6a
Anal. Chem. 1992, 64, 68-74
(5) Huang, E. D.; Wachs, T.; Conboy. J. J.; Henion. J. D. Anal. Chem. 1900, 62. 713A-725A. (6) Dole, M.; Mack, L. L.; Hines, R. L.; Mobley, R. C.; Ferguson, L. D.; Alice, M. B. J. Chem. Phys. 1988, 49, 2240. (7) Yambhita, M.; Fenn, J. B. J. phvs. chem.1984, 88, 4451-4459. (8) Huang, E. C.; Henion, J. D. J. Am. SOC.Mass Spectrom. 1990, 1 , 158-185. (9) Hail, M.; Lewis, S.; Jardine, I.; Liu, J.; Novotny, M. J. Mlcrocdumn Sep. 1990, 2 . 285-292. (IO) Olhrares. J. A.; Nguyen, N. T.; Yonker, C. R.; Smith, R. D. Anal. Chem. 1987. 5 9 , 1230-1232. (11) SmW, R. D.; Barinaga. C. J.; Udseth, H. R. Anal. Chem. 1988, 60, 1948- 1952. (12) Lee, E. D.; Muck, W.; Covey, T. R.; Henion, J. D. J. Chramgtogr. 1988, 458, 313-321. (13) Lee, E. D.; Muck, W.; Covey, T. R.; Henion. J. D. 8bmed. Envkon. Mass Spectram. 1989, 18, 253-257. (14) Lee, E. D.; Muck, W.; Covey, T. R.; Henion, J. D. B b m e d . Envkan. Mass Spectrom. 1989. 18. 844-850. (15) Muck, W.; Henion, J. D. J . chrometogf. 1989. 495, 41-59. (16) (a) Whitehouse. C. M.; Dreyer, R. N.; Yamashlta, M.; Fenn, J. B. Anal. Chem. 1985, 57, 675-679. (17) Wong, S. F.; Meng, C. K.; Fenn, J. B. J. Phys. Chem. 1988. 92, 546-550. (18) Fenn, J. 8.; Mann, M.; Meng, C. K.; Wong, S. F.; Whitehouse, C. M. Science 1980, 246, 64-71. (19) Mann, M.; Meng, C. K.; Fenn. J. B. Anal. Chem. 1989, 61, 1702- 1708. (20) Henry, K. D.; Williams, E. R.; Wang. B. H.; McLafferty, F. W.; Shabanowitz, J.; Hunt, D. F. Roc. Mtl. Aced. S d . U.S.A. 1989, 86, 9075. (21) . . Van Berkel. G. J.; Glish. 0. L.; McLuckey. S. A. Anal. Chem. 1990. 62, 1284-1295. (22) McLuckey, S. A.; Van Berkei, G. J.; Glish, 0. L.; Huang, E. C.; Henion, J. D. Anal. Chem. 1991, 63, 375-383. (23) (a) Bruins, A. P.; Covey. T. R.; Henion, J. D. Anal. Chem. 1987, 5 9 , 2642-2648. (b) Bruins, A. P.; WekJolf, L. 0. 0.;Budde, W. L.; Henion. J. D. Anal. Chem. 1987. 59. 2647-2652. (24) (ajconboy, J. J.; Martin. M..W.; Zweigenbaum, J. A.; Henion, J. D.
(25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37)
Anal. U".1990, 62, 800-807. (b) Covey, T. R.; Huang, E. C.; Henlon, J. D. Anal. chem.1091. 63. 1193-1200. HUang, E. C.; Henion, J. D. Anal. chem.1991, 63, 732-739. Wekklf, L. 0. 0.; Lee, E. D.; Henion, J. D. Bkmed. Envkon. Mass Spectrom. 1088, 15, 283-289. Covey, T. R.; Lee, E. D.; Bruins, A. P.; Henion, J. D. Anal. Chem. 1988, 58, 1451A-146lA. Chowdhury, S. K.; Katta, V.; Chait, B. T. Rapkl Commun. Mass Spec@om. 1990, 4 , 81-87. Katta, V.; Chowdhwy, S. K.; Chait, B. T. Anal. Chem. 1901, 63. 174-178. Caldecorat, V. J.; Zakett. D.; Tou, J. C. Int. J. Mass Spectrom. Ion phvs. 1983, 49, 233-251. Aleksandrov, M. L.; Gail, L. N.; Krasnov, N. V.; Paulenko, V. A,; Shkuruo, V. A. Ddrl. Akd. Ne& USSR 1984, 277, 379. de Silfa, J. A. F.; Strojny, N. J. phenn. Scl. 1971, 60, 1303. Francom, P.; Anbenyak, D.; Um, H. K.; B d d p , R.; Jones, R. T.; F&, R. L. J. Anal. Toxlcol. 1988, 12, 1-8. Henion, J. D. Unpubiiehed results, Come#Unhrerslty, June 1991. Henion, J. D.; Thomon, B. A.; Dawson. P. H. Anal. Chem. 1982, 54. 45 1-458. Mills, T., 111; Price, W. N.; Roberson, J. C. InstwnentelD8fa for Ana&ds; Elsevier Scientific Publishers: New York, 1984; Vol. 2. p 1198. Garland, W.; Mlwa, B.; Webs, 0.;Chen, G.; Saperstein, R.; MacDonaM, A. Anal. Chem. 1980. 5 2 , 842-846.
RECEIVED for review March 6,1991. Accepted September 23, 1991. Portions of this work were first presented at the 38th ASMS Conference on Mass Spectrometry and Allied Topics, Tucson, AZ,June 3-8,1990. T.W. and J.D.H. thank the Shell Development Co. for financial support of this work, and K.L.D. thanks the Monsanto Co. for f i i c i a l support during his stay at Cornell.
Chirality Distributions through Lifetime Resolution in Fluorescence-Detected Circular Dichroism and Circularly Polarized Luminescence: A Theoretical Treatment Lei Geng and Linda B. McGown* Department of Chemistry, P. M . Gross Chemical Laboratory, Duke University, Durham, North Carolina 27706
Theoretical treatments are presented for a new technique, lifetime-resolved fiuorescence-detected circular dichroism (LRFDCD). Two different experlmentai approaches are considered, one based on resolution of the separate emlsslon dgnats for left and right circularly polarized excltath and the other on resolution of the differential and total signals. Both approaches resolve the signals Into the Kuhn dissymmetry factor for each fluorescence iifetlme component, producing the ground-state lifetlme-chlrality distribution for the sample; such resolution of chirality for multkomponent systems Is not posslbk In the statk fluorescencedetected circular dkh" (FDCD) experiment. Slmllar treatments are also given for lifetime-resdved circularly polarized luminescence (LRCPL), which ylekls the exciteddate I l f e t M a l l t y distdbutkn that is composed of the iumim#rcence dissymmetry factor for each lifetime component, and the comblned technique of lifetime resolved circularly polarlzed excltatlon/clrcuiarly polarized emisslon (LRCPECPL), whkh ylelds the product of the Kuhn and lumlnescence dissymmetry factors for each ltfetlme component. Lifetime resolution In both the time and frequency domains Is consldered.
INTRODUCTION Many of the most interesting macromolecules and molecular
assemblies contain helical or otherwise asymmetric structural microenvironments. Examples include nucleic acids, proteins, biological membranes, cyclodextrins, and bile salt aggregates. Distribution of a molecular probe compound among different microenvironmentsin solutions containing such structures will produce a heterogeneous population of free and bound probe molecules with various chiral characteristics. These characteristica are determined by the intrinsic chirality (or achirality) of the probe itself as well as structural and electronic distortions that are induced by association with the binding microenvironment. Circular dichroism spectroscopy (CD) is a chiroptical technique that is an excellent source of information about the chirality, intrineic or induced, of a molecule or macromolecular structure in its ground electronic state. It has been extensively applied in biological research ( I ) and has also found some usea in chemical analysis (2). The major limitation of CD is the poor sensitivity that is associatedwith the CD spectrum,which is obtained by taking the difference between the absorption spectra for left circularly polarized (LCP) and right circularly polarized (RCP) light. When appropriate, the sensitivity of CD measurements can be increased by as much as several orders of magnitude by using fluorescence detection ( 3 , 4 ) . This is analogous to the similar increase in sensitivity of conventional fluorescence over conventional absorption measurements. Thus,fluorescencedeteded CD (FDCD) has
0003-2700/92/0364-0068$03.00/00 1991 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 64, NO. 1, JANUARY 1, 1992
detection limits extending into the micromolar range, compared to the millimolar detectability associated with absorption CD ( 4 , 5 ) . In addition to improved sensitivity, FDCD offers the advantage of greater selectivity relative to CD because not all absorbing compounds fluoresce. The improved selectivity serves to reduce interferences and background signals. The FDCD technique has been used to study proteins (61,nucleic acids (7),and molecular interactions (8-10).A technique for total luminescence detection of CD has been described (11) and applied to studies of bilirubin-albumin binding (10). A major limitation of both CD and FDCD is that they indicate only a single, overall measure of the chirality of an absorbing or fluorescing sample (12). The CD signal is a concentration-weighted average of the individual contributions. In the FDCD signal, the individual contributions are weighted by both concentration and quantum yield. Theoretically, resolution of a CD signal into its individual contributions could be based on differences in the rates of absorption of each component. In practice, it is not yet possible experimentally to resolve individual absorption rates because absorption is too fast a process. Fortunately, fluorescence emission occurs on a much slower time scale than absorption so that fluorescence lifetime resolution can be used to resolve individual contributions to an FDCD signal. Such a technique, lifetime-resolved fluorescence-detected circular dichroism (LRFDCD), has been recently described (131,in which lifetime resolution is accomplished in the frequency domain. Circularly polarized luminescence (CPL) is a chiroptical technique that has been widely applied to the study of excited-state chirality (14,151. Like FDCD, the CPL experiment generates an average signal of the individual contributions. The implementation of time-domain lifetime resolution in the CPL experiment has been recently described (16). Fluorescence lifetime resolution exploits differences in rates of fluorescence emission to resolve an emission signal into the contributions from individual components. It can be achieved in both the time and frequency domains. This is distinct from time-resolved experiments that employ time-domain measurements to monitor chemical reactions or conformational changes. In these kinetic experiments,the signal is measured as a function of time but is not resolved into its component contributions. Such time-resolved measurements of unresolved, overall chirality have been made with CD (17), magnetic CD ( I @ , and CPL (19), and are separate from the lifetime resolution techniques described here which yield the chirality distribution for the system. In this paper, we present theoretical treatments for LRFDCD, LRCPL, and the combined technique of lifetimeresolved circularly polarized excitation/circularly polarized emission (LRCPECPL). Two different experimental approaches were formulated, each yielding a chirality distribution that provides the dissymmetry factors (Kuhn for LRFDCD, luminescence for LRCPL, or a product of the two for LRCPECPL) for each lifetime component. The benefits of lifetime resolution in the chiroptical experiments are 2-fold: (1) it permits the resolution of the static chiroptical signal into the contribution from each lifetime component (chiral and achiral) and (2) the chirality distribution directly links the lifetime of a component with its induced chirality, providing important insight into the location of the lifetime component in the structure. THEORY OF MEASUREMENT The following treatment begins with a brief review of the theories of FDCD and fluorescence lifetime measurement. Theoretical treatments are then presented for two different experimental approaches to LRFDCD, LRCPL, and the combined technique, LRCPECPL. The present work con-
6S
siders simple systems in the absence of photoselection and energy transfer (20). Such effects will be treated in future studies. Fluorescence-Detected Circular Dichroism (FDCD) (12). The signal measured in FDCD is
where F L and F R are the fluorescence intensity excited by left circularly polarized (LCP) light and right circularly polarized (RCP) light, respectively, and K is an instrumental factor. Assuming that the quantum yield of fluorescence is independent of the orientation of the circular polarization (12,21), the FDCD signal of a sample containing a single fluorescent species is
where eFL and cFR are the molar absorptivities of the fluorophore for LCP and RCP light and AL and AR are the total absorbances of the sample, including solvent and all absorbing components (fluorescent and nonfluorescent) for LCP and RCP light. Equation 2 can be rearranged to
(3) where AcF is the molar circular dichroism of the fluorophore ( A ~ F= tFL - cFR), €3 is the molar absorptivity (eF = (eFL + eFR)/2) of the fluorophore, and R is a factor determined by the total circular dichroism AA (AA = A L - A R ) and the total absorbance A of the sample, including the solvent, nonfluorescent, and fluorescent species: AL(1
R=
AL(1
- 10-A~) - A R ( 1 - 10-A~) - 10-AR) + A R ( 1 - 10-AL)
(4)
The Kuhn dissymmetry factor of the fluorophore, g F = A*/q, is obtained from eq 3 and requires three measurements: AA, A, and IFDCD. For a multicomponent system containing more than one fluorescent species, I ~ c Dis the quantum yield- and concentration-weighted sum of the contributions from all of the optically active fluorophores (12):
2R IFDCD
where qi and ci are the quantum yield and concentration of the ith component. The Kuhn dissymmetry factors for the individual components in the system cannot be resolved in the static FDCD experiment. A second, independent measurement dimension must be added to resolve the contribution of each component. In this work, resolution is achieved through the dynamic dimension of fluorescence lifetime. Fluorescence Lifetime Distribution of Multicomponent Systems. In frequency-domain fluorescence lifetime techniques (22-24), the sample is excited with intensitymodulated light, usually of the form
I(t) = U + V sin wt (6) where U and V are the dc intensity and the ac amplitude of the excitation light, respectively, and w is the angular frequency of the sinusoidal modulation. The resulting fluores-
70
ANALYTICAL CHEMISTRY, VOL. 64, NO. 1, JANUARY 1, 1992
cence signal is emitted with the same w but is phase-shifted by angle 9 and demodulated by factor M relative to Z ( t ) due to the finite lifetime of the excited state. The total fluorescence F(t)of a multicomponent system containing more than one independently emitting fluorescent component is the s u m of the fluorescence of each component (24):
F(t) = C a i + C b ; sin (wt - 4J
(7)
where ai, bi, and 4i are the dc intensity, ac amplitude, and the phase shift,respectively, of the ith fluorophore. The observed demodulation M and phase shift 9,are related to the lifetime distribution of the system by
Eai sin 4i cos &/Cai cos2 4i hP = (Eaisin di cos 4J2+ (Cai cos2 $ J 2 tan @ =
(8) (9)
where ai is the fractional intensity contribution of the ith component to the total dc intensity Eai: bi/cos 4i ai (10) ai=-- Cui C(bi/cos 4i) The fluorescence lifetime of the ith component can be calculated from both the phase shift 9, Ti
= ( l / w ) tan 4i
(11)
and the demodulation Mi ( = ( b i / a i ) / ( V / U ) ) :
The fluorescence lifetime distribution of the system (Tl(a1)
72(a2)
Ti(ai)
*a*
Tn(an)I
or a distribution of fluorophores with different fractional contributions to the total fluorescence specified by their lifetimes, can then be calculated from multifrequency excitation data by a nonlinear least squares fit (25) to Weber’s equations (22). In systems where a range of interactions at different stages exist (26a), such as fluorescent probes in macromolecules, membranes, polymers, micelles, or adsorbed on surfaces, continuous lifetime distribution functions (26) are expected. In these cases, the lifetime distribution above is understood to be a multimodal, continuous distribution, with each q(ai) denoting a continuous distribution function. For simplicity, the treatment presented in this paper will assume the discrete form, but it applies equally to continuous cases, with the simple substitution of discrete form ri(ai)by the continuous distribution function. Note that the observed modulation M is the ratio of the modulation of total fluorescence to that of the excitation beam, not the modulation of the driving function, or total absorbed light, as is commonly presented in the derivations in the literature. The total absorbed dc intensity CAI,differs from the incident light by the factor ( C A i ) / U = C[$CiZ(l- 10-A)/A]
(13)
where A is the absorbance of the sample. For natural or plane-polarized excitation, this factor is cancelled out upon W i g the ratio of the ac amplitude to the dc intensity of the total absorption to obtain the modulation:
( C B i ) / ( C A i )= V / u
(14)
In LRFDCD, however, this is no longer true, because of the different absorption cross sections of the optically active sample for LCP and RCP excitation (vide infra).
LRFDCD Measurement Theory. The first instrument for LRFDCD has been recently described (131, consisting of a frequency-domain lifetime instrument that is modified with a linear polarizer and a Babinet-Soleil compensator to create LCP and RCP light. The circularly polarized light (assumed to be propogathg dong the n axis) has the form 1/d2Ad(kwt) (i f ik) where the upper and lower signs are for RCP and LCP light, respectively. The intensity of the circularly polarized light, A2, is invariant with time and can therefore be modulated. In frequency-domain fluorescence lifetime measurements, intensity modulation frequencies in the megahertzgigahertz range (27) are used. Thus, in LRFDCD the electric vector of the circularly polarized W-visible light rotates about 10s cyclea in one cycle of intensity modulation; the modulation frequency is sufficiently low compared to the frequency of the circularly polarized exciting light to enable the frequencydomain lifetime measurement. Two different experimental approaches to LRFDCD are considered in the following theoretical treatments. Experimental Approach I. In the first approach to the LRFDCD experiment, an achiral reference component is added to the sample. In addition to being achiral, the reference compound must not affect the fluorescence or chiral properties of the sample components. Each c h i d component in the sample is excited by LCP and RCP light with different absorption crow sections, resulting in circular dichroism. Each component then decays back to the ground state at a rate that is independent of the circular polarization of the exciting light, giving rise to the same fluorescence lifetime for LCP and RCP light excitation. The fluorescence quantum yield of each component is determined by the rate of the fluorescence proteas relative to the totalrelaxation rate of the excited states and is therefore also independent of the circular polarization of the excitation (12,21). The fluorescence lifetime distributions for the LCP and RCP excitations are then obtained for the sample by nonlinear least squares fit of the multifrequency fluorescence lifetime measurements: LCP excitation: I~l(a1d
7Aa.d
***
Ti(aiL)
...
~n(an~)l
RCP excitation: 72(%R)
fTl(alR)
Ti(%R)
Tn(anR)j
where ~i is the fluorescence lifetime of the ith component and a , and ~ aa are the fractional contributions of the ith component to the total dc fluorescence intensity of the sample for LCP and RCP excitation, respectively: aiL aiR
= aiL/CaiL = aiR/CaiR
(15)
The aiLand a a in eq 15 are the dc fluorescence intensities of the ith component:
aiL = [kqLciqil(l- 1 0 - A ~ ) / A L ] U a a = [k€aCiqil(l- 1 0 - A R ) / A ~ ] U
(16)
where ca and are the molar absorptivities of the ith component for the LCP and RCP excitation, I is the path length of the sample cell, and k is an instrumental factor. With the addition of the achiral reference, which will be referred to as component 0, a function of the lifetime distributions ti can be constructed as %L/aOL
- aiR/aOR
= 2aiL/aoL + a=/aOR
(17)
which can be reduced to %L/EOL - %R/cOR
ti
=
2ciL/coL
+ tiR/eoR
(18)
ANALYTICAL CHEMISTRY, VOL. 64, NO. 1, JANUARY 1, 1992
Since component 0 is achiral, then ti
=
eoL
a = C ( a i L - a*) b sin @ = C(biL- biR) sin r$i b COS = C ( b i L - biR) COS 4 i
= eOR and
A€i/~i
(19)
where Aei = eL - eiR is the molar circular dichroism and ei = (eiL + elR)/2is the molar absorptivity of the ith component. The function ti is simply the Kuhn dissymmetry factor of the ith fluorescent component. Thus, by adding an achiral, noninteracting fluorescent component with known lifetime into the sample, the Kuhn dissymmetry factor of each fluorophore in the multicomponent system is obtained. The chirality distribution is obtained from the two lifetime distributions as
+
71
(25)
The observed phase shift and demodulation M are thus related to the contributions of the individual components by tan@=
-
- b a ) sin 4 i C(bi~-. - biR) COS 4 i C ( a i L - u ~ R ) sin 4 i COS +i C(aL - aiR) cos2 4 i C(biL
(26)
M = -b / a where ti will equal zero if the ith component is achiral. Thus, the Kuhn dissymmetry factor ti is found for each and every lifetime component, chiral or achiral, in the system, forging a direct link between chirality and lifetime that is absent in the individual techniques. As discussed above, a multimodal, continuous chirality distribution is expected for systems where a range of continuous interactions are present. The chirality distribution constructed from multimodal lifetime distributions may also be multimodal and each ~ i ( [ i ) is a continuous distribution function. Experimental Approach I Variation. In the cases where adding an achiral noninteracting fluorophore is not practical, the lifetime distributions for LCP and RCP excitation can be combined with measurements of FL and F R to construct a new function Fi:
v/u
= [(C(a,T-. - a a ) sin
4 i COS d i ) 2 aiR)
+ ( C ~ -L
cos2 4 i ) 2 ] 1 ’ 2 / c ( a L
-
(27) The fractional intensity contribution of the ith component to the total differential fluorescence is defined as ai
= 6,/C6i
(28)
where
is proportional to the differential fluorescence intensity of the ith component. The apparent phase shift and demodulation
Substituting for aiLand ( Y ~ Rfrom eqs 15 and 16 and for FL and FR from eqs 7 (the dc component) and 16 yields
which can be rearranged to give lead to the differential lifetime distribution (71(a1)
where R is a function of the total absorbance A and total circular dichroism AA of the sample (eq 4). In comparison of eqs 22 and 3, it is clear that while Fi has the same form as the static I-, it is now the resolved contribution of the ith component. This signal is denoted by IFDcD,~. Experimental Approach II. In the second approach to LRFDCD, the multiexponential decays of the differential fluorescence, F L - F R , and total fluorescence, FL+ FR, are obtained for sinusoidally-modulated excitation in the frequency domain. The lifetime distributions for the differential and total fluorescence emission are calculated from the multifrequency data and the chirality distribution is obtained. 1. Differential Lifetime Distribution. The differential fluorescence emission intensity, AF(t), of a multicomponent system that is excited by sinusoidally modulated light is given by M(t)= x ( a i L - U ~ R )+ C(biL - b a ) sin (ut - 4 i ) (23) and can be expressed in terms of the modulation frequency o,the observed dc intensity and ac amplitude (a and b, respectively) and the observed phase shift 3,of the emitted light: M(t)= a + b sin (ut - @) (24) Comparison of eqs 23 and 24 yields the relationships
72(a2)
.a*
72(62)
e.*
7i(ai)
7n(an)J
or equivalently {71(61)
7n(6n)1
2. Total Fluorescence Lifetime Distribution. The total
fluorescence lifetime distribution is achieved by excitation with unpolarized light, as in the conventional fluorescence lifetime measurements. The total fluorescence intensity is
F(t) = C ( ~ + L a i R ) + C(b&+ biR) sin (ut - 4 i ) which leads to the total lifetime distribution {71(aJ
72(62)
7i(Ci)
(31)
Tn(un))
in which ui, given as
is proportional to the total fluorescence intensity of the ith component. 3. Construction of the Chirality Distribution. A function qi is constructed from the differential and total lifetime distributions as q i = 6i/Ui (33) Substitution of eqs 29 and 32 into eq 33 yields
72
ANALYTICAL CHEMISTRY, VOL. 64, NO. 1, JANUARY 1, 1992 eiLAR(1
'Ii = t i L A R ( 1
-
(Ati/ei)
- 10-AL) - t i R A L ( 1 - 10-A~) - 10-AL) + e c R A L ( l - 10-A~) - 2R
2 - (Aei/ei)R = zFDCD,i
(34)
Again, as in the approach I variation, we have obtained an signal for each component in the system. LRFDCD: Discussion. LRFDCD combines the dynamic dimension of fluorescence lifetime with the structural information of FDCD. Lifetime measurements resolve the FDCD signal for individual components, in contrast to the single, weighted average that is obtained in the static FDCD experiment. The structural information from FDCD provides a direct link between the lifetime of a component and its location in a structure. In approach I, an achiral, fluorescent reference compound is added to the sample. The reference must not affect the lifetime or FDCD properties of the components of interest, through either direct interaction or modification of a component's microenvironment. Additionally, the fluorescence lifetime of the reference must be known from independent measurements and remain unchanged in the sample. The method is still valid if the achiral reference interacts with the sample as long as the interaction does not affect the components of interest and a detectable amount of the reference remains free. In this case, the fractional contribution and fluorescence lifetime of the achiral reference, a. and so, refer to the subpopulation of free reference molecules instead of the total concentration of the reference compound. Initial results for the experimental realization of approach I have been described (13). It should be noted that the advantage of detectability of fluorescence over absorption is retained in approach I because measurements of total circular dichroism and total absorbance are not involved. In static FDCD, however, the latter measurements are necessary to calculate the Kuhn dissymmetry factor. Addition of an achiral reference is not required in either approach I variation or approach 11. The approach I variation gives the signal, Z m D , i by measurements of the lifetime distributions and total fluorescenceintensities for LCP and RCP excitation. In approach 11,the differential and total lifetime distributions provide the ZFDCD,~signal. To construct the lifetimechirality distribution or the Kuhn dissymmetry factors associated with the lifetimes, measurements of the total circular dichroism and total absorbance of the sample are required for calculation of R in both approach I1 and the approach I variation. An important advantage derives from the use of the internal, achiral reference in approach I. In static FDCD, measurements are subject to errors caused by unequal intensities of LCP and RCP exciting light (15). These errors are overcome in LRFDCD by approach I because of the ratiometric property of ti: the fractional contribution of the component is divided by that of the achiral reference, and the excitation intensities cancel out. Thus, the achiral reference serves as an internal standard to eliminate this source of error in the chirality distribution. In the derivation of both the approach I variation and approach 11, it was assumed as in static FDCD that the LCP and RCP excitation intensities are equal (see eq 16). Practically speaking, it is difficult to generate exactly equal intensities of LCP and RCP excitation (4,@ and this has limited the application of FDCD (15). A correction scheme for unequal intensities has been formulated (28) and will be discussed. elsewhere. LRFDCD in the Time Domain. The signal in frequency
domain is simply a Fourier transform of the time-domain signal (29). Consequently, they carry the same information about the system. By analogy to approach I in the frequency domain, the chirality distribution of a multicomponent system in the time domain is obtained from the multiexponential decay of luminescence (30,311 following LCP and RCP excitation, FL(t)= CfiLe-""iand F R ( t ) = CfiRe-t/Ti, by adding an achiral noninteracting fluorophore:
IF,,,
Here, fL and faare the preexponential fadore for contribution of component i to the decay curves following LCP and RCP excitation, reapectively. Alternatively, the approach I variation in the time domain incorporates the static fluorescence intensities for LCP and RCP excitation in lieu of the internal, achiral reference:
(36) Approach I1 in the time domain uses measurements of the multiexponential decays of the differential fluorescence, FD(t) = CfD,,&/"i, and the total fluorescence, F&) = Cfsie+i, to yield 'Ii
= f D j / f S , i = IFDCD,i
(37)
Lifetime-Resolved CPL in the Frequency and Time Domains. Static FDCD measures the differential intensity of the fluorescence excited by LCP and RCP light. CPL, on the other hand, measures the differential intensity of circularly polarized luminescence that is excited by natural or, in the presence of photoselection, by light that is plane polarized at the magic angle (20b). The signal in CPL is
ZCPL = 2- I L - I R = (38) I - glum IL +IR where ZL and ZR are the intensities of the left and right circularly polarized luminescence, A I is the differential intensity of luminescence (IL- ZR), and I is the total luminescence ((ZL + zR)/2). The signal ZCPL is the luminescence dissymmetry factor gl, (14,15). For a multicomponent system, the observed ZcpL is an average of the contributions from all of the luminophores that are optically active in the excited state: ZCPL
=Cui/CZi
(39)
In LRFDCD, lifetime resolution provides the chirality distribution of the ground state, because the chiral discrimination occurs in the absorption process. Lifetime resolution in CPL, on the other hand, yields the chirality distribution of the excited state and therefore reveals structural information of each excited state or, more exactly, each emission state (14)component because the chiral discrimination occurs in the emission process. The approaches described above for LRFDCD are applicable to lifetime-resolved CPL (LRCPL) as well. The individual luminescence dissymmetry factor, glUj, for each component is obtained through lifetime resolution and the chirality distribution is constructed. In the frequency domain, the chirality of the ith component is calculated from the lifetime distributions for LCP and RCP luminescence. If a i L and aB here are the fractional contributions of the ith component to the LCP and RCP luminescence, respectively, then glmi is given by eq 17 for approach I and by eq 20 for the approach I variation. In approach 11, the lifetime distributions for the differential and totalluminescence are measured and g1+ is calculated by eq
ANALYTICAL CHEMISTRY, VOL. 64, NO. 1, JANUARY 1, 1992
33, where 6i and ai are the fractional contributions of the ith component to the differential and total luminescence, respectively. The time-domain equivalent expressions for LRCPL are obtained by replacing aL and LY~Rby preexponential factors fL and fB in eqs 17 and 20, and 6i and ui by f ~and i fs,i in eq 33. In CPL and LRCPL, the luminescence dissymmetry factors, glm and glwi, are obtained directly from the circularly polarized emission signals. The requirement that the LCP and RCP excitation intensities be equal in FDCD and LRFDCD is therefore irrelevant in the CPL measurements. In both LRFDCD and LRCPL, lifetime resolution results in the measurement of the component chirality and chirality distribution. In LRFDCD, the chirality distribution corresponds to the ground-state structure:
=4 =4
tiCD(A)Im(Piebs-Miabs)
--
fiTA(A)Dpk
n)
-
In LRCPL, the chirality distribution gives the ratio of the rotational to dipole strengths of the emission transition and therefore provides the excited-state chirality of each component:
-
Mi
Ii fFPL(A)Im(P/""*M)m) fiTL(A) IPpy
-
in which R:-(g n) and D:-(g n) are the emission rotational and dipole strengths for the ith component. f z ( X ) and ficpL(X)are normalized line-shape functions for total luminescence and CPL, respectively. In conventional CPL, only an average value is determined:
-CAIi - - 4 CfFpL(A)Rpm(, Eli
ti = 4,
+
[
aiRR] - "iLR aiRL]
~ O L L "ORR
+
"OLR .
r
.
~ORL
(44)
in which (Y~LL,(YQR, aiRL, and a i R R are the fractional contributions of the ith component to the luminescence intensity for LCP/LCP, LCPIRCP, RCP/LCP, and RCP/RCP combinations of excitation/eminsionpolarization. Since the zeroth component is the achiral reference, eq 44 can be reduced to the product of the absorption and emission dissymmetry factors by substitution of the expressions for the fractional contributions (45) si = A%Mi/di = gabs,&lum,i The reference must be achiral in both the ground and excited states. By measurement of the static signals for each of the four polarization combinations (ILL, ILR, ZRL, and IRR), the approach I variation yields
(40)
+
=4
aiLL
fiTA( A) IPpq2 fiCD(A)pJ~(, n)
in which Riab"(g n) is the rotational strength of the absorption transition (Le., the imaginary part of the inner product of the electric and magnetic dipole transition moments Pfb"and Mih) and Dtb(g n) is the dipole strength. fiTA(X) and ficD(A)are normalized line-shape functions for total absorption and CD, respectively, for the ith component. In conventional FDCD, only a ratio of weighted rotational and dipole strengths is experimentally determined
&m,i =
[-
73
CfiTL(A)Di'""&?
--
n) n)
(43)
All of the standard methods described for static FDCD and CPL to analyze the signal and to obtain structural information from the Kuhn dissymmetry factor (12)and the luminescence dissymmetry factor (14,15) can be applied to each component that is resolved in LRFDCD and LRCPL. Lifetime Resolution in CPECPL. Simultaneous circular polarization of the excitation and emission beams results in four possible combinations of excitation and emission orientations. A signal can be constructed from the lifetime distributions for each of the four combinations for approach I:
which is the product of the luminescence dissymmetry factor and IFDCDi 5'i = IFDCD,&lum,i (47) Addition of an achiral species is unnecessary. Approach I1 is achieved by measuring the differential intensity of the LCP and RCP luminescence that is excited by the intensity differential of the LCP and RCP excitation. The lifetime distribution of this signal along with the lifetime distribution of the total luminescence from total excitation also yields the product of the luminescence dissymmetry fador and IFDCDi vi = GiDD/aiSS = IFDCD,&lum,i (48) where 6 n D and u i s are the fractional contributions of the ith component to the differential emission from differential excitation, IDD, and total emission from total excitation, Isp The signal for CPECPL is weaker than signals obtained with FDCD or CPL alone, but the relative difference between components will be increased because the CPECPL signal is the product of two chiral selectivity factors, gabs,i and glm,b CONCLUSIONS In LRFDCD, the signal constructed in approach I is gabs,i, whereas the approach I variation and approach I1 both yield IFDCD,~. In LRCPL, all three approaches yield glu,,i. The signals constructed in LRCPECPL are the products of the respective LRFDCD and LRCPL signals for each approach. In approach I and its variation, the chirality distribution is obtained from the lifetime distributions determined for both the LCP and RCP light generated signals. Approach I employs the addition of a noninteracting, achiral fluorescent compound to the system. It offers the advantages of requiring no measurements additional to the lifetime distribution and automatic, internal correction for unequal intensities of LCP and RCP excitation in LRFDCD and LRCPECPL. The approach I variation does not require the addition of an achiral reference, but the total intensities for the LCP and RCP light-generated signals must be measured. In approach 11, the chirality distribution is obtained from the differential and total lifetime distributions. In LRFDCD using the approach I variation or approach 11, construction of the chirality distribution requires that the total circular dichroism and the total absorbance of the sample also be measured. The experimental realizations of LRFDCD approach I in the frequency domain (13)and LRCPL approach I1 in the
74
ANALYTICAL CHEMISTRY, VOL. 64, NO. 1, JANUARY 1, 1992
time domain (16)have been demonstrated recently. The other techniques discussed in the theoretical treatment have yet to be explored by researchers in the field.
(20)
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RECEIVED for review August 22,1991. Accepted October 11, 1991. This work was supported by the United States Department of Energy Office of Basic Energy Sciences (Grant No. DE-FG05-88ER13931) and by the National Science Foundation (Grant No. CHE-9111928).
