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Chemical Physics 341 (2007) 240–257

Aqueous bimolecular proton transfer in acid–base neutralization

Omar F. Mohammed a, Dina Pines b, Ehud Pines b,*, Erik T.J. Nibbering a,*

a Max Born Institut fur Nichtlineare Optik und Kurzzeitspektroskopie, Max Born Strasse 2A, D-12489 Berlin, Germanyb Department of Chemistry, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva 84125, Israel

Received 27 March 2007; accepted 26 June 2007Available online 6 July 2007

Abstract

We report on a comparative femtosecond infrared study of the bimolecular proton transfer reaction dynamics of the photoacid pyr-anine (8-hydroxy-1,3,6-trisulfonate-pyrene, abbreviated as HPTS) with the family of carboxylate bases �OOCCH(3�x)Clx (x = 0–3) inaqueous solution. We use a generalized reaction model consisting of n proton transfer reaction pathways between photoacid and base,each pathway characterized by the number n of water molecules functioning as solvent switch facilitating an efficient transfer. Thedynamics of the different proton transfer pathways have been followed by inspection of appropriate vibrational modes marking the pro-gress of the reaction, and allow the direct observation of the transient relay mechanism of proton through one bridging water molecule ina loose photoacid–base configuration of the type HPTS�� H3O+� � ��OOCCH(3�x) Clx (x = 0–3). By applying a global fit procedure onthe n-coupled reaction pathways, with full reversibility and detailed balance, we find for the reaction series that the encounter complexformed after mutual diffusion between photoacid and base, and subsequent desolvation, follows in general the loose complex pathwaywith one water molecule bridging acid and base. Only for the weakest base studied, trichloroacetate, larger solvent switches with n P 2water molecules are important in the transfer dynamics. Whereas transfer in the tight complex with no water spacer (n = 0) occurs withintime resolution of 150 fs, the transfer in the loose (n = 1) complex proceeds in a sequential fashion where the first transfer occurs withintime resolution, irrespective of base strength, whereas the second transfer from the water to the base is activated and conforms to a cor-relation between free energy and reaction rate.� 2007 Elsevier B.V. All rights reserved.

Keywords: Proton transfer; Acid–base neutralization; Bimolecular reaction dynamics; Femtochemistry; Hydrated proton; Grotthuss mechanism; Ultr-afast infrared spectroscopy

1. Introduction

One of the most fundamental and common, yet elusive,chemical reactions is proton transfer in aqueous solution[1–5]. In aqueous proton transfer an exchange occurs ofH+-ions between donor and accepting groups stronglymediated by the protic solvent water, where the orderand reaction yields of proton transfer events is dictatedby the acidity and basicity of donating and acceptinggroups of the molecules. In the case that proton donorand acceptor groups are found on different molecules,

0301-0104/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.chemphys.2007.06.040

* Corresponding authors.E-mail addresses: [email protected] (E. Pines), nibberin@

mbi-berlin.de (E.T.J. Nibbering).

namely when bimolecular solution phase neutralizationbetween Brønsted acids and bases [6] is under consider-ation, diffusion comes into play, as both donor and accep-tor molecules will move with respect to each other, as wellas that the proton charge may be transported through thewater solvent. As a result the complex microscopic mecha-nisms of bimolecular aqueous proton transfer betweenBrønsted acids and bases have yet to be fully resolvedand thus remain a research subject of intense effort [7–17].

Eigen has reported four different general reaction path-ways in his classic overview published in 1963/1964 [8](Fig. 1). In the hydrolysis pathway a strong base first takesup a proton from the solvent, followed by neutralization ofthe OH�-ion by a weak acid. In the protolysis pathway astrong acid first dissociates a proton to the solvent, forming

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XH B+ + HB++ +X− H2OH2O

Self-neutralization of water: strong acid and strong base

XH B+ + H3O+ B+ + HB+X− + +X− H2OH2O

Neutralization of base by (H3O+)aq: strong acid and weak base

XH B+ + OH−+ + HB++ +X− H2OH2O

Neutralization of acid by (OH−)aq: weak acid and strong base

XH HB+

OH−+ + HB+H3O++X−

H2O+ +H2O

B+H2O+ H3O++X−

XH B+ HB++X−

Direct collisional neutralization: weak acid and weak base

XH B HB+X−

Fig. 1. Aqueous acid–base neutralization pathways, where the order of proton transfer events depend on the relative acid and base strengths.

O.F. Mohammed et al. / Chemical Physics 341 (2007) 240–257 241

hydronium H3O+, after which a weak base neutralizes thehydrated proton. In the case of having both a strong acidand a strong base in solution, both protolysis and hydroly-sis pathways occur simultaneously, and the neutralizationoccurs between hydrated proton and hydrated hydroxide,which is the reverse case of the auto-ionization process ofwater. In the case of weak acids and weak bases the protonexchange with the solvent may be slow enough to favour adirect neutralization pathway between acids and basesupon formation of a reactive collisional encounter complexafter mutual diffusion.

The classical kinetic approach to the essentially many-body process of proton exchange between weak acids andweak bases is to apply the diffusion equation to modelthe mutual approach of the intact reactants towards form-ing an encounter (reactive) complex [7,18–20]. The reactionwithin the encounter complex is then simply modelled bytwo empiric reaction parameters: an on-contact rate con-stant and a contact (reaction) radius a between acid andbase. Both parameters represent effective parameters aver-aged over all possible reactive configurations. When furtherassuming steady-state conditions and full reversibility ofthe reaction the kinetic model consists of only two (kinetic)stages describing a constant flux of reactants in a diffusionspace (the presumed non-reactive mutual approachingstage) moving into a constant reaction volume where thereactants disappear (the close-contact reactive stage). Thisdescription of bimolecular acid–base neutralization in solu-tion is known as the Eigen–Weller (EW) model [8,9,21–24].In the EW approach the reactive (close-contact) stage ismodeled by two reaction parameters: The distance a

between acid and base at which the proton transfer occursand the rate coefficient of the proton transfer k0 at this dis-tance. Several questions have remained unsolved within thecontext of the EW model:

(i) What is (are) the actual structure(s) of the reactivecomplex(es) for the conventional proton transferreactions that are adequately described by the EWmodel.

(ii) Is there only one reactive ‘‘on contact’’ complex for aclosely related family of acid–base reactions? In otherwords, is the contact radius a a constant for a closelyrelated family of reactions and does it represent a sin-gle value or an averaged one?

(iii) Is there a single mechanism of proton transfer for agiven reactive complex of a radius a, i.e., step-wiseor concerted? In addition extensive solvent rearrange-ments within the reaction volume are possible so theactual proton transfer within a given reactive volumemay involve several reactive steps perpendicular tothe reaction coordinate.

In the EW model a value for the contact radius a impliesa certain amount of water molecules n separating the reac-tants upon formation of the reactive complex [25]. Cur-rently accepted values for the contact radius a are around6 ± 1 A for a large number of acids and bases [1], includingthe ones on which we report in this work, implying by geo-metrical considerations that a typical reactive encountercomplex consists of an acid and a base bridged by one ortwo water molecules. When acid and base are well sepa-rated by a large number of solvent shells (meaning thenumber of water molecules n between acid and base islarge), the mutual approach of the reactive pair towardforming the encounter complex may be viewed as a gradualdesolvation process of both acid and base that can beapproximated by mutual diffusional motion until theencounter complex configuration is reached, from wherethey will react with each other. From there, a furthernon-diffusional desolvation may occur before acid and base

D+(D2O)n ( )n

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ROD B−

ROD B−… …

ROD B−… …( )n

+ + D3O+

kdif ksep

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D2O

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Loose Complex (n=1)

Tight Complex (n=0)k–p

B−RO− … …

kswn1

k–swn1

kswn2

k–swn2

Fig. 2. Reaction scheme used to model the experimental results obtained for the photoacid–base pair HPTS (ROD) + carboxylate (B�) in deuteratedwater. Abbreviations: w: deuteron dissociation to water; gem: geminate recombination; sc: deuteron scavenging; dif: diffusion; sep: separation; swn: switchconsisting of n water molecules; (de)solv: (de)solvation; p: direct deuteron between acid and base.

242 O.F. Mohammed et al. / Chemical Physics 341 (2007) 240–257

actually exchange a proton, the exact pathway beingdependent on the particular acid and base reactivities andreaction rates and (de)solvation energetics and dynamics(Fig. 2). When a complete desolvation occurs before pro-ton exchange in a tight ‘‘inner-sphere’’ (n = 0) acid–basecomplex, the solvent will only play a secondary role inthe actual proton transfer reaction dynamics, assistingthe single reaction step of proton transfer between thedonating and accepting groups that are directly linked bya hydrogen bond. In contrast, for reactive complexes witha bridge of water molecules (n P 1) separating acid andbase, water plays an active role of mediating proton trans-port between the donor and acceptor, through a von Grot-thuss-type mechanism.

Transmission of protons through protic solvents isknown as the von Grotthuss mechanism [26], as a dedica-tion to Theodor von Grotthuss whose landmark achieve-ments on modeling the electrolysis of water, published aspamphlet in 1805 in Rome and in scientific journals inFrench [27] and English [28] in 1806 and in later years inGerman, as an appendix [29] to what is now understoodto be the first report on the first law of photochemistry(known as the Grotthuss–Draper law) and as independentreports [30,31] (for a recent translation of this importantmanuscript in English, see Ref. [32]). As explained in his-torical overviews [17,33–37] this work does not deal explic-itly with transmission of protons (H+) through water(H2O), as protons as elementary particles still had to awaitdiscovery. Nevertheless the explanation of diffusion of neg-ative and positive (denoted as o or h, respectively) chargedbodies between a chain of neighbouring water molecules byvon Grotthuss is a rudimentary – but an important – foun-dation in the current understanding of the anomalouslyfast proton transmission as a topological defect along a

hydrogen bonded chain of water molecules [26], whichcan occur not only in bulk water or other protic solvents[38–46] (we refer to the reviews [16,17] for a complete over-view on this), but also in acid dissociation in water [47–57],in acid–base neutralization reactions [58–68], in fuel cells[69,70], and in protein ion channels in biological mem-branes [3,4,71–75], where besides water other functional-ities such as carboxylate groups may assist the protontransmission process.

It follows that proton transfer in acid–base reactionsmay involve in general a reactive stage where the protonneeds to move through the solvent before ultimately react-ing with the base. The onset of this stage depends on thepKa of the acid and may also depend to a lesser degreeon the properties of the base when in close proximity tothe acid. Two approaches may be thus used for modelingthe dynamics of proton transfer in acid–base reaction. Inthe first one the reaction may be described formally with-out an explicit participation of the solvent using time-dependent solutions of the diffusion equation [76]. In thesecond approach one may use a reaction model whichexplicitly includes the solvent and the mechanism by whichthe proton is shuttled in between acid and base (the vonGrotthuss mechanism). Clearly, the latter approach is froma microscopic point of view closer to the actual mechanismof acid–base reactions but in practice is extremely cumber-some to apply. This is because the nature of the hydratedproton in these proton exchange processes is not wellunderstood and has been much debated. Hydrated protonsdo not necessarily exist as hydronium (oxonium) ions,H3O+, but are likely part of larger cluster configurationsHðH2OÞþn . Key examples of hydrated proton are the Zun-del cation H5Oþ2 , a hydrated proton symmetrically locatedbetween two water molecules [77,78], and the Eigen cation


H9Oþ4 , a hydronium ion symmetrically solvated by threewater molecules H3O+(H2O)3 [8,21]. Infrared spectroscopyis a prime tool to characterize the proton hydrated with aknown number of water molecules in the gas phase [79–87], as the vibrational band patterns are highly sensitiveto the local configuration of the hydrated proton, eventhough the theoretical vibrational mode analysis is due toanharmonic couplings far from trivial and remains a topicfor debate [88–91]. From these gas phase studies it is nowknown that the symmetrically solvated hydronium in theEigen cation has a pronounced vibrational resonance at2650 cm�1 in the gas phase, whereas the Zundel cationhas its resonances in other vibrational spectral regions.The Eigen and Zundel cations are limiting cases for thehydrated proton as other configurations can be envisaged,that in particular will be important for disordered liquidsurroundings, where besides a distribution of hydrated pro-ton configurations a fluxional exchange between these con-figurations will occur [45,92]. With this in mind it becomesclear why the infrared spectra of acidic aqueous solutionsdo not show distinct narrow resonances of the differenthydrated proton clusters, but in general a broad featurelessabsorption due to strongly overlapping transitions occurs[75,78,93–98].

The von Grotthuss mechanism in bulk water is a contin-uous process, without a well defined start and end. Aciddissociation in water has a well-defined onset, when theacid initiates the release of the proton to the nearby watermolecule in the first solvation shell [52–57,99,100]. Acid–base neutralization in water, as well as proton transferthrough membranes or ion channels, has well-defined ini-tial and final stages in the proton transmission, althoughthe elementary steps may be numerous and complex. Toperform time-resolved studies photoacids as optical trig-gered means for initiating proton transfer have beenapplied for decades [1,7–9,14,101–103]. Photoacids areorganic molecules that exhibit a large change in the aciddissociation constant Ka upon photoexcitation to electron-ically excited states (typical changes in pKa values on theorder of 6–10 units). As a result photoexcitation initiatesproton transfer reaction dynamics to accommodate to thenew equilibrium situation. It has been demonstrated thatone can by altering the conditions, strongly determine theoutcome of these reaction dynamics. E.g. one can adjustthe fraction of photoacid molecules that will release a pro-ton to the solvent upon photoexcitation, by adjusting thepH of the solution [47–51,66,104]. In the presence of a neu-tralizing agent in solution, one can perform ultrafast titra-tion experiments in solution using photoacids. Now ingeneral the bimolecular neutralization dynamics of an opti-cally excited photoacid by a base will be dominated by theslow diffusional motions of the two reactants. However, atbase concentrations in the molar range a significant frac-tion of photoacid exists in such a close proximity to thebase, that it becomes feasible to access the ‘‘on contact’’reaction dynamics from the observed early time-dependentsignals [58]. This approach has been followed in ultrafast

studies of the neutralization dynamics of photoacids withcarboxylate bases. When using techniques probing elec-tronic transitions, such as time-resolved single photoncounting [58,60,61] or UV/Vis pump–probe [59], one cantypically probe the first event of proton transfer, i.e. whenthe proton leaves the excited photoacid. Recently we dem-onstrated in a neutralization study of the photoacid pyra-nine (HPTS; pKa(S0) = 7 and pKa(S1) = 0.3 at 1 M ionicstrength solutions) with several carboxylate bases that withtransient infrared spectroscopy it is possible to probe theinitial event of proton dissociation from the photoacid,the arrival event of the proton at the base (forming the con-jugate acid of the carboxylates), as well as the transientappearance of a hydrated proton species in a water bridgebetween the photoacid and the base [62–65,67]. We havesuccessfully analyzed the proton transfer reaction betweenthe stronger carboxylate bases (acetate and chloroacetate)and HPTS using a time-dependent solution of the diffusionequation due to Collins and Kimball [76,105,106]. Basedon the kinetic analysis of the transient behaviour of thespecies specific vibrational marker modes measured in deu-terated water solution we inferred the existence of at leasttwo different photoacid–base complexes:

(i) Tightly linked complexes (no water bridge: n = 0),enabling a deuteron transfer within the experimentaltemporal resolution of 150 fs [62] .

(ii) Loosely linked complexes where a sequential deu-teron transfer occurs with a fast first step (<150 fs)from photoacid to the water bridge consisting of asingle water molecule (n = 1), and a slower secondand final transfer to the carboxylate base on picosec-ond time scales [65]. Analysing the proton transferdynamics of the initially uncomplexed photoacidreveals on-contact reaction time constants that lieclearly in the picosecond time scale [63,65], suggestingstrongly that that for these photoacid–base reactivesystems the encounter complexes are much alike theloose complexes.

The case of the weakest base investigated, �OOCCCl3(x = 3), was found to follow a more complex pathway. Inaddition to having to include both forward and backwarddeuteron transfer steps in the description, a consistentdescription could only be obtained when abandoning thesingle encounter complex approach by assuming thatbesides tight and loose complexes, reactive complexes con-sisting of bridges with several water molecules (n P 2) playa significant role in the exchange of deuterons [67]. Thismodel potentially represents an important generalizationof the EW model, but until now has only been appliedfor the case of trichloroacetate base.

The purpose of the present manuscript is to apply thisnew model to the proton transfer reaction between HPTSand the full set of the acetate-base family. In addition toreanalyzing the data for acetate and chloroacetate we havealso studied the reaction between HPTS and dichloroace-

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Fig. 3. Steady-state and transient mid-infrared spectra of HPTS acid(solid black) and conjugate HPTS� base (solid grey) in the electronicground state (b) and upon electronic excitation to the S1-state (a), wherethe largest changes can be observed between 1400 and 1600 cm�1. Thecarboxylate bases (solid grey) and conjugate carboxylate acids (solidblack) for acetate (c; x = 0), monochloroacetate (d; x = 1), dichloroacetate(e; x = 2) and trichloroacetate (f; x = 3), showing clearly the C@Ostretching band between 1720 and 1750 cm�1.


tate which represents an intermediate case between thestrong and weak acetate bases. We are now, thus, able toprovide for the first time a comparative femtosecond infra-red study of the reaction dynamics of HPTS with the fullfamily of carboxylate bases �OOCCH(3�x)Clx (x = 0–3)in D2O. In doing so, we have gradually tuned the overalldeuteron transfer reaction from being diffusion controlled(diffusion much slower than the on-contact reaction rateas in the case of acetate; �OOCCH3 ; x = 0) to being acti-vation controlled (where the on-contact reaction rate isslower than the rate of diffusion as in the case of trichloro-acetate; �OOCCCl3; x = 3). Our analysis of the observedtransient behaviour of the vibrational marker modesreveals the reaction time scales of the different inner stepsin bimolecular deuteron transfer, allowing us to make gen-eral statements of water-mediated proton transfer dynam-ics in solution unattainable by our previous analysis.

2. Experimental

To follow the temporal evolution of vibrational markermodes we used a femtosecond infrared spectroscopic lasersystem consisting of a home built 1 kHz amplified Ti:sap-phire laser system and frequency conversion stages. Thesecond harmonic output of the amplified laser system(wavelength 400 nm, pulse duration 55 fs, energy 3–7 lJ,spot diameter 300 lm) was used to excite the photoacidmolecules. Tunable mid-IR probe pulses (100–150 fs dura-tion, 10 nJ energy) were generated by difference frequencymixing of signal and idler pulses from a near-infrared opti-cal parametric amplifier [107]. After spectral dispersionwith a polychromator the probe pulses were detected bya multichannel mid-IR detector array (IR associates) witha spectral resolution of 4–8 cm�1, depending on the spec-tral region probed.

Sample solutions were circulated through a flow cellconsisting of 1 mm thick BaF2 windows separated by a50 lm thick teflon spacer, to guarantee that for every lasershot a new fraction of the solution was excited. We used20 mM solutions of pyranine (8-hydroxy-1,3,6-trisulfo-nate-pyrene, abbreviated as HPTS, used as delivered fromAldrich) in deuteriumoxide (Deutero GmbH, 99.8% deu-teration grade) or double distilled water. Sodium acetatemonochloroacetate, dichloroacetate and trichloroacetate(Aldrich) were used in the studies as the proton acceptorbase in the concentration range of (0.5–3 M). A smallamount of the conjugate acid (Aldrich) was added to thecarboxylate salt solutions to ensure that HPTS was presentin the ground state in the acid form. Typical working con-ditions included pD = 3.6–4. All measurements were per-formed at room temperature, T = 25 ± 2 �C.

Fig. 3 shows the steady-state spectra for HPTS in acidand base form in the electronic ground state, as well asthose of the carboxylate bases and their respective conju-gate acids. The transient spectra of HPTS are shown inthe top panel, marking the fingerprint vibrations of S1

HPTS in the photoacid form at early pulse delays, and

those of HPTS� in the photobase form at long pulse delays[62,63,65,108]. It is clear that most species-specific vibra-tional marker modes can be found in the frequency range1400–1900 cm�1. However due to the fact that the basesare present at molar concentrations significant regions ofthe spectral range become opaque, delimiting the optionsof probing transient kinetics of the different species. Fortu-nately, for most cases it is possible to follow the rise of theHPTS� S1 photobase species by measuring the fingerprintvibrations located at 1503 and 1435 cm�1. The magnitudeof these transient vibrational bands as function of pulsedelay between UV pump and IR probe is determined byeither fitting the line shapes to Gaussian functions or byapplying singular value decomposition [109]. We havefound that the early time dynamics, of particular impor-tance to determine the fraction of HPTS that dissociate adeuteron within time resolution, can most appropriatelybe probed on the 1435 cm�1 band. This HPTS� photobasetransition can more easily be separated from nearby vibra-tional bands than the 1503 cm�1 HPTS� photobase markertransition, that is located near two strong HPTS S1 bandsindicative of the photoacid form. A small spectral blue-shifting can be observed for the HPTS� photobase markerband at early pulse delays up to 5 ps, indicating minoreffects by intramolecular vibrational redistribution andvibrational cooling [64,65,108]. This effect is the main causefor the uncertainty in the estimated early time componentof the HPTS� photobase marker band.

On the other hand, the arrival time of the deuterons atthe accepting carboxylate base is more easily detected bymeasuring the rise of the C@O stretching bands of the con-jugate acids of the carboxylates, located between 1720 and1750 cm�1 (depending on the particular carboxylate acid).We also detect a distinct transient vibrational band at


1850 cm�1 in D2O (2570 cm�1 in H2O) that we haveascribed to a hydrated deuteron (hydrated proton) bandwith a hydronium ion in a configuration similar to thatof the Eigen-core in H9Oþ4 [65,67]. We use this hydrateddeuteron band as a signature of the deuteron transientlyresiding of the water bridge while sequentially shuttlingthrough the loose complex (with n = 1 water moleculebridging between HPTS and the carboxylate base).

The temporal resolution in the experiment was 150–200 fs, delimited by group velocity dispersion betweenUV pump and IR probe pulses, and by a significantlystrong broad featureless absorption rising with the pulsecross correlation and decaying with several time constantsfrom sub-100 fs to a few picoseconds. This transient broadfeatureless IR absorption, that leads to a floating baseline,originates partially from the solvent and cell windows andpartially from HPTS solution, making it hard to deciphermolecular response in the photoacid–base reaction fromcompeting processes such as multiphoton ionisation andfree carrier generation, and subsequent relaxation phenom-ena. We refrain from fully trying to assign these spectralfeatureless signals apart from referring to a previous reporton HPTS in different solvents, where we tentatively ascribethese effects to changes in hydrogen bonded O–H stretch-ing absorbance of excited HPTS at the hydroxyl-groupand/or of strongly bound water at the sulfonate-groups[108]. We note here that the solvents H2O and D2O havesignificant absorption in all spectral ranges, even inbetweenthe bending and stretching fundamentals, due to combina-tion overtone bands of the solvent. Since the vibrationalbands of the solvent are extremely broad, any transientresponse by the solvent will result in a broad featurelessfloating-baseline signal. In principle broad featurelessabsorption can also be caused by hydrated protons or deu-terons present in larger water clusters, approaching thefully solvated proton/deuteron case, even though this hasbeen found to be weaker in magnitude than the early timeresponse of HPTS, when clearly the proton/deuteron hasnot dissociated from the photoacid [108]. The electronicexcited state decay of HPTS in photoacid and photobaseforms occur with lifetimes of 4.8 and 5.3 ns respectively,and have consequently no influence on the much fasterdynamics of proton transfer discussed here.

The data fits have been carried out taking into accountthe following: (i) each closed reaction loop obeys detailedbalance kinetics; (ii) all reaction steps in bulk water withdiffusion have diffusion-controlled reaction rates with val-ues similar to mentioned in previous reports [48–50,58–63]; (iii) for all bulk proton transfer steps the ratio of theforward and backward rate constants should conform toacceptable pKa-values for both HPTS and all carboxylateacids [48,58,110,111] as listed in Tables 2–4; (iv) all rateconstants were assumed to be time independent and wereinitially varied one at a time to search for their best values;(v) in the next round of fits the best values of the variousrate constants were slightly modified to obey detailed bal-ancing; (vi) a final round of fits where then carried out

by simultaneously changing each time the values of tworate constants to ascertain detailed balancing while opti-mising for the best fit parameters; (vii) uncertainties remainin the values (a) for the rates of the first proton transfersteps in the loose (n = 1) and tight (n = 0) complexes asthese steps appear to be faster than the time resolutionand (b) for the rates of the solvation/desolvation stepsbetween the different complexes, albeit that the found val-ues are not unlikely [112]; and in closing this section (viii)the most important thing to point out is the fact that therelative yields for the the majority of the various reactionbranches is a direct outcome of our experimental measure-ments, emphasizing that individual rate constants areadjustable but their relative magnitudes are not becausethey were directly determined by experiment.

3. Results

Transient IR spectroscopy reveals the reaction regimesof the different reaction pathways, each dominated by par-ticular reaction time scales, as depicted in Fig. 2. Here thevibrational marker modes of the HPTS� photobase (at1435 and 1503 cm�1) and of the conjugate carboxylate acid(the C@O stretching mode located between 1720 and1750 cm�1) indicate the deuteron transfer from the photo-acid (first step) and the arrival of the deuteron at the base(final step). For every pathway the transient signal is –within measurement accuracy – similar in spectral shape.The characteristic time scale for the signal rise, however,is strongly dependent on the reaction pathway. Thus adetermination of the relative signal contributions of thereactive species, tight (n = 0), loose (n = 1) and larger sol-vent switch (n P 2) complexes or uncomplexed solvent sep-arated photoacid and base, can be made. The hydrateddeuteron (D3O+) band is on the other hand (to be dis-cussed below) a marker mode for the loose (n = 1) com-plexes only. In this case the initial fast rise and muchslower decay enables us to make statements of the sequen-tial deuteron transfer steps that occur within this reactionpathway. Although these observations have already beenreported before for particular carboxylate bases[62,63,65,67], a comparison of experimental data for allcarboxylate bases allows for making statements on theinfluence of the base reactivity on the different reactionpathways, or even on particular deuteron transfer steps.

Fig. 4 shows a comparison of transient spectra recordedin the range of the C@O stretching mode of carboxylateconjugate acid and the hydrated deuteron band at specificpulse delays for different concentrations of the base�OOCCH2Cl (x = 1). For every concentration used (1–3 M) a hydrated deuteron band appears within time resolu-tion, followed by a decay on an extended time scale, with-out any significant change in spectral shape. The C@Ostretching carboxylate acid marker mode only appears atpicosecond time scales for 1 M base, whereas for the higherbase concentration an initial component exists that appearswithin time resolution. Fig. 5 shows a comparison of the

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Fig. 4. Transient mid-IR spectra recorded for the neutralization reactionof HPTS + monochloroacetate (x = 1) in D2O for 1 M (a), 2 M (b) and3 M (c) base concentration, showing a time-resolution limited appearanceof the hydrated deuteron band of the loose (n = 1) complexes at1850 cm�1, followed by a decay on picosecond time scales, accompaniedby a rise of the C@O stretching marker mode of monochloroacetic acid at1720 cm�1. At higher base concentrations the C@O stretching band alsohas an ultrafast component indicative of transfer in tight (n = 0)complexes within time resolution.

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(d) -100 ps 0.7 ps 5 ps 20 ps 80 ps 150 ps 300 ps 500 ps 700 ps 1000 ps

Wavenumber (cm-1)

Fig. 5. Transient mid-IR spectra recorded for HPTS + 2 M carboxylatebase in D2O, showing the initial appearance of the hydrated deuteron andsubsequent decay on picosecond time scales, and the rising C@Ostretching band of the conjugate carboxylate acids, for acetate (a;x = 0), monochloroacetate (b; x = 1), dichloroacetate (c; x = 2) andtrichloroacetate (d; x = 3).


transient IR spectra obtained for the same vibrational mar-ker modes, now for the whole series of carboxylate baseseach at 2 M concentration. It appears that the transientcharacteristics of these two vibrational marker modes arevery similar for each base studied. However, a closerinspection reveals important base-dependent differences inthe temporal behaviour of the signal strengths of the vibra-tional marker modes. Whereas the hydrated deuteronappears within time resolution for all bases studied, thedecay appears to proceed on longer picosecond time scalesfor weaker basicity. The same observation can be noted onthe rise of the C@O stretching band of the conjugate car-boxylate acid. Here again an initial fast component – witha magnitude dependent on the base concentration –appears within time resolution independent on the strengthof the base, whereas the subsequent slower rise has a timescale that becomes longer the weaker the basicity is. Similarconclusions can be drawn on the rise of the HPTS� photo-base marker bands (data not shown here, but publishedbefore [65,67]).

Fig. 6 shows the integrated signal strength of the C@Ostretching marker band as function pulse delay for the car-boxylate bases for 1 and 3 M base concentration. Here it isclear that for higher base concentration (i) the magnitudeof the initial instrument-response limited rise of the markerband increases as function of base concentration; (ii) thesubsequent rise also is faster for higher base concentration;(iii) the absorption rise appears to be completed within 1 nsfor the stronger bases �OOCCH(3�x)Clx (x = 0–1) but hasnot risen to the same value for the weaker bases (x = 2–3).Fig. 7 shows that the decay of the magnitude of thehydrated deuteron band at 2 M base concentration is alsobase-dependent: the weaker the base the slower this markerband diminishes. Whereas this transient band has fully dis-appeared at 1 ns for the stronger bases (x = 0–1), the bandhas a significant magnitude for the weaker (x = 2–3) bases.

The decay of the hydrated deuteron band at 1850 cm�1

in D2O, and the equivalent hydrated proton band at2570 cm�1 measured in H2O, is not accompanied by signif-icant spectral shifts, which hints at a particular kinetically

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x = 2

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x = 1

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(a)

Fig. 6. Kinetics of the C@O stretching band of the carboxylate acid(symbols: experimental results; solid lines: fits using the model described inSection 4.2 and in Fig. 2), marking the final deuteron transfer to the basefor 1 M (a) and 3 M (b) base concentrations, showing a base dependentdegree of initial fast rise (due to transfer in tight (n = 0) complexes), andsubsequent slower dynamics dictated by transfer in the loose (n = 1) andsolvent switch (n P 2) complexes and by mutual diffusion between acidand base for the carboxylate bases �OOCCH(3�x)Clx (x = 0–3).

0 200 400 600 800 1000

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0.5

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x = 3

x = 2

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Pulse Delay (ps)

Fig. 7. Kinetics of the hydrated deuteron D3O+ band (symbols: exper-imental results for 2 M base concentration; solid lines: fits using the modeldescribed in Section 4.2 and in Fig. 2), showing a base dependent degree ofdecay dynamics dictated by the ratio of second forward and backwardtransfer in the loose (n = 1) complexes and by mutual diffusion betweenacid and base reactants forming the complexes and separation ofconjugate base and conjugate acid products.

0.0

0.2

0.4

0.6

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D3O+

H3O+

Pulse Delay (ps)

(a)

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0.2

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0.6

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D3O+

H3O+

Sig

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(b)

Fig. 8. Hydrated proton and deuteron band kinetics (symbols: experi-mental results; solid lines: biexponential fits) at 1 M base concentration fortwo carboxylate bases: (a) monochloroacetate (x = 1); (b) dichloroacetate(x = 2). Biexponential fitting of the data (A1exp(�t/s1) + A2 exp(�t/s2))resulted in the following fit values. (a) For D3O+: A1 = 0.28, s1 = 36 psand A2 = 0.72, s2 = 194 ps; for H3O+: A1 = 0.17, s1 = 17 ps andA2 = 0.83, s2 = 100 ps. (b) For D3O+: A1 = 0.28, s1 = 81 ps andA2 = 0.72, s2 = 392 ps; for H3O+: A1 = 0.31, s1 = 27 ps and A2= 0.69,s2 = 194 ps.


stable configuration for D3O+ (H3O+) [62,63,65,67]. Inter-estingly an isotope effect is observed when comparing thedecay curves obtained in D2O and in H2O solution(Fig. 8). Bi-exponential fitting of the data reveals a ratioin rate constants of kH/kD � 2–3 with the exact value vary-ing as the reaction progresses and showing a dependencyon the proton acceptor strength of the base.

4. Discussion

4.1. Base-induced solvent switches

HPTS dissociates a deuteron to D2O solvent with a250 ps time constant (the equivalent proton transfer inH2O solvent occurs with a 90 ps time constant) [48]. Recentreports based on ultrafast UV/Vis pump–probe spectro-scopic results suggest the initial formation of an ion pairof unspecified character on the order of a few picoseconds[113–115]. These recent reports are at odd however withpreviously reported interpretations of time-resolved fluo-rescence [116], UV/Vis pump–probe [117] and transientIR [108] measurements where no indications of an ion pairformed by initial proton/deuteron dissociation on a timescale of 1–2 ps from the electronically excited HPTS photo-acid have been found. Our own transient IR absorptionmeasurements described in Refs. [62,63,65,67] do not indi-cate a rapid pre-equilibrium whatsoever prior to HPTS dis-sociation in water or to a base and we do not consider thispossibility in our modeling of the acid–base neutralizationreaction.


When a neutralizing base is added to the solution, theoverall transfer of a proton or deuteron is accelerated byup to three orders of magnitude, depending on the partic-ular configuration of acid and base at close contact inaqueous solution [58,59,62,63,65,67]. When acid and baseare directly linked by a hydrogen bond between donatingand accepting groups, this increase of reaction rate is deter-mined to a large extent by the free energy differencesbetween reactant and product sides of the reaction, whichconsists of a single proton/deuteron transfer assisted bythe surrounding solvent. In contrast, for configurationswhere acid and base are separated by a small number ofwater molecules, the proton/deuteron transfer can activelybe facilitated by water, functioning like a solvent switch ofwell-defined geometry (Fig. 2) [65,67]. A short solventswitch has the ability of increasing both the proton dissoci-ation rate of the acid and the rate at which the protonspans the distance between acid and base. We point outhere that water separating acid and base may also mediatethe transfer of protons/deuterons in a diffusional fashion(similar to the von Grotthuss mechanism in bulk water)functioning as a long-range, non-specific, solvent switchconnecting between acid and base. Water may also bealigned as wires, that are essentially linear hydrogen-bonded chains temporarily connecting acid and base,where within the lifetime of these water wires the protonpropagates concertedly or sequentially from acid to baseover large distances. Such water wires can be consideredas specific long-range solvent switches having the abilityof efficiently facilitating point-to-point transfer of the pro-ton over relatively long distances in solution. Although wehave not found explicit evidence for water wires mediatingproton transfer in our experiments, we do not exclude thepossibility of these. We thus use the more general conceptof solvent switch, as this includes several physically differ-ent mechanisms mediating proton transfer between acidand base in aqueous solution.

Our experimental transient IR results shown in Figs. 4–8reveal the time scales for the first event, deuteron dissocia-tion from the photoacid, for the two smallest solventswitches for the HPTS-carboxylate base reaction pair.For the tight complex, where no water separates acid andbase (n = 0) it follows that for all carboxylate bases thedeuteron transfer occurs within 150 fs. This point out toa higher intrinsic (gas-phase) basicity of all carboxylatesas compared to the intrinsic (gas-phase) basicity of the elec-tronically excited HPTS. Interestingly this is also found tooccur for the loose complex with one water moleculebetween acid and base (n = 1), irrespective of the basicityof the carboxylate present. This result is surprising whenone considers the basicity of the carboxylate (as repre-sented by the (bulk water) pKa value of the conjugate car-boxylate acid) to be indicative of reaction time scale. Whilethe strong bases acetate and monochloroacetate (x = 0–1)are expected to have fast deuteron transfer rates, this willbe less likely for di- and trichloroacetate (x = 2–3). Thisfact points to different factors playing a key role in this ini-

tial transfer of a deuteron, e.g. different values for pKa forthe photoacid and conjugate carboxyate acid in the tightand loose complexes compared to those of in the bulkwater solvent, even when a single water molecule is the pro-ton acceptor in the first reaction step for all carboxylates(see below). In addition, the influence of Coulombic inter-action between the photoacid and the (negatively charged)carboxylate base will mainly depend on the total charge ofthe carboxylate which is a constant in this reaction series.On the other hand, the time scale of the second deuterontransfer in the loose complex correlates with the basicityof the carboxylate base: the weaker the base the slowerthe second transfer.

We have ascribed the observation of the hydrated deu-teron band at 1850 cm�1 to a photoacid–base reaction pairwith one water molecule bridging acid and base [65]. Thisconclusion is based on the observation of the ultrafast firsttransfer (within 150 fs) from photoacid to the bridgingwater, and the spectral location of the hydrated deuteron,that is very similar to that of the symmetrically solvatedD3O+ in the Eigen cation D3O+(D2O)3 [86]. A small fre-quency upshift is observed when going from the strongestbase acetate (x = 0) to the weakest base trichloroacetate(x = 3), revealing differences in the hydrogen bond interac-tions of D3O+ in the ionic complex consisting of theHPTS� photobase and the carboxylate bases. Formallywith current spectroscopic knowledge one cannot distin-guish between a D3O+ fully symmetrically hydrogen-bonded between the (partially) negatively charged oxygenatom of the HPTS� photobase and the two oxygen atomsof the carboxylate base (which also has one net negativecharge), a D3O+ hydrogen-bonded to HPTS� and twowater molecules, or even a case of a pure contact ion pairwithout hydrogen bonds. However, in light of the fact thatthe transient band of the hydrated deuteron does not sig-nificantly change in spectral shape at longer pulse delayshints at a preferred geometric configuration of the hydrateddeuteron having increased stability over a simple solvent-stabilized contact ion-pair. In contrast a hydrated deuteronin water would exchange between different hydration con-figurations at ultrafast time scales. This is the reason whyaqueous solutions at low pH do not show well distin-guished vibrational bands of the hydrated proton at desig-nated frequencies [78,96]. This is also the reason why wehave not transiently observed a hydrated deuteron bandfor the photoacid dissociation in deuterated water (withoutneutralizing base), as upon dissociation with a time con-stant of 250 ps, an ultrafast equilibration within fractionsof a picosecond will erase any spectral signatures of thehydrated deuteron: only a small increase of a spectral fea-tureless absorbance occurs over a large spectral range, ashas been reported by us before [108]. A third remark inthe context why we are inclined to conclude that thehydrated deuteron assumes a special geometric configura-tion in the loose complex, can be made by referring torecent reports on calculations of infrared spectra ofhydrated protons in condensed phase. For the case of


HF acid dissociation in water [56] and of the hydrated pro-ton species in bacteriorhodopsin [75] a large degree of flux-ional motions is mirrored by much broader IR transitions.Finally, we feel that a more sophisticated and definitive testfor our suggestion of a transient special ionic complex con-sisting of HPTS�� (D3O)+� � ��OOCCH(3�x)Clx occursshould be pursued using state-of-the-art ab initio quantumchemical molecular dynamics combined with IR spectros-copy while the proton is transferring. In this light we referto recent numerical approaches to study acetic acid dissoci-ation [57], where the important role of water in the stabil-ization of the ionic complex has been noted.

While the spectral shape of the hydrated deuteron bandas observed at 1850 cm�1 appears to be largely unchanged,its dynamics occurs on multiple time scales. A decline inmagnitude up to a few picoseconds is not perfectly matchedwith an accordingly magnitude rise of the C@O stretchingmarker mode of the carboxylate acids [65]. This feature is astrong indication we deal with the observation of a hydro-gen bonded O–H/O–D stretching modes of the transienthydrated proton/deuteron in the loose (n = 1) complex,subject to strong couplings with the electric dipolemoments and Coulombic fields of the nearby chargedHPTS� photobase and the carboxylate base, the surround-ing solvent layers showing ultrafast motional rearrange-ments and the counterions present in solution. Asignificant change in IR transition cross section in hydro-gen-bonded O–H stretching bands of phenol-dimers dueto large changes in electric dipole moment of a nearby cou-marin dye has been reported [118]. Here the dynamics wasinduced upon electronic excitation of a neutral species(coumarin 102 hydrogen bonded to a phenol-dimer) innonpolar solvent (C2Cl4). In the current case of acid–baseneutralization we deal, besides the positively chargedhydrated proton/deuteron, with a fourth-fold negativelycharged photobase (HPTS�), electronically excited to anew charge distribution, and one-fold negatively chargedcarboxylate base, as well as positively charged counterions(Na+ or K+). As a result the partially screened Coulombicpotentials will strongly influence the time-dependent O–H/O–D stretching oscillator of the hydrated proton/deuteron.In addition the fluctuating hydrogen-bond network withthe water solvent shells will have a significant influenceon the dynamics of the hydrated proton/deuteron markermode. In this light elucidation of the dephasing and spec-tral diffusion dynamics of the marker band of the hydratedproton/deuteron will provide more insight into the reorga-nizational motions associated with the intermediate stageof the loose complex. With photon echo spectroscopydephasing and spectral diffusion of transitions subject toline broadening by coupling to a fluctuating heat bathcan be determined [119–131]. Here vibrational photon ech-oes on the O–H/O–D stretching band of the hydrated pro-ton/deuteron may reveal these ultrafast motions of thehydrogen bonds within the intermediate complex and ofthe surrounding water solvent shells [132]. It would beinteresting to determine whether the frequency fluctuation

correlation function will behave more like that of bulkwater [133–143], where most of the dephasing and spectraldiffusion dynamics occurs in a few hundreds of femtosec-onds, or that dynamical components on picosecond timescales are more dominant [112,144–146]. Photon echo spec-troscopy would thus provide insight into the rigidity andfluxional degree and associated time scales of the hydratedproton/deuteron in the intermediate stage of the loosecomplex.

The observation of the loose (n = 1) complex is facili-tated by the transient occurrence of a hydrated deuteronband at 1850 cm�1 spectrally separated from solventbands. This is not the case for other hydrated deuteronconfigurations, where the marker modes are closer to theD2O bending and stretching vibrations [81,83–86,147,148]. Based on the transient IR spectra we thus can-not exclude a priori the possibility of other solvent switches(n P 2) facilitating the transfer between acid and base. Thetransient observation of larger solvent switches may onlybecome possible upon further developments of the methodin signal detection sensitivity.

Finally the observation of the C@O stretching mode oftrichloroacetic acid growing in at longer times provides evi-dence that this carboxylate exists as a true acid species atlow pH. Considering the fact that deuterated HPTS inthe excited state has a pKa value of about 0.7 (in 1 M ionicstrength solutions), trichloroacetic acid cannot differ muchin its pKa value, in accordance with literature values [149],but excluding reports by others [150,151] who suggestedthat trichloroacetic acid to a large extent exists as ion pairsin aqueous solution. In the case of an ion pair consisting ofa hydrated deuteron and trichloroacetate one would notobserve a C@O stretching vibrational marker mode.

4.2. Modelling aqueous bimolecular proton transfer

The kinetic data of the HPTS� photobase, the hydrateddeuteron D3O+ in the loose (n = 1) complex, and the car-boxylate acid species, as derived from the time-dependentbehaviour of the respective vibrational marker modes, arecomposed of the time-dependent contributions of the dif-ferent reaction pathways, as indicated in Fig. 2. Fittingthe observed reaction kinetics is thus based on the time-dependent absorption of the vibrational marker modesindicating the initial deuteron release from the HPTS�

photobase, the transient occurrence of the deuteron onthe water bridge in the loose (n = 1) complex, and the finaldeuteron arrival at the carboxylate. Whereas the initialdeuteron release from the photoacid, and the arrival atthe carboxylate base occur through numerous reactionpathways, the hydrated deuteron band is solely indicativeof the deuteron transfer reaction between HPTS photoacidand carboxylate base through a solvent switch consisting ofa single water molecule (n = 1). When a general fitting pro-cedure is applied, the possibility of a large variation inparameter values has a priori to be considered. It is how-ever because of the strongly different reaction time scales


and the existence of preformed populations of complexesof acid and base that one can make a distinction of the rel-ative contributions of tight (n = 0) and loose (n = 1) com-plexes on the one side, and other solvent switches (n P 2)up to fully solvent separated acid and base on the otherside. Here we can directly deduce reaction time scales forthe tight and loose complexes by inspection of the vibra-tional marker modes at early times (from femtosecondsto picoseconds) [62,63,65,67], whereas the desolvationand solvation steps connecting the different solvent switchpathways are found to occur on much longer time scales(tens of picoseconds or longer). The mutual diffusionbetween acid and base also occurs on longer time scalesbefore an encounter complex with n water molecules isformed. In addition to the short solvent switch pathwayswe have to include the protolysis reaction channel, whereHPTS photoacid first dissociates to the solvent (250 ps timeconstant for deuteron transfer to D2O in high ionicstrength solutions), followed by diffusion of the hydrateddeuteron and eventually a deuteron pick-up by the base.

In bimolecular reaction dynamics in solution the diffu-sional process between the two reactants typically isdescribed using the Debye–Smoluchoswki equation [7,18–20,152], where molecular diffusion in three-dimensionalspace is described by the diffusion equation, and a reactionoccurs when the two reactants collide at the contact reac-tion distance a. Collins and Kimball have derived a math-ematical formalism for bimolecular reaction dynamics forfinite reaction probabilities k0 (so-called radiative bound-ary condition) [76], where not every arrival at contact dis-

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Fig. 9. Kinetics of the HPTS� photobase band, the hydrated deuteron D3O+

experimental results; solid lines: fits using the model described in Section 4.2 a(a)–(d) 3, 2, 1 and 0.5 M, respectively.

tance necessarily leads to reaction. This approach can berefined for cases where interaction potentials between thereactants exist, such as Coulombic interactions betweencharged ions [106]. We have used the von Smoluchowski–Collins–Kimball (SCK) approach with Szabo’s refinementfor finite ionic strength to model the diffusion-controlledreaction dynamics between HPTS and the strong bases ace-tate (x = 0) [62,63] and monochloroacetate (x = 1) [65]. Wehave found on-contact reaction rates of (6 ps)�1 and(20 ps)�1 for acetate and monochloroacetate, respectively.These on-contact reaction rates are similar to the overallreaction rate of the loose (n = 1) complexes [65], providingstrong support – but not unequivocal evidence – for thehypothesis that the loose (n = 1) complex is identical tothe encounter complex formed after mutual diffusion ofacid and base. In other wording, the encounter distance(reaction radius) used to model diffusion assisted reactionsbetween acid and bases is the distance where further desol-vation occurs more slowly than the respective deuterontransfer through the solvent switch at the particular acid–base separation. The diffusion limited reaction rate isapproached when the solvent switch is faster than bulk-diffusion.

A further exploration of the carboxylate base family canbe pursued along these lines. One problem arising wheninvestigating the weaker di- and trichloroacetate (x = 2,3)bases, however, is the increasing importance of reversibilityof proton transfer with decreasing base strength. A moreappropriate modeling of the observed reaction kineticsincludes forward and backward proton transfer obeying

0

HPTS_

DOOCH2Cl

D3O+

(c)

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HPTS_

DOOCH2Cl D

3O+

(d)

Pulse Delay (ps)

band and the C@O stretching band of monochloroacetic acid (symbols:nd in Fig. 2), as function of the concentration of monochloroacetate base:

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D3O+

DOOCCl3

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Fig. 11. Kinetics of the HPTS� photobase band, the hydrated deuteronD3O+ band and the C@O stretching band of trichloroacetic acid (symbols:experimental results; solid lines: fits using the model described in Section4.2 and in Fig. 2), for 2 M concentration of trichloroacetate base. Whenimposing that the deuteron transfer only can occur through tight (n = 0)and loose (n = 1) pathways, reasonable fits are obtained for the HPTS�

photobase and trichloroacetic acid C@O stretching marker bands. Astrong deviation occurs in contrast between experiment and fit of thehydrated deuteron D3O+ band.

Table 1


detailed balancing for every reaction step. We thus solvethe rate equations using time-independent rate constants,that could be diffusion-limited for a fraction of the possiblereaction steps. We avoid the inclusion of time-dependentreaction rates, such as in the SCK model, that have dimin-ished importance in slower on-contact reactions, makingthe inclusion of detailed balancing is a nontrivial proce-dure. Instead the slower the on-contact proton transferproceeds, the more useful steady-state rate constantsbecome. We have recently applied this approach to the caseHPTS + trichloroacetate (x = 3) [67]. Here we show thecomparative fitting result for �OOCCH(3�x)Clx (x = 1–3).The data set for acetate (x = 0) was not sufficiently largeenough (the hydrated deuteron band is much weaker, echo-ing the smaller fraction of loose complexes in solution) tohave a quantitative fit result.

The results of the fitting procedure are shown in Figs. 9–11 (the full fit result in the case of trichloroacetate base canbe found in Ref. [67]), as well as in Tables 1–4. By compar-ing the rate constants for the different reaction steps ofFig. 2 as function of the base we can make the followingremarks:

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DOOCHCl2

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Fig. 10. Kinetics of the HPTS� photobase band, the hydrated deuteronD3O+ band and the C@O stretching band of dichloroacetic acid (symbols:experimental results; solid lines: fits using the model described in Section4.2 and in Fig. 2), as function of the concentration of dichloroacetate base:(a)–(c) 3, 2 and 1 M, respectively.

Rate constant fit values in the bimolecular deuteron transfer betweenHPTS and carboxylate base

1/k (ps)�1 �OOCCH2Cl �OOCCHCl2�OOCCCl3

1/ksw1 40 40 401/k�sw1 240 240 2401/ksw2 10 15 2001/k�sw2 300 65 601/k1 0.15 0.15 0.151/k�1 0.27 0.26 0.251/k2 25 75 1751/k�2 90 85 231/kp 0.15 0.15 0.151/k�p 2 2 21/ksolv1 220 220 3301/kdesolv1 10 70 6001/ksolv0 25 100 2501/kdesolv0 1000 1000 10001=k0solv1 45 45 131=k0desolv1 120 180 1801=k0solv0 50 70 15001=k0desolv0 1000 100 100

(i) In the tight (n = 0) complex the forward transferreaction occurs an order of magnitude faster thanthe backward reaction.

(ii) In the loose (n = 1) complex the first transfer occurswithin time resolution and the second occurs on pico-second time scales. This second step is base depen-dent: the weaker the base, the smaller the forwardreaction rate (k2), but the larger the backward reac-tion rate (k�2). Whereas for monochloroacetate(x = 1) the progress of deuteron transfer in the loosecomplex is dominated by the forward reaction steps,making it complete within 500 ps, this is not the casefor the weaker bases (x = 2,3). Here the intermediatestage of the loose complex can be observed beyond

Table 3Diffusion constants, contact distances, pKa values and rate constantsa usedin global fitting of the dichloroacetate data

Base concentration (M) �OOCCHCl2 1 2 3D · 105 (cm2 s�1)b 0.9 0.8 0.7aeff (A)c 4.7 5.2 5.5pKHPTS(S1) 1.10 1.13 1.16pKDOOCCHCl2 1.78 1.92 2.00kdif (ps M)�1 (312)�1 (318)�1 (330)�1

ksep (ps)�1 (65)�1 (85)�1 (100)�1

kw (ps)�1 (290)�1 (295)�1 (300)�1

kgem (ps M)�1 (23)�1 (22)�1 (21)�1

ksc (ps M)�1 (200)�1 (150)�1 (130)�1

k�sc (ps)�1 (12000)�1 (12500)�1 (13000)�1

a,b,c See footnotes of Table 2.

Table 4Diffusion constants, contact distances, pKa values and rate constantsa usedin global fitting of the trichloroacetate data

Base concentration (M)�OOCCCl3 1 2 3D · 105 (cm2 s�1)b 0.70 0.32 0.30aeff (A)c 4.7 5.2 5.5pKHPTS(S1) 1.12 1.13 1.18pKDOOCCCl3 0.90 1.00 1.11kdif (ps M)�1 (400)�1 (795)�1 (730)�1

ksep (ps)�1 (85)�1 (210)�1 (230)�1

kw (ps)�1 (240)�1 (245)�1 (270)�1

kgem (ps M)�1 (18)�1 (18)�1 (18)�1

ksc (ps M)�1 (250)�1 (300)�1 (300)�1

k�sc (ps)�1 (2000)�1 (3000)�1 (3900)�1

a,b,c See footnotes of Table 2.

Table 2Diffusion constants, contact distances, pKa values and rate constants usedin global fitting of the monochloroacetate dataa

Base concentration (M)�OOCCH2Cl

0.5 1 2 3

D · 105 (cm2s�1)b 1.1 1 0.9 0.8aeff (A)c 4.0 4.7 5.2 5.5pKHPTS(S1) 1.05 1.12 1.14 1.18pKDOOCCH2Cl 2.86 2.86 2.99 3.12kdif (ps M)�1 300 281 282 290ksep (ps)�1 48 58 75 97kw (ps)�1 260 274 290 300kgem (ps M)�1 23 21 21 20ksc (ps M)�1 125 110 100 90k�sc (ps)�1 60,000 80,000 97,000 120,000

a Values optimized in the range of the accepted literature values, see forexample Refs. [1,50,58–63].

b D is the mutual diffusion coefficient of HPTS and the carboxylate base.c aeff is an effective reaction radius which includes the interaction cal-

culated with a = 6.3 A, a contact radius of HPTS and carboxylate base(z1 = �1, z2 = �3 are the charge numbers of the carboxylate base andHPTS, respectively).


1 ns, a consequence of a much larger stability (as dic-tated by the ratio K = k2/k�2) of the intermediatecomplex HPTS�� D3O+� � ��OOCCH(3�x)Clx.

(iii) The fact that both forward and backward transferreaction steps play an important role in the dynamics

and that all reaction pathways should in principle beconnected (as indicated by the scheme of Fig. 2),leads to a highly non-exponential decay of thehydrated deuteron marker band at 1850 cm�1 forthe weaker bases where several coupled reactionpathways are important, extending well beyond thetime scale expected from the magnitude of the secondforward reaction time constant.

(iv) The solvent switch swn has been invoked to obtain asatisfactory fit of the trichloroacetate (x = 3) data[67]. Here again the first step, deuteron transfer towater in the switch bridge, is insensitive to basestrength (but much faster than the bulk transfer rate),whereas the second transfer to the base becomesslower when the basicity of the carboxylate decreases,whereas the opposite is true for the backward trans-fer. In similar fashion to the loose (n = 1) complex,the reaction of monochloroacetate through the sol-vent switch swn pathway will be short lived, whereasthe increased stability of the intermediate configura-tion for the weaker bases as compared to those ofthe conjugate carboxylate acids will lead to longereffective lifetimes. We note here that the hydrateddeuteron likely will exist in a highly fluxional config-uration, where the location of the deuteron will betuned by the motions of nearby photobase and car-boxylate base and by the surrounding solvent.

(v) A more detailed description of the evolution ofthe intermediate complex HPTS�� D+(D2O)n� � ��OOCCH(3�x)Clx (x = 1–3; n P 2) cannot be given,without available kinetic information of vibrationalmarker modes of this species. However, the fit resultscan be understood as indicators of the importance ofadditional pathways in the acid–base neutralizationreaction. By making a comparison between the trans-fer rates of this swn reaction pathway with the desol-vation/solvation steps to the loose complex pathway,it becomes clear that for monochloro- and dichloro-acetate (x = 1,2) the majority of photoacid–basereactants will be channelled through the loose com-plex pathway. This is different for the weakest basestudied, where the overall reaction dynamics becomesslow enough to make the reaction pathways throughthe larger solvent switch configurations importantenough. It is of no surprise that excluding the sol-vent switch swn pathway in the modelling is notproblematic when fitting the results for monochloroand dichloroacetate. The reaction rates obtained forthe loose complex are then close to the ones obtainedhere (with differences in fitting values less than 20%).In contrast, strongly deviating unsatisfactory fits areobtained for �OOCCCl3 (x = 3) without the inclu-sion of the additional solvent switch swn (Fig. 11).

(vi) In solvent switches of finite size proton transferoccurs to and from water. One may conclude fromour results that the chemical reactivity of the watermolecules in-between acid and base is considerably

-10 -5 0 10 15-8

-6

-4

-2

0

2

4

6

8

10

12

10lo

g(k

[s])

ΔpKa

5

Fig. 12. Free energy correlation: DpKa (acid–base) vs. the overall proton-transfer rate on contact. The free-energy vs. reaction-rate curves arecalculated using the Marcus equation for proton-transfer, Eq. (2) (solidline) and using Marcus theory for electron-transfer, Eq. (3) (dashed line)and are the best fits of a large family of proton transfer reaction fromphotoacids to water [14,102]. The solid dots denote the fit values found fork2 and the open squares those for k�2, after correcting for the small isotopeeffect for the deuteron transfer, kþH=kþD ¼ 1:5. The open triangles indicatephotoacid dissociation to bulk water assuming pKa (D3O+)complex = 1.5 ,whereas the open circle is the rate for H2O self-dissociation.


modified by the length of the solvent switch and itscharge density and to a lesser effect by its chemicalreactivity.

4.3. Water-mediated proton transfer

We thus have found that for the second transfer steps ofthe loose (n = 1) and larger solvent switch swn (n P 2) com-plexes the reaction rate is dependent on the base strength ofthe carboxylates. The question now is whether this informa-tion can be used in finding a correlation between free-energyand deuteron transfer reaction rate and to relate it to previ-ously reported free-energy reaction-rate correlations onphotoacid dissociation in neat aqueous solvent and in reac-tions between photoacids and carboxylate bases [58,153]. Asemi-empiric correlation between the proton transfer rateand the difference between the pKa of acid and conjugateacid of the base in aqueous solution has been defined usingthe free-energy relationship:

kp ¼ k� expð�DGa=RT Þ; ð1Þ

where (k*)�1 is the frequency factor for the specific familyof reactions, R is the gas constant and T is the absolutetemperature. The effective activation energy of the protontransfer reaction, DGa, may be estimated using the Marcusbond-energy bond-order (BEBO) equation [154]:

DGa ¼ DG0=2þ DG#0 þ DG#

0 cosh½DG0 ln 2=ð2DG#0 Þ�= ln 2;

ð2Þ

or alternatively using Marcus charge-transfer theory(MCT), applied in the normal activated region [155–157]:

DGa ¼ ð1þ DG0=4DG#0 Þ

2DG#0 : ð3Þ

The MCT theory was originally developed for the activa-tion free-energy of electron transfer reactions in solution.Here the reaction is assumed to takes place in the ‘‘normal’’region where the activation energy decreases when the reac-tion is more favorable thermodynamically. For both ap-proaches DG#

0 is the solvent-dependent activation energyof the charge-exchange reaction when the total free energychange DG0:

DG0 ¼ RT ln 10pKa ð4Þ

in the proton-transfer reaction is equal to zero. Eqs. (2) and(3) are practically equivalent for excited state photoaciddissociation to solvent in the photoacidity range that hasbeen studied so far. Here only normal reaction behaviourhas been observed where the proton transfer rate betweenphotoacids and bases monotonously increases as a functionof the increase in the relative strength of the conjugate acidof the base compared to the excited photoacid.

The deuteron transfer rates measured in the currentstudy for the loose (n = 1) and solvent switch (n P 2) com-plexes, where a hydrated deuteron transfers to an accepting

carboxylate base, correlate reasonably well with a similarcorrelation found in large group of photoacid-dissociationto water [14,58,153] when one assumes that the proton dis-sociation occurs from a bound H3O+ (D3O+) ion beingabout 1000 times more basic than a H3O+ (D3O+) ionresiding in bulk water (see Fig. 12). For deuteron transferthe absolute values of the rate constant from the D3O+

ion to the various acetate bases as well as the correspond-ing back proton-transfer rate constants have been corre-lated with the (bulk) pKa values of the carboxylates whenassuming pKa (D3O+) = 1.5. The assignment of a consider-ably more basic pKa value to the hydronium ion in theloose and solvent switch complexes, pKa = 1.5, instead ofits formal value in bulk water of �1.74 [1] is corroboratedby our kinetic analysis of the dichloroacetate-HPTS reac-tion. The pKa-value of deuterated dichloroacetic acid inpresence of 1 M of the dichloroacetate base according toour analysis is 1.78 (Table 3). We have found the rate ofthe proton transfer from D3O+ to dichloroacetate andthe back deuteron transfer from dichloroacetic acid toD2O to be almost equal (Table 1). This means comparablebasicity for D2O and �OOCCHCl2 within the HPTS� � �D2O� � ��OOCCHCl2 complex, i.e. pKa (D3O+)complex ofabout 1.7 in a good agreement with the value estimatedfrom the free-energy correlation. The increased basicityof the complexed water molecule points to a water mole-cule strongly bound within the acid–base complex akin to


situations encountered for water molecules bound to mac-romolecules, enzymes and surfaces.

The isotope effect on the decay kinetics of the hydratedproton/deuteron intermediate (Fig. 8) exhibits featuresindicating that the observed kinetics are not caused byan elementary process such as the unimolecular dissocia-tion of an O–H bond. These features are: (a) non-expo-nential decay of both the H3O+ and D3O+ kinetics thatcan only be satisfactorily fitted with at least two exponen-tial decay curves, (b) an apparent isotope effect thatchanges with reaction time, and (c) an isotope effect thatdepends on the relative reactivity of the acid–base pair.The apparent magnitude of the isotope effect changesbetween 1.9 and 3 getting larger at long decay times.The isotope effect is visibly larger for the weaker�OOCCHCl2 base in accord with theories of solvent med-iated isotope effect in acid base reactions [156–159]. Insuch cases the maximum isotope effect for a family of sim-ilar reactions is found for the symmetric case when DG0 ofthe proton transfer between donor and acceptor is zero.This is roughly the case for the proton transfer to�OOCCHCl2 from the intermediate where we have foundthe forward and backward rate constants of the protonintermediate – base system to be almost equal, ie,(75 ps)�1 and (85 ps)�1, see Table 1. Using our detailedkinetic model we are led to conclude that the measuredpulse delay dependent isotope effect in the observed kinet-ics may be decomposed into several elementary contribu-tions. For �OOCCH2Cl base we have found an isotopeeffect in the elementary reaction steps to lie around�1.45. Despite the fact that in this case the decay curvesfor the hydrated proton/deuteron do not extend so muchto long delay times and a kinetic analysis cannot be per-formed in such detail we reckon that the elementary reac-tion steps also exhibit a much larger range for the isotopeeffect up to values of 1.7–2.0.

In any case our current findings points to a similar medi-ating role of water in both proton transfer from photoacidto bulk water solvent, and from hydrated proton in theloose and solvent switches to the carboxylate bases. In con-trast, the proton transfer reactions in tight complexes, thatdo not proceed through water, but instead directly betweendonating and accepting groups of acid and base, are toofast to fit on the same correlation curve. This shows thatthe highly polar solvent water exerts much less control onthe rate of proton transfer reactions occurring directlybetween an acid and a base. This implies that slower morecollective solvent relaxation modes, as indicated in theoret-ical studies [158,159], will only strongly affect the dynamicsof mineral acid dissociation when at least several watermolecules directly participate in the proton transfer reac-tion. When only one or two water molecules separatebetween acid and base they control the proton transfer ratechemically and participate directly in the proton transferprocess on individual molecular levels rather than collec-tively as part of highly polar and highly fluxional solventmedium.

5. Conclusions

We have presented for the first time a full set of experi-mental results and performed a novel kinetic analysis on anultrafast infrared spectroscopic study of the neutralizationreaction of the photoacid pyranine (HPTS) with the car-boxylate base family �OOCCH(3�x)Clx (x = 0–3) in aque-ous solution. Based on the dynamics of IR-activevibrational marker modes of the conjugate photobase ofthe photoacid (HPTS�), of the hydrated proton/deuteronin the loose complex (H3O+/D3O+), and of the carboxylateacids, we have derived the time-dependent kinetics of themany steps in the different reaction pathways of Fig. 2.Assuming fully reversible kinetics for every proton/deu-teron transfer, and of molecular diffusion in a fitting modelprovides a quantitative insight into the reaction rates ofthese different reaction steps. We can now conclude withthe following general observations:

(i) Only three different populations of acid–base pairscan directly be identified by our method: Acid–baseseparated by more than one water molecule (solventswitches n P 2 up to fully separated acid–base), theone having one water molecule directly spacingbetween acid and base (loose complex; n = 1), andthe one which forms a directly linked reactive com-plex with no solvent in between acid and base (tightcomplex; n = 0).

(ii) The relative abundance of the various acid–base pairsis controlled thermodynamically, the stability con-stants at 1 M of base being for all different popula-tions on the same order of magnitude.

(iii) Within the smallest reactive complexes (n = 0,1) weobserve the first reactive step to be always proton dis-sociation from the acid either directly to the protonacceptor or to the water molecule spacing betweenacid and base occurring within experimental time res-olution (150 fs). This is irrespective of the acidity ofthe carboxylate acid used in the range of 0 < pKa < 5.

(iv) The overall proton transfer rate between acid (HPTS)and all the bases studied has always the highest valuein directly linked acid–base pairs without waterspacer and the slowest for the completely separatedacid and base at relatively low concentrations. Theproton transfer rate within complexes containingone water molecule (n = 1), or a few (n P 2), is inbetween the two limiting reaction rates.

(v) In all cases the aqueous proton shuttling in betweenacid and base in a reactive loose (n = 1) complexhas been identified as assuming the Eigen-core config-uration with symmetric hydrogen bond configura-tion, H3O+(L3).

(vi) The rise of the solvated proton band always occurswithin time resolution. This is even true for the rela-tively slow proton transfer reaction from HPTS to�OOCCCl3 (x = 3). These points to a base-assistedsolvent switch mechanism within the reactive


(n = 1) complexes that we tentatively ascribe to Cou-lomb interactions between the charged acid andbases.

(vii) The final transfer step of the aqueous proton in theloose and solvent switch swn complexes arriving atthe base is activated and controlled by the basicityof the proton acceptor: the lower the basicity theslower the proton transfer rate. The key role playedby the mediating water is clear when comparing thereaction rates found here with those of previouslyinvestigated proton transfer of photoacid to waterand to accepting bases.

(viii) The proton transfer reaction within the reactive com-plexes always are best-fitted by a reversible kineticmodel. For most carboxylate bases �OOCCH(3�x)Clx(x = 0–2), the proton transfer is to a large extentchanneled through the loose (n = 1) complex path-way after formation of an encounter photoacid–basecomplex. Only for the weakest base �OOCCCl3(x = 3) the second transfer step is slowed down tosuch an extent that larger solvent switch (n P 2)route assume a role with increasing importance.

In light of current results it is recommendable to explorefurther the potential of the method in elucidation of bimo-lecular aqueous neutralization reactions for different clas-ses of photoacids and of bases.

Acknowledgments

This work has been supported by the German–IsraeliFoundation for Scientific Research and Development(GIF 722/01 for E.T.J.N. and E.P.), the Israeli ScienceFoundation (ISF 562/04 for E.P.), the James Franck centrefor Laser–Matter Interactions (E.P.), and by a long termmission fellowship by the Egyptian government (O.F.M.).We thank Prof. Dr. Andrius Baltuska in translating essen-tial text sources on Theodor von Grotthuss from the Balticregion. This work is dedicated to Douwe A. Wiersma, whosince 30 years has been a pioneer in ultrafast spectroscopyof condensed phase chemical dynamics. This work is justone demonstration of his unshakeable conviction that pro-gress in the field ultimately will lead to essential insight intoelementary condensed phase chemical reactions.

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