Excited-state proton transfer reactions I. Fundamentals and intermolecular reactions

J. Photo&em. Photobiol. A: Chem., 75 (1993) I-20

1

Invited Review

Excited-state proton transfer reactions 3. Fundamentals and intermolecular reactions Luis G. Arnaut

and Sebasti%o J. Formosinho

Depariamento de Q&mica, Universidtzde de Coimbra, 3049 Coimbm (Portugal) (Received November 17, 1992; accepted April 22, 1993)

Abstract Theoretical models that have been proposed and applied to proton transfer reactions are reviewed in this work. Simple models, like the Eigen model, Marcus theory and the intersecting state model, are applied to excitedstate intermolecular proton transfers. The kinetics and thermodynamics of proton transfers occuring in the singlet states of aromatic molecules with -OH, -NH,+, -NH2 and -CO substituents are reviewed.

1. Introduction Ground-state proton transfer reactions are one of the simplest and most important processes found in chemistry. They have an outstanding place in all general chemistry books and are the favourite subject of many first year chemistry students. Excited-state proton transfers (ESPT) are much less popular, even in the realm of photochemistry, despite their unquestionable importance in fundamental and applied photochemistry. The understanding of ESPT is an indispensible building block of photochemistry and approaches for its introduction at an undergraduate level have been presented [l]. Intermolecular ESPT have been employed as mechanistic tools and in technological applications in pH 123 and pOH [3] jump experiments aimed at the study of proton hydration dynamics [4,5], photolithography [6], and as probes of the environment around proteins 17-91, micelles [IO,1II, reversed micelles [ 121, @yclodextrin [13-151 and films [16]. Analogous intramolecular reactions have been applied in chemical lasers [17], energy storage systems and information storage devices at a molecular level [18], high-energy radiation detectors [19], and polymer stabilizers [20,21]. In 1931, Weber [22] reported for the first time that the shift of an acid-base equilibrium of some

lOlO-6030/93/$6.00

organic molecules, occurred at a different pH depending on whether it was observed by absorption or fluorescence spectroscopy. In 1949 Fiirster 1233 provided the correct explanation for this observation and initiated the field of excited state intermolecular proton transfers (ESI,,PT). Soon thereafter, Fiirster proposed a valuable method to estimate the pK of a molecule in an excited state (pp) based on its ground state pK and the absorption and/or emission spectra of the molecule [24], which became known as the Fiirster cycle. In 1955 Weller [25] found that methyl salicylate presented an unusually large Stokes-shifted fluorescence emission. When the acidic proton of the phenol group was methylated, the fluorescence became t&e common mirror image of the absorption. He proposed that the red-shifted fluorescence corresponded to an excited state isomer, formed via a proton transfer (PT) in the excited state. Since Weller’s initial work, excited-state intramolecular proton transfers (ESI,PT) have been intensively studied. An early review was made by Weller in 1961 1261. The field was yet incipient if compared with the knowledge accumulated in ground state proton transfers at that time [27,28], but in the following decade the reviews published attest to the rapid Q 1993 - Elsevier Sequoia. All rights reserved

2

LG.

Amaut.

S.J. Fonnosilrho

I Excited-stntc profon

development of this area. Vander Donckt [29] reviewed ESI,,PT with a view to rationalize excitedstate acid-base equilibria based on charge transfer and resonance theories. Fijrster [30] discussed the adiabatic nature of these reactions. Schulman and Winefordner [31,32] discussed possible analytical applications of ESPT. The extensive review on thermodynamic acidities of ESI,,PT published by Ireland and Wyatt in 1976 [33] gives a good picture of the development of the field at this stage. At that time a large body of data on pK* of oxygen and nitrogen acids and bases had been accumulated, but comparatively little was known about the excited state behaviour of carbon acids or bases. Shortly after, KlGpffer [34] reviewed ESI,,PT and proposed a phenomenological classification of this field in terms of emission properties, providing also the spectroscopic data for many of typical molecules in each class. More attention to the kinetics of these reactions was given in the review by Kuzmin et al. ]35]. Wubbels addressed the topics of acid and basi: photocatalysis emphazising the role of the catalyst in the quantum yield of the products [36]. Until the SOS, the kinetics of the PT step in singlet states was mainly assessed through the steady-state method initially proposed by Weller [37]. In this method, the pH dependences of the fluorescence efficiencies of the conjugate acids and bases in the lowest excited singlet state are related to the competition between PT and photophysical deactivation. This method enables one to measure protonation and deprotonation rates and, therefore, pK*s, and is still very useful today 1381. Owing to the relatively short lifetime of many singlet states, the real-time determination of many rates had to wait for the development of experimental techniques with fast time resolution. This is especially true for ESI,,PT, which are among the fastest processes known in chemistry. Gutman [9] discussed the application of ESI,,PT of aro.matic alcohols as probes for macromolecules and solutions, emphasizing the potential role of pH jump experiments in biochemistry. Dynamic analysis with nanosecond resolution became popular in the early 8Os, and opened a new window on this field. Shizuka [39] reviewed photoreactions of naphthylamines and naphthols and showed the importance of nonadiabatic protonation of the excited state of aromatic compounds. Picosecond spectroscopic techniques have also been introduced in the study of chemical kinetics 140,411 and a few laboratories have applied them to ESPT. Some early work was reviewed by Huppert [42,43], including inter- and intramolecular ESPT. Another effort to rationalize intramolecular PTs was made

trmsfcr

readions

(i)

by Kasha in 198G [44]. More recently, some kinetic data with femtosecond time-resolution has become :~vailable. This work has not yet been reviewed, despite its relevant impact on the understanding of intramolecular PTs, and will be addressed in the following paper [45]. It is now well established that upon photoexcitation the functional groups R-OH, R-NH2, R-NH,+ become stronger acids (weaker bases), while the groups R,C=OH+, R-C02H, R-COZH2+, R-S03H2+, R-POSH3 +, R-As03H3 + , R-NO,H become stronger bases (weaker acids). It is a genera1 rule in aromatic molecules that electron donating substituents become stronger donors in the excited state, while acceptors will attract the electrons more strongly. This is certainly related to the observation that substituent effects in these photoreactions are better correlated by u+ or u- Hammett substituent constants than by u constants, because ionic resonance structures make much larger contributions to the excited states than to the ground states [46]. After the pKs of the triplet states became available [47], it became clear that, in general, the pK* of the triplet state is intermediate between those of the ground and the singlet states, although exceptions are known. It is also well known that the effect of electronic excitation may be quite dramatic: it may increase the acidity of organic acids up to 32 pK units [48] and increase the rate of protonation by 11-14 orders of magnitude [49]. This review is focused on the thermodynamics and kinetics of intermolecular PTs occurring in the lowest excited singlet state of organic compounds and, unless otherwise stated, pK*, kd and k, refers to the acidity constant, deprotonation and protonation rates of this electronic state. It covers the kinetic data collected in the last ‘tao decades and some of the theories put forward to rationalize and predict trends in the data. Such an exercise may be useful to provide guidelines for future experiments and improvements in the current theories. This is not intended to be a comprehensive review of the vast and rather disperse literature published on ESPT. The emphasis of the present work is on providing tools to rationalize trends in the experimental data representative of ESI,,PT, rather than in describing all the data. This review is extended in the following paper [45] to the field of excited-state intramolecular PTs. Recently ESI,,PT of inorganic compounds have been addressed by several authors. The readers interested in this topic are advised to consult the latest research papers available [SO-581.

LG. rlmattt, S.J. Fonnosinlro / &cited-state proton transfer mactions (I)

2. Thermodynamics A convenient starting point to address the thermodynamics of ESPT is the Fiirster cycle [24]. This thermodynamic cycle combines thermodynamic and spectroscopic data to predict the chemical equilibrium constants in the excited states. An early discussion on this method to determine pK* was published by Jaffe [46] in 1965. More recently the aproximations involved in the F&ster cycle were reconsidered by Grabowski 1591 and generalized to relate also redox potentials to pKs and electronic excitation 1603. The cycle is applicable to the simple indicator equilibrium BH+ =

B+H+

(1)

and based in the energy relations she-tin in Fig. 1, gives e

- AEI=N&(vB -I-l++C)

(2)

where w and m are the enthalpy changes in the excited and in the ground states, vB and VBH+ are the frequencies of the lowest absorption bands of B and BH+, h is Planck’s constant and NA is the Avogadro number. Assuming that m AH= AG*‘- AGo, one obtains f@K=N,h(v,

+ vBH+)/(2.303RT)

(3)

The derivation of this relation assumes that: (i) the solutions are dilute enough such that the enthalpy differences are the same as their differences in the standard state; (ii) the entropy of protonation, ASo, must be the same in the ground and excited states; (iii) the O-O bands of either absorption or emission are accurately known; (iv) the absorption or emission bands of the conjugate acid-base pair must belong to the same electronic B*

AH* (BH + )*

h”, T hv Ml+ _i

B

AH BH+

Fig. 1. FGrster (BH+)* +B*+H+.

cycle

for

the

acid-base

equilibrium

3

configuration and to the same irreproducible representation of the highest common subgroup. The Forster cycle is Q prfori applicable to absorption or emission spectra. In practise the ApK measured by these spectra may be different for two reasons: (i) relaxation of the solvent shell; (ii) relaxation of bond lengths and bond angles. The success of this method can best be appreciated comparing the literature pK* values with the values presently available from direct measurement of protonation and deprotonation rates. Such a comparison is made in Table 1. For 1-naphthol and its conjugate base the emission is from the ‘L, state, whereas the ‘L is the emitting state for 2-naphthol. The IL, state has more charge-transfer character, which leads to a much faster deprotcsnation and proton-induced quenching rates [61]. The quenching rate of the excited-state conjugated base, kq, is particularly large and competes with the protonation rate, kp. The discrepancy between pflF, and pK*, was attributed to solvent relaxation around the conjugated pair and to extreme difficulty in measuring the very weak fluorescence of 1-naphthol in aqueous solution 1621. Substitution by electronwithdrawing groups in the C-5 or C-8 positions of Znaphthol should lower the energy of its IL,, state and enhance the excited-state acidity. This has been verified using cyano-substituted 2-naphthols, which lead to discrepancies between pK*, and PK*~, approaching 3 units [63]. The pK+, values of aromatic amines are very negative compared with the ply** values. In naphthylamines this has been assigned to the inversion of the electronic levels of these molecules during the lifetime of the excited state. However, in phenanthrylamines a significant interaction between their IL,, state and water molecules was assumed and related to the electron migration from the amino group to the phenanthrene ring in the relaxed fluorescent state. The large Stokes shifts in water that result from this charge transfer have been correlated to the discrepancy between Another consequence of PK*dyn and PK*~, [a]. the increase in negative charge at a carbon atom of the aromatic ring, is the more facile electrophilic protonation of this carbon atom, which leads to proton-induced quenching [64]. The rate constants for this quenching have been related to the rr charge densities at the appropriate C-atoms in the excited state of aromatic compounds, calculated using a SCF-MO-C1 method, although a low correlation coefficient was obtained, rc0.8 (651. When such a quenching mechanism competes with k,, simple acid-base equilibrium cannot occur in

H20

H20

H20

H20

H20:CH,CN D20:CH3CN H,O:CH,CN D,O:CH,CN H20:CH3CN D,O:CH$N H#CH,CN D20:CH3CN H@CH3CN D20:CHJCN H20:CH,CN D20:CH3CN H,O:CH,CN DrOCH,CN H20:CHJCN D@CH,CN H20:CH3CN D,O:CH,CN H20:CH3CN D,O:CH,CN Hz0

D20

H20

40

Hz0

H20

&O

D20

H20

H20

D2’3

H20

D2O

H20

Solvent

(1~1) (1:l) (8~2) (8:2) (91) (9:l) (9:1) (9:l) (91) (9:l) (9:l) (91) (9:l) (91) (95:s) (9%) (95:s) (95:s) (95:s) (95:s) -5.6 -2.6 -1.6 -4.5 -3.2 -5.9 -4.1 -5.4’

2.83 -1.8 1.7 1.6’

4.1 3.9 3.2 3.5 3.9 4.1 4.6

- 2.35’ - 0.33 2.28 - 0.32’

-5.5 -5.5

2.51 2.5’ 1.6’

1.49 1.49b

2.0’

PK*rc

3.4

8.lt

9.12f 9.33’

9.30’

9.23’

PK

0.4lb 0.81 1.58 2.0zb 0.04c 2.72b 3.Eb 1.95s 0.13’ 0.71’ 2.19’ 1.28” 1.7’ -1.2 -1.2 - 0.64 - 0.61 - 0.76 - 0.68 - 0.92 - 0.93 - 0.43 -0.40 - 0.95 - 0.93 - 0.77 - 0.86 - 1.0 -1.2 -0.8 -0.96 2.5 2.8

2.5’

2.74 2.79 - 1.6 1.8 1.71’

-0.15 0.15 - 0.56 - 0.55 - 0.01 0.05 - 0.45 - 0.25 - 0.40 - 0.35 2.7 2.6 0.8 0.3

-1.1 -1.1

0.4’

1.66’

2.8’

~K*dy.

pK*c

2.5 x 10’0” 7.9 x 109 8.8x 109 3.2x lo9 5.8x 1O’O 1.ox1os 3.9 x 10’ 1 ox 109s 1:7x101c 5.8 x 10s 1.6x 20s 8.0x IO9 1.7x109 2.2x LO9 1.5x 109 3.5 x 108 9.8 x 10’ 8.1 x lo* 6.2~108 9.2 x 10s 7.7 x 105 7.5 x 10s 5.6 x 10” 8.0~1~ 6.8X 20s 7.0 x 10s 6.5 x 10s 1.3x 109 1.1 x 109 1.0x109 8.5x 10s 9.6 x 10’ 1.7 x 106 8.6X107 7.7 x 10’ 4.0 x 109 2.0 x lo8 2.9 x 10s

kd W’)

1.0x1os 1.0x10’0 1.5xWJ

6.8x10’* 4.8~10’~ 3.3 x 10’0 3.3 x 10’0 6.4 X 10” 5.8 x 1O’O 5.1 x 10’0 9.0 x 10’0 2.3x 10” 3.0 x IO9 2.5 x 10’ 1.0 x 10” 8.3 x lOto 1.3x108 9.1 x 10’ 8.0 x 10’ 2.4 x 10’ 1.4x108 1.3x108 l.lXlos 9.0 x 10’ 2.8 x lo8 2.2 x 10s 9.0 x 10’ 8.0 x 10’ 1.2x109 9.0 x 10’ 1.2x108 7.5 x 10’ l.SXloB 9.4x 10’ 3.0 x 109 1.1 x109

kP (M-1 s-‘)

1.3x 10’ 6.8 x 106 1.2x 108 2.0 x 10’ 1.6x 10’ 5.4 x 10’ 4.4 x 10s 3.4 x 108 9.3 x 10’ 4.4 x 10’ 2SXloB 2.1 x lee 1.9x108 1.6~1~ 8.9x 10’ 6.0 x 10’ 3.3 x roe 3.3 x 108 4.1 x 109 1.0x lo9

(M-‘s-‘)

kq

protonation and proton-induced

_

‘(331. ‘=[128]. ‘[129]. d[130]. c[131]. 9121. g[2]. h[132]. The ESI$T to the adjacent sulfonate group of 2-naphthol-3,6*disulfonate has [133J kd= LSX 10” s-‘, with k,,+/ko+ =2.2, and kp=4.SX109 s”, withku+/kn+ = 1.6. $1341. k[13Ss]. ‘[136]. m[173]. “[174]. “[64]. p[17S]. q[18S]. ‘[186]. ‘11761. ‘[19S].

z I-aminopyrene” I-aminopyrenem 1-aminoanthracene” 1-aminoanthracene” I-phenanthrylamine” 1-phenanthtylamine” Zphenanthtylamine” Zphenanthrylamine” 3-phenanthtylamine” 3-phenanthrylamine” 4-phenanthtylamine” 4-phenanth@amineO 9-phenanthtylamine” 9-phenanthtylamine” I-naphthyfamine” 1-naphthylaminer 2-naphthylaminer 2-naphthylaminer (CH&-l-naphthylamineP (CH&-l-naphthylaminer) I-naphthylamideq 2-naphthylamideq 2quinoloner 4-quinolone’ acridone

I-naphthol 1-naphtholb l-naphthol-Z-sulfonateb I-naphthol-2.sulfonate I-naphthol.3,6-disulfonate Znaphthol 2-naphthol 2-naphtholb-sulfonate 2-naphthol-6,8-disulfonate 2-naphthold,ddisulfonate 2-naphthol-3,6_disulfonate

Acid

TABLE 1. Comparison between pk? values obtained by the Wrster cycle, fluorescence titration and dynamical analysis. Deprotonation, quenching rates of some aromatic hydroxy compounds and amines are also shown

LG. Amaut, S.J. Fomosinho

I Ercitd-slate pvlon

the excited state and fluorescence titration does not yield the correct deprotonation and protonation rate constants [64]. The Weller method requires that both acid and base forms are fluorescent. An alternative method that requires only one of the forms to be fluorescent has been proposed 1663; however, this method requires two other assumptions which may be difficult to verify in practice: the PT must be the only fluorescence quenching mechanism, and the rate of PTs must be determined by the pKdi!ference between the excited molecule and the quencher. 3. Kinetics Far from the diffusion controlled limit, linear free-energy relationships are frequently employed to rationalize PT reactions. The most popular is the Brgnsted relation [67,68]

k,=G,K,"

or

kd=GdKa+

(4)

where K, is the equilibrium constint of the catalyst, G, and Gd are constants dependent on the temperature, pressure, medium and substrate, and a and p, which are independent of the nature of the substrate, have constant values for acids of the same type and are usually between 0 and 1. These relations require a + p= 1. Application of the Brgnsted relation to ESPT is limited by the diffusion control of the protonation of weak and moderately strong acids, which leads to the trivia! result of /3=1, and by the sparse data available for homogeneous series of acid-base photocatalysis. Yates and coworkers 149,691 studied the photoprotonation of aromatic alkenes and a!!cynes using a reasonably uniform set of genera! acid catalysts, and obtained curved Bronsted plots with a coefficients in the 0.14-0.18 range. As the acid strength of the catalyst is increased, the a values appear to decrease, as predicted by Eigen [28]. However, the upper limit for the photohydration rates is 2 to 3 orders of magnitude lower than the diffusion-controlled limit for thermal PTs in aqueous solution involving oxygen atoms. The mechanism proposed by Eigen for genera! acid-base reactions presumes an association step preceeding PT, which is then followed by the separation of the acid-base pair by the solvent. AJ-J+B-

&

AH..

.B-

A

k-1

A- *..HB

+

A- +HB

(5)

transfer wactio!u (I)

5

This leads to the fonvard and reverse rates for the overall process kc=k,k,k,l(k,k,+k_,k,+k,k_3

(64

k,=k_,k,k_,l(k,k,+k_,k,+k,k_,)

(W

which has a free energy of AGO= -RT In KC,=RT !n(2)(pK,u - PKBH)

(7)

where K,, = k,lk,. From this mode!, it follows that a-l for the endothermic deprotonations and a=0 for the exothermic ones. Eigen-type diagrams have been particularly useful to rationalize PTs involving oxygen and nitrogen acids [28]. For these “normal” acids and bases, Eigen defines as idea! behaviour the transition from a= 1 to a= 0 as pKAH- pKs, varies from - 1 to 1. T!rir would corrrespond to a PT step free of any hindrance. However, even for “normal” acids the transition from a= 1 to a=0 occurs over a range of cu. S pK units. This range is much wider for carbon acids and eqn. (4) may be regarded as a reflection of an unperceptible transition of the Brgnsted coefficient within the experimentally accessible data. Johnston and Parr [70,71] introduced a practical procedure to calculate activation energies and rate constants of elementary bimolecular reactions with no adjustable parameters from kinetic data, the bond energy-bond order method (BEBO). The BEBO mode! reasons that, in the transfer of an H atom behveen two atoms or molecules in the gas phase, there is a strong correlation between the changes in the bond that is broken and the bond that is formed AH+B+A+HB

(8)

where charges are omitted for generality. Then, it is assumed that along the minimum-energy path from reactants to products the sum of the bond orders is constant and is equal to unity, nAHfnHD = 1. This assumption was confirmed by ab initio calculations (721, although it was also pointed out that there is a lack of coincidence of the inflection point in the bond order profile with the saddle point in the corresponding energy plot of some unsymmetrical atom-transfer reactions ]731. In 1968 Marcus (741 adapted to the case of proton transfers the theory he initially derived for weak-interaction electron-transfer reactions. Although the assumption of weak overlap is not expected to hold for PTs, Marcus theory was

LG. Amatrt, S.J. Fonnusi~~ho I &cited-state protorlttwsfcr rcactiorts(I)

6

successfully applied also in this field 175-771. According to Marcus theory, the relation between the free energy barrier for a PT in solution (AG*) and the “standard” free energy of reaction at the prevaling temperature and electrolyte condition (AGO) is AGS= w,+ AG:[l -t (AGO+ wp- w,)/(lrAG$)}’ =[w,+AG~+~(~~-w,)+(w~-w,)*/(~~AG~)] f [3+ (wp- w,)/(SAG;)] AGO+ (16AGi)- ‘(AGO)’ (AG~+W,-W,~~~AG~

AG* = w,

AG’+w,-W,B

AG* = AGO+ w,

-4AG:

AGO+w,-w,>rlAG;

PaI

(9bI (9c)

where AG$ is the value of AG* at AGO=0 and w, (or w,) is the work required to bring the reactants (or products) together to the mean separation in the activated complex. AGO may be replaced by AGO’= AGO+RT ln(sr/s”)

(10) to account for the statistical factors s* and sp. The intrinsic barrier AG$ of the cross reaction (8) is expected to follow the well-known additivity property which relates it to the exchange reactions AH +A and BH+ B. Marcus and Cohen applied eqn. (9) to many PTs without explicit consideration of the work terms [75]. They calculated t+ PT rates using kM = 2s’

exp( - AG*IRT)

(11) where Z is a collision number in solution (= IO” M-’ s-l). It is possible to estimate the values AG& wp and w, by fitting eqn. (9a) to a secondorder polynomial in AGO. Kresge calculated the intrinsic barriers and work terms of several PTs to and from carbon [68], and obtained an average w, larger than 50 kJ mol-‘, whereas the average AGi for the same reaction is only 17 kJ moP’. These work terms are too large to represent simple encounter of reactants, and it was suggested that they also include the energy necessary to desolvate the reactants and reorient the solvent, while AG; corresponds to the activation energy of the PT step. The separation of the observed freeenergy of activation of an adiabatic reaction in two events is open to criticism. This situation is distinct from electron transfer reactions, where the electronic motion is uncoupled from nuclear changes. Koeppl and Kresge presented an alternative model based on the intersection of two harmonic oscillators and in the BEB0 method [78], and

argued that Marcus theory tends to underestimate AGX and consequently to overestimate w, [79]. It should be pointed out that the curvature of the Bransted plots predicted by Marcus theory is quite different from the curvature discussed by Eigen. According to Marcus, curvatures will lz.z observed when the rate determining process is the actual PT, while Eigen associated the curvature with the change of the rate-determining step from the PT step to the diffusion of reactants or products. Reaction series with a small AG$ value will give sharply curved Eigen plots, whereas a large value for AG: gives the opposite behaviour. With the work of Marcus, it became very common to rationalize ground state PTs in terms of intrinsic barriers to the reaction 168,801. An application of Marcus theory to thermal PTs between fluorenes and g-substituted fluorenyllithium [81] showed that the cross relation was not verified and that changes in substituents produce changes in the intrinsic barriers. Gould and Farid recently reported a similar variation in the intrinsic barriers of a series of aromatic hydrocarbons undergoing electron transfer [82]. Nevertheless, the cross relation was obeyed in PTs between transition metals 1831. Despite the relative success of Marcus theory in the interpretation of thermal PTs, Yates [84] argued that Marcus theory needs to be modified to be applied to ESPT. Marcus also derived an alternative relation from BEB0 premises [74] AG* = AGjj+&AGO-!-[AG&/lnf2)] ‘x In cosh[AG0/(2AGi)

ln(2)]

(12)

which has the same limits as eqns. (9b) and (9c.1, an? at low [AG0/(4AG6] differs from eqn. (9a) by &AGO. Agmon and Levine criticized the ad hoc restriction of eqns. (9a-c) noting that for the X+H, family one finds AG; = 27.6 kJ mol-I, yet for either F+ Hz and I + Hz IAGo is well outside the limit of 4AGb [85,86]. Alternatively, these authors adopted the basic assumption of the BEB0 method to define a reaction coordinate of constant bond order; and introduced an entropy term to derive a more general relation AG$ =n* AGo + AM(n*)

(13)

where n* is the order of the BC bond of eqn. (8) at the transition state. The above expression can be used to obtain the energy profile along the reaction coordinate, making rzH3 vary from zero in the reactants to unity in the products.

LG. Amaut, S.J. Fomosinho I Ewiled-stale proton

This model assumes that M(n) is a function only of the bond orders of reactant and product. Depending on its functional form, different relations can be obtained, namely [86-883: (i) the model proposed by Thornton [89]; (ii) the empirical form proposed by Rehm and Weller to account for the quenching rate of excited states by electron transfer in solution [go]; (iii) Marcus equation; (iv) the equation derived by Marcus as an approximation to the BEBO potential profile. The latter choice for M(n) gives better agreement with the experimental data [88] and was designated as the mixing entropy of the two bond orders M(n) = -n In n - (1 -n)

ln(1 -n)

(I41

where n =nHB. The location of the transition state is determined by the solution of a[AG”(n)]/&z=C n*=[l+exp(-AGO/A)]-’

WJ

and A= - (AG&bn 2). The transition state theory is then used to obtain the reaction rate constant k = (k,T/ht) exp[ - AG*/(R’7’!j

(I61

The Agmon-Levine model has been applied to many thermal [88,91] and to photochemical PTs 1921. It is important to realize that although the BEBO, Marcus and Agmon-Levine models can be mathematically related, they result from two different approaches to reactivity. Marcus theory is a nonadiabatic (weak-interaction) model that relates the rate to the properties of the unperturbed reactants. The formulations that assume the conservation of the bond order in the course of the reaction lead to adiabatic (strong-interaction) models, and calculate a more gradual change of the properties of the reactive system with the reaction coordinate. Which models give the most meaningful results is still an open question [93]. The intersecting-state model (ISM) proposed by Formosinho and Varandas [94,95] goes one step further in the direction of generalizing and flexibilizing the thermodynamic and intrinsic kinetic contributions to AG*. ISM utilizes eqns. (13) and (i4) together with the Pauling relation to calculate the sum of the reactive bond extensions at the transition state, scaled by the sum of the equilibrium bond lengths of AH and HB [96], IAH+ZHB d =a’(Z,

+ZHB) In

1 + exp( AGO/h) 1 - [ 1 + exp(AGVh)] - ’

(17)

where a’ is a constant (0.156) and A the mixing entropy parameter. Generalizing eqn. (17) to situations where the resonance effect at the transition

mmsfcr reactions (I)

7

state may be significant and act as to reduce the reaction energy barrier, one obtains [95,96] 1 + exp( fir* AG?A)

d= $

VAH+ h-A In

1 - [1 + exp(&*

AGO/A)]- r

(I81 It is obvious that when the effect of resonance on the energy barrier is translated by a transition state bond order n* >+, d no longer corresponds to the bond extensions to the transition state configuration. For a bond-breaking bond-forming process, the limiting case of n* = + corresponds to transfers where resonance is negligible. The value of n* acquires a special meaning in electron transfer reactions, where no bonds are broken or formed and n* = 1 is expected not as a result of resonance but of weak-adiabaticity [97-UIO]. Expanding eqn. (18) in Taylor series one obtains d = (Zm +I,,J[u’

ln(2)/n* + (a’/2)(A.GOlh)2]

(1% The energy profile along the reaction coordinate can be calculated from the displacement between the reactant and product potential energy curves, d, assuming the reactive bonds behave as harmonic oscillators

(~lffxr'=(3)fp(d-x,)'+AGD (20) where frand fpare the force constants of the A-H and H-B bonds, and X, is the bond extension of the reactant to the transition state configuration. The intersection of the two curves gives AG* = &f,xr2, which, together with eqn. (16), gives the PT rate. ISM does not separate the observed free-energy of activation into a step for tlte encounter of reactants and solvent reorganization and another one for the proton motion from the acid to the base. The energy barrier for the PT is calculated with parameters essentially determined by the nature of the reactants cf,, fpand Zr+Zp)and by parameters that depend both on the reactants and the medium (n* and h). As a result, free-energy barriers will be found in very exothermic reactions, expected to be diffusion controlled, without explicit consideration of dilfusion barriers. Electron transfers are treated differently in this respect, because the frequency of these weak-adiabatic reactions may have to be corrected for the frequency of encounter of the reactants. ISM may represent reactant and product by Morse oscillators, which becomes critical for reactions involving large a AG* in the forward or reverse direction [95,101]. ISM has been applied to PT reactions in the ground [102-1051 and excited states [106]. This

8

L.C. Amaut, S.J. Fortnoshho

I Excited-stafc proton trmsfer rcacliom (I)

model was also fruitfully applied to acid-base catalysis [107,108] and photocatalysis [loll. ISM can explain anomalous free-energy relationships like those observed for nitroalkanes and 9-alkylfluorcnes in terms of field/inductive, resonance and polarizability effects on the transition state bond order [lOS]. It was shown that for photochemical reactions [109,110] and hydride and PTs [ill], the energy barriers calculated by ISM can be used to obtain tunneling rates through the Tunnel Effect Theory [112,113]. For an adiabatic reaction by incorporating the correction of Englman and Ranfani [114] for small energy barriers, the tunneling rate is k,un= ~(1.t exp[(2&)(2p

Al’)“’ AX]}-’

(21) where u is an effective frequency, ~1is the reduced mass of the oscillators, AV and AX are the height and width of the barrier. With the procedure used by ISM to calculate the configurational changes along the chemical reaction, one can make AV= AG* and the width of the barrier is given bY Ax = Id - (2~AG”~lf)‘“~ (22) where f is the force constant of the oscillator and AGO the reaction energy. Yates [115] tested the applicability of eqns. (9) and (12), the hyperbolic equation proposed by Lewis and More O’Ferral [I161 and various modifications of Marcus equation, to the photoprotonation of alkenes and alkynes. He concluded that, among these theories, only unrealistic modifications of Marcus theory gave reasonable agreement with experimental data. Yates also applied ISM to these reactions and obtained remarkable agreement between the rates calculated with reasonable parameters and the experimental data. This study must be regarded with some caution because Yates assumed that the photoprotonation was adiabatic and there is evidence that, in some cases, it may be diabatic [lOI]. This issue will be addressed in Section 4.4. A6 inirio molecular orbital calculations have also been performed on many PTs. Some results obtained at the SCF/4 - 3IG level were reviewed by Scheiner [117]. They provide information on the location of stationary points in the potential energy surface and do not address solvent effects. These calculations show a systematic increase of the energy barriers to PT with the increase in the Hbond Length between AH and B. When the Hatom is bonded to a second row atom like sulfur, where the electron cloud is more diffuse, the

potential energy profile collapses into a singlewell function at much longer H-bond lengths, and the energy barrier increases more smoothly with the H-bond length. Studies of bent H-bonds [118] revealed that deviations of even up to 40-50” from linearity (180”) do not affect the barrier to PT very much, but then it rises quickly as the deformation increases. The energy of the transition state is more sensitive to the nonlinearity of the H-bonds than the equilibrium geometry. The a6 in& studies also indicate that the major source of the kinetic isotope effects is the difference in zero point energy, while tunnelling gives a minor contribution. The effect of various basis sets in the calculation of PT barriers has also been assessed [119]. Warshel developed an empirical valence bond method [120] to obtain a simple potential energy surface that allows simulation of the dynamics of PTs in polar solvents [121]. This author considered that the solute vibrations are faster than the solvent fluctuations and that the potential energy barrier along the proton coordinate is almost the same for any solvent configuration that gives the same reaction energy along the solute coordinate. This was invoked to justify the treatement of the proton, Q, and solvent, 4, coordinates separately. The probability of reaching Qs was expressed as the product of the probability that the solvent reaches y*, where the charge distribution of the products is stabilized relative to that of the reactants, times the probability that the solute will jump from the reactants equilibrium configuration to Q* and the given q*. Later, Warshel recognized the difficulty in separating solute and solvent fluctuations in adiabatic reactions, and defined two limiting situations for reactions in polar solvents: solventdriven and solute-driven reactions 11221. In the solvent-driven limit, the reaction does not occur until the solvent reaches a polarization that stabilizes either the charge distribution of the transition state or the the product state and the activation barrier along the solute coordinate becomes small. In the solute-driven limit the solute changes its configuration to that of the transition state, while the solvent responds by moving towards its transition state polarization. Gutman [123] used the molecular dynamics simulations carried out by Warshel 11241 in the solvent-driven limit to argue that the rotation of water molecules, which has to act cooperatively, becomes dominant in energetically favourable PTs: in no case will a proton leave the donor site unless the acceptor nest is ready.

L.G.

.haW,

S.J. Fotmositrho

/ E&cd-slate

More recently, Hynes et al. [125] proposed a dynamical theory of diabatic PI’s, applicable to H-bonded complexes meeting two conditions. Firstly, the distance between the heavy atoms between which the H transfers is sufficiently large to ensure a significant barrier and thus weak coupling between the two H wells. Secondly, this theory assumes that the time scale for H motion is short compared to the relevant heavy atom intramolecular vibrations and solvent molecule translations and rotations, so the dynamics of the latter dominate the tunneling rate. This may be difficult to reconcile in practice because an appreciable separation between the heavy atoms will lead to sloti PTs.

4. Intermolecular

proton

transfers

4.1. Aroma tic hydroxy compounds

Earlier work on the PT kinetics of substituted 2-naphthols made use of steady-state methods [126,127], but more recently ESI,,PT of aromatic alcohols have been extensively studied by timeresolved techniques [4,5,43,61,62,92,128-1551. The kinetic and thermodynamic acidities of several aromatic alcohols in the excited state are shown in Table 1 and their relationship is shown in Fig. 2. This Fig. also shows an application of the idealized Eigen model to the deprotonation of naphthols, i.e. it was assumed that the PT step 12

F 1

a

Ga

B

1

4

0

-4

I

1 .

-100

0

-50

AC’

50

100

, kJ/mol

Fig. 2. Deprotonation (circles) of aromatic hydroxy compound in water and reverse reactions (squares). The open symbols refer to 2.naphthol-3,Cdisulfonate. The calculations with the idealized Eigen model, Marcus theory without explicit consideration of work term (AG*,,=S.OS k.I mol-‘) and KM (n*= 1.14, A=84 kJ mol-*) are also presented.

ptwfon frutufcr tractions

(I)

9

in mechanism (5) occurs rapidly compared with the diffusion steps. In this application of the Eigen model we used /~,=&_,-6X10~~ M-* s-l; the values of k-, and k, do not influence these calculations. The dissociation rates were expressed in M-l s-l, taking [HZ01 =SS.S M, which yields - 1.74. The ESI,,PT of naphthols follow PKH~O= approximately the trends expected from Eigen plots, with @=0.94 and a correlation coefficient r = 0.98, excluding the deprotonation of 2-naphthol3,ddisulfonate (2N36S) where competition with intramolecular PT is observed 1331. The groundstate kinetic and thermodynamic acidities of 8hydroxypyrene-1,3,6-trisulfonate (HPTS), 2N36S, 2-naphthol-6-sulfonate and 2-naphthol were also included in Fig. 2 and fall on the same correlation [9,123]. Including thermal and photochemical reactloons i;l the same plot one obtains p=O.996 with r=0.996. The collinearity between the measured rate of the acid dissociation of excited naphthol and pyrene derivatives with the acid dissociation constants of the excited compound has been known for a long time [135]. An application of Marcus theory to the excitedstate deprotonation of aromatic hydroxy compounds is also shown in Fig. 2. The theoretical line was calculated with AGz==8.05 k.I mol-’ using eqns. (6) associated with eqn. (11). The average intrinsic barrier for the ESI,,PT of the aromatic alcohols plotted is AGi=7.34 kJ mol-‘. A fit of the ESI,,PT data to a second-order polynomial in AGO gives AGg=3.71, w,=6.62 and w,,=O.84 W molt. However, the fit is nearly as good for a straight line as it is for a second-order polynomial, and the coefficient of the second-order term is affected by a large uncertainty. An attempt to include thermal and photochemicai deprotonations in the same polynomial fit yielded AGi= 18.24, wr= - 35.46 and w,= -0.06 k.J mol-‘. This is a rather unrealistic set of parameters and advises against the separation of work terms from the intrinsic barrier in reactions series with small Brsnsted curvatures. These ESI,,PT were first analysed within the formalism of ISM in 1988 (106]. In Fig. 2 we present the rates calculated with n*= 1.14 and A=84 W mol-l. These parameters were obtained from a fit of eqn. (19) to the bimolecular deprotonation rates of all the aromatic alcohols of Table 1, except those with competitive intramolecular PTs. Better agreement with ESI,,PT can be obtained in the fit to eqn. (19) if the ground-state PTs are not considered. This last fit yietds tr*= 1.18 and A=58 W mol-‘, which reveals that, for these aromatic alcohols, the reactivity differences can

10

L.G. Anraut, S.J. Fomosi~~ho I Excited-stutc proton transfer reactions (I}

be ascribed essentially to the entropy parameter. A lower A was associated with a lower entropy in the excited state 11061. The small differences in the parameter values between these and earlier calculations with ISM have to do with the use of [Hz01 =55.5 M. The decrease in rate calculated for PTs with AGO>50 k.I mol-’ is an artifact caused by the use of harmonic oscillators to represent reactant and product, The use of Morse oscillators would displace this effect to much lower reaction energies, as will be seen later in the case of PTs to carbon. The very fast PT of some of these alcohols make them excellent probes to study the structure of proton solvation dynamics. From time-resolved studies carried out in a picosecond scale, two different views have emerged, one from the group of Robinson and Lee, and the other owing to Huppert, Pines and Agmon. Robinson and Lee have argued that the ESI,,PT rates of aromatic alcohols in aqueous solutions are limited by the time water takes to wrap itself around the charge [5]. Analogous processes are considered to occur with the elementary ions e-, OH- and H+. In pure water, the irreversible rotations of the polar water molecules are measured by the Debye rotational relaxation T,,-‘, and the rate expression for weak acids dissociation and recombination rates are [128,152] kai,(S-

‘) =

TD-*

$2

exp(AS’JR)

exp( - AHOi/RT) (23)

k&M-’

s-‘)=r,,-1

fi

(24) where the reactants are at 1 M, C! is a stericj mobility factor and ASoi and m”i are the ionization entropy and enthalpy. According to this formulation, AGSdi, = AGoi and no barrier stands in the way of the recombination reaction of weak acids. The only unknown factor iu these equations is the steric/mobility factor introduced by Eigen [156], which lies between.narrow limits (0.20-1.0) and can be estimated fairly accurately 151. Evidence in favour of this model comes from the values of AsOi and m”i obtained in temperature studies of ESI,,PT of l- and Znaphthols in aqueous solutions [28,150,151]. The proton dissociation rates divided by the entropy and enthalpy exponential factors were found to be very close to r,,-l, r,(H,O, 298 K) = 7.0 ps and rD(D20, 298 K) = 8.9 ps [5]. One would cxpe.c! to obtain a pre-exponential factor that is also temperature-dependent, as in the transition state theory. Indeed, ~,,-l depends on the temperature, as do ASoi and Woi. Iiowever, some compensation is expected to occur and a near-

constant activation energy for proton dissociation is found. Robinson and Lee have also argued that the proton dissociation requires a common (Hz0)4*t cluster as the proton acceptor. This cluster had already been proposed as proton acceptor based on transport, thermodynamic and structural studies 1281. The dynamical evidence in its favour comes from ESI,,PT rates in mixed water-alcohol solvents. The proton dissociation rate of naphthols was found to decrease as the alcohol concentration increases. An application of the Markov randomwalk method for cooperative solvent behaviour indicated that the proton acceptor is most likely to be a water cluster containing 4f 1 molecules [149]. Further support in favour of these clusters was claimed from the decrease in the deprotonation rate of naphthols with an increase in electrolyte concentration [153,154]. This salt effect was rationalized in terms of a decrease in the number of solvent molecules available to form proton acceptor clusters, as the increase in the number of ions in solution ties up a larger fraction of solvent molecules [ 123,157]. However, ESI,,PT in aqueous urea solutions showed that the deprotonaticm rate is not related to the activity of water in a simple manner [148]. Indirect evidence from gas-phase studies where relatively strong intermolecular bonding in clusters containing up to three water molecules surrounding H30+, was also invoked in support of the water cluster model [5]. However, ESI,,PT in l-naphthol - (H,O), clusters requires cluster sizes with n > 30 to occur [158]. It is interesting to note that ESI,,PT from 1-naphthol appears to be compIetely suppressed in ice, which seems to be a general phenomenon of hydroxynaphthalenzs [158]. This was attributed to the rigidity of the solvent in ice or cold clusters, and was taken as evidence of the role of orientation relaxation of the water molecules during PT. Similar results were obtained with 2naphthol [159]. However, as the proton affinity of the base in the cluster increases, the critical cluster size for ESPT to occur decreases [159]. A similar dependence on the basic@ of the cluster and its size was found for phenol: ESPT from phenol to (NH3), solvent clusters occurs abruptly at n=5 with k d = 1.7~10’~ s- ’ (1601. Similar results were obtained in matrix isolated Znaphthol.(NH& complexes, where ESPT occurs when n =3 and probably n =4; the barrier for PT was estimated to be 15-53 kJ mol-‘, depending on the tunnelling model used [161]. ESPT was also studied in nonpolar rigid matrices at 77 K, between 1-naphthol and triethyiamine [162]. These molecules are

L.G. Arnaut,

SJ

Fonrrosinho I Emited-state

known to form a ground-state H-bonded complex in non-polar media. Irradiation of this complex in the above-mentioned conditions leads to PT rate larger than 10’ s-l, with the formation of contact and separated ion pairs. It was pointed out that for ESPT to occur in clusters, both the proton and the anion need to be well solvated and the proton affinity of the solvent must be large [163,164]. The proton affmity of the base increases with the cluster size [165], so there is normally a critical cluster size for ESPT to be observed. The model of Robinson and Lee is an extension of Eigen’s concepts [Z&28,156], and lead to the suggestion that single water molecules can play no role in electron or proton hydration [S]. It is clear that in ethanol-water solvent mixtures log kd of photoexcited hydroxyaromatics is a linear function of the mole fraction of ethanol when this mole fraction is smaller than 0.5 [166]. In solvent mixtures with higher ethanol contents PT is not observable. Schulman and Kelly claimed evidence for the participation of a water cluster with I2 molecules in these deprotonations. The alternative model of Huppert, Pines and Agmon is based on the solution of the Debye-Smoluchowski equation (DSE) for translational pair diffusion in the field of the pair coulombic interaction, with a boundary condition at contact applicable to reversible reactions. According to these authors, the spatial inhomogeneity in the concentration profile cannot generally be ignored, and only at long times is the geminate proton-anion recombination governed mainly by diffusive motion [146,167,168]. The ESI,,PT of an aromatic alcohol is regarded as a transient, nonequilibrium dissociation of an excited-state molecule ROH” 5

[RO*-.

. .J-J+]

z

RO*-

+H+

(25) where a first chemical step is followed by a diffusional one. This model has been supported by the nonexponential fluorescence decay of S-hydroxy-1,3,6pyrene trisulfonate, HPTS, which is best fited by reversible time-dependent geminate recombination kinetics [145]. The deprotonation lifetimes measured directly by picosecond time-resolved spectroscopy are shorter than the lifetimes found by relative quantum yield measurements (1321. This was interpreted considering that the time-resolved studies provide the initial deprotonation rates,

proton transfer reactiorw (I)

11

while the rates derived from quantum yield measurements are average, geminate-recombinationinfluenced rates [132]. ESI,,PT studies in water-methanol mixtures have been extended and reinterpreted [129]. It was found that that PTs between HPTS and water or methanol are approximately 2 orders of magnitude slower than the solvent relaxation. times recently measured, 1 ps for water and 10 ps for methanol 11691. Proton dissociation rates of 1-naphthol in these solvent mixtures are even faster than those of HPTS. These results showed that solvent effects in the dissociation rate coefficient are equal to effects in the dissociation equiiibrium constant [129], and conflict with the model that postulates the availability of large water clusters as the only factor governing the rate of PT to solvent. In water-methanol mixtures the stability of all clusters seems to be nearly identical, provided they are centered around a protonated water core [129]. In addition, the effect of pressure on the PT from HPTS to HZ0 and DzO is much larger than on solvent parameters like the reorientational or dielectric relaxation times, leading to an activation volume of -6 cm3 mol-’ [143]. Thus the reorientation of HZ0 molecules cannot be the rate determining step. Strong electrolytes in aqueous solution diminish the yield of the geminate recombination process due to their ability to screen the coulombic interaction between the proton and the molecular anion [132]. The same effect may be observed with mild bases capable of reacting the proton before it recombines with the anion [ 1701. A recent model suggesting that the rate-determining step in PT from HPTS to water-alcohol mixtures is the diffusion of a water molecule to the excited dye molecule [155], seems to have been motivated by a faulty deconvolution procedure [ 1291. 4.2. Aromatic amines The excited state acidities of phenanthrylamines were initially obtained through the Forster cycle [171] and fluorimetric titrations 11721. Subsequently, Tsutsumi and Shizuka [64,173-175, 177,178] carried out extensive determinations of pK* values of aromatic amines by dynamical analyses. The time-resolved work corrected the earlier work, whose sources of error were already discussed. More recently this type of compound was used to probe complexes with crown ethers 11791 and proton solvation models 1921. From the purely kinetic point of view, the dissociation of protonated nitrogen acids and un-

L.C. Antauf,

12

S.J. Fonnosird~o ! Em?cd-state

protonated oxygen acids that form ion pairs have always been considered examples of the same type of PT reaction [92]. Thus, one would expect to find the same pattern of free-energy relationships with both types of acids. Figure 3, which includes the amines of Table 1 studied in solvents containing more than 80% of water, together with the groundstate deprotonations of ammonia, trimethylamine, triethylamine and dibenzylmethylamine in water [180], shows that this is not the case. The bimolecular rates plotted in Fig. 3 were calculated assuming [H,O] =55.5 M in pure water. The ESI,,PT of the aromatic amines plotted are nearly thermoneutral and the features of the plot are appreciably distinct from those of typical Eigen diagrams. The calculations with the Eigen model used k,=k_,=6x109 M-’ s-l and cannot reproduce the trends in the data. Comparative analysis of Figs. 2 and 3 reveals that the excited state deprotonations of protonated nitrogen acids are much slower, for the same pK*, than the analogous aromatic alcohol reactions. Furthermore, the linear correlation of the ESI,,PT to H,O with the acidity constants gives p-O.66 with r -0.985. The analogous ground-state reactions have p=O.91 with r =0.988 and behave like normal acids. Including both thermal and photochemical reactions in the same linear correlation we obtain p=O.77 with r = 0.998. In Fig. 3 we also show an application of Marcus theory to these reactions. The calculations were

-100

-50

so

0

AC0

IOU

, kJ/mol

Fig. 3. Protonation (squares) ofaromatic amines in solvent mixlures with more than 80% water content and reverse reactions (circles). The calculations with the idealized Eigen model, Marcus theory without explicit consideration of work term (AG*,=23.69 kJ mol-*) and ISM (/$=0.84, A= 100 kJ mol-‘) are also presented.

proforr framji?r reactions (I)

made in the same way as for aromatic alcohols but using AG,,* = 23.69 kJ mot- *. The average intrinsic barrier for the excited state reactions is slightly lower, A@= 22.29 kJ mol-‘. ‘Ihe fit to obtain the work terms of these ESI,,PT yields AG&=22.29, ~~524.55 and w,=i2.87 kJ mot-‘. The inclusion of thermal and photochemical reactions in the same second-order polynomial fit gave rather unrealistic parameters: AG$ = 20.57, wr= -3.82 and w, =6.15 kJ mol-‘, owing to the linearity of the plot. ISM was also applied to these reactions [106]. The calculated rates presented in Fig. 3 were obtained with II* =0.83 and A = 126 kJ mol”, obtained in the same manner as for aromatic alcohols. The best fit to the ESI,,PT of aromatic amines of Table 1 is obtained with n* =0.84 and A = 100 kJ mol-‘, which supports the observation that the differences between the rates of ground and excited-state PT, have to do with entropy differences. In contrast with aromatic hydroxy compounds, there is an increase in deprotonation rate of protonated l-aminopyrene in water-organic solvent mixtures up to 60-70% of organic soIvent content [92]. At even larger organic solvent concentrations the PT rate decreases sharply. A ‘linear dependence of the PT rate on the water concentration below 4 M was also observed in these solvent mixtures. These observations, together with the fact that the bimolecular rate for proton abstraction by water is one order of magnitude less than the diffusion controlled rate, conflict with the idea that deprotonation rates are determined by the kinetic availability of large water molecule clusters [92]. Alternatively, Pines correlated the proton dissociation rate with the pK* values of the precursor acid in the different solvents. Such linear free-energy relationships 1151 can also be interpreted in the framework of ISM, and the slight curvature observed can be expected from the decrease of II* and increase of h as the water content of the solvent increases [107]. Robinson has expressed the view that the results obtained with aromatic amines are not directly comparable with those of aromatic alcohols and are not suilnbte to test the various water-cluster models, because the cationic acids prepolarize the water structure around them [92]. In related molecules, like l-@-aminophenyl)pyrene cation in ethanol-water, the deprotonation rate could be measured, k, = 3.0 X 10’ s-r, but the proton-induced quenching on the pyrene ring is too fast, kg= 7.4 X 10’ M-l s-l, to permit the measurement of the protonation rate [181,182]. Apparently, the decay rate of the 4-(9anthryl)-N,N-dimethylaniline cation is faster than

L.G. Amauf, S.J. Fonnosinko I E*citcd-state proton transfir tractions (I]

its kd and no prototropic equilibrium is observed in water [183]. In phenanthrylammonium ions-f8crown-6 complexes there is a large steric effect on the protonation of the amino group and k, is negligibly small compared with the rate of the other competitive decay processes and the prototropic equilibrium is also absent [184]. In methanol-water mixtures, the measured rates of l- and Zuaphthylammonium:crown complexes are k, = 7.8 X lo6 s-’ and k., = 2.7 x lo6 s-l, respectively, and k,=1.5x108 M-‘s-l and k,=2 2X109 M-’ s-’ [179]. The PT rates of l- and 2-naphthamide [185], 2- and 4-quinolone 11861 in water, obtained by fluorescence titration, are shown in Table 1. Wubbels et al. [187] studied the phot+Smiles rearrangement of 4-O,NC,H,OCH,CH,NHPh in acetonitrile and found that it is subject to general base catalysis. Like in the amine:; of Fig. 3, the rates of ESI,,PT to the ground-state base catalyst approach 10’ ha-’ s-’ for exothermic reactions and have a Bronsted slope p= 0.6 for the endothermic ones. Table 2 shows the kinetic and thermodynamic data for the deprotonation of 2naphthylamine [188], diphenylamine, indole and carbazole [189,190], with OH’ acting as base. For 2-naphthylamine this corresponds to the second PT equilibrium, the first being reported in Table 1. The singlet-state behaviour of aromatic amines as bases in H20 has also been studied. Table 2 also includes data relative to the protonation of 5,6- and 7,8-benzoquinolines and phenanthridine

13

11911, of 4-methoxyacridine [192], 6-methoxyquinoline and acridine [3,144,193,194], acridone 11951, and trans-styrylpyridines [196] by H,O. The homogeneous series of 4’-substituted 3+rylpyridines, studied at room temperature in water containing 10% (v/v) ethanol, showed a satisfactory Hammett correlation if U+ is used [196]. The excited-state Hammett reaction constant (p = 0.7) is significantly larger than the ground-state one (p =0.3), which indicates a relevant resonance contribution by the sty@ part of the molecule in the excited state. The dynamic studies by Marzzacco er al. [191] on quinolines showed that an increase in the fraction of methanol in the aqueous solution leads to a decrease in k,. However, increasing the concentration of LiC104 results in an increase in k, The effect of the electrolyte on k, is weaker with larger cations. It was presumed that metal ions cause water to become a stronger proton donor, in support of the Huppert, Pines and Agmon model. 4.3. Proton transfers to the carbortyi group In the excited singlet state the carbonyl group becomes a stronger base. For example, the acidity constants of the conjugated cations of l- and 2naphthaldehyde and l- and Zacetonaphthone are 8-9 pK units larger in the singlet state than in the ground state 11971. Watkins [198] reported that the protonation of methyl-Znaphthyl ketone in the singlet state by

TABLE 2. Thermodynamic and kinetic basicities and acidities of some aromatic amines Acid

Base

2.naphthylamine’

PK

OHOHOHOH-

<14

carhazole diphcnylamined indoled Base

Acid

PK

4.methoxyacridine acridine acridine (triplet)g 6.methoxyquinoline 6.methoxyquinoline 5,6-benzoquinolinch 7,8-benzoquinoline” phcnanthridineh 3.styrylpyridine’ 4’.CHJ-3-styrylpyridinej 4’.Cl-3-styrylpyridine’ 4’.Br-3-stytylpyridine’ “[MS].

h[33].

c[189].

pK*‘c,

PK*Fc

21.1s

5.3” 5.5”

H20 H2O

11.6e 10.3b

5.1gh

H,O

5.1 4.2 4.6 4.76 4.77 4.74 4.77

Hz0 H20 HP H2O H2O H2O HP

‘[192].

‘[144].

r[194].

h[191).

(s-l) 1.5 x lc+

9.0x lo* 2.1 x loto 2.6X IO’O

8.5 x tp

kd

k,

W’)

(M-’ s-‘)

PK+W

2.7 x 10soc

11.6’ 1o.d 5.6 11.9‘ 12.3’

3.6 x IO”’ 3.1 x 10’” 1.4x 10’0

11.4 10.6

10.1 12.4 12.6 12.4 12.5

b

7.2 x 10’

11.8’ 11.7’

D2O

(M-’ s-‘)

10.98=

PK*I,

PK*Fc

kd

12.28

12.3h

H2O

“[190].

PK+,.

12.3 12.5 12.3 12.4 ‘[196].

5.5XlO~ 5.5 x 10” 5.5 x lo* 5.5 x 109

l.lXW 1.1 x 103’ 9.0x lo’ 2.9 x ld 8.3 x 10’ 1.8X 10’ 3.0x ld 1.0x 106 2.2x lb 3.5 x low 2.2x ld 3.1 x 1oJ

14

L.G. Amauf,

S.J. Formosinho

/ Exited-state

proton tramfir

reactions (I)

TABLE 3. Thermodynamic and kinetic acidities of some aromatic ketones

Base

Solvent

methyl-Z-naphriq! ketonce I-naphthoic acidb 2-naphthoic acidb xanthoneb benzophcnonc (triplet)

Hz0 H,O Hz0

‘[198].

b[199].

E[33].

~:cxI,CN

PK

(4:l)

- 7.70 -7.68 -4.17 -5.7’

PK*F=

- 0.2 - 0.35 3.2 - o.4c

pK*n

PK*W

2.0 0.7 1.8 O.lSd

kd (s-V 7.0 x 1.7x 4.0x 8.3 x 3.3 x

kP (M-’ s-*) 10’ 108 109 10’ IO9

3.8 x lOto 1.7x 10’0 5.6 x 109 5.0 x ld

d[200].

mineral acids in water proceeds with a rate, k =3 .8x10” M-’ s-l very close to the diffusion c&trolled rate calculaied from the Smoluchowski equation, kdifE4.7 X 10” M-’ s-i. Watkins [199] also studied the protonation of naphthoic acids and, again, k, was found to be very close to kdif. The difference between these quantities was assigned to steric requirements for PT. Hoshi and Shizuka [200] measured the protonation and deprotonation rates of benzophenone in H,O:CH,CN (4~1) solution and based on the relatively large protonation rate and pK* value, suggested that 3(r,#) is the reactive state. ESI,,PT of Znaphthoic acid was also studied in ethanol:water solutions [201]. It was found that k, decreases from 2.9X lo9 M-’ s-’ for solvent compositions containing 0.10% of H,O, to 1.5 X lo9 M-’ s- 1 for solutions with 4% of H,O. At the same time, kd increases from 1.5 X 10’ to 1.5 X 10’ s-l. As the amount of water present increases, the systems achieve a state of dynamic equilibrium in the excited state. The rate of protonation was considered to be diffusion-controlled and the decrease observed was associated with variations in the mobility of the proton. The rate of deprotonation was found to be directly proportional to [H,O] and the second-order rate was estimated to be 8.1 x 10’ M-l s-l. It was proposed that the proton exists in these solvent mixtures both as hydronium ion and ethanol-solvated species, and that both of them can react with the excited naphthoic acid. Water is more effective in the deprotonation reaction because of its higher proton affinity. 4.4. Proton transfers to and j?om carbon atom Ground state PTs to or from carbon atoms are usually much slower than the analogous reactions involving oxygen or nitrogen atoms. This is usually attributed to the lack of H-bonding to the solvent and the substantial geometrical and solvation changes generally required by PTs to or from carbon atoms. The much faster PT rates to carb-

anions observed in solvents which only weakly solvate anions, like dimethylsulphoxide, support this interpretation [180]. One must be careful when comparing rates in different solvents, because AGO also changes with the solvent. Actually, there is a decrease in 1w* as the solvent is changed from methanol to dimethylsulphoxide which tends to increase the PT, but this tends to be compensated by an observed decrease in AS* [180]. Yates and coworkers [49,69,202,203] carried out extensive experimental studies on the photohydration of styrenes and phenylacetylenes. For nonnitro-substituted substrates, the photohydration products are formed via Markovnikov addition of water to the alkene or alkyne moiety. The nitrosubstituted styrenes and phenylacetylenes gave anti-Markovnikov addition products. Fluorescence quenching and product quantum yield studies showed that the protonation of the excited substrate is the rate determining step in these photohydrations. While the photohydration of nitrostyrenes and (nitrophenyl)acetylenes proceeds via the triplet state, in all the other photohydrations the rate determining step is the protonation of the excited singlet state. The excited-state protonation of these carbon bases was found to be 10’1-1014 times faster than in the ground-state, although it remained two orders of magnitude slower than the diffusion-controlled limit. The general acid photocatalysis gave curved Bronsted plots with cy values in the range 0.14-0.18, in contrast to the range 0.5-0.85 found for the analogous ground-state reactions. No fluorescence from the photogenerated carbocations was observed and their electronic nature could not be assessed by the experimental studies. The photohydration of aromatic allenes was also shown to involve the protonation of the central carbon of phenylallenes in their singlet excited state [204]. In order to clarify whether these ESI,,PT are adiabatic or diabatic, Yates and coworkers 12051 studied the Dhotodehydroxylation of 9-phenylxanthen-g-01 (FXOL), which generates a fluorescent

L.G. Amaut, SJ Fomosinho

I Excited-state proton tmnsfer reactions (I)

triaryl carbocation. The photoprocess was proposed to involve the water-assisted dehydroxylation from the singlet state of PXOL in a single adiabatic step. It was emphazised [205] that this system satisfies two important requirements for a photoreaction to be adiabatic: (i) there are only minor structural changes; (ii) the backbone molecular structure is rigid. Yates adopted the view that these reactions are adiabatic and applied Marcus theory and ISM to interpret the observed free-energy relationships [84,115]. In collaboration with Csizmadia, he carried out SCF calculations on the adiabatic acidcatalysed hydration of acetylenes [206-2101 and allenes [211,212] in the ground and excited states. Similar calculations were performed for the adiabatic PT to simple substituted nitriles in the ground and excited state [213,214]. A different view was recently offered [loll, based on the fact that the adiabatic protonation of naphthylacetylenes would require a ApK change of 30 units upon electronic excitation, which is larger than the changes observed for similar compounds [33]. The features of ESI,,PT to styrenes can best be interpreted in terms of a rate determining diabatic PT step, as can be appreciated from Fig. 9

4

3 g

-1

rt i 1-400

-300

-200

AC0

-100

0

100

, kJ/mol

Fig. 4. Photoprotonation of 4-methylstyrene (squares) and /3naphthylacetylene (triangle) in water. Thermal hydration of 4methylstyrene by H,O’ (closed circle) and base-catalysed styrene formation from I-(4-methylphenyl)ethyl chloride (open circles) in trifluoroethanol-water. The calculations with Marcus theory were performed with AG*c-31.14, wr= 17.95 and ~~~34.46 kI mol”). For the thermal reactions the calculations with ISM emptoyed n* - 0.88, A = 340 kJ mol- t, and for the photochemical ones the parameters used were d ~0.55, A = 107 kJ mol-’ for 4-methylstyrcne uud tr*-0.50, A = 147 kJ mol-’ for &naphthylacetylene.

15

4. In this Fig. we plot rates of ESI,,PT from inorganic oxygen acids and water to I-methylstyrene and /3-naphthylacetylene [69], treated as diabatic reactions generating the ground-state carbocation [loll. For comparison, we also include the rates available for the closest thermal analogue of this reaction: the rate for thermal hydration of 4-methylstyrene in trifluoroethanol-water by H,O+ (closed circle) and the rates for base-catalysed styrene formation from 1-(4-methylphenyl)ethyl chloride in the same solvent mixture (open circles) [215]. We employed Marcus theory without explicit consideration of work terms to calculate the rates for the base-catalysed reactions. The average intrinsic energy obtained, AC&= 59.89 kJ mol- *,does not reproduce well the slope of the thermal rates plot. Determination of the work terms lead to the parameters AG$ = 31.14, w, = 17.95 and wp = 34.46 kI mol”, which were used in conjunction with eqns. (9) and (11) to obtain the calculated values ploted. Attempts to reproduce the rates of ESI,$T to 4-methylstyrene with Marcus theory, lead to intrinsic barriers larger than 95 W mol-‘, with or without separation of the work terms. Such large intrinsic barriers are not physically meaningful in view of the results obtained with the analogous thermal reactions and other carbon bases. ESI,,PT to P-naphthylacetylene lead to a lower intrinsinc barrier, ca. 20 kJ mol- ‘, but an unreasonably high wp, ca. 150 kJ mol-‘. The features of these calculations are not appreciably changed by the introduction of an electronic forbidden factor to acccount for the proposed diabaticity of these reactions. As mentioned before, Yates has shown [84,115] that Marcus theory is not suitable to treat these reactions as adiabatic. In Fig. 4 we also plot the ISM calculations made [loll, using n* = 0.55 and A = 107 kI mol-’ for 4methylstyrene and n *=O.SO and A=147 kJ mol-’ for /I-naphthylacetylene. The CH bond in the products was represented by a Morse curve. In both these calculations, eqn. (16) was employed but the pre-exponential factor was multiplied by a nonadiabatic factor ~=10’~, to account for the fact that the reaction is initated in the 2, state of the twisted ethylene that does not correlate with the ground state ion pair of the products. The value ofn*is in the range observed for GSIJI’ to or from carbon acids and the value of A is PTs ground-state in the smaller than [102,105,107,108]. The kinetics of the ground-state 4-methylstyrene formation from the carbocation can be reproduced invoking the participation of the C-C bond in the reaction coordinate and

II5

L.G. Amarct, S.3. Fonnosinrlo I Exci~cd-state prorot rransfcr reactions (J)

n*= 0.88and A = 340 W mol- ‘[loll. The enhanced value of n* isconsistent with the participation of a double bond in the reaction coordinate. The value for the thermal hydration of 4-methylstyrene by H,O+ (closed circle) is not reproduced by these calculations as, in fact, it should not be. This reaction is the reverse of the carbocation deprotonation, thus fr and fpshould be reversed and n*, h and 2, +Zp maintained to reproduce it. Indeed, these changes in parameters, necessary for all assymetric reactions, bring the theory and the experiment into agreement. It is instructive to compare the free-energy relationships of Pig. 4 with those reported for thermal acid-base catalysis. Br@nsted coefficients ranging from (Y= -0.48 to 1.6 have been reported [68], but the evidence of curved Eigen plots in PTs to or from carbon is still controversial. The distinct curvatures observed in the photoprotonation of styrenes and phcnylacetylenes are unusual. Perhaps the most distinct case of a curved Bronsted plot in the realm of ground-state PTs far from the diffusion-controlled limit, is the trialkylammonium ion catalysed hydrolysis of diazoacetate ion, where, in a 8 pK units range, cy varies from ca. 0.5 for the weakest to ca. 0 for the strongest acid catalyst, while the protonation rates reach a maximum of lo3 M-l s-’ [216]. Within Marcus theory, such curved Bronsted plots can be explained in terms of a high AGfi- w, +w, term. According to ISM a curvature may result from a low A value [102], which is the typical case of ESI,,PT [106]. The catalysis by the hydronium ion may show either positive or negative deviations from the correlation obtained with other catalysts [68]. It is appropriate to compare the behaviour of the hydronium ion in these photocatalysis with its behaviour in thermal catalysis with ffUO.2. In thermal catalysis with such low cy values the protonation rates approach lo8 M- ’ s- ’ when carboxylic acids are used as catalysts, while the rate of the catalysis by the hydronium ion approaches 10” M-l s-’ [217]. The higher rates of the hydronium ion are usually attributed to the abnormal mobility of the proton in water [218]. The photocatalyses of styrenes and phenylacetylenes by the hydronium ion is slower than expected and this has been attributed to an inverted effect [ 101). The first example of C-H bond heterolysis in the excited state was recently reported by Wan [219]. SH-dibenzo[a,b]cycloheptene (suberene) on photolysis in D,O/CH&N undergoes rapid PT to water giving the suberenyl carbanion as primary product. In a related molecule, SH-dibenzo[a,c]cycloheptene (DBacC), competition between using

PT and forma1 d&-methane rearrangement in the singlet state was observed [220]. The addition of a sufficient amount of water to a Cl&CN solution leads to the dominance of the PT quenching mechanism over the rearrangement. The triplet state of DBacC in a CH,CN solution undergoes d&r-methane rearrangement exclusively. Fluorescence quenchiilg of DBacC by added water to a CI-I,CN solution gave a quenching rate of 2.05~10~ M-' s-l,which may be taken as a measure of its rate of ESI,,PT to water. For structurally less rigid systems like 1,2- or 3,3benzotropilidene, formal d&-methane rearrangement dominates the singlet deactivation process. Another related molecule, dibenzosuberenol, was also shown to ionize via a CH bond cleavage in the singlet state [221]. A thorough study of suberene [48] revealed that the fluorescence quenching rate in CH&N with increasing amounts of water was 1.7 ~10~ M-’ s-l, with a kinetic isotope effect of 2.8kO.4. The carbon acid behaviour is exclusively a singlet-state process. The fluorescence quantum yield of suberene drops from 0.8S_tO.O5 in CHJCN to ~0.05 in 7:3 D20:CH3CN, however the quantum yield for exchange of H by D in this solvent mixture is only 0.029 + 0.004, which indicates that the same proton which was deprotonated very efficiently rebounds to the carbanion. Forster cycle calculations for suberene using a singlet energy of 142 for the anion and pK=32, yield kJ mol-’ Fluorescence pK*Fc= -7. titration gives 1. This is the largest pK-pK* ever rePK*, = ported. Comparative studies with fluorene and lO,lldihydro-5H-dibenzo[a,d]cycloheptene (suberane) showed that these compounds do not undergo observable benzylic proton exchange on excitation [219], although the thermodynamic acidity of fluorene in the singlet state is very high pK*, = - 8.5. This argues in favour of an enhanced photoreactivity of 4n vs. 4tt + 2 systems in ionic reactions. In order to perform useful calculations on these systems, more experimental information is required, namely rate constants for systems with different pKs and information on whether the PT is diabatic or not. Nevertheless, the reactivity differences associated with the aromaticity seem to imply that 4n systems in the singlet state may have values of n* approaching those of nitrogen and oxygen acids. Proton-induced fluorescence quenching of aromatic compounds has been known since the work of Tsutsumi and Shizuka [177]. Shizuka demonstratcd that, in polar media, the proton-induced

LG.

Amour,

S.J. Fomzosinko

I Excited-state proton tramfir reactions (IJ

quenching of the ‘L, state of l-methoxynaphthalene proceeds via electrophilic protonation at one of the proper carbons of the aromatic ring, leading to H or D exchange. The rate of this protonation, 6.0x108 M-’ s-l in (4:l) H20:CH,CN, is very close to kg [222]. Other proto-induced fluorescence quenching rates of afomatic molecules with appreciable charge transfer structure in the fluorescent state are shown in Table 1. Intramolecular quenching via the same mechanism was observed in tryptamine at the C-4 position, with a rate of 9.1x107 s-’ at 290 K in (9:l) CH30H:D20 [223]. Extensive studies of carbon protonation of aromatic compounds have also been carried out by McClelland and coworkers [224-227j. Presently the solvent of choice for these studies is 1,1,1,3,3,3hexafluoroisopropanol, where the carbocations generated are sufficiently long-lived to be observable by nanosecond laser flash photolysis. The studies of Shizuka and McClelland have shown that there is a change in selectivity between ground and excited states, which can be explained by the shift of w-electron density upon excitation. 5. Conclusions The kinetics of ESI,,PT have been intensively studied in the last two decades, complementing and sometimes permitting correction the older thermodynamic data or dissociation constants. The rate constants now available can be associated with the acidity constants to draw free-energy relationships that help rationalize and predict trends in the data. Simple models that offer structure-reactivity relationships are particularly useful at this stage. The functional form of most freeenergy relationships in ESI,,PT are sufficiently simple that more than one model can reproduce them. However, the most useful kinetic models will be those that provide some insight into why those functional forms are observed and can relate them to the structure of the reactants. In this respect, it is particularly important to question the physical meaning of the empirical parameters employed by the kinetic models to fit the observed free-energy relationships. The idealized Eigen model, which neglects the energy barrier for the PT step of 0- and N-acids, is at variance with the experimental data. Marcus theory can give values for the intrinsic barrier and work terms of these and C-acids or bases PTs. In order to go one step further and interrogate why these barriers vary with the type of acid, it is convenient to use ISM, which provides a relationship with the struc-

17

ture of the acid and base involved in the PTs. It is particularly enlightening to note that n* varies from cu. 0.55 for C-acids or bases to ~0.85 for N-acids and ~1.1 for O-acids, accompaning the increase in nonbonding electron pairs close to the reaction center. The role played by the solvent during the PT is a subject that requires more conceptual work in the future. The detailed knowledge of ESI,,PTs involving 0 and N-acids and the fast rates observed, stimulate the use of those atoms as probes of increasingly more complex structures. This is an area where much development can be expected in the future and where some controversy exists. C-acids and bases show much slower, often diabatic, rates and may be useful in mechanistic or synthetic work. The use of compounds where ESI,,PT may occur in more than one site competitively is still an incipient field [228].

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