correction for unequal intensities of left and right circularly polarized light in steady-state and...

submitted papers

Correction for Unequal Intensities of Left and Right Circularly Polarized Light in Steady-State and Lifetime-Resolved Fluorescence-Detected Circular Dichroism

LEI GENG and LINDA B. McGOWN* Department of Chemistry, P.M. Gross Chemical Laboratory, Box 90346, Duke University, Durham, North Carolina 27708-0346

A major difficulty in fluorescence-detected circular diehroism (FDCD) and lifetime-resolved fluorescence-detected circular dichroism (LRFDCD) is the generation of equal excitation intensities of left circularly polarized light (LCPL) and right circularly polarized light (RCPL). In the presence of unequal intensities, the observed FDCD signal of an optically active sample, or the resolved FDCD signals of a multicomponent system in the case of LRFDCD, will be contaminated by a factor that is the ratio of the two unequal intensities. For optically inactive samples, a sample- independent, artifactual, nonzero signal of constant magnitude is observed. A general scheme is presented for the correction of these inac- curacies caused by unequal intensities of LCPL and RCPL. Large differences between LCPL and RCPL excitation intensities were artificially introduced in steady-state FDCD measurements, and the artifact was accurately corrected by the scheme. Corrected results for the different experimental approaches that have been described for LRFDCD showed similarly good accuracy. In a related consideration, inclusion of the total absorbance and absorption circular dichroism of the sample in the calculation of the FDCD signal is shown to be essential for samples with high absorbances. Index Headings: Circular dichroism; Fluorescence-detected circular dichroism; Fluorescence lifetime; Fluorescence spectroscopy; Circularly polarized light.

INTRODUCTION

In fluorescence-detected circular dichroism (FDCD), the optical activity of ground-state molecules is measured through fluorescence detection. 1,2 FDCD offers higher sensitivity and detectability than absorption circular dichroism (CD) due to lower background signals and direct dependence of fluorescence emission on the intensity of the excitation beam. The lowest absolute detection limit for measurement of optical activity has been achieved by FDCD with laser excitation, 3 making it attractive for analytical applications such as detection in HPLC 4 and cap- illary electrophoresis, 3 especially for chiral separations. Moreover, FDCD is highly selective because nonfluorescent chirophores do not contribute to the FDCD signal. The selectivity of FDCD and its sensitivity to structural and conformational changes make it a powerful tool for studies of macromolecular systems and complex samples such as proteins, 5 nucleic acids, 6 and human serum. 7

Received 14 July 1993; revision received 5 November 1993. * Author to wbom correspondence should be sent.

In a complex sample with multiple contributions to its optical activity, both CD and FDCD provide only a single, overall optical activity for the sample. This optical activity is an average weighted by concentrations of each contributing chirophore in CD, and by concentrations and quantum yields of the chirophores in FDCD. The resolution of the optical activity of each component in such a sample is not achieved with these techniques. One important example is the induced optical activity in a probe molecule that is bound to a macromolecule or mo- lecular assembly and possibly distributed among multiple binding sites. Both CD and FDCD measure an average signal of the probe among all binding sites. Information about the individual binding sites or local structures cannot be obtained. This consideration limits the application of FDCD to systems with a single fluorophore, such as proteins with a single tryptophan that experiences a single, unique microenvironment in the protein.

A new technique that overcomes these limitations is lifetime-resolved fluorescence-detected circular dichroism (LRFDCD). s-l° In LRFDCD, the optical activity of each fluorescent component in a multicomponent system can be obtained through fluorescence lifetime resolution of the signals produced from excitation by left circularly polarized light (LCPL) and right circularly polarized light (RCPL). 9,1° The multicomponent system may be a mixture of compounds or a single compound that is distributed among multiple chemical microenvironments. Thus, LRFDCD offers potential not only for resolution of simple mixtures but for detailed studies of local structure, conformation, and binding interactions in heterogeneous, macromolecular systems as well.

The measurement theories of FDCD 2 and LRFDCD 9 assume that the intensities of LCPL and RCPL used for excitation are equal. This state can be difficult to achieve in the actual experiment 4,11 and has been a primary lim- itation in the implementation of FDCD.12 Unequal LCPL and RCPL intensities result in an artifactual Kuhn dissymmetry factor for optically inactive molecules and inaccurate measurements of optically active molecules. A correction scheme based on subtraction has been described at the limit of very low concentration and total absorbance, and its application has been successfully

Volume 48, Number 2, 1994 0003-7028/94/4802-016752.00/0 APPLIED SPECTROSCOPY 167 © 1994 Society for Applied Spectroscopy

demonstrated for FDCD in the context of HPLC detection. 4 For macromolecular systems of biological interest, however, the total absorbance of the sample can easily exceed the low absorbance limit. FDCD measurement has been routinely performed for samples with absorbance above 0.1, where the R term (see below) is not negligible.

In this paper, we present a general correction scheme for unequal intensities of LCPL and RCPL in both FDCD and LRFDCD measurements, with consideration of the total absorbance and CD. Successful application of the correction scheme is demonstra ted in FDCD and LRFDCD measurements of individual chirophores and simple mixtures.

T H E O R Y

Fluorescence-Detected Circular Diehroism. In FDCD, the optical activity of a sample is observed by fluorescence detection. The measured FDCD is the difference between the fluorescence intensities that are excited with LCPL and RCPL (FL and FR, respectively) divided by the average intensity:

IFDCD - - A I _ 2 FL - FR (1) I FL ~ FR"

The fluorescence intensities FL and FR are related to the molar absorptivities (eL and ~R), concentrations (c), and quantum yields (q) of the fluorescent components and the total absorbance (A) of the sample, including all fluorescent and nonfluorescent absorbers. In the case of a sample containing a single optically active fluorescent component, the intensity produced from LCPL or RCPL excitation is expressed as:

Fp = %clq(1 - 10 -Ao) i0 (2) Ap

where the subscript p indicates the sense of circular polarization (L for LCPL or R for RCPL) and l°p is the intensity of the exciting light.

The IvDCD signal can be rearranged, after substitution of Eq. 2 into Eq. 1, to include an intensity ratio 3 = I ° / IO:

3eL ' ~R -- R IVDCD = 2 (3)

1 - \&L + eR/

in which R is a term accounting for the differential absorption of LCPL and RCPL by the whole sample, including all fluorescent and non fluorescent chromophores:

AL(1 -- 10 -AR) --AR(1 -- 10--A0 R = (4)

AL(1 -- 10 -A") + AR(1 - 10-A0 "

Experimentally, R is generally calculated from measurements of the total CD (AA = A L - A R ) and total absorbance (A = (AL + AR)/2) of the sample.

When a sample contains multiple optically active components with overlapping absorption spectra, the FDCD signal is a concentration and quantum yield-weighted average of contributions from all of the components:

ciqi(~eiL - eiR) - R

ciq i (~eiL + eiR) IvocD = 2 . (5)

ciq i (~eiL -- e;R) R 1 - -

ciqi(3eiL + ';R)

The subscript i denotes the ith component in the multicomponent system. If the intensities of the LCPL and RCPL are exactly equal (I°L = IOR), then /3 = 1 and the FDCD signal is given by:

z

IVOCD = 2 (6)

where Ae; = em - e m is the molar circular dichroism, and e; = (e,3. + e,R)/2 is the molar absorptivity, of the ith component.

Lifetime-Resolved Fluorescence-Detected Circular Di- chroism. In LRFDCD, the resolution of the overall steady- state FDCD signal into the contributions from each of the components can be accomplished with the use of two different approaches? In Approach I, a static device is used to create LCPL and RCPL sequentially. The fluorescence lifetime measurement is performed individually for LCPL and RCPL excitation, and the corresponding lifetime distributions are recovered:

LCPL excitation: {a,L(T,0, a2dT20 . . . . a;L(T;L),--, a.L(T.0, a0dT00}

RCPL excitation: { a , . ( T , . ) . a2 . (T2 . ) . . . . a,~(T,~) . . . . a . . (T .R ) , ao.(~oR)}

where aiL and air are the fract ional intensi ty contr ibut ions of the ith component to the emission signals for LCPL and RCPL excitation, respectively. The zeroth component is a noninteracting, optically inactive reference that is added to the sample. A function can then be constructed from these lifetime distributions:

~i "~ 2 aiL/a0L -- aiR/a0R -- A e i (7) aiL/aOL -~- aiR/O/0R ei

which yields the Kuhn dissymmetry factor (gv.; = Aei/~;) of each component. The Kuhn dissymmetry factor of a molecule is proportional to the ratio of its rotational strength and dipole strength 2,~2 and contains structural information about the molecule.

In a variation of the first approach to LRFDCD (Ap- proach I variation), the addition of an optically inactive reference into the sample is unnecessary. Instead, the steady-state fluorescence intensities for LCPL and RCPL excitation (FL and FR) are measured in addition to the lifetime distributions:

LCPL excitation: {alL(TiL), a 2 L ( T 2 L ) , . . , aiL(TiL) . . . . anL(TnL)} EL.

RCPL excitation: {alR(TIR), a2R(T2R) . . . . aiR(T/R) . . . . anR(rnR} F . .

168 Volume 48, Number 2, 1994

The FDCD signals for individual components can then be calculated by

-- e ,R] __ R

~i ~ 2 e%FL - OIiRFiR = 2 \~3ELL ~ EiR] (8) Oe,LFl. + o~,,Fm (/3~,L - ~,R]R"

1 - \/3~,~ -£ ~,R/

In the second LRFDCD approach, Approach II, a dynamic device is used to provide alternating LCPL and RCPL, and the lifetime distributions for differential fluorescence intensity and total fluorescence are recovered:

Differential fluorescence lifetime distribution: {6,(~,), 6&2), . . . 6,0-,) . . . . 6.0-.)}.

Total fluorescence lifetime distribution: {~,(~,), ~&2),--- ~,0",) . . . . ~.(~.)}-

The resolved signals are constructed as

~i = 2ai/cYi = 2 (9)

1 (/3e~L-- E,RIR" In both LRFDCD approaches, the distribution of FDCD

signals is constructed from the lifetime distributions

and contains the Kuhn dissymmetry factors of the individual components.

Cerrectien Scheme. In the presence of unequal LCPL and RCPL intensities, the recovered FDCD signal of an optically active component is no longer the expected dissymmetry factor of the component, but contains the/3 factor:

/3~,L T ~,R/

1 - - \ / 3 ' i L T ¢CiR]

Only if/3 = 1, or if the LCPL and RCPL intensities are exactly equal, is the signal reduced to the FDCD signal for the component: 9

(AEi/ei) -- 2R IFDCD., -- 2 2 - (,5~,/,,)R (11)

from which the Kuhn dissymmetry factor gF,~ = ~Ei/~ can be calculated.

For an optically inactive component, an artifactual nonzero signal is observed in the presence of unequal intensities:

/ 3 - 1

~. = 2 . ( 1 2 ) ~ - 1

If an optically inactive compound is used as a reference,

the absorbances for LCPL and RCPL are equal even in the presence of unequal intensities. Therefore, Ra is always zero. The recovered artifactual signal is thus a function of the/3 factor only and is independent of the prop- erties of the reference. This is a useful feature of the correction scheme because any optically inactive solution can be used as a reference to yield equivalent results:

/ 3 - 1 ~a = 2 / 3 +------i-" ( 1 3 )

A value of zero is obtained for the signal of an optically inactive component only if LCPL and RCPL intensities are exactly equal.

The correction factor/3 is readily calculated from the optically inactive reference measurement with the use of a rearranged form of Eq. 12:

(2 + ~a)(1 + R,) /3 = (2 - ~a)(1 -- Ra)" ( 1 4 )

The Kuhn dissymmetry factor of an optically active component is then found by substitution of the/3 factor into the measured FDCD signal (Eq. 10):

(1 + .a)(1- . ) p + a)p- ~ " - 21 - \ T - 2 - ~ / \ - i - ~ J \ 2 _~a / \~ -U~ ! (15) e~ (1 + Ra~(l - R~(2 + ( a ~ ( 2 - '~i~"

1 + \ 1 - R a / \ l + R / \ 2 - ~ . / \ 2 + ~,/

Clearly, the error introduced by unequal intensities is not additive in the general case in which the R terms are considered. The Kuhn dissymmetry factor of an optically active component cannot therefore be calculated by subtraction of the measured signal of an optically inactive component from that of the optically active component. In other words, correction of the artifactual error due to unequal LCPL and RCPL intensities cannot be accomplished by simple subtraction of the reference signal in the general case of nonzero R.

In FDCD and LRFDCD measurements, the following two special cases with different experiment schemes are considered:

(1) The optically inactive reference is added directly to the sample. This case applies to LRFDCD Approach I measurements only. Since the optically inactive reference and the component of interest are in the same solution, R = Ra. Note that R is a function of the total CD and absorbance of the solution, including all the absorb- ing species. The expression of the Kuhn dissymmetry factor (Eq. 15) reduces to

~6i ~ i - ~a - 4 - - . ( 1 6 )

~i 4 - - ~i~a

~i~a is generally negligible in comparison to 4 because FDCD signals are generally less that 10 -2. The Kuhn dissymmetry factor is then simply the difference between the FDCD signal of the optically active component and the optically inactive reference recovered in LRFDCD:

- ~, - ~a- ( 1 7 ) Ei

Alternatively, the Kuhn dissymmetry factor can simply

APPLIED SPECTROSCOPY 169

S: light source

M: monochromator

P: polarizing cube

PC: Pockels cell

m: mirror

bs: beam splitter

LP1-4: linear polarizers

BSC: Babinet-Soleil Compensator Sam: sample chamber

F: filters

F iG. 1.

m

N bs \

LPI ~ .-.--A

BSC 'l . . . . . . . . . . . . . . . . . . . . . .

', LP2 1 ~ ~ J i . . . . . . . . . . . . . . . . . . . . . . .

~ L

LP3 L L F LP4

S c h e m a t i c d i a g r a m o f t h e F D C D / L R F D C D i n s t r u m e n t .

be obtained by using Eq. 7, in which case subsequent correction for unequal intensities is unnecessary because the correction is intrinsically accomplished in the Ap- proach I calculation; the functions constructed from lifetime distributions are straightforwardly the Kuhn dissymmetry factors of the individual components.

(2) The optically inactive reference measurement is made separately. Steady-state FDCD measurements and LRFDCD Approach I variation and Approach II fall into this case. Since a pure, optically inactive reference is measured separately, the artifactual signal obtained is free of the R term, as in Eq. 13. With the realization that ~ a << 1 usually holds, Eq. 15 is simplified to

A e i ,~ ( ~ i - ~a ) -~- 2R - - z . . . . . . . . 0 8 )

E, R ( ( , - ~a) -q- 2

When total absorbance of the sample is low, R~, R~a <<

1 and

A ~ i - - (~ i - - ~ a ) -~ 2 R . ( 1 9 )

Ei

I fR << ~, ~a, the above equation reduces to the subtraction scheme at low absorbance, as has been previously described in the context of chromatographic detection. 4 The Kuhn dissymmetry factor of a chiral component is then simply the difference between the measured FDCD signal of the optically active component (contaminated by the /3 factor) and the artifactual signal for the optically inactive reference:

- - ~i - - ~a" ( 2 0 ) c/

EXPERIMENTAL

Reagents. Carbazole, pyrene (99%), (R)-( - ) - l , l ' -b i - naphthyl-2,2'-diyl hydrogen phosphate (RBNPA, 99%), and (S)-(+)- 1, l ' -binaphthyl-2,2'-diyl hydrogen phos-

phate (SBNPA, 99%) were purchased from Aldrich (Mil- waukee, WI). Benzo(a)pyrene (BaP) was purchased from Ultra Scientific (N. Kingstown, RI). The (1S)-(+)-10- camphorsulfonic acid (CSA, 99%) was purchased from Sigma (St. Louis, MO). All reagents were used as purchased, without further purification. The CSA solution was prepared in HPLC-grade deionized water. All other solutions were prepared in ethanol (Aaper Alcohol and Chemical Co., Shelbyville, KY).

Instrumentation. The FDCD and LRFDCD measurements were performed on a commercial phase-modulation spectrofluorometer (48000S, SLM Instruments, Inc., Urbana, IL) that was modified in-house to generate circularly polarized light. 8,~° A schematic diagram of the instrument is shown in Fig. 1. Light generated by a 450-W xenon arc lamp or sharp lines from a 500-W xenon/mer- cury arc lamp were selected by an excitation monochromator with the use o f a 1-nm bandwidth. In steady-state FDCD measurements, the light is reflected directly into the excitation channel by a mirror (m). In LRFDCD measurements, the light passes through a Pockels cell (PC) to sinusoidally modulate the beam intensity to accomplish lifetime resolution in the frequency domain. In either case, a beamsplitter (hs) then sends a small portion of the modulated beam to a reference PMT (Hamamatsu Model R928P) to compensate for source intensity fluc- tuations in FDCD or to serve as a phase-stopping channel in the dynamic LRFDCD measurements. A combination ofa Glan-Thompson polarizer (LP1) set to pass vertically polarized light and a motorized Babinet-Soleil Compen- sator (BSC) then renders the excitation light circularly polarized. The thickness of the BSC is set by computer to generate quarter wave retardation (X/4) and three-quarter wave retardation (3M4) for LCPL and RCPL, respectively, at each wavelength. Here, the samples were measured in strain-free fused-silica fluorescence cells. The temperature of the sample compartment was maintained by a temperature controller (Haake A81) at 25.0 _+ 0. I°C. In the emission channel, a combination of short-pass and long-pass filters was used to eliminate the major Raman scattering peak and the first- and second-order Rayleigh scattering. Fluorescence was collected with right-angle configuration by a PMT (Hamamatsu Model R928P).

In steady-state FDCD measurements, a macro program written in-house in the SLM software environment con- trois the collection of fluorescence intensity at alternating left and right circular polarizations. Each experimental FDCD value is the average of 25 consecutive pairs of alternating LCPL and RCPL excitation measurements, in which each intensity measurement is collected as the average of 50 internal samplings. In LRFDCD, the fluorescence lifetime measurements were made with the use of ten modulation frequencies in the range of 8.9 to 141.3 MHz. An ethanolic solution of carbazole was used as the lifetime reference (r = 9.3 ns) in order to reduce color effects of the PMT. 13 Measurements of reference-sample pairs were taken until phase deviations were smaller than 0.5 ° and modulation deviations were smaller than 0.005, or until the number of pairs reached 20.

Photoselection effects may introduce errors in both FDCD 14 and LRFDCD measurements 15 due to aniso- tropic distributions of transition dipole moments of excited-state molecules when the rotational reorientation of


molecules is slow. In order to determine the need for correction of photoselection effects in this work, the fluorescence lifetimes and rotational correlation times of SBNPA and carbazole were determined. A multihar- monic Fourier transform phase-modulation spectrofluorometer (Model 48000 MHF, SLM Instruments, Inc, Ur- bana, IL) excited at the 325-nm line of a He-Cd laser was used for these measurements. The rotational correlation times of SBNPA and carbazole in ethanol at 25°C were determined to be 110 ps and < 100 ps, respectively, which are significantly smaller than their respective fluorescence lifetimes of 2.8 ns for SBNPA and 9.3 ns for carbazole. Correction for photoselection effects was thus unnecessary, and no polarizer was used in the emission channel for the FDCD and LRFDCD measurements. Since the orientations of the excited-state molecules are effi- ciently randomized by rotational diffusion, the polarization dependence of the PMT did not present a problem.

Fluorescence lifetime data analysis was performed with the use of commercial nonlinear least-squares software (Globals Unlimited, Urbana, IL) . 16 For LRFDCD, the multifrequency data files for LCPL and RCPL excitation were globally linked by fluorescence lifetimes, which is valid since fluorescence lifetime is independent of the sense of the circular polarization of the exciting light. By the procedure of globally linking the two data sets, the chi-squares surface around the minimum is better defined for accurate estimation of the parameters. 17 The lifetimes in the fits were fixed to values determined for the same mixture with the use of the MHF instrument. Global linking ofLCPL, RCPL, and linearly polarized excitation (MHF) data files yielded results similar to those obtained by linking the LCPL and RCPL files only.

Absorbance was measured on a Hewlett-Packard 8451A diode array spectrophotometer. An Aviv 40DS circular dichroism spectropolarimeter was used for the absorption CD measurements.

RESULTS AND DISCUSSION

Generation of Circular Polarization. The circular polarization is generated by passing the excitation beam through LP1 and the BSC. In the alignment procedure, the BSC is removed and a linear polarizer LP2 is inserted between LP1 and the sample chamber and set to pass horizontally polarized light. LP1 is then rotated until the extinction point is reached, at which point it is set to vertical polarization. The orientation of LP1 is also ad- justed to make its optical surface perpendicular to the exciting beam. The BSC is then inserted between LP1 and LP2 and also positioned to be perpendicular to the exciting beam. The BSC is rotated to again reach extinction. One of the two optic axes of the BSC now lies parallel with the LP1 polarization, or vertically oriented. The optic axes of the BSC are then rotated by 45 ° to be bisected by the electric field vector of the incident, linearly polarized beam. The thickness of the motorized BSC is computer controlled to generate X/4 or 3X/4 retardation to generate LCPL or RCPL at the excitation wavelength.

The linear polarizer LP2 also acts as an analyzer to check the purity of circular polarization. If the light is perfectly circularly polarized, the intensity of the beam transmitted through LP2 should be independent of the

angle setting of LP2. In the alignment procedure, the intensity is measured at four angle settings of L P 2 : 0 ° (vertical), 35.26 °, 54.74 °, and 90 ° (horizontal). Since the PMT efficiency is polarization dependent, the purity of circular polarization cannot be measured by directly send- ing the light into a PMT. Instead, a fluorophore solution with fast rotational reorientation is employed to random- ize the linear polarization. The excitation intensity is measured via the fluorescence of this solution. An ethanolic solution of carbazole is a good candidate because its fluorescence lifetime is at least 100 times longer than its rotational correlation time. Several other fluorophores were also used, and yielded essentially identical results to the carbazole solution.

Because the image of the incident light on LP2 is fixed in the orientation of the excitation monochromator exit slit while the square window of LP2 must be rotated to achieve different polarization angle settings, the image and intensity of light transmitted through LP2 are polarization angle dependent and vary with the window shape of LP2 viewed by the exit slit at different angles. A mask is therefore inserted between LP2 and the sample in order to select only the center portion of the beam for excitation and thereby ensure a constant beam shape. The fluorescence intensity detected by the PMT is then free of polarization effects, and the intensities at the four different angles of LP2 can be compared. Verification of the purity of circular polarization proved to be very crucial in the FDCD and LRFDCD measurements. Imperfect circular polarization resulted in large, inaccurate signals. We found that accurate measurements could be achieved ifLP1 and the BSC were aligned so that the intensities (steady state for FDCD, dc component for LRFDCD) measured at the four angle settings of LP2 were within one percent of each other for both LCPL and RCPL. LP2 is removed once the alignment process has been completed. The mask is replaced by a lens which focuses the excitation beam into the sample cell. The lens did not have any detectable effects on the FDCD or LRFDCD measurements.

Ideally, the excitation beam should be perpendicular to the optical surfaces of both LP1 and the BSC, and the polarization of LP1 should exactly bisect the two optic axes of the BSC to ensure circular polarization. In the actual experiment, deviations from these ideal conditions may occur. Several experiments were performed to eval- uate the relative importance of these different aspects of alignment. The angle of incidence of the light on LP1 proved to have small effects on the quality of circular polarization, and only slight changes in the polarization shape were observed when the LP1 orientation was al- tered relative to the excitation beam because of the large acceptance angle of the Glan-Thompson polarizer. The angle between LP1 and the optic axes of the BSC also shifts the polarization shape. If one changes this angle from <45 °, through 45 ° and then >45 °, the light emerging from the BSC changes from elliptically polarized to circularly polarized, and then to elliptically polarized again but with the major and minor axes of the ellipse reversed. The effect was significant, however, only when the angle deviated from 45 ° by a degree or more. In routine align- ments, much smaller variations in this angle occur (less than 0.3 ° ) and result in relatively small changes in the polarization shape.


5.0e-03 @ 1. Pyrene

4.0e-03 H N

2, Carbazole L9

3.0e 03 o o o o o 3. RBNPA ~ O x /OH

4. (±)BNPA ~ / ~ O

2.0e-03 5. SBNPA

6. BaP (1)

CZV 1.0e-03 I I ~ ¢ I r I 7. BaP (II) I 2 3 4 5 6 7

Compound

FiG. 2. F D C D s igna l s o f s o m e o p t i c a l l y a c t i v e a n d i n a c t i v e c o m - p o u n d s . T h e e x c i t a t i o n w a v e l e n g t h w a s 3 1 4 n m . B a P (II) w a s m e a s u r e d 14 h a f t e r B a P (I) fo r t h e s a m e s o l u t i o n .

The most significant change in polarization was observed when the incident angle of the excitation beam on the BSC was varied. The deviation of the incident light from the normal of the optical surface results in both uneven amplitude projection onto the fast and slow axes and changes in the propagation length of the excitation beam in the crystal, leading to deviations from the quarter wave and three-quarter wave thicknesses that are required to generate LCPL and RCPL, respectively. Within the possible alignment variations, the polarization shape can change significantly from circular polarization to elliptical polarization with varying degrees of ellipticity that may be quite large. Although this aspect of alignment is clearly the most critical, it is important to minimize deviations in all aspects of alignment--the incident angle on LP1, the optical axis angle of the BSC, and the incident angle on the BSC--in order to ensure accurate results because of the very small intensity differences that must be detected in FDCD or resolved in LRFDCD.

Note that an optical configuration that generates perfect LCPL at quarter wave retardation does not guarantee perfect circular polarization for RCPL at three-quarter wave retardation. The angle between the plane of linear polarization and the optic axes of the BSC could be skewed from 45 ° and still allow pure LCPL to be generated if the light beam is passed through the BSC at an angle slightly off the crystal surface normal, which produces the nec- essary additional retardation adjustment. When the thickness of the crystal is subsequently changed for RCPL, the additional retardation adjustment may no longer exactly compensate for the deviation in the angle between linear polarization and the BSC optic axis, resulting in elliptically polarized light. In this work, the optical components were very carefully aligned to produce high-purity circular polarization for both LCPL and RCPL.

An important finding was that, even when the optical alignment was significantly skewed away from circular polarization, a statistically significant FDCD signal was never observed for two optically inactive samples: 2.0 uM pyrene solution and 2.8 uM BaP solution. This ob- servation indicates that the absence of a significant FDCD signal as reported by an optically inactive sample is not a reliable indicator of the purity of circular polarization. The optically inactive samples are sensitive only to the excitation intensity and not to the circular polarization.

T A B L E I. FDCD signals, standard deviations, and signal-to-noise r a - t ios for several optically active and inactive compounds (excitation a t 3 1 4 nm) .

C o m p o u n d IFDCD S D S / N

P y r e n e 2 .9 x 10 -3 6 x 10 " 5 C a r b a z o l e 2 .9 x 10 3 4 x 10 -4 7 R B N P A 4 .0 x 10 -3 5 x 10 " 8 (_+) B N P A 3 .0 x 10 -3 4 x 10 4 8 S B N P A 2 .0 X 10 -3 3 X 10 -4 7 B a P (I) a 3 .0 x 10 -3 4 x 10 4 8 B a P (II)" 3 .0 x 10 -3 4 x 10 4 8

a Measurement II was made 14 h after measurement I.

Purity of circular polarization must be checked by place- ment of an analyzer (LP2) in the beam after the BSC, as described above in the alignment procedure. On the other hand, a significant FDCD signal for an optically inactive sample is not always an indication of noncircularly polarized light. It may be a result of unequal excitation intensities of LCPL and RCPL, as illustrated in the next section.

Steady-State FDCD Measurements. FDCD measurements were made for four optically inactive samples and two optically active samples. Pyrene, carbazole, and BaP are planar molecules without centers of asymmetry and are therefore intrinsically optically inactive. The other optically inactive sample was the racemate (+)BNPA. The two optically active samples were solutions of the individual enantiomers RBNPA and SBNPA. If the intensities of LCPL and RCPL are exactly equal, the four optically inactive samples should show negligible FDCD signals, while the two enantiomers should have FDCD signals of opposite polarity and equal amplitudes.

The experimental results are shown in Fig. 2 and Table I. The ratios of FDCD signal to standard deviation range from 5 to 8, indicating good signal-to-noise (S/N) ratios. The four optically inactive samples show significant artifactual FDCD signals, with essentially equal amplitudes. As expected from Eq. 13, the error introduced by unequal intensities is an instrumental error and thus should be independent of which optically inactive sample we use. The artifactual signal is proved to be invariant with the concentration of the optically inactive samples. The sta- bility of the instrument is demonstrated by the two FDCD measurements of the 2.8-uM BaP sample, which were made 14 h apart. RBNPA and SBNPA both show positive FDCD signals, but lying on opposite sides of the straight line formed by the four optically inactive samples and equidistant from the line. With correction for unequal intensities with the use of the average FDCD signal of the optically inactive samples (3.0 x 10-3), the Kuhn dissymmetry factors of the RBNPA and SBNPA solutions were calculated to be 1.0 x 10 -3 and - 1 . 0 x 10 -3, respectively. The fact that the magnitudes of these corrected FDCD signals are equal for the two enantiomers indicates that the excitation light, both LCPL and RCPL, is circularly polarized. The small standard deviation of 0.05 × 10 -3 in the FDCD signals of the optically inactive samples (2% relative standard deviation) shows that the artifactual FDCD signal is not dependent on the prop- erties of the optically inactive samples used.

The /3 factor, or the ratio of excitation intensities of LCPL and RCPL, was calculated by the following rela-


e,i

-2.0

-3.0

-4.0

-5.0

-6.0

-7.0

-8.0

-9.0

- 10.0 -6.0

I I I I I

10% of,5~/E 5.0X10 . ~ . f j r . . . . . . . .

z:// 'z// ' // ,.oxlo-2

,t. / /¢~V / / 5"0X10-3

~ / * AA/A 1.0Xl0 -3

7 ~ / " 5.Ox10 "4

e/e 1.0xl0 -4

a b c d

, , ,

-5.0 -4.0 -3.0 -2.0 -1.0 0.0

log A

FIG. 3. Effect of the 2R term on the FDCD signal as a function of total absorbance and circular dichroism of the sample. For a dissymmetry factor of 5.0 x 10 4, the magnitude of 2R reaches 10% of the signal if the sample absorbance A is greater than (a) 4.3 x 10 3, for zXA/A = 1.0 x 10-2; (b) 8.7 x 10 3, for LkA/A = 5.0 x 10-3; (c) 0.044, for,:kA/A = 1.0 x 10-3; and (d) 0.090, for ,SA/A = 5.0 x 10 -4.

t i onsh ip (which is a s impl i f ica t ion o f Eq. 14 when R a

= 0)

2 + ~ , /3 (21)

2 - ( ,

to be 1.003. Thus , the slight i m b a l a n c e be tween the ex- c i ta t ion in tens i t i es o f L C P L a n d R C P L o f 0.3% results in a shift o f over 300% in the F D C D signal o f R B N P A a n d yields the incorrec t m a g n i t u d e and sign for SBNPA.

The significance o f the R factor in the accurate calcu- la t ion of K u h n d i s s y m m e t r y factors is shown in Fig. 3. The R factor increased m o n o t o n i c a l l y wi th increas ing abso rbance a n d / o r C D o f the whole sample. For a typical K u h n d i s s y m m e t r y factor o f 5.0 x 10 -4, the m a g n i t u d e of 2R can easily exceed 10% of the signal. W h e n the rat io o f total C D to total ab so rbance zXA/A = 5.0 x 10 4, a 10% error is i n t r o d u c e d i f the c o n t r i b u t i o n o f 2R is ne-

glected w h e n ma t r ix a b s o r b a n c e exceeds 0.090. W h e n z2xA/A = 1.0 x 10 -3, the same percentage error results w h e n ma t r ix abso rbance exceeds 0.044. The co r respond- ing a b s o r b a n c e th resholds for 10% error are as low as 8.7 x 10 -3 a n d 4.3 x 10 -3 for & A / A values of 5.0 × 10 -3 a n d 1.0 × 10 -2. W h e n the ra t io o f total C D to the total ab so rbance increases, to le rance in a b s o r b a n c e becomes lower. The effect o f the R t e rm is mos t s ignif icant for samples with high c i rcular d i c h r o i sm a nd absorbance . Samples of biological in teres t of ten exceed these thresh- olds in total ab so rbance a n d CD, a n d samples with abso rbance higher t han 0.1 are rou t ine ly s tudied by F D C D . Signif icant errors in m e a s u r e d d i s s y m m e t r y factors could result i f s imple base l ine sub t r ac t ion were used to correct for u n e q u a l in tensi t ies . It is also shown in Fig. 3 tha t Eq. 19 is a va l id cor rec t ion scheme in mos t cases, because the m a g n i t u d e o f the R factor is usual ly smal ler t h a n 10 -2 a n d c o n d i t i o n s R~, R~a << 1 are usual ly satisfied.

The F D C D spec t rum of a 1 .0 -mM CSA so lu t ion is shown in Fig. 4. The er ror bars show typical va r i a t i ons in the F D C D m e a s u r e m e n t s o b t a i n e d with the use of the modi f i ed F D C D / L R F D C D i n s t r u m e n t . The F D C D signals, the co r r e spond ing s t anda rd dev ia t ions , a n d the ra- t ios o f the two are t abu la t ed in Tab le II. The rat io var ies f rom 7 at 260 n m to over 30 at 300 a n d 320 nm. The s igna l - to -noise rat io general ly increases with increas ing K u h n d i s s y m m e t r y factor. The opt ical ly inac t ive reference BaP shows smal l F D C D signals at all wave leng ths (Fig. 4 or Tab le II), wi th S /N rat ios be tween 0.2 a n d 2.1, i nd i ca t ing the absence of large art ifacts due to unequa l in tensi t ies .

A neu t r a l -dens i t y filter wi th 0.03 optical dens i ty was inser ted in to the R C P L exci ta t ion channe l to artificially i n t roduce u n e q u a l in tens i t i es be tween L C P L a n d RCPL, a n d the F D C D spectra o f the CSA a n d BaP so lu t ions were again m e a s u r e d (Fig. 5). The F D C D spec t rum o f CSA shows a s ignif icant increase in signal i n t ens i ty o f a p p r o x i m a t e l y 100%. M e a n w h i l e a significant, ar t i factual F D C D spec t rum was obse rved for BaP. The in t ens i ty ra t io of I°L/I~ i n t r o d u c e d by the neu t r a l -dens i ty filter is 1.072. The expected ar t i factual F D C D signal is then calcu la ted to be 0.069, which agrees well wi th the m e a s u r e d signal for BaP. The gradual increase in the ar t i factual F D C D signal wi th the decrease in wave leng th results f rom the gradual increase in opt ical dens i ty o f the neu t ra l - dens i ty filter wi th decreas ing wavelength . Correc t ing for

TABLE II. FDCD signals, standard deviations, and signal-to-noise ratios of CSA (1.0 mM) and BaP ~ at sequential excitation wavelengths.

CSA BaP

X (nm) IVDCD SD S/N IF~o SD S/N

260 2.7 x 10 -2 4 x 10 -3 7 2.0 x 10 s 2.2 x 10 3 0.9 265 2.3 x 10 -z 2 x 10 -3 12 0.3 x 10 -4 1.9 x 10 3 0.2 270 2.8 x 10 -2 4 x 10 -3 7 1.4 x 10 -3 1.5 x 10 3 0.9 275 3.6 x 10 2 2 x 10 3 18 -0.3 × 10 -3 1.6 x 10 -3 0.2 280 4.3 x 10 -2 2 x 10 3 22 1.6 x l0 -3 1.8 x 10 -s 0.9 285 4.8 x 10 2 2 x 10 3 24 1.2 x 10 3 1.6 x 10 -a 0.8 290 5.6 x 10 .2 3 x 10 .3 19 1.3 x 10 .3 1.9 x 10 -3 0.7 295 5.6 x 10 2 2 x 10 .3 28 1.0 x 10 .3 0.8 x 10 -3 1.2 300 5.9 x 10 2 2 x 10 3 30 1.7 x 10 3 0.8 x 10 -3 2.1 305 5.5 x 10 .2 2 x 10 .3 28 0.7 x 10 3 1.5 x 10 -3 0.5 310 4.7 x 10 2 2 x 10 3 24 1.4 x 10 3 1.3 x 10 -3 1.1 315 3.8 x 10 2 4 x 10 3 10 0.5 x 10 3 1.6 x 10 .3 0.3 320 3.1 x 10 2 1 x 10 3 31 0.9 x 10 3 1.3 x 10 3 0.7

- The concentration of BaP was intensity matched with the CSA solution at corresponding wavelengths.

APPLIED SPECTROSCOPY 17:3

e~

0.06

0.04

0.02

0.00

I I i 1

/ \ O : \ O

/ o O

o,j/

o'~,o., . .~,~ o ~ . O - - o - - o - - I ~ O ~ o - - O ~ o _ ~

I I I I

260 280 300 320

W a v e l e n g t h ( n m )

FiG. 4. FDCD spectra of CSA (-O-) and BaP (-O-). The BaP concentration was set so that the fluorescence intensity was approximately equal to that of the CSA at the corresponding wavelengths. Error bars (_+ 1 standard deviation) are shown for several points, including those with the largest standard deviations.

0.15 I I I I

t~

0.12

0.09

0.06

0.03

/ o / N o

/ O ~ O ~ O IIP~ I

V ~ V " V ~ V ~ V~.V~..V._ V. . V ~ v _ . V ~ v ~ V

, . , . / / "%,, 0.00 I I I I

260 280 300 320

Wavelength (nm)

FiG. 5. FDCD spectra of CSA (-O-) and BaP (-v-) in the presence of unequal LCPL and RCPL intensities, created by placing a neutral-density filter with 0.03 optical density into the RCPL excitation; and dissymmetry factor spectra of CSA after correction for unequal intensities (-v-) and in the absence of unequal intensities (-O-).

unequal intensities using Eq. 19 and BaP as the optically inactive reference results in a corrected FDCD spectrum of CSA that is consistent with the spectrum obtained in the absence o f the introduced unequal intensities (Fig. 5). This result illustrates accurate correction for the unequal intensities by the der ived scheme•

LRFDCD. L R F D C D was performed on a mixture of carbazole and SBNPA. The Kuhn dissymmetry factor of SBNPA was calculated in the Approach I experiment with the use o f Eq. 7, with carbazole serving as the added optically inactive reference. The recovered value was - 0 . 9 × 10 -3. With the incorporat ion of the steady-state fluorescence intensities upon excitation with LCPL and RCPL in Approach I variat ion (Eq. 8), the F D C D signals recovered by L R F D C D for carbazole and SBNPA were --0.5 x 10 -3 and - 1 . 4 x l 0 - 3 , respectively. The artifactual F DC D signal for the optically inactive carbazole is again caused by unequal intensities o f LCPL and RCPL: I°L/I~ = 0.9995 (the RCPL intensity exceeds the LCPL intensity by 0.05%), as calculated from the artifactual F D C D signal of carbazole. The result o f this small imbalance between LCPL and RCPL intensities is the in- t roduct ion o f a large error o f 56% in the calculated F D CD signal of SBNPA.

The recovered Kuhn dissymmetry factor of SBNPA with the use o f the Approach I variat ion after correction for unequal intensities was - 0 . 9 x 1 0 - 3 , which is the same value that was recovered with Approach I. The consistency between Approach I, which only utilizes the parameters recovered in the dynamic lifetime experiment, and Approach I variation, which utilizes both steady-state and dynamic fluorescence measurements , indicates the applicability o f the correction scheme in the L R F D C D measurements and verifies the L R F D C D the-

ory. The d issymmetry factors recovered in the L R F D C D experiments are in good agreement with the d issymmetry factor o f - 1 . 0 x 10 -3 measured for pure SBNPA by steady-state FDCD.

E f f e c t s o f I m p u r e C i r c u l a r P o l a r i z a t i o n . The scheme presented in this paper corrects for unequal intensities of pure LCPL and RCPL excitation. Extreme care was taken to ensure the purity o f circular polarization and, thus, accurate measurement . In the event that a linear polarization residue is present in the circularly polarized light, a dual P M T configuration can be used to partially eliminate the artifact? The following correction scheme, which is der ived similarly to the correction scheme presented for unequal intensities of perfectly circularly polarized light, can be used to fully correct for imperfectly circularly polarized excitation because any polarization state can be decomposed into a linear combinat ion o f left and right circularly polarized light, which form an or thonormal basis. I f the imperfect left (or right) circularly polarized light is decomposed into a pure left (or right) circularly polarized light beam, I ° (or I°), and a right (or left) circularly polarized "residue", I~ (or I°'), the measured FDCD signal is

eeA . (1 - 10-AL)(IOL -- [0L') -- eRAL(1 -- 10--A")(I0. -- I0. ' ) IFDCD eLAR(1 - - 10-A,)(I ° + I °') + eRAL(1 -- 10--AR)(I ° + I °')

= 6L(I~ - - I f ) + eR(I~ -- I f ) EL(I ° -Jr I o') + %(1 ° + I o')

ek(IO -- I o') -- %(1 ° -- I o') - R

%(1 ° - i o,) + eR(I ° -- I o') X

1 - %(1° + I° ' ) - eR(I° + I°')R eL(/° q- I o') + ER(I ° + I o')

(22)

1 7 4 V o l u m e 4 8 , N u m b e r 2 , 1 9 9 4

Three parameters are needed to characterize the intensity ratios between IOL, IOR, I0L ', and I~, from which accurate F D C D signals can then be calculated. The three parameters are determined by measuring the F D C D signals for three standards which can be solutions o f any three compounds with different, known Kuhn dissymmetry factors (one o f which may be optically inactive). In this way, it should be possible to accomplish accurate measurements in F D C D or L R F D C D despite imperfect circular polarization. This correction scheme is currently under inves- tigation.

C O N C L U S I O N S

The mathematical treatment for the correction of artifactual signals due to unequal LCPL and RCPL excitation intensities was introduced, and its successful ap- p l ica t ion to s imple so lu t ions o f ch i rophore s was demonstrated for both F D C D and LRFDCD. With the use o f a correct approach to optical alignment, and proper consideration and correction of experimental artifacts, accurate measurements were achieved. The imbalance between LCPL and RCPL intensities is one of the major artifacts in F D C D and L R F D C D measurements. For most of the samples used in this work, sample absorbance was low enough to allow correction o f unequal intensities by simple subtraction. For many biological samples, where the L R F D C D technique promises the most potential, the unequal intensities must be treated in the general case, with consideration o f matrix absorbance and CD.

It is important to note the limitations of using optically inactive reference samples for checking optical alignment. An optically inactive reference solution of an achiral compound will have an artifactual F D C D signal if the intensities of LCPL and RCPL are significantly different, but not if the intensities are equal, even if the light is not perfectly circularly polarized. An optically inactive solution o f a racemic mixture will have a significant artifactual signal in the case of unequal intensities or in the case of incomplete circular polarization, unless the latter contains equal but opposite linear residues for RCPL and LCPL, in which case they will cancel out and the racemate also will fail to indicate the impure circular polarization. The best approach is the one used in this work, in which an achiral reference is used to check for unequal inten-

sities and a linear polarizer is used as an analyzer to ensure complete circular polarization o f the individual LCPL and R C P L beams, which is made possible by the use of a static device to generate the circularly polarized light.

ACKNOWLEDGMENTS

This work was supported by the National Science Foundation through Grant No. CHE-9111928. L. Geng thanks the American Chemical So- ciety Division of Analytical Chemistry for a Full Year Graduate Fel- lowship sponsored by Eli Lilly and Corporation.

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