distances shorter than RD, the Coulomb potential is greater than the thermal energy and vice versa. Since the proton has a finite probability of recombining with the RO-*, the geminate recombination reforms the excited ROH*. The ROH* photoacid can subsequently undergo a second photocycle and so on. The end result of the quasi-equilibrium between the proton and the RO-* and ROH* forms of the photoacid, leads to a long-time nonexponential fluorescence tail of the ROH* timeresolved fluorescence signal. The time-resolved fluorescence, ROH(t) signal shape and time-dependent decay can be fitted by a theoretical model that takes into account the reversibility and the diffusional motion of the proton in solution.20,21 The Spherical Symmetrical Diffusion Program (SSDP) of Krissinel' and Agmon25 numerically solves the reversible geminate-recombination model of photoacids and provides the time-resolved fluorescence, I FROH (t ) , signal fit. There are several parameters and assumptions involved in this solution. If the proton-diffusion coefficient and the fluorescence lifetimes of both the ROH and RO- forms are known, there are two parameters that are used in the simulation and fit: the ESPT and



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recombination rate constants. The asymptotic long-time fluorescence decay of the ROH signal is given by20,21

P(t ) = I FROH (t )exp(

t -

τ FRO

)=

Keq (4π Dt )3/ 2

3

The fluorescence decay at long times follows a power law of time (t-3/2) for proton diffusion in three-dimensional space. Figures 2b and 2d show that the ROH signals have a long-time nonexponential fluorescence tail, that at long times, obeys a power law of t-3/2. Figures 2c and 2d show, on linear and semilog scales, the time-resolved fluorescence of the ROH form of HPTS in H2O-rich mixtures of H2O and D2O. Fitting procedure and fit results The fluorescence lifetimes of both ROH and RO- of HPTS are about the same; for H2O it is 5.4ns and for D2O it is somewhat shorter, τF=5.3ns. For the signals fit, we used a reaction-sphere radius of 6Å. This reaction sphere radius was used in the past by us and also by others.9 The proton diffusion in H2O/D2O mixtures is taken from the seminal work of Weingärtner and Dreismann.1 They found anomalous H+/D+ conductance in H2O/D2O mixtures. In the current study, we find similar anomalous behavior in the ESPT rate constant, kPT, of HPTS in H2O/D2O mixtures. The kPT values of a mixture do not follow the H2O mole-ratio relation given by D 2O H 2O D2 O k PT ( xH 2O ) = kPT + xH 2O ( kPT − kPT ).

4

kPT is determined by the fit of the early time of the ROH time-resolved fluorescence. At these times, the proton-recombination contribution to the signal is rather small. We estimate that the error in the determination of kPT values is ±7%, whereas the error for kr values is larger at ±10%. The largest deviation of kPT from a linear relation with

xH 2O is 27% at xH 2O ≈0.4. We are confident that the signal to noise ratio of the experimental signals is excellent and the main cause for error in the determination of kPT is due to the proton recombination process that causes the HPTS ROH signal to deviate from an exponential decay. At longer times, the geminate recombination repopulates the ROH* and the deviation from exponential decay is determined by both kr and DH + . Since DH + was previously measured by Dreismann,1 we change only the values of kPT and kr in order to obtain the best fit. 8 Environment ACS Paragon Plus

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Figure 3 shows the experimental time-resolved fluorescence of the ROH decay and the SSDP fit for pure H2O, pure D2O and a mixture of H2O/D2O with xH 2O =0.54. b)

1.0

Norm. Signal

0.8

1

H2O fit

H2O fit

xH O=0.54 fit

xH O=0.54 fit

D2O fit

D2O fit

2

2

Norm. Signal

a)

H2O

0.6

xH O=0.54 2

D2O

0.4

H2O

0.1

xH O=0.54 2

D2O

0.01

0.2 0.0

1E-3 0.0

0.5

1.0

1.5

2.0

2.5

3.0

0

1

2

Time (ns)

3

4

5

6

7

8

Time (ns)

Figure 3: Time-resolved fluorescence decay curves of HPTS in pure H2O, pure D2O and a mixture with xH 2O = 0.54, showing the SSDP fit for each curve. a. shown on a linear scale b. shown on a semilog scale.

As seen in the figure, the fits are rather good for all curves. Table S1 in the supporting information section provides the fitting parameters of the numerical solution by the SSDP25 program. Figure 4a shows the plot of the electrical conductance of HCl/DCl in H2O/D2O mixtures as a function of the mole ratio of H2O in the mixture. a)

440

Λ0 Exponential Fit

y=267+43⋅exp(1.3⋅xH O) 2

b) proton diffusion (cm2/s)

420

Λ0 (S⋅cm2/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


400 380 360 340 320

-5

9.5x10

proton diffusion

9.0x10-5 8.5x10-5 8.0x10-5 7.5x10-5 7.0x10-5 -5

6.5x10

300 0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.5

1.0

xH O

xH O

2

2



c)

9

kESPT

y=0.05+2.6⋅exp(1.25⋅xH O)

Exponential Fit

2

8 7

kESPT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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6 5 4 3 2 0.0

0.2

0.4

0.6

0.8

1.0

xH O 2

Figure 4: a. Molar conductance results that were taken from ref 1. b. proton diffusion as a function of xH 2O of H2O/D2O mixtures. c. ESPT rate constant of HPTS as a function of xH 2O of H2O/D2O mixtures.

The curve is taken from the work of Weingärtner and Dreismann.1 Figure 4b shows the values of the proton-diffusion coefficient calculated from the fit of the values of Λ0 of Reference 1, shown in Table 1, by the following equation:

Λ 0 = 267 + 43exp(1.3 ⋅ xH2O )

5

Table 1: Conductance and proton diffusion as a function of xH 2O .a

xH 2 O

Λ0(S·cm2/mol)

Proton diffusion (105cm2/s)

0

312.70

6.80

0.091

316.88

6.77

0.178

322.69

6.89

0.256

328.49

7.02

0.326

334.23

7.14

0.388

339.77

7.26

0.44

344.77

7.36

0.492

350.13

7.48

0.5

350.98

7.50

0.542

355.63

7.60

0.545

355.97

7.60


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a

0.6

362.48

7.74

0.66

370.14

7.91

0.73

379.86

8.11

0.805

391.31

8.36

0.896

406.81

8.70

1

426.92

9.12

Calculated, by eq. 5, from the experimental results of Dreismann et al26

The Einstein equation relates ion conductance, λ, and diffusion, D,

λ=

qD k BT

6

where q is the charge of the ion. Figure 4c shows the plot of the ESPT rate constant of HPTS in H2O/D2O mixtures as a function of the mole ratio of H2O in the mixture. The ESPT rate constant is obtained through the SSDP by fitting the time-resolved fluorescence decay signals of the ROH form of HPTS in the H2O/D2O mixtures. As seen in both plots, there is substantial deviation of both kESPT and the conductance, λH + , from the mole-fraction curve. Figure 5 shows the relative deviation of kESPT from mole-ratio dependence in H2O/D2O mixtures. exp ∆k ESPT / kL (H 2O) = {k ESPT ( xH 2O ) − k L ( xH 2O )}/ kL (H 2O)

7

where k L (H 2 O) is the value of kESPT that would be obtained if it followed linear exp ( x H 2O ) − k L ( xH 2 O ) . dependence on xH 2O , and ∆kESPT = kESPT



0.30 ∆kESPT/kL(xH O) 2

0.25

2

∆kESPT/kL(xH O)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.20 0.15 0.10 0.05 0.00 0.0

0.2

0.4

0.6

0.8

1.0

xH O 2

Figure 5: Relative deviation of kESPT from mole-ratio dependence in H2O/D2O mixtures.

k ( xH 2O ) is the ESPT rate expected from the mole ratio of the H2O/D2O mixtures as plotted by the straight line in Figure 4c. The maximum deviation occurs at xH 2O ≈0.4 and not at xH 2O ≈0.5. The maximum relative deviation is about 27%, much greater than the estimated error in the determination of kESPT which is ±5%. The maximum relative deviation from mole-fraction dependence in λH + at about xH 2O =0.5 is about 13.5 (see Figure 4a), about half that of the ∆kESPT (see Figure 5). Figure 6 shows the rate of geminate recombination, kr, as a function of xH 2O in H2O/D2O mixtures.


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7

kr

6 5

kr (Å/ps)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4 3 2 1 0 0.0

0.2

0.4

0.6

0.8

1.0

xH O 2

Figure 6: Rate of geminate recombination, kr, of HPTS as a function of xH 2O in H2O/D2O mixtures.

kr is obtained from fitting of the time-resolved fluorescence signals of the ROH form by the SSDP in mixtures of H2O/D2O. As seen in the figure, kr also deviated in D2Orich H2O/D2O mixtures from the expected xH 2O mole-ratio curve. The maximal deviation of kr also occurs at about xH 2O ≈0.4 as is found for kESPT and the relative deviation is about 25%, close to the value of kESPT of 27%.

Discussion Anomalous H+ and D+ conductance in H2O/D2O mixtures was experimentally measured by Weingärtner and Dreismann.1 The conductance of deuterons in D2O is about 2/3 that of protons in water. When KCl conductance is measured as a function of the molar ratio of D2O in H2O/D2O mixtures, it follows the molar ratio of D2O. Since D2O viscosity is greater than that of water, the conductance of KCl in D2O is lower than in H2O. When the conductance of KCl is plotted as a function of the mole fraction of D2O in the mixture, it follows the mole fraction linearly. The overall proton and deuteron conductances of H2O/D2O mixtures do not follow a straight line with xD2O . Figure 4a shows the conductance results of Weingärtner and Dreismann of three values of xD2O in H2O/D2O mixtures and in neat H2O and D2O. The results deviate from a straight line in the plot of Λ versus xH 2O . In a review article,



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Dreismann26 explained that the deviation is a consequence of fundamental quantum phenomena, because of the large thermal de Broglie wavelength, λdB. Quoting Dreismann: "protons may show short-time and spatially-restricted quantum correlations even at high temperatures".26 The definition of the thermal de Broglie wavelength is

λdB = h / 2π kBTm

8

For a quasi-free proton at 300K, λdB≈1Å. The thermal λdB of a proton in water may reach other protons of the water system and therefore "exhibits quantum interference (or correlation) effects within sufficiently short time intervals". In the current study we tested the excited-state proton-transfer rate of a commonly used photoacid – HPTS - as a function of the mole ratio of D2O in H2O/D2O mixtures. The time-resolved fluorescence of the ROH form of HPTS provides the excited-state proton-transfer (ESPT) rate. To obtain this rate, we used the SSDP of Krissinel' and Agmon.25 It numerically solved the Debye–Smoluchowski equation (DSE) coupled to a chemical kinetic equation, which includes the proton transfer to the solvent and the proton geminate recombination.20-22 It is based on the reversible geminate-recombination model of Pines, Huppert and Agmon.20,21 At short times after excitation, the fluorescence-decay rate provides the ESPT rate constant kPT. At longer times, the diffusion-assisted reversible geminate recombination repopulates the protonated form of the photoacid and the decay rate deviates from exponential decay. At long times, the fluorescence of the ROH form decays asymptotically according to a power law of t-3/2. Figure 4c shows a plot of the ESPT rate constant, kPT, versus the mole ratio of H2O in the H2O/D2O mixture. The deviation from linear dependence on xH 2O is similar to that of the proton conductance shown in Figure 4a. We tested 17 mixtures of H2O/D2O in the mole-ratio range of 0
0.325 the following equilibrium is also important:



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K ''

eq  → ROD + H 2O ROH + HOD ← 

13

Since we did not consider the above equilibrium, the rate constants determined from solving Equation 11 provided one or two negative rate constants out of the four obtained. Since maximum deviation from linear dependence of kPT on xH 2O occurs at

xH 2O ≈0.5, we conclude that xD2Ok HD2O + xH2OkDH2O + xHODk DHOD + xHODk HHOD < xH° 2Ok HH2O + xD° 2OkDD2O

14

where xH° 2O and xD° 2O are the premix mole fractions of H2O and D2O. We assume that in the xH 2O =0.5 mixture, the overall rate of all four kinds of reactions HOD

kD ROD* + HOD  → RO-* + D2OH + HOD

kH ROH* + HOD  → RO-* + H 2OD+ D2 O

kH ROH* + D2O  → RO-* + D2OH + H 2O

kD ROD* + H 2O  → RO-* + H 2OD+

is smaller than the mean of the known rate constants,

15a 15b 15c 15d

k HH 2O + k DD2O . Under these 2

assumptions, the deviation of kPT from linear dependence on xH 2 O 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 xH 2 O of the mixtures. The overall maximum deviation from linear dependence on xH 2 O is about 27% at xH 2 O ≈0.5, where the solvent is HOD.

Summary and Conclusions The electrical conductance of D+, Λ 0D , in D2O is smaller than that in H2O and its prototropic value is lower by a factor of 1.45. In the beginning of the 1990s, Weingärtner and Dreismann1 measured the proton/deuteron electrical conductance, Λ, in H2O/D2O mixtures. They found that Λ0 does not follow the mole fraction of D2O,

xD2O , but deviates from a linear relation with xD2O in H2O/D2O solvent mixtures. Dreismann ascribed this deviation to fundamental quantum-mechanical phenomena


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such as interference and/or correlation of the proton or deuteron with hydrogen or deuterium atoms of the H2O or D2O. In a review article by Dreismann26 he found other related phenomena that deviate from linear dependence on xD2O in H2O/D2O mixtures. In the current study we chose a commonly used photoacid, 8-hydroxy-1,3,6pyrenetrisulfonate (HPTS), shown in Scheme 1, to measure the rate of excited-state proton transfer (ESPT) in H2O/D2O mixtures. The ESPT rate was obtained by measuring the time-resolved fluorescence of the protonated form, the ROH*, of the photoacid. For data analysis, we used the reversible proton-geminate-recombination (GR) model20,21 which accounts for the complex shape of the time-resolved fluorescence of the ROH form of HPTS because of the diffusion-assisted reversible GR process. We plotted the ESPT rate constant, kPT, that was obtained versus the mole fraction of H2O. The plot, shown in Figure 4c, shows that, as in the case of Λ0 (see Figure 4a), there is a deviation of kPT from linearity with xH 2O . The relative deviation of kPT is about twice that of Λ0 found by Weingärtner and Dreismann1. We explain the larger deviation of kPT qualitatively by the fact that the kinetic isotope effect of kPT of HPTS is twice that of Λ0. In the discussion, we present an explanation of the deviation of kPT from mole-ratio dependence. The model presented is based on some reasonable assumptions. The combined ESPT rate from ROD and ROH to the HOD, D2O and H2O solvent mixture is smaller for all mixtures than the mean rate constant kd = xH° 2Ok HH2O + xD° 2OkDD2O where kDD2O and kHH2O are the ESPT rate constants in neat D2O and H2O solvents and xH° 2O and xD° 2O are the premix mole ratios.

Supporting Information Available A. Table of HPTS kinetics parameters calculated with use of the SSDP.25

Acknowledgement This work was supported by a grant from the Israel Science Foundation 914/12.

References 1. Weingärtner, H.; Chatzidimttriou-Dreismann, C. Anomalous H+ and D+ Conductance in H2O–D2O Mixtures. Nature 1990, 346, 548-550.



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2. Martynov, Y.; Demyashkevich, A.; Uzhinov, B.; Kuzmin, M. Proton-Transfer Reactions in Excited States of Aromatic Molecules. Usp. Khim. 1977, 44, 3-31. 3. Ireland, J. F.;Wyatt, P.A. Acid-Base Properties of Electronically Excited States of Organic Molecules. Adv. Phys. Org. Chem. 1976, 12, 131–221. 4. Gutman, M.; Nachliel, E. The Dynamic Aspects of Proton Transfer Processes .Biochem. Biophys. Acta 1990, 1015, 391–414. 5. 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 6. Rini, M.; Magnes, B. Z.; Pines, E.; Nibbering, E.T. Real-Time Observation of Bimodal Proton Transfer in Acid-Base Pairs in Water. J. Science 2003, 301, 349–352. 7. Mohammed, O. F.; Pines, D.; Dreyer, J.; Pines, E.; Nibbering, E. T. Sequential Proton Transfer Through Water Bridges in Acid-Base Reactions. J. Science 2005, 310, 83–86. 8. Tran-Thi, T. H.; Gustavsson, T.; Prayer, C.; Pommeret, S.; Hynes, J. T. Primary Ultrafast Events Preceding the Photoinduced Proton Transfer from Pyranine to Water. Chem. Phys. Lett. 2000, 329, 421–430. 9. Agmon, N. Elementary Steps in Excited-State Proton Transfer. J. Phys. Chem. A

2005, 109, 13–35. 10. Spry, D. B.; Fayer, M. D. Charge Redistribution and Photoacidity: Neutral Versus Cationic Photoacids. J. Chem. Phys. 2008, 128, 084508-1-084508-9. 11. Siwick, B. J.; Cox, M. J.; Bakker, H. J. Long-Range Proton Transfer in Aqueous Acid−Base Reactions. J. Phys. Chem. B 2008, 112, 378–389. 12. Mohammed, O. F.; Pines, D.; Nibbering, E. T. J.; Pines, E. Base-Induced Solvent Switches in Acid–Base Reactions. Agnew. Chem. Int. Ed. 2007, 46, 1458–1461. 13. Mondal, S.K.; Sahu, K.; Sen, P.; Roy, D.; Ghosh, S.; Bhattacharyya, K. Excited State Proton Transfer of Pyranine in a γ-cyclodextrin Cavity. Chem. Phys. Lett. 2005, 412, 228–234. 14. Prasun, M. K.; Samanta, A. Evidence of Ground-State Proton-Transfer Reaction of 3-Hydroxyflavone in Neutral Alcoholic Solvents. J. Phys. Chem. A 2003, 107, 6334–6339. 15. Bhattacharya, B.; Samanta, A. Excited-State Proton-Transfer Dynamics of 7Hydroxyquinoline in Room Temperature Ionic Liquids. J. Phys. Chem. B 2008, 112, 10101–10106. 20 Environment ACS Paragon Plus

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16. Pérez Lustres, J. L.; Kovalenko, S. A.; Mosquera, M.; Senyushkina, T.; Flasche, W.; Ernsting, N. P. Ultrafast Solvation of N-Methyl-6-Quinolone Probes Local IR Spectrum. Angew. Chem., Int. Ed. 2005, 44, 5635-5639. 17. Pérez -Lustres, J.; Rodriguez-Prieto, F.; Mosquera, M.; Senyushkina, T.; Ernsting, N.; Kovalenko, S. Ultrafast Proton Transfer to Solvent: Molecularity and Intermediates from Solvation-and Diffusion-Controlled Regimes. J. Am. Chem. Soc.

2007, 129, 5408-5418. 18. Mojumdar, S. S.; Chowdhury, R.; Mandal, A. K.; Bhattacharyya, K. In what Time Scale Proton Transfer Takes Place in a Live CHO Cell? J. Chem. Phys. 2013, 138, 06B603_1. 19. Weller, A. Intramolecular Proton Transfer in Excited States. Z.Elektrochem 1956, 60, 1144. 20. Pines, E.; Huppert, D.; Agmon, N. Geminate Recombination in Excited‐State Proton‐Transfer Reactions: Numerical Solution of the Debye–Smoluchowski Equation with Back reaction and Comparison with Experimental Results. J. Chem. Phys. 1988, 88, 5620-5630. 21. N. Agmon, E. Pines and D. Huppert. Geminate Recombination in Proton Transfer Reactions. II. Comparison of Diffusional and Kinetic Schemes. J. Chem. Phys. 1988, 88, 5631-5638. 22. Simkovitch, R.; Pines, D.; Agmon, N.; Pines, E.; Huppert, D. Reversible ExcitedState Proton Geminate Recombination: Revisited. J. Phys. Chem. B 2016, 120, 12615-12632. 23. Chattoraj, M.; King, B. A.; Bublitz, G. U.; Boxer, S. G. Ultra-Fast Excited State Dynamics in Green Fluorescent Protein: Multiple States and Proton Transfer. Proc. Natl. Acad. Sci. U. S. A. 1996, 93, 8362-8367. 24. Weller, A. Fast Reactions of Excited Molecules. Prog.React.Kinet 1961, 1, 187214. 25. Krissinel', E. B.; Agmon, N. Spherical Symmetric Diffusion Problem. J. Comput. Chem. 1996, 17, 1085-1098 26. Chatzidimitriou-Dreismann, C. Proton Nonlocality and Decoherence in Condensed Matter—Predictions and Experimental Results. Advances in Chemical Physics, Volume 99: Resonances, Instability, and Irreversibility 2009, 216, 393-430. 27. Kaatze, U. Dielectric Relaxation of H2O/D2O Mixtures. Chem. Phys. Lett. 1993, 203, 1-4. 21 Environment ACS Paragon Plus


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28. Chatzidimitriou-Dreismann, C.; Krieger, U.; Möller, A.; Stern, M. Evidence of Quantum Correlation Effects of Protons and Deuterons in the Raman Spectra of Liquid H2O-D2O. Phys. Rev. Lett. 1995, 75, 3008. 29. Takeda, S.; Tsuzumitani, A.; Chatzidimitriou-Dreismann, C. Evidence of quantum correlations in the H/D-transfer dynamics in the hydrogen bonds in partially deuterated benzoic acid crystals. Chem. Phys. Lett. 1992, 198, 316-320. 30. 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. 31. Duplan, J. C.; Mahi, L.; Brunet, J. L. NMR Determination of the Equilibrium Constant for the Liquid H2O–D2O Mixture. Chem. Phys. Lett. 2005, 413, 400-403.


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TOC Graphic 9 HO

SO3-

8 7

kESPT

Page 23 of 23

6

-

-

5

SO3

SO3

deviation from linearity

4

kESPT

3 2 0.0

Exponential Fit 0.2

0.4

0.6

0.8

1.0

xH O 2


Anomalous H+ and D+ Excited-State Proton ... - ACS Publications

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