94
J. Phys. Chem. 1980, 84, 94-98
Circularly Polarized Luminescence from a Model Molecular System James P. Riehl Department of Chemistry, University of Missouri-St.
Louis, St. Louis, Missouri 63121 (Received July 25, 1979)
Publication costs assisted by the Petroleum Research Fund and the Research Corporation
Expressions relating the differential circularly polarized emission intensity to conformation are developed for a model molecular system. The model is composed of two isolated chromophores. The emitting chromophore is populated through radiationless energy transfer from a donor chromophore, and this same chromophore is the source of optical activity through a dynamic coupling mechanism. Specific results are presented for the special case of rigid molecules whose donor and acceptor dipoles are situated in parallel planes.
Introduction Circularly polarized luminescence (CPL) is rapidly developing into an extremely useful experimental tool for many chemical and biochemical studies. Experimental and theoretical aspects of CPL spectroscopy have been discussed in detail in two recent reviews.‘P2 In CPL spectroscopy one measures the differential spontaneous emission of left minus right circularly polarized radiation by chiral luminescent systems. This technique is then the emission analog of circular dichroism (CD), and reflects the chirality of molecular excited (luminescent) states in the same way that CD probes the chirality of molecular ground states. Theoretical interest in these chiroptical methods is primarily concerned with the development of useful spectra-structure relationships. In CD such efforts have led, for example, to so-called “sector rules”, which have been fairly successful in predicting the absolute sign of the observed spectrum for certain classes of optically active molecules. Of primary concern in these studies is the origin of optical activity in the particular system under study, and the evaluation of the appropriate transition matrix elements in order to relate specific structural parameters to the observed CD s p e ~ t r u m . ~ The first detailed theoretical treatment of CPL was undertaken by Snir and S ~ h e l l m a n .In ~ their model the source of optical activity was the “correlative” coupling of two transition dipoles. Their model was restrictive in that they assumed that the absorption and emission transition dipoles were parallel. They did, however, consider the effects of photoselection and orientational relaxation on the CPL observables. Steinberg and Ehrenberg5 extended these results to include polarized exciting radiation and variable absorption and emission transition moment directions. Riehl and Richardson have subsequently reported a general theory of CPL from molecular ~ystems.~J Experimental research involving CPL spectroscopy covers a broad area of chemistry limited only by the requirements that the system under study be optically active and luminescent. Of particular interest in our research group are the current and potential uses of the technique as a molecular structural probe. I t has been shown, for example, that CPL observed from certain biological macromolecules (e.g., proteins) may be interpreted in terms of particular structural parameters associated with the chiral environmental of the luminescent chromophore.6 A number of interesting results have been reported for comparative CD vs. CPL s t ~ d i e s .Only ~ in a relatively few cases, however, has the interpretation of the CPL spectrum in terms of structure or structural changes been very 0022-3654/80/2084-0094$0 1.OO/O
specific. More often, the results lead to important but qualitative information. Brittain, Richardson, and Martin,1° for example, have discussed the intensity of CPL observed from Tb3+- (substituted for Ca2+)protein systems in terms of exterior vs. interior binding sites. They also concluded that, since the sign of the observed CPL varied from protein to protein, the absolute configuration at asymmetric a carbons is probably less important than the spatial arrangement of aromatic groups. The Tb3+ ions in these systems were excited through radiationless energy transfer from these aromatic residues. It is clear from the experimental results reported to date that, in order to fully exploit the technique of CPL spectroscopy, appropriate theoretical models must be developed and analyzed. Specifically, all of the dynamics, molecular and electronic, beginning with the absorption process and ending with the emission must be considered. Molecular and intramolecular reorientation, vibrational and electronic relaxation, and the geometric dependence of energy transfer, as well as the optical activity mechanisms, must be described and related to observables in order to be able to ascertain or predict the effect of these phenomena on the measured emission intensities. In the work reported here, we examine theoretically a specific model system which we believe to be of some relevance in real systems. Theory and Model We consider in this study the model system depicted schematically in Figure 1. The “molecule” of interest is assumed to have two localized chromophores separated by a distance r, and situated in a particular conformation denoted by Bc. More specifically we choose a system in which an initial absorption is assumed to be localized on chromophore D (donor), and luminescence is observed from chromophore A (acceptor). The absorption is a transition from the ground state of the donor, D , to an intermediate excited state, De. The molecule is t i e n allowed to (1) vibrationally relax to another excited state, Der,(2) undergo radiationless transfer to the acceptor state, A,, and (3) luminesce to state A,. Other possible decay modes are also illustrated in this figure. For molecules with orientation, Q, with respect to a fixed laboratory coordinate system, the differential circularly polarized luminescence intensity is given by the following equation = h~lf~p~(o)N,(Q,B,,t)aw(s2,eot) (1)
u(u,oc,Q,t) Ileft - Iright
where fcpL(w) is a normalized line shape function centered at ul; N,(Q,B,,t) denotes the number of molecules (popu0 1980 American Chemical Society
The Journal of Physical Chemistry, Vol. 84, No. 7, 7980 95
Circularly Polarized Luminescence from Molecules DONOR
ACCEPTOR
De '
Yet
f
ABSORPTION Flgure 2. (a) Dipole-dipole energy transfer model. GA denotes the transition dipole of the acceptor, &,that of the donor. fl is the distance between the chromophores. (b) Conformation angles (eo) for special case of jiD and ,?i perpendicular A to ?. (see text). Figure 1. Energy level diagram for a particular model system showing absorption, emission, and various radiationlessprocesses. The emitting (acceptor) chromophore is excited through radlationlessenergy transfer ( k m ) from the aibsorbing chromophore.
minescence and quenching from donor state De!; TD is the lifetime of state De/ in the presence of the acceptor
lation) in the emitting state; and A W(O,d,,t)is the quantum mechanical differential transition rate. The specific dependence of AI, N,,, and AW on conformation (ec), time (t),and orientation (a)has been included in this equation. In order to relate eq 1to an experimental observable, we must integrate this equation over the appropriate spatial distribution of molecules. In addition, we wish to allow for a distribution (possibly weighted) of allowed conformations. These two averaging problems are formally illustrated below
and
TD
rAo
= (kET
+ k4 t
rZb)-l
is the lifetime of the emitting state 7.4' = (k t kq)-'
a m
AI(w) =
J,
iU(w,t) dt
(3)
(8)
In many cases of interest the emitting state is long lived compared to the donor state, Le., .Ao >> TD In this special case eq 6 may be simplified as follows:
= ~(oc)fe~Ne(Q,O)e-t/'A0
where the brackets denote an ensemble spatial average. It has been explicitly assumed in this equation that the line shape and energy of the transition are independent of orientation and conformation. Although the time dependence of iV will also be of some importance, the more common experimental technique is the so-called "steadystate" experiment. The correct expression for the observable in this case is obtained by integrating over long times.
(7)
(10)
In eq 7 we have introduced the transfer efficiency, v(Oc), which depends on conformation through the energy transfer rate constant dec) = ~ E T ( ~ J / ( ~ E T ( O J + k4 + k5) (11) In addition, we have replaced Ne&,0) by fedVe(Q,O), where is the fraction of molecules initially excited to state A, that decay to state Act. This substitution is valid in the limit that the relaxation is rapid, as assumed above. The most commonly proposed mechanism for radiationless energy transfer in the types of systems we wish to model is the Forster dipole-dipole mechanism12 (see Figure 2). The rate constant for this mechanism is written as
fep
~ET(O,) = C(k4 + k5)~2(6'c)r+
( 12)
N,,(Q,e,,t). Assuming that the vibrational relaxation processes (kl, kz,and k3 in Figure 1)are much faster than the other phenomena, we can write the following rate equation
where C is a proportionality constant depending upon spectroscopic details of the donor and acceptor transitions, and K ~ ( O , ) , the orientation factor, is a function of the relative orientation of the donor and acceptor transition dipoles
dNn(fi,Bc,t)/'dt = kET(ec)Ne'(a,t) - (k + kq)Nn(Q,eJ)
~~(0,)= jiA*jiD - 3 ( j i A * i ) ( j i D * i )
(5) where k ~ T ( d ~is) the rate constant for energy transfer and k and k, are, respectively, luminescence and quenching rate constants for state A,,. If, in addition, we assume that conformational changes occur much more slowly than energy transfer, i.e., kET(Oc) is not a function of time, eq 5 may be easily integrated.ll The result is
where k4 and k5 are, respectively, rate constants for lu-
(13)
The transition dipoles, jiA and jiD, are given in our model as follows $A
= (AgliWn)
t
PWgn
f i =~ (DgljilD,f) E fi(D)ge'
(14)
(15)
where ji is the electric dipole moment operator. Substituting for kET (eq 12) into eq 11, we are able to express the transfer efficiency in terms of the orientation factor K~ T(d,) =
K2(8c)/[C-1re+ K 2 ( e c ) ]
(16)
96
The Journal of Physical Chemisfry, Vol. 84, No. 1, 1980
Riehl
I I
Figure 3. Schematic diagram of a qenen_eralizedemission experiment. The laboratory axes are denoted by (1, 2, and 3). The angle a denotes the orientation ofJhe eleqric vector of the incident beam with respect to the laboratory 1 axis. kdenotes the direction of the incident exciting beam.
The number of molecules initially excited to state De is proportional to the absorption beam intensity, Io, the absorption dipole transition moment, fi(D)eg,and the concentration, C, A2Cm~oI~(D)eg12~o(Qo) (17) where A’ is a proportionality constant and Po(Qo)is the probability that an excited molecule has an orientation Qo at time t = 0. This probability is related to the incident polarization and direction of the exciting beam as follows:l
the very fine and often subtle details of electronic and molecular structure. From a theoretical point of view, a useful approach to such a spectra-structure correlation is to analyze the particular system under study within the context of a proposed optical activity mechanism. An important and, perhaps, dominant mechanism for optical activity in many luminescent systems is dynamic (or correlative) coupling of transition dipoles. We consider here such a mechanism, and, in our model, assume that the donor chromophore is also the perturber chromophore so that the optical activity (as well as the energy transfer) depends upon the relative orientation of the donor-acceptor pair. The rotatory strength in the dynamic coupling model is given by the following e q ~ a t i o n : ~
AEDand AEA are, respectively, the energies of the donor and acceptor transitions; and
Ne(Q0,O) =
Po(Q0) =
(4~)-’[1- FPZ(COS eo)]
F is a geometrical factor defined as F = 1 - 3 sin2 a sin2 ,8
(18) (19)
(angles a and @ are illustrated in Figure 3); P2 is the Legendre polynomial of order 2; and Bo is the angle between the absorption dipole, assumed to define the molecular 2 axis and the laboratory 3 axis at t = 0. The reorientational relaxation of the excited molecules due to rotary Brownian motion in the time interval between absorption and emission must be described in order to determine the orientational distribution of excited molecules at the time of emission. Assuming random orientation in the ground state the probability that an excited molecule will have an orientation Q at time t is given by the following e q ~ a t i o n : ~
P(Q,t)= (4~)-’[1- FC(t)Pz(cos e)]
(20)
The time-dependent coefficient, C(t), has a relatively simple form if we assume that the molecules are treated as rotating (so-called Einstein) spheres C ( t ) = exp(-6Dt) (21) where D is the rotational diffusion constant. The number of molecules which have an orientation Q at time t and are in the emitting state D, is then given by
N,,(Q,B,,t) = ~(e,)f,~A2CmIo(~.(D)ep(2p(Q,t) (22) AW(Q,O,,t). The differential emission transition rate may be written in the following form AW(Q,e,,t) = K ( w ~ ’ ) R ~ ” ( Q , ~ , ) (23) where K(w$)is a constant appropriate for spontaneous emission, and R”(Q,8,) is the rotatory strength for the emissive transition Ag A,. Note that there is no explicit time dependence on the right-hand side of eq 23, since, in fact, the time dependence of this quantity is solely through reorientational and conformational relaxation. The correlation of rotatory strength with conformation is not trivial, since, in general, this quantity depends on
-
V D =~ (DelAgIVIDeAn)
(25)
where V is the interaction energy between the two chromophoric groups.
Results The formulas presented in the previous section may be applied to any system which can be treated within the general model. To do so one needs to know the relative orientations of the relevant transition dipoles, various lifetimes and rate constants, and an assumed model for intramolecular and intermolecular motion. Clearly, the number of parameters is larger than the number of observables, thus it is not possible, in general, to unambiguously determine all the unknown values from the limited number of polarization experiments that can be performed. It is, however, quite feasible to determine if a particular choice of molecular parameters is consistent with experimental observations, and this would be of significant importance in many instances. In order to illustrate precisely how conformation can effect the observed differential intensity, we consider the following system: (1) We assume that the molecules are randomly oriented and rigid (Le., D = 0 and 0, = constant); (2) fi(D)gdis assumed to be parallel to fi(D)ge;and (3) fi(D)ge and ji(A)”g are assumed to be in parallel planes perpendicular to 3 (see Figure 2). 8, in this case is defined as the dihedral twist angle between the two vectors. Substituting eq 22 and 24 into eq 4 and performing the time integral ( Q and 0, are now time independent), one obtains the result
WW)= T A ~ ~ W ~ C P L ((P(Q,O)Rgn(Q,fl,) U)B~~,) ) (26) where B is a constant. The transfer efficiency, given by eq 16, reduces to the following
s(e,)
= cos2 B,/(c-Y + COS^
e,)
(27)
and the dependence of the rotatory strength on conformation has the form Rgn(Q,6,) = R l Q )sin
e,
(28)
From eq 27 and 28 it is seen that the maximum values for the energy transfer efficiency occur at angles where the optical activity in our model is zero, and vice versa. Although this might seem to be a disadvantage, it actually results in the measurement being very sensitive to conformation.
The Journal of Physical Chemistty, Vol. 84, No. 1, 1980 97
Circularly Polarized Luminescence from Molecules
CONFORMATION ANGLE ( o c )
Figure 6. Differential emlssion Intensity ( A I )vs. conformation angle for speck1case of jiAand ir, perpenducutar to 7. The energy transfer is assumed to be independent of 0,. The source of optical activity is the dynamic cwplng between the donor and acceptor-transition dlpnles. Q denotes an absorption polarization para151to the 1 axis; 7~ den~tes an absorption polarization parallel to the 3 axls (see Figure 3).
(e,)
0
n/z
n CONFORMATION ANGLE
3nl2
2n
(Bc)
n/z
n
3V2
2 11
CONFORMATION AI~GLE ( e c )
Figure 7. Differential emlssion Intensity (AI) vs. conformation angle for special case of ZA and ZD perpendicular to ?. The emitting chromophore is excited by direct excitation. The of optical acPivity is the dynamic coupling between the donor and acceptor tra_nsltion dipoles. Q denotes an absorption polarization paraJie1 to the 1 axis; ir denotes an absorption polarization parallel to the 3 axis (see Figure
Figure 5. Differemtial emisslon intensity (AI) vs. conformation angle (e,) for special case of PAand Z, perpendicular to 7. The donor chromophore is excited through dipole-dipole energy transfer, however, the optical activity is lndepcndent of angle e,. Q denotes an absorption polarization pargllel to the 1 axis; ir denotes an absorption polarlzation parallel to the 3 (axis (see Figure 3).
(e,)
In Figure 4 we plot M(in arbitrary units) vs. conformation angle, O,, for two different orientations of the excitation beam for the complete model described above. These two excitation geometries are denoted ir (a= 0, /3 = arbitrary) and Q (a = ~ / 2 , / 3= 7112). Note that there are conformations in which the measurement yields a result greater than the r and vice versa. In Figure 5 we plot AZ vs. conformation angle for the situation in which the emitting chromophore is populated through dipoledipole energy transfer, but the donor chromophore is not involved in the optical activity. In this case, note that there are no zeros at 8, = 0, T which correspond to zero chirality in the previous model. In Figure 6 we illustrate the result expected for energy transfer from donor to acceptor that is not orientation dependent, perhaps, because of an exchange mechanism. The optical activity, in this case, is due to dynamic coupling as described above. Finally in Figure 7, we show the results expected for direct excitation of the acceptor chromophore, assuming that the absorption transition moment is parallel to the emitting transition moment.
concerning optical activity and energy transfer mechanisms, a8 well as intramolecular orientation. The depolarization of linearly polarized light, in systems where the emitting molecules are rigid, may be related to the angle between the absorption and emission transition moment directions. In addition, Dale and Eisenger12have examined (linearly) polarized excitation energy transfer for a large number of model systems, and have shown hiow one can determine appproximately the relative orientation of donor and acceptor chromophores. The measurement of the circular polarization of the luminescence is, in principle, more sensitive to molecular structure for the reasons described above, and thus, within the context, of an appropriate model, has great potential as a structural probe. When used in combination, the two techniques should prove to be a valuable experimental tool. A number of assumptions have been made in the derivation of the expression for the differential emission intensity described above. Some of the more restrictive assumptions are that (1) the molecules have a single conformation that does not change during the lifetime of the excited state, (2) the emitting state is long lived compared to all other excited state processes, and (3) the molecules do not rotate in the time interval between absorption and emission. These assumptions lead to a final result which has a relatively simple form, and is easily interpretable. However, modification of what is presented here to include
Discussion Figures 4-7 illustrate, for a particularly simple model, how CPL spectroscopy may be used as a specific molecular-structural probe. It is seen how a relatively simple change in incident polarization may lead to information
3).
98
J. Phys. Chem. 1980, 84, 98-105
(1)a range of possible excited state conformations, (2) an emitting state that is not long lived, and (3) a model for reorientational motion may be performed in a straightforward manner. Rather than attempt to map out the result for a large number of possible models, the approach that we have chosen to use in our research group is to examine specific luminescent chiral systems. Preliminary work is currently underway on combining computer-assisted conformational analysis on small polypeptides with our theoretical expressions, with the goal of being able to suggest specific experiments to probe the conformation, or to verify existing experimental results. In addition, we are currently examining macromolecular systems in order to determine the applicability of CPL as a specific structural probe in such systems. The results are also being extended to include the time dependence of the differential emission intensity. Acknowledgment. Acknowledgments are made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, and to the Research Corporation for support of this research. In addition, the
author acknowledges Dr. Frederick S. Richardson for many helpful discussions concerning various aspects of this work. References and Notes (1) Richardson, F. S.; Rlehl, J. P. Chem. Rev. 1977, 77, 773-792. (2) Steinberg, I.In “Biochemical Fluorescence: Concepts”; Chen, R. F.; Edelhoch, H., Ed.; Marcel Dekker: New York, 1975; Vol. I, Chapter 3. (3) See, for example, Snatzke 0. In ”Optlcal Activity and Chlral Discrirninatlon”;Mason, S. F., Ed.; Riedel: London, 1979; Chapter 11. (4) Snlr, J.; Scheilman, J. A. J. Phys. Chem. 1974, 78, 387-392. (5) Steinberg, I.Ehrenberg, ; B. J. Chem. Phys. 1974, 61, 3382-3386. (6) Riehl, J. P.; Rlchardson, F. S.J. Chem. Phys. 1976, 65, 1011-1021. (7) Riehl, J. P.; Richardson, F. S. J. Chem. Phys. 1977, 66, 1988-1998. (8) Stelnberg, I. 2.; Schlesslnger, J.; Gafnl, A. In “Peptkles, Polypeptides and Proteins”; Blout, E. R.; Bovey, F. A.; Goodman, M.; Lotan, N., Ed.; Wlley: New York, 1974; pp 351-369. (9) Schlessinger, J.; Gafni. A,; Steinberg, I. J. Am. Chem. SOC.1974, 9 6 , 7396-7400. IO) Brlttain, H. 0.; Richardson, F. S.; Martin, R. B. J. Am. Chem. SOC. 1976, 9 8 , 8255-8260. 11) Schiller, P.W. In “Biochemlcai Fluorescence: Concepts”; Chen, R. F.;Edelhoch, H., Ed.; Marcel Dekker: New York, 1975; Vol. I, Chapter 5. 12) Dale, R. E.; Elsinger, J. In “Blochemical Fluorescence: Concepts”; Chen, R. F.; Edelhoch, H., Ed.; Marcel Dekker: New York, 1975; Vol. I,Chapter 4.
A Study on the Vibronlc Intensification of Absorption Bands by Means of the Floating-Orbital Method Kazuo Akagl, Toklo Yamabe, Hlroshl Kate,+ and Kenlchl Fukul” Depadment of Hydrocarbon Chemlstw, Faculty of Englneerlng, Kyoto university, Kyoto 606, Japan, and College of General Education, Nagoya University, Chlkusa-ku, Nagoya 464, Japan (Recelved July 9, 1979)
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The mechanism of the intensificationof the absorption band due to the vibronic no r * m transition in lactone is investigated in detail by partitioning the transition moment into the electronically alllowed part and the electronically forbidden but vibronically allowed part, where the latter is evaluated by the method of a Herzberg-Teller expansion over floating orbitals. The results by INDO-CI calculation indicate that the increase in the oscillator strength of this transition results from the electronically allowed character generated by the symmetry lowering (C2u C,) rather than the vibronically allowed one. The vibronic couplings of the no-a*C=O states through ring out-of-plane molecular vibrations excited state with the 1A’ (no-a*) and 2A’ (ao-a*~=o) (modes 2 and 4) are found to make predominant contributions to the vibronically induced intensity. The delocalization of the electron density of the no orbital is verified to give rise to the intensification by vibronic coupling as well as the electronically allowed intensity.
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Introduction There have been a number of studies of vibronic coupling observed in molecular spectroscopies,l-12radiation or radiationless p r o c e s ~ e s , ~and ~-~ photochemical ~ react i o n ~ . ~The * ~ ~development of spectroscopy has enabled investigators to detect the vibrational structure on the weak absorption band of electronically forbidden transitions. This has presented interesting subjects concerning the vibronic intensity borrowing as well as the analysis of vibrational structures. Such a vibronically induced intensification is usually treated by the Herzberg-Teller (H-T) perturbation theory.14 The systems treated by this theory have centered around the compounds having high symmetry such as formaldehyde (C2v)4p24 or benzene (D6h),3924925 partly because there are a lot of experimental t College of General Education, Nagoya University.
* Address correspondence of this author at Kyoto University. 0022-3654/80/2084-0098$01 .OO/O
results for these compounds to be compared with the theoretical ones and partly because one only needs to evaluate the vibronically allowed transition moment, that is, the first order in the H-T expansion. In actual cases, however, one often encounters a more complicated situation in a lower symmetry compound (e.g., C, symmetry) involving the carbonyl chromophore. In this case the intengity for the vibronic n T* transition, being locally electronic dipole forbidden, consists of both the electronically allowed part and the electronically forbidden, vibronically allowed part. In the cases of conjugated aldehyde and ketones, McMurryZ6suggested that the latter is more significant than the former for the intensification r* transition, which has been verified to be of the n valid only in the case of benzophenone.n On the contrary, in aldehydes such as a c r ~ l e i np, r~~~p ~y n~ a~land , ~ ~benzaldehyde,31 the former has been predicted to be more significant than the latter, although a convincing argument
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0 1980 American Chemical Society
