J . Phys. Chem. 1989, 93, 6069-6073
C. Rotational Contours. Analysis of the rotational fine structure in electronic transitions furnishes added symmetry information of the excited-state vibrations.” As mentioned earlier, the rotational contours of all three origin bands are extremely sharp with little intensity in the wings, indicative of a strong Q branch. An analysis of the vibrational peak contours requires a more detailed examination of the rotational constants for each structure (see Table XI1 in ref 14). While T H P has a reflection plane, it has no rotational symmetry. Its rotational contours for various vibrational modes are therefore somewhat mixed between A-, B-, and C-type bands. The maximum inertial axis (I,) for T H P lies perpendicular to the ring plane while the minimum axis (Z,) lies perpendicular to I , along the reflection plane. and 1 , (174.3) have In dioxane-hs, I , (168.5 g cm2 X similar values while I, (304.3: perpendicular to the ring plane) is significantly greater.14 The C, axis lies along I,. For dioxane-ds, the two lowest axes of inertia are also approximately equal and substantially less than the third axis (Io = 200.9, Ib = 218.3, and I, = 357.0), but the C, rotational axis now lies along I,. That is, the increased mass of the D atoms has increased I, from 168.5 to 218.3 while the original Ib = 174.3 has increased to 200.9. This switch in the two lowest moments of inertia appears to account for the differences in peak contours between the de and hs spectra. For example, vibrations along the axis containing both ring oxygens would be predominantly B-type in dioxane-hs and A-type in dioxane-ds. The symmetric C-0-C stretch lies approximately along this axis which changes from Ib to I, in the two isotopes. Although the contours are expected to be somewhat mixed between A- and B-type bands due to rotational constants of nearly equal magnitude, the presence of a Q branch in the A-type band of the hs spectrum could enhance this peak‘s intensity over the B-type band in the ds spectrum. If this were true, then the 732-cm-’ peak in the h8 structure would appear more intense than the 672-cm-’ band in dioxane-d8 as is observed. D. Comparison to Rydberg Spectra of Cyclic Ketones. In both the ether and ketone ring systems, the lone pair orbitals centered mainly on oxygen (but with significant contributions from the carbon atoms C,-C3) represent the highest occupied MO. The Hartree-Fock calculations also show that in each case the lowest Rydberg level is predominantly of 3s character. Why then does (17) Ueda, T.; Shimanouchi, T. J . Mol. Specrrosc. 1968, 28, 350.
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the two-photon polarization ratio indicate that the n 3s transition in ethers (SI < 0.2) is of opposite symmetry compared to 3s in ketones for which the SI values are 3 / 2 ? 1 The the n HOMO of the oxygen in the sp2 carbonyl group is located within the plane of the acetone chromophore, while the symmetry of this orbital (in point group C,) is a”. This is different from the situation in T H P and dioxane (sp3 hybridization) where the nonbonding orbitals are located above and below the plane of the ether chromophore (a’ symmetry). The excited Rydberg states of both cyclic ethers and ketones are found to have predominant s character and consequently a’ symmetry. This transition in ketones is therefore a’’ a’ whereas the ether transitions are a’ a’. In summary, the difference in the transition symmetry between the ketones and ethers is a result of the different orientation of the lone pair orbitals in the ground electronic state.
-
-
-
V. Conclusions The lowest electronic transitions of THP, dioxane-hs, and dioxane-ds cooled in a free jet expansion have been examined by 2 1 REMPI spectroscopy. The resonant two-photon intermediate state of T H P has been assigned as the 3s Rydberg level in agreement with previous studies, while the equivalent transition in dioxane has been observed for the first time. This new state has likewise been attributed to the 3s Rydberg level and is accessible only through two-photon absorptions. Polarization ratio measurements, as well as ab initio calculations, indicate that the symmetry of this transition is A’ A’ for T H P and A, A, for 1,4-dioxane. By use of hot and sequence band intervals, several of the low-frequency ring vibrations in the excited-state spectra have been assigned. It has been proposed that the relaxation of the C-0-C u bonds is the major consequence of electronic excitation.
+
-
-
Acknowledgment. We are grateful to GLAXO for the support of T.J.C. In addition, we thank the National Science Foundation through Grant CHE-8706766 for the purchase of chemicals, solvents, and laser dyes. The ab initio calculations were preformed on the National Cancer Center (NCI) CRAY XMP; access to NCI through the NIEHS, RTP computing center is gratefully acknowledged. Registry No. THP, 142-68-7;D, 7782-39-0; 1,4-dioxane,123-91-1; 1,4-dioxane-d8,17647-74-4;40Ar,7440-37-1.
Perrin Revisited: Parametric Theory of the Motional Depolarization of Fluorescence Gregorio Weber Department of Biochemistry, School of Chemical Sciences, University of Illinois, Urbana, Illinois 61801 (Received: December 27, 1988)
The usual derivations of the depolarization of fluorescence under continuous illumination treat it as a problem of rotational diffusion following the creation of a gradient of oscillator orientations by photoselection. An alternative formulation is presented in which the depolarization results from exchanges between a fixed number of oscillator orientations in thermodynamic equilibrium. In this formulation the parameters that determine the observed stationary polarization are the relative populations of the allowed orientations, the loss of polarization owing to the orientation exchanges, and the rates of reorientation during the fluorescence lifetime. The standard enthalpy and volume changes in the orientational equilibria determine the changes in polarization with temperature and pressure. This treatment predicts temperature dependencies of the polarization like those observed in the local motions of tyrosines and tryptophans in peptides and proteins and of the porphyrin in its specific complexes with apomyoglobin and apohemoglobin.
The description of the depolarization of the fluorescence of organic molecules by molecular rotations begins with Perrinls2 whose theories envisioned only the depolarization owing to unrestricted motion of rigid particles. The application of his ideas ( I ) Perrin, F. J . Phys. 1926, 7, 390-401. (2) Perrin, F. J . Phys. Radium 1936, VII.7, 1-11.
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and methodology to the fluorescence of complex systems, particularly those of biological origin, has demanded a number of extensions in order to accommodate them to the phenomena observed in macromolecule^,^*^ polymer^,^*^ micelles,’ lipid bi( 3 ) Weber, G. Biochem. J . 1952, 51, 145-154.
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The Journal of Physical Chemistry, Vol. 93, No. 16, 1989
Weber a. is the limiting anisotropy due to emission without reorientation and aI2= azl is the exchange anisotropy that would be observed if only the emissions after change of direction were observed. Similarly 02
=
aow22
+ Q2lW21
(3)
The observed anisotropy, ( a ) is the weighted sum of a l and a2: (a) =
Figure 1. Schematic representation of the exchanging oscillator directions in a particle that is effectively motionless during the fluorescence lifetime.
layers,*q9biological membranes,I0 etc. The intention of this note is to draw connections between these various cases and the original treatment of Perrin by developing a theory of the depolarization of fluorescence emitted by molecules that occupy a finite number of positions. Our point of departure is the remark” that in every case the depolarization results from the exchange of orientations between excited and unexcited molecules in a molecular population in thermodynamic equilibrium. This process resembles in all respects the exchange between isotopically and nonisotopically labeled components in chemical equilibrium. It is convenient to start by a phenomenological analysis of the simplest possible case, one in which the depolarization is determined by potential differences between oscillators that can only exist in one of two different orientations. To this purpose consider irregular objects, as macromolecules of some size or microscopic pieces of membrane suspended in a transparent medium. Let the suspended particles that carry the oscillators be large enough so that we can neglect completely their motions during the fluorescence lifetime; then any depolarization must be the result of changes in orientation of the excited oscillators that take place within each particle. Let the two oscillators along the permitted directions, at an arbitrary angle to each other, be distinguished by the subscripts 1 and 2 (Figure 1). Because of the random orientation of the carrying particles with respect to the direction of polarization of the exciting beam, the fractionsf, andf2 of the total excitation corresponding to the respective oscillators are proportional to their numbers in the ground state. These are determined by the equilibrium constant K , : Kl
= k,2/k2,
=f2/f,
a, =
sow,, + al2wl2
(5)
-
m
w,, = cwIzjw21j-I(I- w2,) j=O
or Wl2
=
Wl2(1
- w21)/(1 - WI2W21)
(6)
Equation 6 shows that W,, approaches w12when the probability of reversal is negligible; otherwise it remains smaller than w12. If w12and w2, are close to unity W12approaches w12is related to the probability of reorientation during the fluorescence lifetime T by the equation wl2
= k127/(1
+ k127);
w21
=
...
(7)
with k2, and k I 2defined by eq 1 . From (6) and (7) we obtain w12=
k 1 2 ~ / ( 1+
w21= k217/(1
k 1 2+ ~ k2i~)
+ k 1 2 +~ k 2 1 ~ )
(8)
and flWI2
= f2W2I
(9)
From eq 4, 8, and 9 it follows that a0
= ( a ) = (a0 - al2)2fikl27/(1
+ k127 + k21T)
(10)
which may be put in the convenient form ((0)-
Gottlieb, Y. Y.; Wahl, Ph. J . Chim. Phys. 1956, 849-856. Wahl, Ph. J . Polym. Sci. 1958, 29, 357-361. Valeur, B.; Monnerie, L. J . Polym. Sci. 1976, 14, 11-27. Shinitzky, M.; Dianoux, A.-C.;Gittler, C.; Weber, G . Biochemisfry 1971, IO, 2106-2113. (8) Shinitzky, M.; Barenholz, Y. J. Biol. Chem. 1974, 249, 2653-2657. (9) Kawato, S.; Kinosita, K.; Ikegami, A . Biochemistry 1977, 16, 23 19-2324. (IO) Zannoni, C. Mol. Phys. 1981, 42, 1303-1320. (1 1) Weber, G . In Fluorescence and Phosphorescence Analysis;Hercules, D. M., Ed.; Interscience: New York, 1966; Chapter 8, p 233. ‘The difference in orientation applies only to the excited molecules, not to the molecular population as a whole that remains randomly oriented at all times, the excited molecules exchanging orientations with the unexcited ones. The process of diffusion may be said to be maintained by the entropy of mixing of the two types of molecules rather than by the existence of a true gradient in the orientations of the whole molecular population.” (4) (5) (6) (7)
(4)
applies also to oscillators in the excited state. The difference between the probabilities WI2appearing in eq 2 and w12in eq 5 should be carefully noted: W12 is the ~ i s i b l e probability of reorientation while w12is the a priori probability of reorientation. WI2is generally smaller than w I z because reversals of orientation during the fluorescence lifetime do not result in depolarization of the emission. Invisible and visible probabilities of reorientation are related as follows: The probability of j changes of orientation 1 2 followed by j - 1 reversals and emission from orientation 2 is w I ~ w 2 1 ~ ‘-1 wZ1). (1 The average probability of visible reorientation, W12,is thus
(2)
where W,, (0 < W < 1) is the probability that the emission will take place from the originally excited oscillator and W12 the complementary probability, that of emission from the 2-oriented oscillator following reorientation during the fluorescence lifetime.
=h W 2 1
fIWl2
(1)
In eq 1 k 1 2is the number of transitions per unit time per molecule from the position of the first subscript to that of the second and k2, the number of transitions in the opposite direction. If the excitation falls exclusively upon the 1-oriented oscillators the observed anisotropy is
ao(fiw11 +f2W22) + al2Cflwl2 +f2W2I)
Equation 4 indicates that the depolarization results from the magnitude and fractional weight of the exchange anisotropy. The distribution of the excited molecules between the states 1 and 2 will not be altered by the exchanges between them unless the equilibria for excited and unexcited molecules differ from each other. For the time being we disregard this latter possibility and assume that if the a priori probabilities of reciprocal changes in orientation are w I 2 and w21 then the ground-state equilibrium condition
a12)/(ao - a121 = 1 - (2fik127)/[1 + k12(1 + f i / f 2 ) ~ 1
(11) In the fast exchange limit (kI27 >> 1, k 2 l T >> l , f l = f 2 = the right-hand side of (1 1) equals On the other hand when reversals of orientation are virtually absent during the excited-state lifetime ( k l 2 T 1 , k237 >> 1 , and eq 18 takes the limiting form 00
- (a) =
(a0 - al21fH12
+ (aO
- a231fH23
For times much longer than the reorientation times, that is when >> 1, k237 >> 1, the anisotropy difference a. - a(t) tends to a constant value (u,, - ul2)Fl2 (ao- a23)fH23. The plots of Figure 5 show clearly these limiting values of the time-dependent anisotropy which can serve as a practically important restriction in the fitting of eq 18 or 21 to the experimental data of the stationary fluorescence anisotropy. The phase and modulation of the fluorescence emitted upon harmonic excitation are easily obtained from the sine and cosine Fourier transforms of the impulse response described by eq 24.13 kl27
(21)
In eq 2lfHIZ = 2/(1/fi+ I / f i ) a n d f H 2 3 = 2 / ( 1 / f 2 + l / f 3 ) “fe respectively the harmonic means of the fractional populations in each separate equilibrium. The distribution of orientations at emission directly reflects then the ground-state equilibria. In the original diffusion theory the data of the stationary fluorescence depolarization contain exclusively kinetic information about the fluorophore, more explicitly about the relative magnitudes of the rates of emission and rotation. Evidently no kinetic information is conveyed by eq 21; Instead it contains information on the thermodynamic parameters that determine the distribution of the exchanging orientations. Equations 18 and 21 allow us to describe the effects of temperature and pressure on the system from the changes in standard enthalpy and volume for the equilibria 1 2 and 2 3. The
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(12) Gratton, E.; Alacala, R. J.; Marriott, G. Eiochem. SOC.Trans. 1986, 14, 835-838.
+
Advantages and Limitations The preceding computational procedure does not offer any interest in the calculation of the free rotations of molecules. Its proper place is in the specification and testing of models of the restricted rotations of fluorophores in heterogeneous media like macromolecules or biological membranes. In these cases we expect that the interaction of the fluorophore with the surroundings will reduce its possible orientations to a small number. Because of the limited precision of the measurements of stationary polarization we restricted consideration to the case of three allowed orientations described by eq 17, although the extension of this equation to the description of depolarization following jumps between a larger number of successive orientations is straightforward. We note that in considering the depolarization involving three different directions we neglected to include in the calculation the case in which excitations of oscillators in the directions 1 and 3 are followed by emissions in the directions 3 and 1, respectively. The resulting visible probabilities WI3 = W12W23 and W31 = W3,W2, give rise to an additional term in eq 17: 2(ao - a3l)f&WlzW23. It can be numerically shown that this term makes a negligible contribution, even if 031 is set equal to zero, and for that reason we did not consider it necessary to include it in (18) and following equations. We also assumed in the derivation of this equation a single fluorescence lifetime 7 , the same for all fluorophore surroundings. The extension to the case of different lifetimes associated to the several orientations is straightforward. A more (13) Weber, G.J . Chem. Phys. 1977, 66, 4081-4091.
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The Journal of Physical Chemistry, Vol. 93, No. 16, 1989
interesting limitation of our formulation concerns the imposed condition of the exact correspondence of the motions of the fluorophore in the ground and excited state. This assumption is less likely to be valid in the case of polar fluorophores with appreciable different electronic distributions in ground and excited states. In this case the rates kij of eq 8 will be those of molecules in the excited state, kij* and will differ from those in the ground state which appear in eq 5. However, if the free energies of ground-state interaction of the fluorophore in the two exchanging orientations are increased or decreased by the same amount upon excitation, that is, if kij*/kij= kji*/kji,eq 5 remains valid with k,* replacing k,. Equation 10 will only require modification to the extent that the free energies of interaction of fluorophore and surroundings in the different orientations are unequally modified by the electronic excitation. Of particular interest is the possibility of estimating the enthalpies or the volume changes associated to the orientational equilibria. We show below that variations in the two enthalpies result in characteristic patterns of the dependence of depolarization upon the temperature. From these patterns it is possible to obtain information on the energetic characteristics of the surroundings of the fluorophore in the macromolecule or membrane. Discontinuous jump models of depolarization have been previously e ~ a m i n e d ' ~but, , ' ~ as in the classical Perrin theory, always in the context of a particular geometry. The present treatment achieves simplicity, at the cost of losing some information, by discarding the geometrical context and treating the exchange anisotropies as adjustable parameters.
Modeling the Experimental Observations of Local Fluorophore Motions in Proteins The local rotations of the natural fluorophores of peptides and proteins (tyrosine and tryptophan) can be examined by employing solvents of viscosity sufficiently high to effectively cancel the overall motion of the polypeptide within the restricted range of temperatures under study.3 The dependence of the viscosity of liquids upon the temperature, n(7'), over a restricted range of temperature, is well described by an expression of the form
In the last equation no is the viscosity at a fixed temperature To and b is the thermal coefficient of the viscosity. From eq 26 and 22 it follows that approximately h = b R p . With the expansion in eq 26 Perrin equation, of the form shown in eq 13, may be written as a o / a - 1 = RTr/Vno exp[b(T- T o ) ]
(27)
where Vis the effective volume of the rotating unit, and in logarithmic form as
Y = In [ a o / a - 11 - In [ R T r / q O U = b(To- T) (28) In almost every case the change of the fluorescence lifetime with temperature is small enough to make unimportant the contribution from the second term in the left. Then, a plot of In [ a o / a- 13 against T - Toyields a straight line with a slope equal to the thermal coefficient of the resistance to the fluorophore rotation.I5 Employing 75-90% glycerol-water mixtures the fluorescence polarization of a number of peptidesI6 and protein^"-'^ has been measured in the range of temperatures of -30 to +30 "C, in which case To is conveniently set at 0 "C. In most of them the plot of (14) Szabo, A. J . Chem. Phys. 1984, 81, 150-167. (15) Weber, G.; Scarlata, S.; Rholam, M. Biochemisrry 1984, 23, 6785-6788. (16) Scarlata, S.; Rholam, M.; Weber, G. Biochemistry 1984, 23, 6789-6792. (17) Rholam, M . ; Scarlata, S.; Weber, G. Biochemisrry 1984, 23, 6793-6796. (18) Royer, C.; Alpert, B. Chem. Phys. Lett. 1987, 134, 454-460. (19) Scarlata, S., to be published.
Weber
-2'40v V
I
-24.0
-16.0
-8.0
0.0
I
E.0
16.0
24.0
I
CELSIUS TEMPERATURE Figure 2. Yplot according to eq 20 with exchange anisotropies q,= 0.35, a,, = 0.30, = 0.05. The orientational equilibria a t 0 OC arefi/fi = 0.25;f2/f3 = 7. The Corresponding enthalpies are AHl2= -22RT0, AH23 = -8RTo. The plots should be compared with those of Figures 1 and 2 of ref 16 and Figures 1 and 2 of ref 17. In Figures 2, 3, and 4 computations have been made by eq 21 rather than (18) to reduce the number of parameters and reach the condition of thermodynamic rather than kinetic significance.
-
-2.19
*
I 4 \
-
z-2.49 4
Y
z -1
-2'Eol/ W
-24
-16
-E
0
E
16
24
CELSIUS TEMPERATURE Figure 3. Y plot with the same parameters of Figure 2 except AHl, = -20RT0, AH,, = -12RT0,f,/f2(0 "C) = o.3,f2/f,(o"C) = 28. T o be compared with the first panel in Figure 4 of ref 18.
Yvs t ("C) shows two distinct slopes joined by an abrupt change at a temperature Tc characteristic of the protein or peptide. This was found to vary between -20 and +10 O C and from the polarizations involved (Soleillet equation20) the abrupt change is shown to correspond to rotational angles of 10-30' of arc. These findings already suggest a model of three oscillator directions with a I 2= 0 . 8 5 (corresponding ~~ to an 18" rotation) and a23 = ao/3 to 0. Figure 2 shows one such Y plot (In ( a o / ( a )- 1) vs temperature ("C)) which characteristically shows an abrupt change in the slope in the span of a few degrees Celcius, just as the peptides16and proteins" studied by this method. A more complex pattern of the fluorescence polarization from protoporphyrin in complex with apomyoglobin (desFCMb),has been observed by Royer and Alpert:I6 the polarization remains almost constant over a considerable temperature range between two regions of decreasing polarization at lower and higher temperatures (Figure 3). Figures 2 and 3 show that both characteristic Y plots can be reproduced when eq 21 rather than (18) is used in the computations. Equation 21 requires values of k, large enough to make Wi, approach f H i j , a case in which the thermal profile becomes independent of the rate of orientation exchange and reflects directly the equilibrium distribution of orientations. In these cases the thermodynamic information refers to that of the immediate protein surroundings. Figure 4 is the Y plot for a case that differs from that of Figure 3 only in the orientational distribution at 0 "C. It shows that thermal repolarization is possible when temperature (20) Soleilett, P. Ann. Phys. 1929, 12, 23-97.
J. Phys. Chem. 1989. 93. 6073-6079
-1.30
-
-
c-(
I
4
\
-a
s-l.ElI
I
/
z
1
-2’311/ V
I
-24
-16
-E
0
E
16
24
I
CELSIUS TEMPERATURE Figure 4. Y plot showing thermal repolarization. Same parameters as “C) = 0.2. those of Figure 3 exceptfi/f2(0 “C) = l,fi/h(O
I
I
-3.0
-2.0
at a wavelength for which a. = 0.2’ The plots of Figure 5 explain the origin of the thermal dependence of the long-time constant polarization observed in studies of the decay in real time of the fluorescence polarization of probes included in membra ne^.^ Besides they indicate that observation of the decay of the anisotropy corresponding to the stationary polarization shown in Figure 2 demands a time resolution of 1/ lo0 of the fluorescence lifetime, which in protein fluorophores roughly corresponds to 30 ps. Access to these short decay times is now becoming possible.22
Continuous and Discontinuous Reorientations The classical diffusion theory first used by Perrin to describe the depolarization by molecular rotations implicitly assumes the existence of an “infinite” number of possible oscillator orientations. As the time allowed to the diffusion process lengthens the probability that an oscillator will have at emission the orientation that it had at excitation continuously decreases and becomes vanishingly small for a sufficiently long fluorescent lifetime. On the other hand if the number of possible orientations is finite the probability of finding the oscillator in the orientation that it had at excitation cannot fall below a certain value however lively the motions or however long the time allowed for the diffusion. There is little doubt that the latter is the case in media which introduce appreciable differences in the probability of orientation of the fluorophore with respect to its surroundings, and this may even be the case for fluorophores dissolved in some molecular liquids. By a study of depolarization of the fluorescence at sufficiently high temperatures it should be possible to determine whether the diffusion theory or the parametric approach applies best in this instance.
I
I
-1.0
LOG (TIME/LIFETIME) Figure 5. Plots of the anisotropy against the decimal logarithm of the time, in units of the fluorescence lifetime, computed from eq 24. Anisotropy and thermodynamic parameters are those of Figure 2, with the addition of kl27 = k237 = 10 and thermal coefficients 6 of the 1 2 and 2 3 transitions, respectively O.O7/OC and O.O3/OC. The three curves are for -20, 0, and 20 O C .
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6073
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favors the growth of one fractional orientation at the expense of the other two. Here the repolarization has a very different origin than in the one case in which this phenomenon has this far been observed: the motions from asymmetric free rotors on excitation
Acknowledgment. The present work has been supported by the USPH through grant GM-11223 to the author. The author thanks Dr. Suzanne Scarlata for the many discussions that gave rise to the present treatment of motional depolarization of fluorescence. (21) Weber, G. In Time Resolved Fluorescence Spectroscopy in Biochemistry and Biology; Cundall, R. B., Dale, R. E., Eds.; Plenum: London, 1983; pp 1-19. (22) Lackowicz, J. R. In Modern Physical Methods in Biochemistry; Neuberger, A,, Van Deenen, L. L. M., Eds.; Elsevier: New York, 1988; Part B, pp 1-26.
Calculation of the Distribution of Donor-Acceptor Distances in Flexible Bichromophorlc Molecules. Application to Intramolecular Transfer of Excitation Energy Bernard Valeur,* Jacques Mugnier, Jacques Pouget, Jean Bourson, and Fransoise Santi? Laboratoire de Chimie CZnZralet and Laboratoire d’lnformatique, Conservatoire National des Arts et MZtiers, 292 rue Saint- Martin, 75003 Paris, France (Received: December 28, 1988) The distribution of center-to-center distances between chromophores linked to the ends of a short flexible chain can be calculated by using the rotational isomer theory together with the statistical weights of the conformations of short sequences of three and four bonds. The distance distributions are calculated for five coumarin bichromophoric molecules in which the spacer is a short polymethylene chain with a variable number of methylene groups, or a chain containing C-C and C-0 bonds. Good agreement between the predicted and experimental values of the efficiency of excitation energy transfer supports the validity of the calculations.
Introduction Intramolecular excited-state processes in bichromophoric molecules1 form a subject of considerable interest because of their
’Unite Laboratoire d’lnformatique. associee au CNRS no. 1103 “Physicc-chimie organique appliquk”. f
0022-3654/89/2093-6073$01.50/0
implications in numerous fields: photophysics, photochemistry, biOlogY, polymers, ... For the Processes that require close approach of the two chromophores (formation of excimers Or exciPlexes, photochemical reactions) a certain flexibility of the spacer is (1) De Schryver, F. C.; Boens, N.; Put, J. Adu. Phorochem. 1977, IO, 359.
0 1989 American Chemical Society
