J. Chem. Soc., Faraday Trans. 1, 1982, 78, 1087-1101 Proton-transfer Reactions in the Excited State of Phenanthrylamines by Nanosecond Spectroscopy and Fluorimetry BY KINZO TSUTSUMI, SHIZEN SEKIGUCHI AND HARUO SHIZUKA* Department of Chemistry, Gunma University, Kiryu, Gunma 376, Japan Received 22nd April, 198 1 Proton-transfer reactions in the excited singlet state of phenanthrylamines at 300 K have been studied by means of nanosecond time-resolved spectroscopy and fluorimetry. On the basis of dynamic analyses involving proton-induced fluorescence quenching, the proton dissociation (k,) and association (k,) rate constants and the acidity constants pK,* in the excited singlet state of phenanthrylamines were determined. The pK,* values are discussed theoretically by taking account of their electronic structures.An empirical equation to estimate approximately the correct pK,* values of aromatic amines using data from Stokes shifts and (pK,*),, values (determined by the Forster cycle) is proposed. Isotope effects on the rate constants and pK,* values have also been examined. Acid-base properties in the excited state of aromatic compounds are of interest in chemistry and also in biochemistry. They are closely related to the corresponding electronic structures. Since the original work of Forsterl and Weller2 a number of studies on the acidity constants pK,* in the excited state have been It is well-known that the pK,* value can be estimated by means of the Forster the fluorescence titration curve2, and the T, + T, absorbance titration curve? The Forster cycle involves the approximations that an acid-base equilibrium is established during the lifetime of the excited state and that entropy changes associated with proton dissociations both in the ground and excited states are the same.Recently the reliability of the Forster cycle has been questioned in some papers. Grabowski and Grabowskas reconsidered it with emphasis on the thermodynamic approximations and on the necessary experimental precautions. The titration curves also contain the assumptions that proton-transfer reactions in the excited state are very fast and that the acid-base equilibrium is established in the excited state. A laser study of the protonation equilibrium of triplet benzophenone has been reported by Rayner and Wyatt.lo They have shown that the pK,* value of the triplet benzophenone obtained by laser photolyses is almost equal to that estimated from the T, + T, absorbance titration curve, since the lifetime of the triplet benzophenone may be long enough to allow the acid-base equilibrium.However, for the excited singlet state it has been shown by Tsutsumi and Shizuka" that proton-induced fluorescence quenching competitive with proton-transfer reactions is present in the excited singlet state of naphthylamines and the simple acid-base equilibrium cannot be established in the S, state. Dynamic analyses involving proton-induced quenching are therefore needed in order to obtain the correct pK,* values in the S, state. Dynamic analyses by means of nanosecond time-resolved spectroscopy with fluorimetry were applied to P-aminopyrene,12 1 -aminoanthracene13 and naphthols.'* Recently, the Stuttgart group15 has supported our method of determining the pK,* values of naphthylamines.Similar studies on excited naphthols 10871088 PROTON-TRANSFER I N PHENANTHRYLAMINES have been reported by Harris and Selinger.16 The quenching mechanism induced by protons in polar media has been studied very recently by Tobita and Shizuka,17 and it is found that the fluorescence of aromatic compounds having an intramolecular charge-transfer structure is quenched effectively by protons and that the proton-induced quenching is caused by electrophilic protonation at one of the carbon atoms of the aromatic ring leading to proton exchange (or isotope exchange). As for phenanthrylamines, the acidity constants in the excited singlet and triplet states have been studied by means of the Forster cycle.l* The dynamic behaviour of the excited singlet state of phenanthrylamines in the presence of protons has been investigated in the present paper by means of nanosecond time-resolved spectroscopy with fluorimetry. The acid-base properties of the title compounds have been discussed from the viewpoint of n-electronic structures with the aid of a semi-empirical SCF-MO-CI method.EXPERIMENTAL The phenanthrylamines were synthesized except for 9-phenanthrylamine (9A) (Aldrich). Syntheses of 1 -phenanthrylamine (1A) and 4-phenanthrylamine (4A) were as follows. A mixture of p- 1 - and /3-2-naphthoylpropionic acids was prepared from naphthalene and succinic anhydride in nitrobenzene according to the method of Ha~0rth.l~ After each compound had been isolated by fractional crystallization, it was submitted to a Clemensen reduction to give 7-1- or y-2-naphthylbutyric acid, which was cyclized with concentrated H2S04 to produce 1- or 4-keto- 1,2,3,4-tetrahydrophenanthrene, respectively. These were then transformed to the oximes by the usual method, and then submitted to Beckmann rearrangement to give 1A [m.p.145-146 OC (146 "C20)] and 4A [m.p. 50-51 "C (55 "C20)], respectively. The overall yields were 1 and 2% for 1A and 4A, respectively. Syntheses of 2- (2A) and 3- (3A) phenanthrylamines were as follows. Phenanthrene was acetylated with acetyl chloride in the presence of aluminium chloride to give the mixture of 2- and 3-acetylphenanthrenes, which were separated by the method of Mosettig and Kamp.21 The acetylphenanthrenes were transformed to oximes with hydroxylamine hydrochloride, and were then submitted to Beckmann rearrangement22 to give 2A [m.p.85 "C (85 oC23)] and 3A [m.p. 86-87 "C (87.5°C23)]. The overall yields were 10 and 44% for 2A and 3A, respectively. 9A was purified by sublimation. H2S04 (97 %, Junsei), D20 (99.7 %, Merck) and D2S04 (96-98 %, isotopic purity 99 %, Merck) were used without further purification. Deionized water was distilled. Actual acid contents were determined by titration. The concentrations of the samples were 10-4-10-5 mol dm-3 in H20 (or D20) containing 10% acetonitrile in volume. In this study buffer solutions were not used since fluorescence quenching by inorganic anions might 25 All samples were thoroughly degassed by freeze-pumpthaw cycles on a high-vacuum line.Absorption and fluorescence spectra were measured at 300 & 1 K with Hitachi 139 and 124 spectrophotometers and a Hitachi MPF 2A fluorimeter, respectively. The fluorescence quantum yields at 280 nm excitation were measured by comparison with a quinine bisulphate 0.05 H2S04 solution (mF = 0.54).261 27 The fluorescence response functions were recorded at 300 & 1 K with a Hitachi nanosecond time-resolved spectrophotometer (1 1 ns pulse width). The kinetic analyses for the fluorescence response functions of A* and (A+H)* were carried out using an electronic computer (FACOM 230-25). METHOD OF CALCULATION Calculations were carried out on the basis of a semi-empirical SCF-MO-CI method according to the procedure described in a previous work.l* The C-C and C-N bond lengths were assumed to be 139 and 138 pm, respectively.All bond angles were assumed to be 120'. The computation was carried out with a HITAC 8800/8700 computer located at the Computer Centre of the University of Tokyo.K. TSUTSUMI, S. SEKIGUCHI AND H. SHIZUKA 1089 RESULTS AND DISCUSSION FLUORESCENCE TITRATION CURVES AND LIFETIMES IN THE EXCITED SINGLET STATE OF PHENANTHRYLAMINES Absorption and fluorescence spectra of the protonated and neutral phenanthryl- amines are shown in fig. 1. In the presence of protons ([H+] > mol dm-3), phenanthrylamines are protonated on the nitrogen atom in the ground state since the pK, values in the ground state of lA, 2A, 3A, 4A and 9A are 3.4, 4.1, 3.9, 3.18 and 3.5, respectively.18 The absorption spectra of the corresponding protonated amines A+H are similar to that of phenanthrene.There was no isotope effect on the shapes of the absorption and fluorescence spectra. On irradiation with 280 nm light, the neutral (A) and cation (A+H) fluorescence spectra were observed, de- pending upon proton concentrations. 3 A 15 20 25 30 35 15 20 25 30 35 h WY u .- E 15 20 25 30 35 15 20 25 30 35 15 20 25 30 35 wavenumber,’cm -* FIG. 1 .--(a) Absorption and (b) fluorescence spectra of neutral and protonated phenanthrylamines. lA, 2A, 3A, 4A and 9A denote I-, 2-, 3-, 4- and 9-phenanthrylamines, respectively. Logarithmic plots of the fluorescence quantum yields of neutral amines OA and cations (PAH as a function of [H+] are shown in fig.2. For example, the @A value for neutral 1A decreased considerably with increasing [H+]. In the range [H+] -c 1.5 mol dm-3, the OAH value increased slightly with increasing [H+]. Further- more, on over 1.5 mol dmP3 H,SO, being added, the QAH value increased appreciably with increasing [H+] to give a maximum value (PiH of 3 x lo-, at [H+] = 24.3 mol dm-3. Similar results for the fluorescence titration curves were also obtained in the case of FAR 1 36c TABLE 1 .-FLUORESCENCE QUANTUM YIELDS (mi,, a",), LIFETIMES (zi, z0AH), PROTON DISSOCIATION (k,), PROTONATION (k,) AND QUENCHING (kb) RATE CONSTANTS OF PHENANTHRYLAMINES AT 300 K sample" mi/ 10-2 zO,/ns khl k,/ a",/ 10-2 &/ns lo8 mol-l dm3 s-' kl/108 s-l lo8 mol-l dm3 s-I 1A H+ D+ 2A H+ D+ 3A H+ D+ 4A H+ D+ 9A H+ D+ 8.0, f 0.7 8.7, f 0.8 4.1 , +_ 0.4 4.2, f 0.4 4.5, f 0.5 4.5, _+ 0.4 4.8, f 0.5 4.6, f 0.2 4.7, f 0.3 3.86 f 0.3 8.5 f0.8 13.5 f0.9 13.5f0.5 14.4 f 0.5 10.7 k0.5 16.8f0.7 7.3k0.5 14.5+ 1 13.0 f 0.9 14.1 f0.5 2.9, f 0.3 4.4, f0.5 4-58 f 0.4 5.0, f0.3 6.2, f 0.3 6.9, f 0.4 4.4 f 0.4 3.1 f 0.3 3.3, +_ 0.4 3-38 f0.3 49f3 47., f 4 49., f 1 62., f 2 37f 1 52., f 1 49.1 f 5 37., f 4 35, k 1 38.,f 1 1.6 & 0.2 0.5, & 0.05 4.3, & 0.4 3.3,&0.3 0.93 & 0.08 0.44 & 0.04 2.4, k 0.3 2.1 & 0.2 1.9, & 0.2 1.6, k 0.2 8.1 f 0.9 6.2 f 0.9 9.2 f 0.6 7.7 f 0.5 7.5 f0.8 5.6 +_ 0.5 8.0 f 0.8 6.8 f 0.7 7.0 +_ 0.5 6.5k0.5 1.4k0.3 1.3 k0.3 1.1 kO.1 0.9 f 0.08 2.8 & 0.3 2.2 f 0.3 0.9 f 0.1 0.8 & 0.08 1.2 f 0.1 0.9 & 0.1 ~~ a For abbreviations see caption to fig.1. w P 0 cl 0 2 I clK. TSUTSUMI, S. SEKIGUCHI AND H. SHIZUKA 1091 - 3 - 2 - 1 0 1 2 - 3 - 2 - 1 0 1 2 - 1 - 2 - 3 - 3 - 2 - 1 0 1 2 log [H,O+l FIG. 2.-Logarithmic plots of the fluorescence quantum yields of (a) neutral amines (mA) and (b) cations (@AH) as a function of [H,O+]. 0, H,SO,+H,O; 0, D,SO,+D,O. other phenanthrylamines (fig. 2). The midpoints of the fluorescence titration curves of A* and (A+H)* differ, as can be seen in fig. 2. The discrepancy between the midpoints of the curves for @A and @AH indicates that for phenanthrylamines these curves do not correspond to simple two-component equilibria in the lowest excited singlet state. Therefore the pK,* values cannot be determined directly from the midpoints of the curves.These features are similar to those of naphthylamines," 1 -aminopyrene,12 1-amin~anthracenel~ and 1-naphth01.l~ The isotope effect on the fluorescence quantum yields of the phenanthrylamines is also shown in fig. 2. The fluorescence lifetime of neutral lA(zO, = 8.5 & 0.8 ns at ca. pH 7) decreased with decreasing pH. On the other hand, the apparent fluorescence lifetimes of the cation, rAH, were very short (rAH < 1 ns) in the range [H+] < 1.5 mol dm-3. At higher acid concentrations [H+] > 1.5 mol dm-3, rAH increased significantly with increasing [H+] to give a maximum value, z ; ~ , of 49+3 ns at [H+] = 24.3 mol dm-3. Similar results were also obtained for other phenanthrylamines.These data are listed in table 1. The isotope effect on the fluorescence lifetimes of phenanthrylamines is also shown in table 1. KINETIC ANALYSES The experimental results can be accounted for by the scheme shown in fig. 3,11 where k,, k, and kk denote the rate constants for proton dissociation, association and 36-21092 PROTON-TRANSFER I N PHENANTHRYLAMINES FIG. 3.-Reaction scheme of excited-state phenanthrylamines in the presence of protons. proton-induced quenching, respectively, kf and k; the radiative rate constants of (A+H)* and A*, respectively, and k, and kd the radiationless decay rate constants for (A+H)* and A*, respectively. From the steady-state approximation, the following equation can be obtained: Since the value of following equations should hold : is large and k, > k2 [H,O+] at [H,O+] c 0.5 mol drn-,, the and From the above relations, eqn (1) can be simplified to = 1 + k;zi[H,O+].@A A Stern-Volmer plot of @)"A/@, against [H,O+] gives a linear relationship (fig. 4), which agrees well with eqn (1'). The following experimental equations for phenanthrylamines were obtained : From the slopes of the linear plots and eqn (1') the rate constants for proton-induced quenching (kh) at 300 K were determined to be (1.6 f 0.2) x lo8 (lA), (4.36 f 0.4) x lo8 (2A), (9.3k0.8)~ lo7 (3A), (2.47k0.3) x lo8 (4A) and (1.92kO.2) x lo8 mol-l dm-3 s-l (9A), respectively. A deviation from linearity at higher proton concentrations ([H,O+] > 0.6 mol dm-,) for the phenanthrylamines was observed. This may be due to the variation in ionic strength at higher proton concentrations, and a more specific short-range interaction between A* and H+ seems to be dominant, as reported by Weller.28 In addition to this, the concentration of free water molecules, which act as proton acceptors of (A+H)*, should decrease at higher acid concentrations; the value of the pseudo-first-order rate constant kl(kl = k;[H20]) might also decrease underK. TSUTSUMI, S.SEKIGUCHI AND H. SHIZUKA 1093 . 0; 0 0.2 0.4 0.6 0 0.2 0.4 0.6 2 A 1 5 - 0 0.05 0.1 0 0.2 0.4 0.6 3 .O 2.0 I . o * r I I 0 0.2 0.4 0.6 [ H3 O+] mol dm-3 FIG. 4.-Stern-Volmer plots of against [H,O+]. 0, H,S04+H,0; e, D,SO, +D,O. such condition^.'^ Therefore, kinetic analyses involving proton-induced quenching should be carried out at moderate acid concentrations [H,O+] < 0.5 mol dm-3, where the value of k J k , is constant.mol dmA3 < [H,O+] d 5 x 10-1 mol drn-,), fluorescence from both A* and (A+H)* can be observed (fig. 2). Under a &function pulse excitation the fluorescence response functions FA(t) of A* and FAH(t) of (A+H)* are given by29-32 FA(t) = [k; kl/(A2 - A,)] (e-ll - e-4 t ) (7) and F’H(t) = [k,(A,-X)/(12-A,)J(e-.21t+ Ae-lZt) (8) At medium proton concentrations ( where A = ( X - A1)/(A2 - X). The decay parameters 1, and A, are A,,, = i ( X + Y T (( Y - a 2 + 4 k , k2[H,0+]}a) where x = (Z&)-l+kl and Y = (~;)-l+ (kd + k,) [H,O+]. (9)1094 PROTON-TRANSFER I N PHENANTHRYLAMINES z- 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 7 0 I0 20 30 40 50 60 70 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 tlns FIG. 5.-Decay curves of excited neutral amines in the presence of protons [(a) pulse, (b) ZA(t)].Solid line, computed; dashed line, observed. 1A: [H+] = 4.37 x lo-’ mol dm-3, 1, = 2.3 x lo8 s-l, I , = 1.33 x lo8 s-l; 2A: [H+] = 3.9 x lo-, mol dm-s, I , = 9.1 x lo7 s-,, 1, = 9.5 x lo8 s-l; 3A: [H+] = 7.59 x lob2 mol dm-3, A, = 9.83 x 107s-l, I , = 8.01 x loa s-,; 4A: [H+] = 1.31 x 10-l mol dm-3, I , = 1.67 x lo8 s-I, 1, = 8.41 x lo8 s-l; 9A: [H+] = 3.9 x lo-, mol dm-3, 1, = 8.4 x lo7 s-l, 1, = 7.34 x lo8 s-l. The output of the D, pulser is related to the undistorted fluorescence response function of FA(t) or FAH(t) by the convolution integral or where IL is the corresponding lamp function and IA(t) or IAH(t) the observed fluorescence response function of A* or (A+H)*, respectively. The observed fluores- cence response function IA(t) for the phenanthrylamines was analysed using eqn (7) and (10).A kinetic treatment of the fluorescence response function of (A+H)* was impossible since the intensity was very weak. Using the experimental values of 70,, 7 i H and kb the convolution method was applied, since exact values could be obtained in a convolution system containing a small number of parameters. Typical results for convolution in the H2S0, + H20 system are shown in fig. 5. Fig. 6 shows logarithmic plots of the decay parameters A1 and A2 as a function of [H,O+]. From the values of A1 and A2, both k, and k, values can be obtained. Similarly, kinetic analyses forK. TSUTSUMI, S.SEKIGUCHI AND H. SHIZUKA 1095 10- loo lo-* 10-l loo [H,O+] /mol dm-3 FIG. 6.-Decay constants A, and 1, as a function of [H,O+]. phenanthrylamines in the D2S04 + D20 system have been carried out. Isotope effects on proton-transfer reactions in the excited state may involve complex problems; those in the ground state have been discussed by Bell.33 A study of isotope and temperature effects on proton-transfer reactions in the excited state is in progress and will be reported in the future. PROTON-INDUCED FLUORESCENCE QUENCHING Appreciable proton-induced quenching of phenanthrylamines was observed, as described in the previous section. There was no quenching effect due to the counter-ion SO:- under the experimental conditions. It has been demonstrated for the quenching mechanism induced by protons that (1) intramolecular charge-transfer structure in the excited state is responsible for the proton-induced quenching and (2) the proton-induced quenching is caused by electrophilic protonation at one of the carbon atoms of the aromatic ring.17 In the excited state of phenanthrylamines charge migration from the amino group to the phenanthrene ring (ie.intramolecular charge-transfer) may take place in polar media just as it does in naphthylamines,ll 1 -naphthol,14 1 -methoxynaphthalene17 and 1 -aminopyrene.12 Electron migration in the excited state of aromatic amines is supported by the data on charge densities at the nitrogen atoms of the compounds calculated by a semi-empirical SCF-MO-CI method, as will be shown later (see table 2).However, the charge density at the carbon1096 PROTON-TRANSFER I N PHENANTHRYLAMINES TABLE 2.-ACIDITY CONSTANTS IN THE GROUND (p&) AND EXCITED SINGLET ( p g ) STATES AND 71-CHARGE DENSITIES ON THE NITROGEN ATOM OF PHENANTHRYLAMINES (PN) sample P C b 1A H+ 3.4 D+ 2A H+ 4.1 D+ 3A H+ 3.9 D+ 4A H+ 3.1, D+ 9A H+ 3.5 D+ - 0.76 f 0.08 - 0.68 f 0.05 - 0.92 & 0.08 - 0.93 f 0.08 - 0.43 f 0.04 - 0.40 f 0.04 - 0.95 f 0.09 -0.93 0.09 - 0.77 f 0.07 - 0.86 f 0.08 ~ ~~~~ -0.15f0.02 -5.6 1.8863 1.8370 0.15 * 0.02 -0.56k0.05 -2.6 1.8911 1.8352 -0.55f0.05 -0.01 fO.001 - 1.6 1.8903 1.8494 0.05 & 0.005 -0.45f0.05 -4.5 1.8863 1.8331 - 0.25 f 0.03 - 0.40 f 0.04 - 3.2 1.8864 1.9372 - 0.35 f 0.04 a Taken from ref. (18); determined by dynamic analyses; estimated from the fluorescence titration curve of A*.atom in the phenanthrene ring is not so great (< 1.085), since the migrating electron is widely distributed among the carbon atoms in the ring. Electrophilic protonation at one carbon atom in the aromatic ring (i.e. proton-induced quenching) is locally restricted.,' As a result, the values of kb for phenanthrylamines having such a small charge density on the carbon atom become small (ca. lo8 mol-l dm3 s-l) compared with those of 1-naphthylamine (ca. log mol-l dm3 s-l).ll The proton-induced quenching is competitive with protonation k , in the excited state of phenanthrylamines, as can be seen in table 1. It is therefore obvious that a simple acid-base equilibrium cannot occur in the S, state of phenanthrylamines. This is the reason why the fluorescence titration curves do not correspond to simple two-component equilibria in the S, state.For the excited state of protonated phenanthrylamines, (A+H)*, no proton-induced quenching was observed under experimental conditions. Protons are inactive to the cation (A+H)* owing to the electronic repulsion force between them. EXCITED-STATE p e VALUES OF PHENANTHRYLAMINES Dynamic analyses involving proton-induced quenching are needed in order to obtain the p e values of phenanthrylamines as well as those of naphthylamines.ll Using the values of k, and k, (table l), we can determine the correct p c values where the values of k l / k 2 are constant at moderate acid concentrations. The p c values are listed in table 2. Similarly, the p c values for the D,SO,+D,O system have been determined.The p c values in the excited singlet state of phenanthrylamines are more negative than those in the ground state. This well-known phenomenon is caused by electron migration from the amino group to the phenanthrene ring for the relaxed fluorescent state in polar media. In other words, the charge density or formal charge at the nitrogen atom of the excited singlet state of aromatic amines is closely related to basicity of the species, as will be discussed later. The pK,* values determined by the Forster cycle and by the fluorescence titration curve are also shown in table 2. The p e values obtained by the Forster cycle are very negative in comparison with those obtained by dynamic analyses. The fluorescence spectra of neutral phenanthrylamines in polar media shift considerably to the red, as shown in fig.1. The difference beween the p e values obtained by the Forster cycleK. TSUTSUMI, S. SEKIGUCHI AND H. SHIZUKA 1097 and those obtained by dynamic analyses arise mainly from the large Stokes shift of phenanthrylamines in aqueous media. The reliability of the Forster cycle has been discussed by Grabowski and Grabowskag on the basis of thermodynamic considera- tions. They have suggested that the Forster cycle may fail if the electronic levels of a given molecule invert during the lifetime of the excited state in a solvent-assisted relaxation process. Naphthylaminesll and 1 -naphthol14 are such cases, whereas no inversion of the electronic levels for phenanthrylamines takes place.However, the large Stokes shifts [(3.3-6.4) x lo3 cm-l] indicate a significant interaction between A* (lLa) and water molecules. In contrast, the p c values determined by the midpoint of the fluorescence titration curve of A* are positive in comparison with those obtained by the dynamic analyses. This discrepancy can be understood by taking account of the proton-induced fluorescence quenching, kb. ELECTRONIC STRUCTURES AND ACIDITY CONSTANTS OF PHENANTHRY LAMINES Electron migration from the amino group to the phenanthrene ring in the excited singlet state (lL,) occurs much more intensely than that in the ground state (lA). The charge densities or formal charges on the nitrogen atom of the phenanthrylamines have been estimated by means of a semi-empirical SCF-MO-CI method.The calculated results are shown in table 2. is applied to proton-transfer reactions in the excited state, a linear relation between the n-charge densities (P') or formal n-charges (el) and the excited-state p c values may be anticipated. Fig. 7 shows a plot of Qg If the chemical non-crossing 0.17 QN* QN -1.0 -0.8 -0.6 -0.4 -0.2 PK: 0.1 0.1 0.1 FIG. 7.-Plots of the acidity constants [pK,* (a) and pK, (b)] against the formal charges [QN and Q;], respectively.1098 PROTON-TRANSFER I N PHENANTHRYLAMINES (or QN) as a function of p c (or pKa), where the asterisk indicates the lowest excited singlet state. Calculations by the least-squares method give the following equations : pKa = - 143.4&+ 19.7 (r = 0.950) (12) and p c = -32.50Q;l;+4.50 ( r = 0.965) (13) where r denotes the correlation coefficient.state can be written as The Gibbs free-energy change (AG) for proton-transfer reactions in the ground (14) where Ka denotes the equilibrium constant. On the assumption that the difference in entropy changes between proton dissociation and association processes is small, the value of A H is given approximately by1* AG = - RT In Ka = (2.303 RT)pKa A H = I N - A + C (15) where I N is the valence-state ionization potential of the proper nitrogen atom, and A and C the electron affinity of hydronium ion and a constant value, respectively. Eqn (16) is derived from eqn (14) and (1 5) : IN +constant. (16) 1 2.303 RT - According to eqn (16), the theoretical pKa values should be proportional to the valence-state ionization potential of the nitrogen atom.In order to estimate the I N values (in ev), a parabolic relation between I N and the total valence-shell electron density (q) on the nitrogen atom is assumed:35 I N = a+ bq+cq2. (17) For the nitrogen, which is trigonal, a, b and c are equal to -89.402, 24.6265 and - 1.45 15, respectively. Eqn (1 7) can also be expressed as eqn (1 8) I N = -10.1622QN-2.1130 (18) where QN is the formal n-charge on the nitrogen atom and the term in QR is disregarded since the value of QK is very small. From a substitution of eqn (1 8) into eqn (1 6), eqn (19) is obtained : (10,1622QN + 2.1 130+ A - C) pK,theO= - 1 2.303 RT = - 1.71 x 102Q,+constant (19) where T = 300 K. Thus a linear relationship between pKkheo and QN holds, with a slope equal to - 1.71 x lo2.The slope of the line obtained experimentally is - 1.43 x lo2 for the ground state [eqn @)I. This value is almost the same as that derived by the theoretical method. For the excited singlet state, however, the slope of the straight line obtained experimentally is smaller than that of the theoretical relation for the ground state. This may be attributed to the relatively small dependence of in the S, state upon Q; compared with that of I N upon QN. H ~ y t i n k ~ ~ and also Waluk et have assumed a linear relationship between the logarithm of the protonationK. TSUTSUMI, S. SEKIGUCHI AND H. SHIZUKA 1099 I 1 1.83 1.84 1.85 1 hf ' 36 PN FIG. 8.-Plot of log k, against the n-charge density PN at the nitrogen atom. rate constant k, and the n-electron density P,.Fig. 8 shows a plot of log k, against P,, showing that the linear relation holds fairly well: log k, = 29.88PN -46.34 (r = 0.937). CORRELATION BETWEEN p e VALUES AND STOKES SHIFTS In the course of our studies on proton-transfer reactions in the excited singlet state of aromatic compounds, it has been shown that significant proton-induced quenching is present and that a simple acid-base equilibrium cannot occur in the S, state. Dynamic analyses involving proton-induced quenching are therefore needed in order to obtain the correct p e values. However, the treatment by dynamic analyses is complicated and troublesome in comparison with that by the Forster cycle. The large deviation of the values determined by the Forster cycle from the correct p c values is mainly due to the remarkable Stokes shift, as described above. The plot of A p e [ = p c - (pG)Fc] as a function of the Stokes shift AEst (in eV) is shown in fig.9, where the Stokes shifts were determined from the values of the peaks in the 10 8 6 4 2 n - 0 0.5 1.0 AEstleV FIG. 9.-Plot of A p e [ = p e - @K&c] values against the Stokes shifts (A&). Numbers denote 1, NNdimethyl-I-naphthylamine; 2, 1A; 3, 1-aminoanthracene; 4, 1-naphthylamine; 5, 4A; 6, 9A; 7, 2A; 8, 2-naphthylamine; 9, 1-aminopyrene; 10,3A. 0, H,SO,+H,O; 0, D,SO,+D,O.1100 PROTON-TRANSFER I N PHENANTHRYLAMINES absorption and fluorescence spectra. The following linear relation for aromatic amines is obtained by the least-squares method: A p e = 8.72AEst-2.64 (r = 0.885). (20) This plot also includes the A p e values of naphthylamines,ll NN-dimethyl- 1 - naphthylamine,ll 1 -aminoanthracene13 and 1 -aminopyrene,12 as have been previously reported.Fig. 9 shows that the values of A p e increase with increasing AEst: the AEst values increase with increasing solvation energy, caused by a re-orientation of the polar solvent molecules during the lifetime of the excited singlet state of the aromatic amines. As a result, an intramolecular charge-transfer state of the neutral excited amine is produced in polar media which is susceptible to electrophilic protonation (i.e. proton-induced quenching)l' to the aromatic ring. Using eqn (20') we can estimate approximately the correct p e values for the S, state of aromatic amines: p c = (pc)Fc + 8.7,AEst - 2.64.(20') CONCLUSION Proton-induced fluorescence quenching is involved in the excited singlet state of neutral phenanthrylamines, and a simple acid-base equilibrium cannot be established in the S, state. The relaxed fluorescent state, having an intramolecular charge-transfer structure in polar media, is susceptible to proton-induced quenching. In order to obtain the correct p e values, dynamic analyses involving proton-induced quenching are needed. Linear relations between the formal charges and acidity constants were obtained for both ground and excited singlet states independently. For aromatic amines the values of A p e [ = p e - ( P C ) ~ ~ ] are proportional to those of the Stokes shifts, i.e. Using this equation, the correct p e values can be estimated approximately from the data for ( p c & and AEst.p c = (pe)Fc + 8.72AESt-2.64. This work was supported in part by a Scientific Research Grant-in-Aid from the Ministry of Education of Japan. Th. Forster, Z . Elektrochem. Angew. Phys. Chem., 1950, 54, 42, 531. A. Weller, Ber. Bunsenges. Phys. Chem., 1952, 56, 662; 1956, 66, 1144. A. Weller, Progr. React. Kinet., 1961, 1, 189. E. Vander Donckt, Progr. React. Kinet., 1970, 5, 273. J. F. Ireland and P. A. H. Wyatt, Adv. Phys. Org. Chem., 1976, 12, 131. W. Klopffer, Adv. Photochem., 1977, 10, 31 1. (Wiley-Interscience, New York, 1966), p. 125. G. Jackson and G. Porter, Proc. R. Soc. London, Ser. A, 1961, 200, 13. Z. R. Grabowski and A. Grabowska, Z . Phys. Chem. (N.F.), 1976, 101, 197. ' E. L. Wehry and L. B.Rogers, Fluorescence and Phosphorescence Anulyses, ed. D. M. Hercules lo D. M. Rayner and P. A. H. Wyatt, J . Chem. Soc., Faraday Trans. 2, 1974, 70, 945. l1 K. Tsutsumi and H. Shizuka, Chem. Phys. Lett., 1977,52,485; Z . Yhys. Chem. (N.F.), 1978,111,129. H. Shizuka, K. Tsutsumi, H. Takeuchi and I. Tanaka, Chem. Phys. Lett., 1979,62,408; Chem. Phys., in press. l3 H. Shizuka and K. Tsutsumi, J . Photochem., 1978, 9, 334. l4 K. Tsutsumi and H. Shizuka, Z . Phys. Chem. (N.F.), 1980, 122, 129. l5 F. Hafner, J. Worner, U. Steiner and M. Hauser, Chem. Phys. Lett., 1980, 72, 139. l6 C. M. Hams and B. K. Selinger, J. Phys. Chem., 1980, 84, 891, 1366. l7 S. Tobita and H. Shizuka, Chem. Phys. Lett., 1980, 75, 140.K. TSUTSUMI, S. SEKIGUCHI AND H. SHIZUKA 1101 I" K. Tsutsumi, K. Aoki, H. Shizuka and T. Morita, Bull. Chem. SOC. Jpn, 1971, 44, 3245. Is R. D. Haworth, J. Chem. SOC., 1932, 1125. 2o W. Lagenbeck and K. Qeissenborn, Chem. Ber., 1939,72, 724. 21 E. Mosettig and J. van de Kamp, J. Am. Chem. SOC., 1930, 52, 3704. 22 W. E. Beckmann and C. H. Boatner, J. Am. Chem. SOC., 1936, 58, 2097. 23 A. Werner, Justus Liebigs Ann. Chem., 1902, 321, 312. 24 A. R. Watkins, J. Phys. Chem., 1974, 78, 2555. 25 H. Shizuka, T. Saito and T. Morita, Chem. Phys. Lett., 1978,56,519; H . Shizuka, M. Nakamura and 26 M. H. Melhuish, J. Phys. Chem., 1961, 65, 299. 27 J. N. Demas and G. A. Crosby, J. Phys. Chem., 1971,75, 991. 28 A. Weller, 2. Phys. Chem. (N.F.), 1955, 3, 238. 29 J. B. Birks, Photophysics of Aromatic Molecules (Wiley-Interscience, London, 1970); J. B. Birks, Organic Molecular Photophysics, ed. J . B. Birks (Wiley-Interscience, London, 1975), vol. 2, chap. 9. 30 B. Stevens, Adv. Photochem., 1971, 4, 161. 31 A. Weller, in The Exciplex, ed. M . Gorodon and W. R. Ware (Academic Press, New York, 1975). 32 W. R. Ware, D. Watt and J. D. Holmes, J. Am. Chem. SOC., 1974, %, 7853; M-H. Hui and 3 3 R. P. Bell, The Proton in Chemistry (Chapman and Hall, London, 1973); Chem. SOC. Rev., 1974, 3, 34 C. A. Coulson and H. C. Longuet-Higgm, Proc. R. SOC. London, Ser. A, 1947, 192, 16. 35 M. J. S. Dewar and T. Morita, J. Am. Chem. SOC., 1969, 91, 796. 38 G. J. Hoytink, Red. Trav. Chim. Pays-Bas, 1957, 11, 885. 37 J. Waluk, A. Grabowska and J. Lipinski, Chem. Phys. Lett., 1980, 70, 175. T. Morita, J. Phys. Chem., 1980, 84, 989. W. R. Ware, J. Am. Chem. SOC., 1976,98, 4718. 513; J. Chem. SOC., Faraday Trans. 2, 1980, 76, 954. (PAPER 1 /64 1)