Rate of intramolecular electronic energy transfer in coumarin bichromophoric molecules. An investigation by multifrequency phase-modulation fluorometry

Abstract Dynamics of intramolecular electronic energy transfer in bichromophoric molecules, consisting of two coumarins linked by a variable number of methylene groups, is investigated by multifrequency phase-modulation fluorometry. From observation of the acceptor delayed emission, information on the rate of transfer can be obtained.

(1) Assuming that kT is not time dependent (Stern-Volmer kinetics), the solutions of this system are the impulse response functions [ 111 In phase fluorometry experiments, the exciting light is sinusoidally modulated and the harmonic responses that are observed, are the Fourier transforms of the rmpulse responses_ The quantitres that can be measured are #, the phase shift OF emission with respect to excrtation, and B.f, the modulation ratio (ac/dc ratio) [ 121 where S and G are the sine and cosme transforms of the impulse response 1(t): S = r J(f) sin(wr) df/ { 1(r) dt, (12) 0 0 G = i I(r) cos(wt) dt/ J I(r) dr, (13) 0 0 w is the angular frequency of the exciting light.

Calculation of @
Let US assume first that we can find an exciting wavelength XI at which only the donor absorbs ( [Aflu = 0 in eq (9)) Eqs. ( 4) can be now written rn the following form: wu Furthermore, at a higher exciting wavelength 12 at which only the acceptor absorbs, we have

119)
Denoting by Gx and & the phase shifts correspondmg to eqs ( 18) and ( 19) respectively, it is of interest to calculate tan(@A -#i)_ This calculation can be done by means of eqs.( 12) and ( 13 Therefore, equivalent information is obtained from observation of the donor and the acceptor provided that the phase of reference is appropriately chosen. In practice, there is no wavelength at which the donor can be escited with negligible absorption of the acceptor.When both donor and acceptor absorb ( [A*lo # 0 in eq_ ( 9)). the same procedure of calculation can be used and leads to.A = tar@_& -0:)

It is now worth examining what kid of mformatron can be drawn from the measurement of the modulation ratio.
Using eq (11) together with eqs.( 16) and ( 17  kT( 10 The agreement between steady-state results and time-resolved results indicates that the kinetics are nmple; the small deviations nt low frequencies are more likely accounted for by experimental error than by complex kinetics (the expenment is in fact more difficult to perfonn at the lowest frequencies)_ Scveral phenomena, such as distribution of interchromo-phoric distance, intramolecular motions, etc., could lead to complex kinetics but the effects are expected to be small in the present case since the transfer efficiency is high a molecular chain or frame is still receiving considerable attention because of its unplications tn numero~ fields: photophysi~al processes, biologrcal systems, dye lasers.wavelength shifters, etc.The reader is referred to the recent review by Speiser [ 1]-In a previous paper [2], we have reported a very efficient intramolecular energy transfer in a bichromophoric molecule consrsting of two coumarin dyes linked by a short aliphatic chain.Application to frequency conversion of light was suggested.This new type of bichromophore whose formula is investigated with special attention to the effects of various parameters (temperature, vJscosity, nature of the solvent, number of methylene groups separating the donor and acceptor moreties) on the efficiency of energy trar sfer.The results are being reported separately [3] _ An essential feature of energy transfer is the rate of transfer_ In most studies, rhis rate is calculated from measurements of the transfer efficiency and the lifetime of the donor in the absence of transfer_ Nevertheless, dynamrcs of energy transfer is best analyzed by using time-dependent techniques.especrally when transfer cannot be characterized by a single rate constant.Pulse fluorometry has been currently used for this purpose btrt never phase fluorometry However, thanks to recent improvements based on multifrequency modulation of light and cross-correlation detection [d] , phase fluorometry can provide information equivalent to that obtained with pulse fluorometry 15,6]_ In the present paper, we report the first investigatton of energy-transfer dynamics by phase fluorometry.Furthermore, in most previous studres, attention 0 009-2614/85/g 03.30 0 Elsevier Science Publishers B.V. (North-Holland physics Publishing Division) was paid only to changes in the fluorescence decay of the donor However, when very efficient energy transfer occurs and/or when the quantum yield of the donor is very low, the donor fluorescence is so weak that detection is difficult because of stray h&t.Nevcrtheless, Information on transfer rate is contained in time-dependent acceptor fluorescence via donor ex-citation_ For instance, picosecond pulse fluorometry can be usad for the dctermmation of the rise of the acceptor fluorescence following pulse excitation of the donor [7] _ Alternately, as shown in this paper, phase fluoromctry experiments are based on the measurement of the phase shift between the acceptor fluorescence in the presence of transfer with respect to the acceptor fluorescence in the absence of transfer at various frequencies_ This kind of experiment is reported in the present work using the above-depicted bichromophoric molecules.3_ Experimental The synthesis of the coumarin bichromophoric molecules will be reported elsewhere [S] _ The experiments were carried out in propylene glycol (Aldrich, gold label) at 2SDC.Very dilute solutions (5 X ICtm6 M) were used to prevent spurious effects such as intermolecular energy transfer or reabsorption_ The absorption and emission spectra are given elsewhere [3] _ Lifetime measurements were performed with the multlfrequency phase fluorometer described by Gratton and Limkeman [4] _ The light source used in the experiments reported in this work was an HeCd laser From Liconix Inc., equipped with W optics for 325 nm.The intensity of the laser was sinusoidally modulated using an elcctro-optical modulator (model LMA 1 from lasermetrics Inc_).With this arrangement, contmuously variable modulation frequencies can be obtained from 1 to 160 MHz_ The detection system is based on the cross-correlation techmque introduced by Spencer and Weber [9] _ The photomultipliers employed were from Hamamatsu Inc., model R 928.These tubes show neghgible color effect in the wavelength range used in the present experiments [4] _ Data acquisition was performed using an ISS-ADC interface from ISS Inc. and the lifetime acquisition softward provided by ISS.Phase and modulation 218 data were analyzed for a single and double exponential decay using the KS lifetime analysis software_ Thus analysis is based on a non-linear least-squares method described by Brandt [I 0] _ The equations used and the attainable resolving power have been reported elsewhere [5,6] _ Error analysis is obtained from the computation of the diagonal terms of the covarlance matrix of errors as reported by Brandt [101-3.Theory Jn a first approach, we consider a simple kinetic scheme involving a single rate constant kT for transfer from donor to acceptor.If the emission spectrum of the acceptor does not overlap the absorption spectrum of the donor, there is no back transfer-D-A k, and k, are the emission rate constants of the donor and the acceptor, respectively they are equal to the reciprocal of the lifetimes $ and 7:, respectively, in the absence of transfer_ Following an infinitely short pulse of light, the concentrations in excited donor and acceptor obey the following system of differential cquatlons: d [D'] /dr = -(kD + kT)[D*],

[
At the excitation wavelength, both donor and acceptor absorb and their initial concentrations are [D*10 -and [A*lO, respectively.
It is remarkable that this expression is identical to the tangent of the phase shift of the donor in the presence transfer:tan tpI, = w/(kD + kT)_ (21) lo/[D*lo)[(kT+kD)2+w21/kT' -(22) Once kD and the ratio [~*]o/[D*]o are evaluated.the measurement of A provides a straightforward way to determine k,.
used to calculate & by means of eq.(31).At frequencies higher than 10 MHz, the calculation was performed by using the actual value of (T~)~ at each frequency instead of using the average value, in order to minimize the effect of slight systematic deviations from the average value The values of A = tar@A -&) are reported in fig. 1 Apart from small deviations at low frequencies, the variations of A versus frequency are approxlmately linear, as expected from eq. (28)_ The calculation of the average slopes leads to the values of the rate constant which are reported in table 1_ These values are in the range predicted by Fbrster; dipoledipole interaction is in fact highly probable as a consequence of the large spectral overlap between donor emission and acceptor absorption [3] _ The transfer rate constants are slightly sensitive to the number of methylene groups.This fact is in agreement with the small changes in transfer efficiencies determined by steadystate methods (whereas larger changes were observed when dimethylformamide is used as a solvent) [3] _ The consistency between dynamic and steady-state methods is further confirmed by the values of transfer efficiencies qT calculated from the rate constants (table 1) by means of the following relation: