The Journal of Physical Chemistry, Vol. 83, No. 4, 1979 447
Tautomerizatioln Kinetics of 7-Hydroxy-4-methylcoumarin1
Tautomerization Kinetics of 7-Hydroxy-4-methylcoumarin in the Lowest Excited Singlet State Stephen G. Schulman" and Leonard S. Rosenberg Co//egeof Pharmacy, University of Fbrida, Gainesville, Florida 326 10 (Received June 15, 1978)
The biprotonic phototautomerism of 7-hydroxy-4-methylcoumar~n, in the lowest excited singlet state, was evaluated fluorometrically, using steady-state kinetics. Rate constants for dissociation of the excited neutral molecule and reprotonation of the excited anion to form the neutral molecule were determined unambiguously. However, the present method allows only composite constants, containing the rate constants for prototropism of the excited zwitterion implicitly, to be evaluated. In the absence of exact information about the excited state equilibrium constant for the reactions involving the zwitterion, only limiting values of the rate constants of the latter can be estimated. However, it was possible to establish from these that, in the lowest excited singlet state, the zwitterion is a weaker acid than the neutral molecule.
T h e pH dependence of the fluorescence of 7-hydroxy4-methylcoumarin (/3-methylumbelliferone) is anomalous in that the fluorescence spectrum of the singly charged anion red-shifts while the long-wavelength absorption band blue-shifts ulpon going to lower pH. This has been shown to be the result of tautomerism in the lowest excited singlet state1S2between the neutral molecule (I) and the zwitterion
HO
for the characterization of the dye-solvent system and could be useful to provide a rational approach to the design of related dyes with emission spectral energy distributions contributing to a wider range of laser tunability than that, of 7-hydroxy-4-methylcoumarin itself. With this in mind, the following attempt was made to analyze the pH dependence of the fluorescence of 7-hydroxy-4-methylcoumarin in terims of steady-state kinetics.
xiLoo-AoH+ I
II
(11). Direct excitation of the neutral molecule a t near neutral pH aipparently results in its clissociation during the lifetime of the lowesit excited singlet state and subsequent reprotonation of the resulting excited anion at the carbonyl oxygen atom of the lactone group a t low pH. The variety of emiission wavelengths available from the various prototropic species derived from 7-hydroxy-4-methylcoumarin has been suggested as the basis for the construction of acidity tunable dye laser^.^*^ Although tautomerism in the lowest excited singlet state has been observed for a variety of compounds as well as for P-~ethylumbellnferone~-~ the phenomenon has generally been dealt with in qualitative terms. Quantitativeg and semiquantitativelo methods exist for the calculation of rate and equilibrium constants for simple excited-state proton transfer reactions in which dissociation and reprotonation o~ccursa t the same functional group. However, the kinetic treatmentsg have not, to our knowledge, been applied to proton transfer involving distinct sites of dissociation and reprotonation. The approximate thermodynamic treatmentlo can be applied to tautomeric system^^-^ but only if alkylated models of the various tautomers can be prepared so that ground state pK,'s, and absorption arid fluorescence spectra of each can be taken. In the case of @-methylumbelliferone, the approximate thermodynamic trealtmentlO of prototropic reactions involving the zwitterioin is inapplicable because a derivative methylated at the carbonyl oxygen could not be prepared. Moreover, thlere is no evidence for a measurable presence of the zwitteirion in the ground electronic state. It was of iinterest to us to be able to evaluate, as accurately as plossible, the relative acidities and basicities, in the lowest excited [singletstate, of the various functional groups of 7-hydroxy-4-methylcoumarin which are prototropically reactive. 'This information is highly desirable 0022-3654/79/2083-0447$0 1.OO/O
Experimental Section Chemicals. 7-Hydroxy-4-methylcoumarin (Aldrich Chemical Co., Milwaukee, Wisc.) was recrystallized several times from absolute ethanol. The solutions for measurement of fluorescence and absorption spectra were 1 X lW5 M in 7-hydros.y-4methylcoumarini and had their pH adjusted with HC10, or NaOH solution. The use of standard buffer solutions was avoided because high concentrations of buffer ions complicate the kinetic treatment of the fluorimetric titration data. Apparatus. Fluorescence spectra were taken on a Perkin-Elmer MPF-2A fluorescence spectrophotometer whose monochromators were calibrated against the xenon line emission spectrum and whose output was corrected for instrumental response by means of a rhodamine-B quantum counter. Excitation was effected at the isosblestic point at 335 nm. A Beckman DB-GT spectrophotometer and an Orion 801 p H meter with a Corning silver-silver chloride-glass combination electrode were also used. Lifetimes of the lowest excited singlet states (fluorescence lifetimes) were measured, on nitrogen-purged solutions, on a TRW nanosecond decay-time fluorimeter, with an 18-W pulsed deuterium lamp, interfaced with a Tektronix 556 dual-beam oscilloscope by means of two 1A2 plug-in, dual-channel amlplifiers. With this apparatus fluorescence lifetimes of duration 11.7 ns could be measured. Results and Discussion The pH dependence of the fluorescence spectrum of 7-hydroxy-4-metl?ylcoumarin is shown in Figure 1. At pH >10 the anion is the absorbing species and only the 452-nm fluorescence of the anion is observed. In the interval p H 6.5-10 the anion is converted to the neutral species in the ground state, resulting in the decrease in observed anion emission. From p H 4 to 6.5 considerable fluorescence which is invariant in intensity with p H is observed from the anion even though excitation of the neutral species is virtually exclusive. This results from the dissociation, in the lowest excited singlet state, of the phenolic group of
0 1979 American Chemical Society
the directly excited neutral molecule. In the same pH interval a weak short-wavelength emission is observed on the blue side of the anion fluorescence. This is attributed to fluorescence from that fraction of the directly excited neutral molecules which does not undergo photodissociation. The latter assignment is substantiated by the fact that 7-methoxy-4-methylcoumarin, which should be electronically similar to the neutral 7-hydroxy compound, also fluoresces near 400 nm.' In the interval pH 1-3.5, with decreasing pH, the fluorescence of the anion decreases giving way to the longer-wavelength emission at 477 nm, attributed to the excited zwitterion. Simultaneously, the fluorescence assigned to the neutral molecule increases in intensity. From pH 1 to Ho - 1 the fluorescences of the neutral molecule and zwitterion are maximal in intensity and invariant with respect to solution acidity. Below Ho - 1the short-wavelength emission of the neutral molecule and the long-wavelength emission of the zwitterion give way to a more intense fluorescence (at 424 nm) which is intermediate between those of the two uncharged species in spectral position and is believed to originate from the cation derived from 7-hydroxy-4-methylcoumarin.' However, this will not be considered further here and the remainder of this study will deal with the spectral changes occurring between pH 6 and Ho - 1. The fate of photoexcited 7-hydroxy-4-methylcoumarin in the pH interval 1-6 can be represented by Scheme I. Here, N, A, and Z represent the ground states of the neutral molecule, anion, and zwitterion and N*, A*, and Z*, the lowest excited singlet states of the same species, respectively. Corresponding to N*, A*, and Z* are the rate constants for fluorescence kf,k;, and k;' and the rate Scheme I
N
-
N*
N*
hu
kf
N*
(absorption)
N
(fluorescence)
N
(nonradiative deactivation)
kd
N* + Hz0 A*
A* A* A*
~ N A
A*
-
+ H30+ k
ki
(dissociation)
+ H20
(reprotonation)
N*
(fluorescence)
A
(nonradiative deactivation)
+ H30'
-
kd"
+ H30+
A
d'
AN
-+ - + kAZ
+ H 2 0 kZA z* ki' z z* z Z*
S. G. Schulman and L. S. Rosenberg
The Journal of Physical Chemistry, Vol. 83, No. 4, 1979
448
Z*
A*
HzO
(reprotonation)
H30+
(redissociation) (fluorescence) (nonradiative deactivation)
constants for unimolecular radiationless deactivation kd,
kd,and h$. The lifetimes of N*, A*, and Z* in the absence of proton exchange are 7 N = (kf+ k&l, 7 A = ( k j + hi)-',
+
and 72 = ( k f ' IQ")-', respectively. The rate constants for prototropic dissociation of N* and Z* are kNAand k Z A and the rate constants for reprotonation of A* to form N* and Z* are, respectively, k A N and kAZ. Under conditions of steady-state excitation, deactivation, and proton exchange the rates of disappearance of N*, A*, and Z* from the lowest excited singlet state are -d[N*l/dt = [ ( 1 / 7 ~ )+ ~NA][N*I - ~AN[A*][H~O'I(1) -d[A*]/dt = [ ( 1 / 7 ~ )+ k ~ ~ [ H 3 0 + ] kAZ[H30+ll[A*l- kNA[N*l - IZZAIZ*l (2) and [(1/7z) + ~zAI[Z*I - ~AZ[A*I[H~O'I (3) -d[Z*l/dt Integration of eq 1 from [N*] = 1 when t = 0 to [N*] = 0 when t = Q),eq 2 from [A*] = 0 when t = 0 to [A*] = 0 when t = a,and eq 3 from [Z*] = 0 when t = 0 to [Z*] = 0 when t = and with the aid of the identitiesg
yields
and
where $ N / & N O , 4A/4Ao, and @z/+zo are the relative fluorescence efficiencies of N, A, and Z, respectively. Combination of eq 4-6 yields eq 7-9 from which it follows that (10) ~ A / ~ A +O +z/dzo + ~ N / @ N ' = 1 However, in order to determine ~ A / ~ A O@z/4z0, , and ~ N / @ N O at each point in a fluorometric titration it is necessary to consider the way in which the fluorescences of the anion, zwitterion, and neutral molecule overlap each other. A t any given point in the fluorescence spectrum of 7 hydroxy-Cmethylcoumarin F = FNO(~N/+NO)
+ Fzo(4z/4zo) + F A ' ( ~ A / ~ A ' ) (11)
where F is the measured fluorescence intensity and F N O ,
Tautomerlratlori Klnetlcs of 7-Hydroxy-4-methylcoumarln
The Journal of Physlcal Chemistry, Vol, 83, No, 4, 1979 449
eo#
m
."e C
a
Ll
LF
301
I
-pH
a
100
2'
!i
8
IO
4
6
2
. -
0
PH 440
360
520
WAVELENGTH
Flgure 2. pH dependences of the fluorescence lntenslties at 452 nm (open clrcles) and at 380 nm (fllled clrcles) of 7-hydroxy-4-meithylcoumarln. The fluoirescence at 380 nm Is magnlfled 15X.
600
(nm)
Flgure l,, Fluoralscence spectra of 7-hydroxy-4-methylcoumarln at pH 11.0 (anion), pH 5.0 (anion and neutral molecule), and pH 1,O (rwltterlon and neutral molecule).
where Fo is the fluorescence intensity a t the analytical wavelength when pH 51. Equation 13 can then be rearranged to
F 2 , and FAoare the fluorescence intensities that would be measured under the same conditioris of analyte concentration and instrumental configuration if the analyte was all in the neutral, zwitterionic, or anionic form, respectively. Combination of eq 11 with eq 7-9 yields
(s
(+) t
f 1 t a)[H3Ot1
which can be solved simultaneously with eq 15 to yield b and c. As in the solution for a the emission maximum for the anion, 452 rim, seems the best choice of analytical wavelength because sensitivity is good a t that point and because FNo = 0 at that wavelength which reduces eq 16 to (FAo - F)u
(12) where (2 k h , ~ ? b~ :=, k A N T A , and C = k A Z T A / ( 1 Equation 12 can be rearranged to
( F - Fp?) t ( F - F N ' ) ~ [ H ~ Ot' ] (F(1 f a) - UFzo - FN')C[H~O']
+- ~ Z A Q ) ,
-
(FA'- F ) U (13)
At high pH (in this case pH >4) [ H 3 0 c ] 0 and all terms containing [F130t]become negligible by comparison with those that do not. This accounts for the pH independence of the fluorescence of the anion and neutral species derived from 7-hydroxy-4-methylcoumarinin the interval pH 4-6,5. In this case we find immediately that LZ
=
Fconst - FNO FA'- Fconst
b C
aF,O - Fo(1 + a) Fo
- F(l t b[HaO']) [F(1t a ) - u F z O ] [ H ~ O ~ ]
(17)
Although FAocould be easily evaluated by taking the fluorescence spectrum after raising the pH of the test solution above pH = pK, t 2 the determination of Fzo is complicated by the fact that at no pH in the fluorometric titration is the fluorescence exclusively that of the zwitterion. In order to estimate Fz0 a t 452 nm the following approach was taken, At pH 51 eq 10 and 11 are reduced to (d'S/$No)O
t
($Z/$Zo)O
=1
I(l8)
and
(14)
where FConstisl the fluorescence intensity at the analytical wavelength in the p H interval 4-6.5. If the fluorescence maximum of the anion (452 nm) is chosen as the analytical wavelength, the fluorescence due to the neutral molecule is negligible and a = FcOm,/(FAo - Fconst).Taking FAo = 1.00 and FCollet= 0.686 at 452 nm, a = k N A r A is found to be 2,18, The p H dependence of the fluorescence intensity at 452 nm is shown in Figure 2. At very lour pH (for the present purposes pH 51) all terms not containing [ H 9 0 t ] become negligible by comparison with those that do giving rise to the pH independent fluorescence observed below pH 1for the neutral species and zvvitterion. In this circurnstance eq 13 can be reduced and irearranged to -=:
c=-
(15)
Fo = A!NO($N/$NO)O t Fz0($z/$zo)o (19) where Fo, FNO, and Fz0 are wavelength dependent but ($N/$N')o and ($~/qbzO)~are not. Combination of eq 18 and 19 and subsequent rearrangement gives
which, at wavelengths where FNo is negligible, reduces to
In order to evaluate ($N/$N')~ the fluorescence spectrum in the 360-420-nrn region was taken a t different pH (from p H 11 to Ho-- 1) and at much greater amplifier gain than represented in Figure 1. It was found that a t 380 nm the fluorescence intensity of the neutral molecule could be monitored with good precision and with virtually no
450
S. G. Schulman and L. S. Rosenberg
The Journal of Physical Chemistry, Vol. 83, No. 4, 1979
TABLE I: Kinetic Parameters of Excited-State Proton Exchange in 7-Hydroxy-4-methylcoumarin aa
2.18
i-
TN,
0.02
b
nS
1.1
kNA, S-' 2.0 x
lo9
b,C M - '
T A ,d
ns
15.0 t 0.5
163+ 6
kAN,
M-'
S-'
1.1i. 0.1 x 10"
r Z , f ns
Ce
107
t
4
23.3 i: 1.0
Estimated from the relative absorption and fluorescence spectral intensities of the neutral species and a a = kNATN. anion and the experimentally determined lifetime of the excited anion. b = kANTA. Measured directly at pH 11.0. e c = ~ A Z T A / +( ~h Z A r Z ) . Calculated from the ratio of the decay time of 10.8 * 0.4 ns measured at pW 1.0 t o ( @ Z / @ Z ' )= ~ 0.465 t 0.008. TABLE 11: Comparison of ~ K N A=*-log k N A / k A N with PKNA*(FC) Calculated from the Forster Cycle Employing the Ground State Dissociation Constant PKNA and t h e Average of the LongWavelength Absorption Maxima (Za) and Fluorescence Maxima (Vf) of the Neutral Molecule and Anion -
neutral molecule anion
k~ A l k A N 1.8 x l o - '
PKNA* 0.74
ua(cm-' x Vf(crn-' x 10-4) 3.11 2.75
overlap with the emissions of the anionic and zwitterionic species. In this case $N/$No at any pH could be estimated as F/FNo at 380 nm provided that F N o could be determined. Keeping in mind that a t pH 4-6.5
a t 380 nm. and ($N/$No)o
PKNA 7.78 t 0.01
= FO/FNO
(24)
where Fo here is the fluorescence intensity at 380 nm and a t pH 51. Combination of eq 15, 21, and 22, with ($N/ $No)o = 0.535 and Foand F$ at 452 nm as 0.0980 and 0.211, respectively, permitted the evaluation of b / c as 1.52 which was then used in eq 16, employing ten different values of [H30+]and F taken from the region pH 1 to 4 in Figure 2, to calculate the values of b and c presented in Table I. In order to explicitly obtain the rate constants for proton exchange from a, b , and c it was necessary to determine TA, rz, and rN. The determination of TA by pulsed source fluorometry was a simple matter, since the fluorescence decay time measured at pH >10 is 7A. However, the fluorescence decay time of the zwitterion at low pH does not correspond to $z/$zo = 1and is, therefore, not equal to rz. Moreover, not only does the fluorescence of the neutral molecule at OW pH not correspond to $N/$No = 1but also its intensity is so low throughout the pH region studied that it could not be detected on the pulsed-source instrumentation employed here. Since the lifetime of the lowest excited singlet state of the zwitterion could be measured at pH I 1and since the lifetime is proportional to the absolute quantum yield of fluorescence, T~ could be well estimated simply by dividing the lifetime measured at pH 51 by ($z/$zo)o where ($z/ &o)o could be calculated from eq 18 and 24. Knowledge of the absorption and emission characteristics of 7hydroxy-4-methylcoumarin a t high and low pH also permitted a somewhat cruder estimate of TN. The absolute quantum yield of fluorescence of the anion is related to the rate constant for fluorescence (kd) by $A' = k f ' 7 ~ . Similarly, QNo = kfrN, where kf is the rate constant for fluorescence of the neutral molecule. We then have 7 N = ((pNo/4Ao)(k{/kf)7A.Since emission was excited at the isosbestic point at 335 nm, $No/$Ao = F N o / F A o where FNO and FAoare measured at the respective emission maxima of the neutral species (398 nm) and of the anion (452 nm). The ratio k j / h f can be approximated for molecules such as 7-hydroxy-4-methylcoumarin which are not capable of
PKNA*(FC) 0.9 t 0.4
2.51 2.21
dramatic conformational changes subsequent to excitation by PA2tAAPA1iz/PN2~Na8N1'2,11 where V A ~and PN' are the squares of the wavenumbers and t A and t N the molar absorptivities, at the band maxima, and &jA1I2and AiiN1i2 are the bandwidths (in wavenumbers) at half-maximum intensity, of the longest wavelength absorption bands of the anion and neutral molecule, respectively. These data, as well as the values of 7A, 72, and TN and the rate constants for excited state proton exchange are presented in Table I. The dissociation constant pKNA* corresponding to excited-state equilibrium between N* and A* and calculated from the ratio kNA/kANcompares well with the value of pKNA* estimated from the Forster cyclelo employing the value of PKNA determined spectrophotometrically and the averages of the wavenumbers of the long wavelength absorption and fluorescence maxima of each species as the "pure-electronic transition" wavenumbers of neutral molecule and anion (Table 11). Unfortunately, the ratio C = kAZTA/ (1 kZArz) could not be solved for kAZ and kZAfrom the titration data and the lifetimes of A* and Z* alone. However, it is possible to estimate a range for the value of kAZwhose lower limit is the value calculated for the circumstance that no dissociation of the zwitterion occurs measurably, Le., kZAq
