8536
J . Phys. Chem. 1990, 94, 8536-8542
bond basis functions now serve as basis functions for the complete system. As they are bond functions, they are eigenfunctions of the individual bond Hamiltonians. There is a similar strategy for partitioning a given molecule by Hutchinson and c ~ - w o r k e r s . ~ First, ~ * ~ the ~ * ~full Hamiltonian is partitioned into several one-dimensional, zero-order Hamiltonians, according to different trial coordinates. The corresponding Schrodinger equations are solved in the next step. Finally, the sets of eigenfunctions thus obtained form the basis of the multidimensional problem. The idea of both methods are similar: splitting up a multidimensional problem into several lower dimensional ones and combining these solutions to solve for the larger system. But they differ in their intentions. TAFIM concentrates on basis functions, as its aim is to select a minimal basis set for highly excited selective vibrational states of larger molecules. The strategy of refs 37, 39, and 40 on the other hand concentrates on the internal coordinate representations of vibrational modes. By introduction of (39) Fleming, P. R.; Hutchinson, J. S. J . Chem. Pfiys. 1989, 90, 1735. (40) Hutchinson, J. S. Adu. Cfiem. Pfiys. 1988, 20, 637. (41) Yamada, K.: Nakagawa. T.; Kuchitsu, K.; Morino, M. J . Mol. Srruct. 1970, 38, 70. (42) Patai, S., Ed.; The Chemistry of the Carbonyl Group; Interscience: London, 1966. (43) Moortgat, G. K.; Seiler, W.; Warneck, P. J . Cfiem. Pfiys. 1983,78, 1185. (44) Tran, L. 8.; Huffaker, J. N. J . Cfiem. Pfiys. 1982, 77, 5624. (45) Reisner, D. E.: Field, R. W.; Kinsey, J. L.; Dai, H. L. J . Cfiem. Pfiys. 1984,80, 5968. (46) Sumpter, B. G.; Thompson, D. L. J . Cfiem. Pfiys. 1985, 82, 4557. (47) Ellison. F. 0.J . Am. Cfiem. Soc. 1963. 85. 3540. (48) Polak, R.; Paidarova, 1.; Kuntz, P. J. J . Cfiem. Pfiys. 1985,82, 2352; 1987,87, 2863. (49) Marston, C. C.; Balint-Kurti, G. G. J. Cfiem. Pfiys. 1989, 91(6), 3571.
nonlocal coordinates it is possible to arrive at eigenstates that are mainly governed by one combination of basis functions. It is similar to the representations of hyperspherical modes in local and hyperspherical coordinate systems. TAFIM is not limited to the use of the reduction procedure ROSE. Every method resulting in a set of bond basis functions should be applicable as well. TAFIM strongly depends on sets of bond basis functions (here Morse and harmonic oscillator wave functions) and is, in this way, complementary to another new and general approach to molecular eigenstates and energies using the fast Fourier transform: Fourier grid Hamiltonian (FGH), proposed by Maston and Balint-K~rti.4~ Here no basis wave functions are required. A final outlook to another possibility of saving computation time should include this report. Since no exact values of the fragmental calculation (step 2) enter into step 3, but only the more qualitative results (Le., which of the starting bond basis functions survives reduction), small differences in the molecular parameters might not lead to different reduced bond basis sets. That is to say, a kind of “library of fragmental basis functions” can be set up. For example, the CH2 fragment in H2CCCD2should not have to be calculated anew, but the results of CH2 in C H 2 0 can be used, if the CH2 parameters are similar. Acknowledgment. 1 thank Dr. B. Hartke and Prof. Dr. J. Manz for many fruitful discussions. Financial support by the Deutsche Forschungsgemeinschaft is also gratefully acknowledged. The computations have been carried out on our Micro-VAX-I1 and on the CYBER 180-995E of the Leibniz Rechenzentrum Munich. Last, but not least, I owe my thanks to M. Kreuz for invaluable moral support. Registry No. C H 2 0 , 50-00-0; H N N H , 3618-05-1.
Dual Fluorescence of 2-( 2‘-Pyridyl) benzlmidazole in Aqueous Solution Due to Photoinduced Proton-Transfer Processes Flor Rodriguez Prieto,* Manuel Mosquera, and Mercedes Novo Departamento de Quimica Fisica, Facultad de Quimica, Universidad de Santiago, E-I5706 Santiago de Compostela, Spain (Received: December 4, 1989; In Final Form: May IO, 1990)
The photophysical behavior of 2-(2’-pyridy1)benzimidazole (2PBI) in aqueous solution has been studied over a wide range of acidity by UV absorption and steady-state fluorescence spectroscopy and fluorescence decay measurements. Absorption spectra reveal the presence of four different species in the ground state, depending on acidity: the dication (D), a monocation protonated at the benzimidazole nitrogen atom N3 (C), the neutral molecule (N), and the anion (A). The acidity constants of the acid-base equilibria among these species are reported. In acid media the emission spectra exhibit dual fluorescence, one of the bands having a large Stokes shift and being attributed to the creation of an excited species, T*, due to photoinduced proton transfer. T* appears over a wide range of acidity, the concentration of protons determining whether it is formed from D*, C*, or N*; on the hypothesis that T* is 2PBI monoprotonated at the pyridyl nitrogen atom, a mechanism for its formation is put forward that explains the acidity dependence of the behavior of 2PBI in the excited singlet state. Analysis of the experimental data in accordance with this mechanism yields the rate constants of the various processes taking place in the excited state.
Introduction Proton-transfer reactions are among the most extensively studied chemical processes owing to their importance in nature and their relative simplicity, which facilitates the development and verification of theoretical models. One particular group of protontransfer processes that has received much attention of late consists of photoinduced proton-transfer reactions in molecules whose excitation alters their acid-base properties.’ Since these processes are extremely fast, especially when the proton transfer involves ( 1 ) Ireland, J. F.: Wyatt, P. A . H. Ado. Phys. Org. Chem. 1978, 12, 131.
inter- or intramolecular hydrogen bonds, studies in this field have greatly increased in number since the development of experimental techniques with a temporal resolution of the order of picoseconds. Their interest lies not only in their providing valuable information concerning the structures and energies of the molecules concerned in excited states but also in the search for substances undergoing phototautomerization processes that make them suitable for use as laser dyes2 or photostabilizers for polymer^.^ (2) Parthenopoulos, D. A.; Kasha, M.Cfiem. Phys. Lett. 1988, 146, 77. AcuRa, A. U.;Costela, A,; Muiloz, J. M. J. Pfiys. Cfiem. 1986, 90, 2807. (3) KlBpffer, W. Adu. Photocfiem. 1977, 10, 31 I .
0022~3654/90/2094-8536$02.50/0 0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 23, 1990 8537
Dual Fluorescence of 2 4 2’-Pyridyl)benzimidazole Wavelength/nm 250
300
350
400
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500
1.0,
I!
’
600
’
1.0
I
I1
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10-37 /cm-f
4
0
6
10
12
14
PH
Figure 1. Absorption spectra and corrected fluorescence spectra for ZPBI and H+ in aqueous solutions of pH 13.2 (---), pH 6.9 (-), pH 3.1 = -2.7 (- -). Fluorescence was induced by radiation of 316 nm in acid media and 313 nm in basic media. [2PBI] = 3 X IO” mol L-I for absorption, 4 X IOd mol L-’ for fluorescence.
-
2
(-.a)
The photophysical behavior of 2-pyridylbenzimidazoles in various nonaqueous solvents has been studied by Kondo4 and Brown et aL5 In cyclohexane, excited 2-(2‘-pyridy1)benzimidazole (2PBI) was found to take part in a proton-transfer process when the medium contained an alcohol capable of forming hydrogen bonds with 2PBI. In this article we describe the photophysical behavior of 2PBI in aqueous solution over a wide range of acidities and discuss the nature of the excited singlet states responsible for the observed dual fluorescence.
Figure 2. Peak intensities of 2PBI fluorescence bands plotted against pH: (a) at 380 nm (band I) in neutral-to-acid media; (b) at 460 nm (band 11) in neutral-to-acid media; (c) at 380 nm (band I) in neutral-to-basic media. Curves a and b are the result of fitting eq 6 to the experimental points. Curve c is the result of fitting a simple equilibrium protonation equation. A,, = 316 (a, b), 313 nm (c). [ZPBI] = 2 X IO” (a, b), 4 x 10” mol L-’ (c). Wavelength/nm 300
350
1.0
400
450
500
550 600
1
Experimental Section
2PBI from Aldrich Chemical Co. was purified by recrystallization from ethanol-water. The acidity of the various solutions used was controlled with perchloric acid and sodium hydroxide, and their ionic strength with sodium perchlorate, all three being Merck p.a. products (a fluorescence quenching due to chloride anions has been observed, so the use of hydrochloric acid or sodium chloride has been avoided). U V absorption spectra were recorded in a Kontron Uvikon 820 spectrophotometer, and fluorescence excitation and emission spectra in a Perkin-Elmer 650-40spectrofluorimeter. The emission spectra presented here have been corrected for the frequency dependence of the sensitivity of the spectrofluorimeter, the correction factors having been determined by comparing emission spectra measured in our apparatus with published corrected spectra for standard substance^^^^ over the range 14500-30500 cm-I. Excitation spectra are uncorrected. Except for highly acidic solutions, for which the acidity function H+ was calculated,* pH was measured by using a Radiometer PHM82 pH meter with a Radiometer Type B combined electrode. The fluorescence decay in solutions of various acidities was measured by the time-correlated single-photon-counting technique using an apparatus and deconvolution program described elsewhere.9 Excitation was effected by using the 316-nm line of an N,-filled lamp (199F, from Edinburgh Instruments), and emission decay was measured at 380 and 500 nm. All experiments, including steady-state measurements, were carried out at 25 O C without prior deoxygenation of the solutions (quenching by oxygen, which in view of the latter’s low solubility in water and the short lifetimes concerned was considered negligible a priori, was ruled out completely by the finding that the slowest decay time was the (4) Kondo, M. Bull. Chem. Soc. Jpn. 1978, 51, 3021. ( 5 ) Brown, R.G.;Entwistle, N.; Hepworth, J. D.;Hodgson, K. B. J. Phys. Chem. 1982.86, 2418.
W.;May,
(6) Lippert, E.;NHgele, W.;Seibold-Blankenstein, 1.; Staiger, U.;Voss, W . 2.Anal. Chem. 1959, 170, I . (7) Ghiggino, K. P.; Skilton, P. F.; Thistlethwaite, P. J. J. Photochem. 1985, 31. 113. ( 8 ) Lovell, M. W.; Vogt, B. S.;Schulman, S. G. J . Phys. Chem. 1984,88, 1885.
(9)Masanita, A. L.; Costa, F. P.;Costa, S. M. B.; Melo, E. C.; Santos, H. J . Phys. Chem. 1989. 93. 336.
10-37 /cm-l
Figure 3. Uncorrected 2PBI excitation spectra for pH 3.13 and 370 nm emission (-), pH 3.13 and 500 nm emission (...),and H+ = -1.80 and 500 nm emission (---). Spectra of pH 3.13 have been normalized to facilitate comparison. Corrected ZPBI fluorescence spectra in acid media under excitation at 316 nm: (a) pH 3.13, (b) pH 1.84, (c) pH 1.14, (d) pH 0.63, (e) H+ = -0.82, (f) H+ = -1.80, ( 8 ) H+ = -2.18, (h) H+ = -3.34. [2PB1] = 2 X IO” mol L-I, for excitation spectra, 4 X IO” mol L-’ for emission spectra.
same in a solution that had been deoxygenated by bubbling nitrogen as in the presence of oxygen). Theoretical equations were fitted to experimental data by using a program based on weighted least-squares analysis and Marquardt’s nonlinear optimization algorithm. Results
The absorption spectra of 2PBI over a wide range of acidity are shown in Figure 1. With respect to its location in neutral media, the low-energy absorption band of ZPBI shifted considerably toward smaller wavenumbers as the pH increased but as pH decreased was hardly changed until very high acidities were reached, when it shifted even further toward smaller wavenumbers. Figure 1 also shows the fluorescence emission spectra of solutions of the same acidity. In neutral and basic media, excitation at the isosbestic wavelength 3 13 nm induced a single emission band with maximum around 26200 cm-l (band I) that waned with increasing pH to disappear at pH > 13.5 (Figures 1 and 2). The excitation spectra at this emission wavenumber was independent of pH in these neutral and basic conditions. In acid media, with excitation at the isosbestic wavelength of 316 nm, another band (band 11) appeared with a maximum around 21300 cm-’. As can be seen in Figures 2 and 3, the intensities
Rodriguez Prieto et al.
8538 The Journal of Physical Chemistry, Vol. 94, No. 23, 1990 SCHEME I
r A
i
k
450
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550
500
5.0
600 650
I
1.0,
I 0.8
,
7 0 ,
Wavelength/nm
-5.0
I
1
- 4 0
m
I
-3 0
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-s m
0 -3 W
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-2 0
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- 1 0
0 . 4 .
kC
0 00 00
0.2
0 05
0 10
0
-
15
0 20
[H'l/mol
0 25
0 30
1-'
Figure 5. [H+] dependence of (a) the reciprocal of the lifetime of 380-nm n n
I.I
27
25
23
21
19
17
15
10-3 7 /cm-' Figure 4. Corrected 2PBI fluorescence spectra in strongly acid media under excitation at 350 nm: (a) pH 0.63: (b) H+ = -0.73; (c) H+ = -1.30; (d) H + = -1.80; (e) H+ = -2.10; (f) H+ = -2.65; ( 9 ) H+ = -3.54. [2PBI] = 6 X lod mol L-I.
of both bands increased with acidity to reach maxima at about pH 3 and decline thereafter, band I disappearing in very acidic media while the intensity of band I1 increases again, shifting slightly to smaller wavenumbers for H+ C -1.8. The excitation spectra of both bands (monitored at the emission wavelengths of 370 (band 1) and 500 nm (band II)), once normalized, were practically identical at pH 3.13 (Figure 3) and remained unchanged for acidities as great as pH 0.5 (results not shown), but at higher acidities the excitation spectrum at the emission wavelength of 500 nm shifted to smaller wavenumbers (Figure 3). Only the species present in strongly acid media absorbed radiation at 350 nm. At this excitation wavelength we measured a series of fluorescence spectra at various acidities, obtaining a single band with a maximum around 20800 cm-' that increased with acidity between [H'] = 0.2 M (pH 0.63) and [H'] = 7 M (H, = -3.55) and shifted slightly to smaller wavenumbers for H+ < -2 (Figure 4). The decay of 2PB1 fluorescence was recorded over the pH range 0.5-12. I n the neighborhood of pH 3, the decay of the 380-nm fluorescence (band I) was monoexponential with a lifetime of 0.70 ns, while 500-nm fluorescence (band 11) decayed biexponentially with a rise time of 0.65 ns and a decay time of 1.67 ns. The reciprocals of both the lifetime of band I emission and the rise time of band I 1 emission increased linearly with proton concentration over the pH range 0.5-2.5 (Figure 5), whereas the decay time of band I 1 emission remained constant to within f0.02 ns over the pH range 0.5-5.65. As the pH is increased from acid to neutral media, band 1 emission exhibited a second decay process with a lifetime of about 90 ps whose contribution increased with pH as that of the 0.70-ns process declined. In neutral media, a third exponential decay whose inclusion slightly improves the goodness of fit has been ignored because its contribution would be very small and error ridden, and the goodness of fit achieved with two exponentials is already within the limits of experimental error: it should be borne in mind that the complexity of the system and the Occurrence in these conditions of lifetimes at the resolution
fluorescence (A);(b) the reciprocal of the rise time of 500-nm fluoresand (c) the ratio between the intensities of T* fluorescence cence (0); at 460 nm and C* fluorescence at 380 nm under excitation at 316 nm (A). See text for the equations fitted in each case.
TABLE I: Ground- and Excited-State Acidity Constants of the Various Acid-Base Equilibria of ZPBI PKDC PKCN
PKNA PKDT PKTN
ground state -1.20 f 0.05" 4.41 f 0.03' 12.05 & 0.03" N Ob N
36
lowest excited singlet state 3.19c 4.2S 9.75c N-7b.c N 14b.c
" Values obtained from asorbance/pH experimental data. 3. CValues bEstimated values based on the assumption of PKTN calculated by using the Forster cycle method. limit of the apparatus means that there may be a considerable percentage error in our estimations of such lifetimes.
Discussion Ground-State Acid-Base Equilibria. The pH dependence of its absorption spectrum suggests that four different forms of ZPBI are involved in ground-state acid-base equilibria: the anion A, the neutral molecule N, the monocation C, and the dication D (Scheme I). It seems unlikely that the first protonation of the neutral molecule takes place at the benzimidazole N1 atom, which would make the ring nonaromatic; in view of the great likeness between the absorption spectra of ZPBI and 2-phenylbenzimidazole1° at acidic and neutral pH, it seems probable that the first protonation takes place at the benzimidazole N3 rather than a t the pyridyl nitrogen atom. Analysis of the pH dependence of absorbance at fixed wavelengths yields the ground-state acidity constants listed in Table I; these values are in keeping with those published for other benzimidazoles with aromatic substituents."," Fluorescence Spectra. Since the distance of about 5000 cm-l between the two fluorescence peaks observed in acid media is too large for them to be attributable to transitions between different states of one and the same electron band, two different excited species must be present. However, the virtual identity of the two bands' excitation spectra in the pH range 0.5-3 (Figure 3) means that both must derive from absorption by the same ground-state (IO) Mishra, A. K.; Dogra, S. K . Spectrochim. Acrcl 1983, 39A, 609. ( I I ) Sinha, H. K.; Dogra, S . K. Chem. Phys. 1986.102, 337. Sinha, H. K.: Dogra, S. K . J . Photochem. 1987, 36, 149.
Dual Fluorescence of 2 4 2'-Pyridyl)benzimidazole Wavelength/nm 350
1.0
400
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The Journal of Physical Chemistry, Vol. 94, No. 23, 1990 8539 SCHEME I1
500 550600
A
a
I I
'.(
'.,
I I
10-3 7
fluoresce or at least has a quantum yield very much smaller than that of N*. The above findings show that the formation of T* is favored in acid media. Furthermore, the absorption spectra of Figure 1 show that whereas protonation of the benzimidazole N3 hardly alters the spectrum, there is a significant shift to lower energies when the pyridyl nitrogen is protonated to afford the dication, a shift paralleled by the wide separation between bands I and I1 of the emission spectrum. It therefore seems reasonable to suppose that the formation of T* implies the protonation of the pyridyl nitrogen atom due to an increase in its excited-state basicity. For the similar molecule I-phenylpyridine, it is known that the pyridyl nitrogen is more basic in the first excited singlet state than in the ground state: pK, = 4.55, pK*, = 10, and the difference is even greater for the meta and para isomers.' We accordingly propose that T* is a tautomer of C* as a hypothesis that will have to be confirmed by the subsequent analysis of experimental data. Species T* could actually be written in two resonance forms:
/cm-l
Figure 6. (a) Corrected experimental fluorescence spectrum of 2PBI at pH 3.01 under excitation at 316 nm (-) together with the individual contributions of the fluorescence of C* and T* (- --). The spectrum of T* was obtained by taking the difference between the experimental spectra for pH 3.01 and 0.52, previously normalized at 380 nm-a wavelength at which T*does not emit. The T* and pH 3.01 spectra were then normalized at 600 nm, and the former was subtracted from the latter to give the spectrum for C*. (b) Corrected experimental fluorescencc spectrum of 2PBI at pH 8.85 under excitation at 316 nm (-) together with the individual contributions of the fluorescence of N* and T* (---). [2PBI] = 2 X IOd mol L-I. (.-a)
which, in comparison with those of C* H
N-
C*
\ H
(--a)
species, the monocation C, which predominates at these pH values. This finding that a single excitation band gives rise to two emission bands, one of them (band 11) with an unusually large Stokes shift, implies that this latter band must be due to a structurally distinct species T* formed in the excited state from the excited monocation C*, which is responsible for band I with a normal Stokes shift. Figure 6a shows the individual emission spectra obtained for both species T * and C*. At acidities greater than about pH 0.5, the band I1 excitation spectrum, like the absorption spectrum, shifts to longer wavelengths (Figures 1 and 3), showing that T* is also formed from the dication D when the latter is present. Furthermore, excitation at 350 nm, a wavelength at which only the dication absorbs radiation, produces a single emission band (Figure 4) that once the Raman contribution is removed coincides with the spectrum inferred for T* at much lower acidities (Figure 6a); Figure 4 shows no emission with normal Stokes shift attributable to the excited dication D*. The intensity of the spectra in Figure 4 grows with acidity following the increase in concentration of D. Nevertheless, at concentrations of acid greater than 4 M (H,< -2) and with excitation either at 316 or at 350 nm, band I I shifts slightly and grows faster than can be due to the increase in concentration of D. This fact may be attributed to the considerable changes in the properties of the medium at such high acidities. Figure 6b shows that the band appearing in the fluorescence spectrum obtained at pH 8.85 has too heavy a tail to be attributable solely to "normal" emission by the excited neutral species N*. Normalization of this spectrum at 550 nm with the spectrum inferred for T*, followed by subtraction of the latter, yields a well-shaped band for N* peaking at 26250 cm-I and confirms the contribution of T*to the tail. In more basic media the intensity of the whole spectrum wanes because the anion A* does not
- a;,* H / \ H
suggest quite different electronic structures for both species, as well as they may have different geometric structures, with a more planar conformation of T* than C*. That would account for the shift between C* and T* fluorescence. Acid-Base Processes in the Excited State. According to the above interpretation of the spectra recorded, the excited species of 2PBI are those shown with the corresponding acid-base equilibria in Scheme 11. Table I lists the p P , of these equilibria as calculated by the Forster cycle method] (for calculation of PK*TN,PKDT, and pK*DT, the value of PKTN has been assumed to be around 3; it must be smaller than pKcN because no protonation of the pyridyl nitrogen is observed in the ground state, but published data for the three isomers of phenylpyridine' and our own current work on 2-(4'-pyridyl)benzimidazole suggest that it cannot be very much smaller). The estimated values of pK*DT and pK*TN imply that T* is the thermodynamically advantaged excited species over the whole range of acidities studied, while the value of about 1OIo calculated for the tautomerization equilibrium constant K*a = kc-/kTc from the estimated pK*, values is in keeping with the experimental observation that the transition from C* to T* is highly favored. Of the processes shown in Scheme 11, the only ones that will be observed are those that are fast enough to compete with the deactivation of the excited species, the rate constants for which are shown by the measured lifetimes to be greater than IO8 s-l in all cases. The estimated pK*, values mean that according to Eigen's theory Of proton transferI2 kcD, kNC, kAN, kNT, and kDT should have values similar to the diffusion-controlled limit, say, 5 X 1Olo M-I s-I, and hence that the reverse constants kw, kCN, kNA,kTN,and kTD all fail the above requirement (the greatest, (12)
Eigen, M. Angew. Chem., Int. Ed. Engl. 1964, 3, 1.
8540 The Journal of Physical Chemistry, Vol. 94, No. 23, 1990
Rodriguez Prieto et al.
SCHEME 111
B
H
A
H
H
A
kDl L
k A I:
k C
t
,
*
a0 x
kDc,being about 3 X IO7 s-I); furthermore, since N* and A* exist only at pH > 3, the effective rates of protonation of these species ( k N c [ H + ]k, N T [ H + ]and , k A N [ H + ]are ) not competitive either, leaving only kcD[H+] and k D T as being likely to be observed. Notwithstanding the latter consideration, the tendency of N* to protonate to give T* is so great as to suggest the possibility of water's acting as an acid in the reaction N*
+ HzO
k'm
T*
+ OH-
where k'NT includes the concentration of water. The estimated value of K*TN suggests a value of about unity for k G N / k k T ,and since kGN ought to be close to the diffusion-controlled limit (or somewhat smaller given the pK, of T*, even species of pK, slightly less than 14 often being deprotonated by OH- at a subdiffusion rate)'* krNTmay be large enough to compete with k N ,the deactivation constant of N*. Deprotonation of T* by OH- will not of course be observed, the concentration of O H - being too small under the experimental conditions used. The tautomerization process C* T* remains to be considered, which a priori might occur (i) by deprotonation of C* followed by protonation of N*, (ii) by protonation of C* followed by deprotonation of D*, and (iii) by a one-step concerted reaction in which the involvement of one or more water molecules13achieves the simultaneous deprotonation of benzimidazole and protonation of the pyridyl group. Reaction i is ruled out by the small value of kCN,and it is only in highly acid media that the quenching of C* fluorescence by protons shows the occurrence of reaction ii (see below). Since the conversion of C* to T* is efficient at acidities in the neighborhood of pH 3 that are too low for appreciable quenching to take place (see Figure 5), it must be concluded that the one-step concerted mechanism iii takes place, the rate constant kcT being large enough to allow successful competition with the deactivation of C*, whereas the reverse
-
( I 3) Jencks, W.P. Ace. Chem. Res. 1976, 9, 425
constant kTCmust be very small, given the estimated value K*,-= lolo. This would be an example of the proton-relay mechanism proposed by Kasha.I4 In view of the above considerations, the mechanism we propose to explain the behavior of excited 2PBI is that shown in Scheme 111, in which only processes that are competitive with the deactivation rate constants kA, k N , kc, kD, and kT appear. Since protonation of C takes place at acidities so high that medium effects cannot be neglected and taking into account the great difficulty involved in the quantitative analysis of these effects, our treatment will be limited to a range of acidity not greater than pH 0; in consequence, that protonation process has not been included in the mechanism proposed, D* being formed only by quenching of C*. The time-resolved fluorescence results are in keeping with this mechanism. The lifetime of 1.67 ns measured at 500 nm (at which wavelength emission by C* and N * is practically zero) is independent of pH over the range in which it was measured (pH 0.5-5-65), confirming that band I1 is produced by the single species T* in this range. Measurements at 380 nm in weakly acid media imply a lifetime of 0.70 ns for C*. The lifetime of 90 ps calculated for N* is only very approximate, being at the limit of the resolution of the apparatus. The rise time of 0.65 ns recorded at 500 nm in media of about pH 3 practically coincides with the lifetime of C* and reflects the latter's conversion to T*; the corresponding rise time for the process N* T* at higher pH is too short to be distinguished separately. As acidity increases from pH 2.5 to 0.5, the lifetime of band 1 and the rise time of band I1 both decrease owing to the quenching of C* fluorescence by protons (the kcD[H+]step in Scheme 111). Quantitatioe Analysis. The proposed mechanism satisfactorily explains the pH dependence of the intensities of both bands I and I1 (Figure 2). The reduction in the intensity of band I to practically zero in basic media (Figure 2c) is due to the concentration
-
(14) Kasha, M . J . Chem. SOC.,Faraday Trans. 2 1986,82, 2319.
Dual Fluorescence of 2 4 2‘-Pyridyl)benzimidazole
The Journal of Physical Chemistry, Vol. 94, No. 23, I990 8541
TABLE 11: Reciprocal Values of Experimental Fluorescence Lifetimes for Species N*, C* (in the Absence of Quenching), and T*; Fluorescence Quantum Yields for N* and C* and Relstive Fluorescence Quantum Yields of T’ (See Text); Optimized Values of the Various Parameters in Eqs 3 and 6 for the Data Shown in Figures 5c and 2a.b reciprocal values of fluorescence parameters of parameters of parameters of fluorescence lifetimes, s-I quantum yields eq 3 eq 6 at 380 nm eq 6 at 460 nm TN-l = 1 x 1010 $IN = 0.032 a = 0.834 f 0.006 PKCN= 4.42 f 0.02 pKcN 4.43 f 0.02 TC-l = I .4 x 109 b = 7.3 f 0.1 a3*0= 2.35 f 0.02 ,460 = 11.2 f 0.2 + c c 0.091 7T-’ = 6.0 x lo8 & = 0.16 b / a = 8.8 0.1 B4@= 8.1 f 0.9 6 = 9.5 f 0.1 M-I = 0.86 d = 7 f 5 M-I
*
$iC
of N* decreasing as the result of the deprotonation of ground-state N to A, whose excited state A * has a virtually zero fluorescence quantum yield. Analysis of these data by the corresponding protonation equilibrium equation yields a value of 12.18 f 0.04 for PKNA, in good agreement with the value deduced from absorption measurements. The increase in the intensity of band 1 when pH is reduced from neutral values to about pH 3 (Figure 2a) implies that the quantum yield of C*, dC,must be greater than that of N*, dN;a roughly 3-fold difference was confirmed (Table 11) by quantum yield measurements carried out using quinine sulfate in 1 N H2S04 as the standard (quantum yield 0.546).15 The increase in the 460-nm (band 11) emission over this pH range (Figure 2b) must have a certain contribution from the increase in band I (see Figure 6), but it is too large to be due solely to this contribution and thus suggests that the relative fluorescence quantum yield of T* formed by tautomerization from C*, hC, is greater than that of T* formed by protonation of N*, dTN(see eqs 1 and 2);16 a roughly 5-fold difference was confirmed (Table 11). dTN
=
(1)
(krT/kT)/(krN/k’NT)
d T C = ( k r T / kT) / ( krC / kCT) (2) The decrease in the intensity of both emission bands as acidity is increased from pH 3 to 0.5 may be attributed, in keeping with Scheme 111, to the quenching of C* by protons to give D*, which either is a nonfluorescent species or has a very low quantum yield. The fact that band I 1 is not affected so much as band I by increasing acidity over this range is of course explained by the deprotonation of D* to T*. At high acidity, band I disappears, showing that C* is not efficiently formed from D*, as was predicted from the small estimated value of kDc. This is also consistent with the absence of band I emission under excitation at 350 nm (Figure 4), a wavelength at which only D absorbs radiation (Figure I ) . The quenching mechanism taken to hold between pH 0.5 and 3 implies that the ratio FT460/Fc380 between the intensities of emission by T* at 460 nm-once the contribution of the fluorescence of C * to the 460-nm emission has been subtracted-and by C* at 380 nm should depend linearly on [H+] (eqs 3-5, in which, for the excited species X* and wavelength A, FT460/Fc380 = a b[H+] (3)
[X*],, being the steady-state concentration of X* and krx its radiative deactivation constant). The existence of this mechanism is thus supported by the linear dependence that is in fact observed (Figure 5c); the corresponding least-squares estimations of the intercept a and the slope b and the wavelength-independent ratio b/a are listed in Table 11. According to the Stern-Volmer equation, the reciprocal of the lifetime of C* should depend linearly on the concentration of protons over the quenching range of pH 0.5-3.0, the slope being the quenching constant, kcD, and the intercept being the reciprocal Fox the lifetime in the absence of quenching, 70. Fitting this equation to the experimental 380-nm emission data by a weighted least-squares method (more weight being given to the data with more accurate longer lifetimes) yields kcD = (1.4 f 0.1) x lolo M-I s-I (Figure 5a), which as expected is of the same order as the diffusion-controlled limit, and 70 = 0.69 f 0.07 ns, which agrees, unsurprisingly, with the lifetime of C* measured in the neighborhood of pH 3. The rise time at 500-nm (T*) emission at high acidity (pH 0.5) should in principle depend on both the lifetime of C* and that of D*, the species from which T* is formed under these conditions. However, fitting the equation to the experimental 500-nm emission data by the same weighted least-squares method as above yields (Figure 5b) 70 = 0.70 f 0.08 ns and kcD = (1.7 f 0.2) X 1Olo M-l s-I, which agree with the values obtained above; and since the rise time measured at pH 0.5 does not deviate unduly from this equation, it is clear that what is being measured is the lifetime of C* when subject to quenching (0.17 ns at pH 0.5, close to the limit of resolution of the apparatus), and hence that the lifetime of D* must be at most of the same order, therefore a three-exponential behavior at high acidity could not be observed. The theoretical steady-state concentrations of D*, C*, N*, and T*entailed by the mechanism proposed in Scheme 111 imply that in neutral-to-acid media FA,the intensity of fluorescence at wavelength A, depends on [H+] as in eq 6, in which Foxis the
+
a =
uT460krTkCT c T c ~ ~ ~ ~ ~ c ~ T
(4) (5)
the instrumental-and wavelength-dependent mental parameters defined by oxx =
oxx are experi-
Fxx/(krx[X*Iss)
(15) Melhuish, W. H. J . Phys. Chem. 1961, 63, 229. Demas, J. N.; Crosby, G.A. J. Phys. Chem. 1971, 75, 991. (16) Note that ground-state T does not exist, and hence T* is not formed by absorption of radiation. This implies that the fluorescence quantum yield of T*cannot be directly measured and so we have defined relariue quantum yields, which include the efficiency of the formation of T* from its precursors. This relative quantum yields have been evaluated by calculating the ratios between the integral of the spectrum of T*and those of C* obtained at about pH 3 where T*is formed only from C*) and N* (& , obtained at neutral pH where T* is formed exclusively from N*).
9‘.
(9) intensity of fluorescence at neutral pH, KCN refer to ground state, and ah,PA,and 6 are defined in eqs 7-9. Curves a and b shown in Figure 2 are the result of fitting eq 6 to the experimental data by a nonlinear optimization algorithm, Foxbeing held constant at its experimental value. For the 380-nm emission, to which only is zerosince uT380 the fluorescence of C* and N* contribute, is-and the corresponding reduced form of eq 6 was fitted. The goodness of the fit strongly supports the proposed mechanism. The corresponding optimized values of PKCN, ah,p,and 6 are listed in Table 11. At both wavelengths, pKcN agrees well with the value obtained from absorption data (Table I); the preferred value for 6 must be that obtained at 380 nm, since the smallness of the effect of quenching at 460 nm makes the value calculated at this wavelength rather imprecise.
J . Phys. Chem. 1990, 94, 8542-8547
8542
TABLE 111: Rate Constants for the Various Processes of 2PBI in the Excited Singlet State in AQNS Solution reaction deactivation radiative deactivation rate constants rate constants, s+ rate constants, s-' k'NT = 3.1 X IO8 s'I kN = 9.7 X IO9 krN = 3.2 X IO8 kcT = 6.7 x lo8 S-l kc = 7.3 X IO8 krc = 1.3 X IO8 kcD = I , 3 X IO" 5-I M-' k T = 6.0 X 10' krT = 1.0 X IO8 k D T l k D = 0.5
reasonable as regards their order of magnitude and agree well with the values estimated from the Forster cycle pK*,: the quenching constant kco is of the order of the diffusion-controlled limit and agrees well with the value calculated from the quenching experiments in lifetime measurements; the large tautomerization constant kCT confirms the efficiency of this process; and k;rlT is as expected large enough to compete with the rate of deactivation of N*.
The values obtained for the above parameters estimated from fluorescence steady-state data, together with the lifetimes of the fluorescent species, the quantum yields of N* and C*, and the ratios hN and 4Tc(Table II), jointly allow calculation of the rate constants of the various processes undergone by excited 2PBI in neutral and acid media, and also of the radiative constants of the three fluorescent species. The results'7 (Table 111) are quite
Acknowledgment. Our special thanks go to Dr. Mapnita and the Structural Chemistry Centre, Lisbon, for their invaluable assistance in obtaining time-resolved fluorescence measurements with their time-correlated single-photon-counting apparatus. This work was supported directly by the Spanish Interministerial Science and Technology Commission (CICYT) and the University of Santiago and indirectly by a CICYT postgraduate training grant awarded to M.N.
(17) It is worth noticing that those rate constants derived from lifetime data obtained at the limit of the temporal resolution capacity of the apparatus, notably those referring to N*, probably have a considerable percentage error.
Registry No. D, 129364-68-7; C, 129364-69-8;N, 1137-68-4; A,
129364-70-I .
Boxing Procedure for Estimating Shape Resonance Energies from Stabilization Graphs with the MSXa Method Maurizio Cuerra Istituto dei Composti del Carbonio Contenenti Eteroatomi e lor0 Applicazioni, CNR, Via della Chimica 8, 40064 Ozzano Emilia, Bologna, Italy (Received: February 5, 1990; In Final Form: May 16, 1990)
Shape resonance energies have been estimated with the M S X a method by stabilizing transition-state energies with a positively charged sphere (Watson sphere). Stabilization graphs have been investigated by using as a variable parameter either the Watson sphere radius rw or its charge qw. The importance of determining resonance energies from stabilization graphs as a function of rw by fixing the ratio qw/rw to a large value (boxing procedure) is clearly demonstrated. Resonance energies are better determined from the stability of the transition-state energies of valence anion states rather than by localizing their avoiding crossings with single-centersolutions, owing to a sharp variation of the electronic relaxation energy in the neighborhood of avoided crossing points in the transition-state procedure.
Introduction Over the past few years temporary anion states have been investigated experimentally by using the sharp variations occurring at specific energies in the electron-scattering cross section (shape resonance) in electron transmission (ET) spectra.' A shape resonance arises as a result of the temporary capture of the incoming electron into a normally vacant molecular orbital (MO). The resonance energies are the negative of the gas-phase electron affinities (EAs) and can be estimated with bound-state calculations by using stabilization methods2 The multiple scattering X a (MSXa) method3 has proven to be a powerful tool for characterizing shape resonances4 In fact,
resonance energies have been accurately reproduced for calcophenesI0 and transition-metal comple~es'*~J with little Computational effort. Tossell and c o - ~ o r k e r s 'first ~ attempted to estimate shape resonance energies with the M S X a method, using the transition-state procedure,I4 by stabilizing the positive energy of the unbound electron with an attractive potential generated by an uniformly positive charged (qw = 2e) sphere (Watson sphere). The Watson sphere radius rw was taken as large as twice the outer-sphere radius (To) so as to ensure that all negative eigenvalues were stabilized by qw/rw. The positive energy was then computed by adding this amount to the corresponding transition-state ei-
Schulz, G . J. Reu. Mod. Phys. 1973, 45, 378. Hazi, A . U.; Taylor, H. S.Phys. Rev. A 1970, I , 1109. Johnson, K. H. Adu. Quantum Chem. 1973, 7, 143. A more rigorous theoretical approach for assigning resonances is to compute the total electron-scattering cross section by means of the continuum MSXa method.' However the agreement with experiment is so far only a qualitative one,&* owing to the difficulty of describing accurately the interaction between the target molecule and the incoming e l e ~ t r o n . ~ ( 5 ) Dehmer, J . L.; Dill, D. I n Electron-Molecule and Photon-Molecule Collisions;Rescigno. T.,Mc Koy, V.,Schneider, B., Us.; Plenum Press: New York, 1979. (6) Tossell, J. A.; Davenport, J. W . J . Chem. Phys. 1984, 80, 813. (7) Guerra, M.; Jones, D.; Distefano, G.; Foffani, A,; Modelli, A. J . Am. Chem. SOC.1988, 110. 315
(8) Modelli, A.; Foffani, A.; Scagnolari, F.; Torroni, S.; Guerra, M.; Jones, D. J . Am. Chem. SOC.1989, I l l , 6040. (9) Krylstedt, P.; Elander, N.; Brandas, E. In?. J . Quantum Chem. 1987, 31, 755. (IO) Modelli, A.; Guerra, M.; Jones, D.; Distefano, G.; Irgolic, K. J.; French, K.; Pappalardo, G. C . Chem. P h p . 1984,88, 455. ( I I ) Modelli, A.; Foffani, A.; Guerra, M.; Jones, D.; Distefano, G. Chem. Phys. Lett. 1983, 99, 5 8 . (12) Modelli, A,; Distefano, G.; Guerra, M.; Jones, D. J . Am. Chem. Soc. 1987, 109, 4440. ( I 3) Giordan, J. C.; Moore, J. H.; Tossell, J. A. J . Am. Chem. SOC.1981, 103, 6632. (14) Slater, J. C . In Computational Methods in Band Theory; Marcus, P. M . , Janak, J. F., Williams, A. R., Eds.; Plenum Press: New York, 1971.
(1) (2) (3) (4)
0022-3654/90/2094-8542$02.50/0
0 1990 American Chemical Society
