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Raman Optical Activity, Spectrometers
Raman Optical Activity, Spectrometers Werner Hug, University of Fribourg, Switzerland & 2010 Elsevier Ltd. All rights reserved.
Symbols 2
a b2 aG0 2 bG2 0 ¼ c b2A ¼ d
2
K ¼ Kp n
drp(h)
Dndrp(h)
Dp(h) Sab
isotropic Raman invariant anisotropic Raman invariant isotropic ROA invariant anisotropic ROA invariant due to the optical activity tensor anisotropic ROA invariant due to the quadrupole tensor (if specified for a particular vibration p) defined by Equation [3] differential scattering cross section for Raman scattering into an element of solid angle O under the angle y difference of differential scattering cross sections for left and right circularly polarized light ratio of ROA to Raman scattering similarity of two spectra, defined by Equation [5]
Abbreviations CCDs ICP ROA SCP VCD
charge-coupled devices incident circular polarization Raman optical activity scattered circular polarization vibrational circular dichroism
Raman optical activity (ROA) or, more precisely, spontaneous vibrational ROA scattering is, like vibrational circular dichroism (VCD), a spectroscopic method that directly probes the handedness, or chirality, of molecular vibrations. ROA of molecular origin was the first of the two phenomena to be measured, though not by much, in 1973. The decisive technologies that enabled the experimental demonstration of ROA were the invention of the argon ion laser, the availability of KD*P electrooptic modulators developed for laser Q-switching, and singlephoton counting. Decisive progress on the reliable collection of ROA data has been made since, and commercial spectrometers have made their appearance. Most present instruments use a backscattering configuration first described at the beginning of the 1980s rather than the earlier right angle configuration. Backscattering is expected to remain the preferred arrangement for biological samples, but for analytic purposes, right angle scattering retains the advantage of requiring smaller samples.
The advances in the measurement of ROA over the past three decades fall into three categories. The first reflects the progress in general Raman instrumentation: multichannel detection with backthinned charge-coupled devices (CCDs) combined with high-luminosity spectrographs based on holographic grating technology, and solid state lasers replacing gas lasers. The second is the conceptual solution of the offset problem ubiquitous in optical activity and the scourge of early ROA measurements. The third are improvements in light collection, sample cell, and handling techniques that have led to a reduction in the amount of the sample required by an order of magnitude, to less than a microliter, and also in backscattering.
ROA Variants There is a wide variety of scattering geometries and polarization schemes that can be used for ROA measurements. Some instrumental parts are common to all, such as lasers, spectrographs, and detectors, but light collection optics and offset reduction schemes may differ. This article will concentrate on the practically relevant or promising arrangements and merely point out others. It will discuss neither the potential use of Fourier transform Raman spectroscopy for ROA nor nonlinear ROA, as no experiments have been demonstrated. Basic Measurement Arrangements The scattering geometries of practical importance are right angle (901), backward (1801), and forward (01) scattering. The 01 and 1801 scattering geometries yield different ROA information, in contrast to ordinary Raman scattering where the signals are identical. ROA intensities are, in general, largest for 1801 and smallest for 01 scattering, with 901 somewhere in between, but details depend on the particular Raman band one observes. For any chosen scattering angle, ROA can be observed either by modulating the incident light between right and left circular (ICP, incident circular polarization) or by analyzing the content of the right and left circular component in the scattered light (SCP, scattered circular polarization). This analysis can be done either by separately measuring the intensity of each circular component or by determining the ellipticity of the scattered light, but only the first method has so far found practical application. The simultaneous modulation of the circularity of the incident light and of the analysis of the
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Raman Optical Activity, Spectrometers
Table 1 Invariant combinations of SCP scattering cross sections for different geometries. ICP cross sections are a factor of 2 larger because they apply to the combined results of a distinct right and left modulation period Scattering angle
Incident polarization
Difference 4ðK =cÞ
Sum K
01 1801 901
Unpolarized Unpolarized Polarized Depolarized Unpolarized
90aG 0 þ 2b2G 2b2A 12b2G þ 4b2A 45aG 0 þ 7b2G þ b2A 6b2G 2b2A 2p 0 2 3 ð180aG þ 40bG Þ
90a2 þ 14b2 90a2 þ 14b2 90a2 þ 14b2 12b2
Integral
4p 2 3 ð180a
þ 40b 2 Þ
aG0 , isotropic ROA invariant due to the optical activity tensor; b2, anisotropic Raman invariant; c, speed of light.
circular polarization of the scattered light yields two dual circular polarization schemes, namely, DCPI for in-phase and DCPII for out-of-phase modulation and detection, where in-phase means the detection of the right circular content when the incident light is also right circularly polarized. The information provided by the two schemes differs and DPII only is of stereochemical interest. In an ICP experiment, the scattered light may or may not be polarization analyzed with a linear polarizer, and in an SCP experiment the exciting light can be linearly or naturally (n) polarized. In right angle scattering this allows the determination of a polarized and a depolarized ROA component, depending on whether the orientation of a linear polarizer is chosen perpendicular or parallel to the scattering plane, respectively. Of the multitude of experimental configurations ensuing from the combination of different geometries and polarization schemes, those of practical relevance are collected in Table 1. Included is the theoretically important cross section for scattering into a solid angle of 4p as its combination of tensor invariants is devoid of quadrupole contributions, and as it can readily be obtained from a polarized and a depolarized right angle ROA measurement.
on the dimensionless ratio D of ROA to Raman scattering, which is independent of many instrumental parameters. For SCP backscattering (scattering angle y ¼ p) with naturally (n) polarized exciting light one has for the average value, and the difference, respectively, of the differential scattering cross sections n dspL and n dspR , for vibration p for left (L) and right (R) circularly polarized light n
1 dsp ðpÞSCP ¼ ðn dspR þn d spL Þ 2 ¼ K p ð90a 2p þ 14b2p Þ dO
½1
D n dsp ðpÞSCP ¼ ðn dspL n dspR Þ ¼ Kp ¼
4K p ð12b2Gp þ 4b2Ap Þ dO c
1 m0 2 o0 o3p 90 4p
½2 ½3
The minus sign for Dds renders the standard definition of molecular quantities as left minus right in optical activity compatible with the ROA convention to represent scattering intensities as right minus left. o0 and op are the pulsations of the exciting and the scattered light, respectively, c the speed of light, and m0 is the permeability of the vacuum. D values follow from eqns [1] and [2] as
The Comparison of Experimental Data Except for band positions, measurements that yield different combinations of invariants of the scattering tensors according to Table 1 are not comparable. The ratio of the five Raman and ROA invariants of the scattering tensor can be extracted from three separate measurements, but this has been done only once. A qualitative comparison of backscattering with depolarized right angle ROA spectra can be meaningful if both are determined by the anisotropic invariant b2G . The quantitative comparison of ROA data with the same invariant combination is possible, in the form of recorded photons per joule of exciting energy, if the data have been recorded under identical conditions. Absolute scattering cross sections have so far not been measured in ROA. A better than merely qualitative comparison of ROA spectra measured under different conditions can be based
n
Dp ðpÞSCP ¼ n n
¼n ¼
dI pR ðpÞ n dI pL ðpÞ dI pR ðpÞ þn dI pL ðpÞ dspR ðpÞ n dspL ðpÞ dspR ðpÞ þn dspL ðpÞ
2 2 2 12bGp þ 4bAp c 90a2p þ 14b2p
½4
where n dI pR and n dI pL are the scattering intensities for right and left circularly polarized light, respectively, for scattering into an infinitesimal element of the solid angle O. ds measures the rate at which energy is removed from the incident beam by scattering, relative to the rate at which energy crosses a unit area perpendicular to the direction of propagation of the incident beam. ds/dO relates to the power scattered into a given element of
Raman Optical Activity, Spectrometers
solid angle dO, and dI is therefore proportional to it. Expressions for other scattering geometries follow from the invariant combinations in Table 1. In an actual measurement, a substantial solid angle is used for collecting light, and measured D values depend on this light collection angle. They depend further on the resolution of the instrument because isotropic and anisotropic invariants of the scattering tensor lead to bands of different width. D also depends on the exciting wavelength l as 1/l. This dependence is not explicit in eqn [4] but follows from the frequency dependence of the invariants. A second way to compare two experimental ROA spectra a and b can be based on their similarity Sab defined as: Pn˜2 n˜ ¼n˜1 I a;n˜ I b;n˜ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Sab ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn˜2 Pn˜2 ˜n¼n˜1 I a;n˜ I a;n˜ ˜n¼n˜1 I b;n˜ I b;n˜
½5
The summation is over discrete wavenumbers n˜ between the limits n˜1 and n˜2 . The similarity of spectra with the same intensity ratio of bands has a value of 1. Spectra recorded in a flat window sample cell and a capillary yielding lower scattering intensities will retain this value, except for the influence of a different light collection angle. Sab and D are useful for identifying instrumental artifacts.
Noise and Its Reduction in ROA Measurements ROA is a small difference of two already small quantities, with values of |D| rarely exceeding 103. Noise therefore sets the limits to the measurement of ROA. There are three noise components that can be distinguished: shot noise, flicker noise, and deterministic offset. They affect spectra differently, and their reduction requires distinct approaches. Shot Noise In the shot noise limited case, where the Raman intensity I is represented by N events, in our case detected scattered photons, the statistics of a Poisson distribution hold. With IREILEI, the rms pffiffiffiffiffiffi ffi deviation of DN corresponding to DI ¼ IR IL is 2N : Thus, to recover DN ¼ jDj N with a signal-to-noise ratio of Z, the number of detected photons needs to be pffiffiffiffiffiffiffi Z2 DN ¼ jDj N ¼ Z 2N ; N¯ ¼ 2 2 D
½6
For a typical value of |D| ¼ 5 104 and a desired minimal rms signal-to-noise ratio of Z ¼ 10, one needs to detect close to 109 photons per spectral element of
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resolution. This number is put into perspective by comparing it to the value of 5.5 104 detected photons per second obtained in backscattering at 4 cm1 resolution with a modern commercial Raman instrument, equipped with a CCD detector and a 15 mW He–Ne laser, for the peak height of the exceptionally strong 992 cm1 band of benzene. In comparison to shot noise, in view of the large number of photons needed in ROA, readout noise is negligible for modern slow-scan CCD detectors. The recipes for the reduction in shot noise are simple: an exciting laser with sufficient power, efficient collection of the scattered light, spectrographs with a large e´tendue (the amount of light that an optical system is capable of collecting), and multichannel detectors with a high quantum efficiency. Shot noise reduction has reached limits that cannot easily be pushed much further. It is the one area where ROA has profited most from the general advances in Raman instrumentation. Flicker Noise While shot noise, which follows a Gaussian distribution, increases as the square root of the measurement time, with the signal-to-noise ratio improving at the same rate, the cumulative error due to flicker noise tends to increase faster than shot noise. The improvement in the flicker signal-to-noise ratio with measurement time can therefore be slow or nonexistent. In clocks, for example, after the elimination of all systematic drifts, there remains an error due to flicker noise that is known to increase at least linearly with time. No analysis of flicker noise sources in ROA has been published. The influence of dust in the sample, which tends to get trapped by the optical tweezer effect in the waist of the focused laser beam, is well known, as is the influence of optical schlieren through local heating. Flicker noise in ROA does not seem to follow the 1/f behavior often observed for electronic circuitry, with f being the frequency, but it is prominent at low frequencies. Reducing it requires high modulation rates in ICP, or a switch to SCP where it can be reduced by the simultaneous detection of right and left circularly polarized scattered light. Deterministic Offset Spurious signals due to systematic instrumental offset are akin to deterministic drift in a clockwork. Such artifacts neither are reduced by an increase in observation time, nor they can be detected by the comparison of subsequent measurements done with the same instrument under identical conditions. Deterministic offset is at the root of early erroneous reports of measured vibrational optical activity. The mechanisms leading to spurious signals can have their root in timing errors, electrical and mechanical
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Raman Optical Activity, Spectrometers
perturbations synchronized with the data acquisition cycle, or optical errors leading to unequal intensities for right and left circular light unrelated to the sample’s ROA properties. The sample itself might exhibit undesirable characteristics such as turbidity, an optically active fluorescent background, or differential absorption for right and left circularly polarized light. From the point of view of optical offset, depolarized right angle ICP is the easiest ROA measurement as imprecisions in the circular polarization of the exciting light do not produce artificial scattering differences. This is true for small light collection angles. The reliable recording with large collection angles requires optics such as the dual-lens light collection system used for the first recording of polarized right angle ICP ROA. The successful measurement of ICP backscattering depends, in turn, on the depolarization of the scattered light because dispersive systems and detectors are polarization sensitive. SCP backscattering is highly sensitive to a component of circularly polarized light in the exciting light, as it will show up, depending on the polarization of Raman bands, as a spurious ROA signal. With linearly polarized exciting light, optical birefringences in the focusing lens and the scattering cell, even with otherwise perfect optics, tend to render the light in the scattering zone elliptical. Routine SCP measurements therefore require depolarized exciting light. An often overlooked problem are reflections of the exciting and the scattered light on optical surfaces, including the walls of the scattering cell.
Instrument Building Blocks Figure 1 gives an overview of the major functional parts of a backscattering SCP ROA spectrometer. In an ICP instrument, a circular polarization modulator in the incident light would replace the circular polarization analyzer in the scattered light. A DCP instrument would be obtained by combining the SCP and ICP building blocks. A dual-arm system is not mandatory for ICP and DCP, but switching the scattered light between two arms, synchronized with a rapid modulation of the exciting light, is a way to reduce flicker noise. Lasers Except for sufficient power, no particular requirements exist for the exciting laser. The tiny ROA effects of chirally deuterated neopentane were measured in backscattering with a frequency-doubled Yb:YAG thin-disk laser intended for display and machining purposes. Such lasers have no longitudinal coherence and are not transverse single mode. A laser’s transverse mode properties can matter in right angle scattering where the waist of the focused beam is imaged onto the entrance slit of the spectrograph.
The choice of exciting wavelengths in ROA has followed the availability of sufficiently reliable and powerful lasers: the 488 and 514.5 nm lines of the argon ion laser were initially used, but now the 532 nm line of the frequency-doubled YAG is common. Excitation in the red or near-infrared region would be preferable for reducing Raman spectroscopy’s ubiquitous fluorescence problem. The 1/l dependence of D, in addition to the fourth power 1/l dependence of Raman scattering, and the lack of sufficiently powerful and reliable continuous wave lasers in the 650–800 nm range, have hampered ROA at these longer wavelengths. CW laser powers of tens of watts are easily available at 1.06 mm, the wavelength of the nondoubled YAG, but problems with sample heating by the absorption of vibrational overtones, and the lack of suitable multichannel detectors, render 1.06 mm excitation unattractive. With green exciting light, 100–400 mW of laser power at the sample is typical for measurements of organic liquids, but 1000 mW can be desirable for aqueous solutions of proteins. Focusing and Light Collection Optics Figure 2 shows the focusing and light collection optics of an SCP instrument capable of measuring forward and backward scattering. A single Gradium lens is often used for focusing and collecting the backscattered light, but separate lenses as depicted in the figure allow for a softer focusing of the laser in the sample, and they eliminate stray light from fluorescence and Raman scattering produced inside a focusing lens also used for light collection. The nonimaging optics collect the light from a 2–3 mm long segment of the focused beam in the sample, as discussed in the context of sample cells (‘see Sample Cells’). This length is determined by the focal length of 30 mm of the light collection lens, 100 mm of the lens focusing light onto the fiber optics, and the diameter of approximately 1.56 mm of each of the two circular entrance ends of the fiber optics cross section transformer. Its two branches guide the light due to the right and left circular component of the scattered light into the spectrograph, as shown in Figure 1. Figure 3 shows a light collection optics capable of filling, also in right angle scattering, the e´tendue of a modern holographic planar grating spectrograph. In ICP, the dual-lens system also suppresses offsets otherwise caused by a deviation from circular of the polarization of the exciting light. Throughput can exceed that achievable with fiber optics in backscattering. Polarization Conditioning and Polarization Analyzing Optics Precise polarization control is quintessential to the elimination of offset in all but depolarized ICP right
Raman Optical Activity, Spectrometers
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Laser
Mechanical shutter
Polarization conditioner
Polarizing beam splitting cube
Sample cell
Fiber optics cross section transformer
Gradium lens Notch filter
Liquid crystal retarder
Spectrograph
Instrument control, data acquisition, and treatment Figure 1
CCD detector
Building blocks of an SCP ROA backscattering spectrometer.
angle scattering. The decisive advance that makes the recording of ROA routine and advantageous for other arrangements is the optical creation of a virtual enantiomer, combined with scrambling of linearly polarized components in the exciting and the scattered light. Figure 4 shows the optical arrangement used in a modern SCP backscattering instrument. A detailed analysis requires the Stokes–Mu¨ller formalism, but the principle can be understood without it. There are two related properties of half-wave plates that are exploited. The first is the interconversion of right
and left circular light passing through them, and the second is the rotation of the plane of polarization of linear incident light by twice the angle it makes with a wave plate’s fast optical axis. As a consequence, all chiroptical properties of a molecule, as observed from the outside, correspond to those of its enantiomer if the molecule is placed between half-wave plates with aligned axes. The circularity converters CC1 and CC2 in Figure 4, which are moved into and out of the exciting and scattered light, respectively, serve the purpose of forming a half-wave cage about the sample. Two measurements are made, one
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Raman Optical Activity, Spectrometers
M1 L1 S
M3
M2
L2
L3
BD
Figure 2 Focusing and light collection optics for backward and forward scattering. L1: 100 mm focusing lens; L2 and L3: 30 mm f/1.1 Gradium light collection lenses; M1, M2, and M3: beam deviation mirrors; BD: beam dump; S: sample. The actual orientation of M1 and M2 is at 901 to each other so that their polarizing properties cancel.
S
L4
L1 M1
L2
L3
I1 P
M2 Figure 3 Offset compensating dual-lens light collection optics for right angle scattering with less than 0.5 ml samples. L1 and L2 form the intermediate image I1, which is projected by L4 onto the spectrograph entrance slit S. L3 is a field lens.
without and one with the half-wave plates in place. The second measurement is treated as if it had been performed for a real enantiomer. Subtracting it from the first one yields twice the value of a single measurement. The sequence of four measurements used in practice is more complicated but based on this idea. Offsets other than those that depend on the chiroptical properties of the sample, and on imperfections of the optics between the circularity converters CC1 and CC2, are eliminated. The linear rotators LR1 and LR2 linearly depolarize the exciting light, and LR3 the scattered light. This cancels the effect optical rotation and stray birefringences may have, and it obviates the need to orient the axes of CC1 and CC2. Counter-rotating halfwave plates in the incident light increases the speed of rotation of the plane of polarization to over 50 000 rpm, and their relative rate of rotation of 29:33 reduces the influence of their imperfections. Spectrographs and Detectors
LR1 M1
LR2 CC1
S L M2 LR3 CC2 Figure 4 Offset elimination optics for collinear scattering. LR1, LR2, and LR3: rotating half-wave plates; CC1 and CC2: half-wave plates moved into the optical train for creating a virtual enantiomer. The mirrors M1 and M2 provide polarization neutral beam deflection.
Spectrographs with planar holographic transmission gratings have become the norm in ROA spectroscopy. The high-speed entrance optics of commercial spectrographs is ill-suited for coupling with the fiber optics of the dual-arm SCP backscattering arrangement of Figure 1. The 2 31 fibers with a 215 mm core and a 245 mm overall diameter have a low f-ratio degradation and accept light in an approximately f/2.2 cone. The length of the curved output surface of the cross section transformer, which directly substitutes for the entrance slit of the spectrograph, amounts to 15.5 mm and requires large diameter optics in order to avoid vignetting. The speed of the light coupled into the fiber optics is f/3.65. Aberration correction can thus be modest, and a single achromatic lens with 76 mm diameter and 200 mm focal length suffices as entrance optics. The modified spectrograph, based on a Kaiser Optical Systems HoloSpec, is shown in Figure 5. Efficiencies of holographic transmission gratings for s and p polarization (perpendicular and parallel to the plane of incidence of the grating) is claimed to be close to
Raman Optical Activity, Spectrometers L1
2393
G
S
L2
FP Figure 5 Holographic plane transmission grating spectrograph with an e´tendue of 1.6 mm2 sr (steradian) and an f/3.3 entrance speed for fiber optics coupling. S: curved entrance slit formed by fiber optics on a 217 mm diameter circle, length 15.5 mm, average optical width 0.169 mm; curvature is determined by f ¼ 401 and y ¼ 501 and is the same with 532 nm excitation for a 0–2400 and a 1555– 3825 cm1 grating G; L1: achromat, f ¼ 200 mm, + ¼ 75 mm; L2: photographic lens, f ¼ 85 mm, f/1.4; FP: focal plane with 6.6 27 mm2 (256 1024 pixel) backthinned CCD detector. Average optical resolution is 7 cm1, and one column of the detector covers a spectral interval of approximately 2.4 cm1.
100 and 60%, respectively. Owing to right angle bends in perpendicular planes, the output light of the fiber optics is partially depolarized, and the efficiency for light coming from the s and p arm of the polarization analyzer is similar. The two halves of the fiber optics are each imaged onto a 128-pixel-wide strip of a backthinned CCD with 256 1024 pixels. The curvature of the slitlike part of the fiber optics corresponds to a circle with a 217 mm diameter fitted to the central segment of a parabola. It leads to a straight line image on the detector so that binning can be used when the CCD is read.
Four dual acquisition cycles +45° LCR −45° On Illumination Off
Figure 6 SCP acquisition cycle for a single fixed position of the circularity converters CC1 and CC2. The CCD detector is read, and the liquid crystal retarder (LCR) is switched, when illumination of the sample is off. The circularity converters are moved to the next of four relative positions during the last dark interval.
Data Acquisition Logic A basic acquisition cycle of a circular intensity difference measurement consists in measuring and subtracting the Raman intensity for right and left circular polarization. Synchronization is required for the illumination of the sample, for reading the detector while illumination is switched off, and in ICP for switching the circular polarization of the exciting light. The basic cycle is complicated by the need to synchronize the motion of the optical elements that create the virtual enantiomer and that scramble components of linear polarization. The timing diagram of Figure 6 summarizes important aspects for the SCP instrument of Figure 1. The two arms of the instrument each measure the intensity of either the right or the left circular component of the scattered light, depending on the switching state of the liquid crystal quarter-wave retarder of the circular polarization analyzer. The sum for two switching states, a dual acquisition cycle, has a vastly increased precision as differences in the arms’ transmissions are eliminated. The polarization scramblers LR1 and LR2 rotate the plane of polarization of the exciting light by an integral number of turns during an illumination window. A trick
to reduce the required high timing precision is to consider not individual dual acquisition cycles but rather blocks of four of them, and to start consecutive dual cycles with the plane rotated by 451, by slightly extending every second dark period. Synchronization of the polarization scrambler LR3 in the scattered light is not needed for long acquisition times, but it is important for short acquisitions, such as the recording of the spectra of the anomers of glucose discussed in the section entitled ‘Experiment ROA Data’. The two half-wave plates used to create the virtual enantiomer are moved into and out of the optical train after four dual acquisition cycles. It is more effective to move them individually instead of together, resulting in four different relative positions. The shortest complete ROA data acquisition cycle then comprises 4 4 2 individual illuminations of the sample. Sample Cells The amount of substance required is a decisive characteristic of any analytical method. Early right angle
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Raman Optical Activity, Spectrometers
Figure 7 Quartz (35 ml) and black Teflon (22 ml) cylindrical sample cells. The inlets are shaped to fit standard 100 ml polypropylene pipette tips. O-joints are made from Kalrez. (DuPont Performance Elastomers L.L.C.).
1.566
0.462 n2
n1
n2
n1
Figure 8 Light collection zone of the nonimaging optics for a sample with an index of refraction n2 ¼ 1.47 (fused quartz) and a cell with flat windows. The curved surface of capillaries increases the internal light collection angle and shortens the zone of light collection.
measurements with micro-capillaries proved that ROA can be determined with less than 1 ml of sample, but sample volumes of more than 100 ml were standard. Rectangular cells requiring 100 ml are still common today in backscattering, even though cylindrical cells with less than a quarter of this volume yield data of the same quality. Figure 7 shows a cylindrical quartz cell for backscattering with a volume of 35 ml and a cell fabricated from black Teflon with a pathlength of only 3 mm and a volume of 22 ml. Small microscope cover glasses are used as its windows. Their thickness of only 0.15 mm reduces collection of Raman light from glass, and they can be replaced should material get burned to their surface. The shape of the zone from which light can be collected by the optics matters for the design of sample cells. The nonimaging optics in Figures 1 and 2 collect light
from a volume situated within a double-sided cone as shown in Figure 8. For a central diamond-shaped zone, light with a solid angle filling the f/1.1 Gradium lens is collected, with efficiency falling off outside this boundary. This makes for efficient light collection from the 50–100 mm diameter waist of a multimode laser beam focused by a 100 mm lens at the center of the light collection zone. The curved surface of a capillary shortens the light collection volume, similar to a reduction in the value of n2, for light scattered in a plane perpendicular to the capillary’s axis. This explains why the loss of Raman intensity amounts to 40% only for capillaries with an inner diameter (ID) of 1.4 mm, as compared to larger flat window cells. The loss increases for 0.56 mm ID capillaries required for sample volumes of 1 ml or less. For organic liquids, the collection of Raman scattered light
Raman Optical Activity, Spectrometers
from a capillary’s thin glass envelope (p0.15 mm) is negligible. It is comparable to that of water when measured in a 1.4 mm ID capillary. For all types of cells, it is of utmost importance to avoid the collection of Raman light reflected under oblique angles from walls. For capillaries, experience indicates that the scattering zone needs to be situated at a distance of about twice the capillary’s ID from either end of the column formed by the sample. For cylindrical cells that are longer than wide, the focus of the light collection optics needs to be placed deep enough into the sample.
Experimental ROA Data a and b Anomers of Glucose Depending on the conditions under which it is crystallized, solid D-glucose consists of the a-pyranose or the b-pyranose form of the molecule. On dissolution in water, the initial value of the specific angle of rotation is 112.21 for the a form and 18.71 for the b form. The two anomers interconvert in solution, and the measured
1.5 0.0
angles converge to a common value of 52.71 over a duration of approximately 3 h. Until about a decade ago, ROA measurements took far too long for determining the spectra of individual anomers, but recent instrumentation has changed this. Figure 9 displays spectra of the a and b forms of glucose, each measured with a total exposure time of 600 s with an SCP instrument based on the schematic of Figure 1. Recording was done in four slices completed within 5 min of the start of the preparation of fresh solutions by the vigorous shaking of powdered a- and b-glucose for 60 and 30 s, respectively, in distilled water. Each slice comprises only two of the acquisition cycles of 32 exposures discussed in the section ‘Data acquisition logic.’ Also shown are the spectra of the same solutions after their equilibration for 3 h. The Raman and ROA intensities, expressed in detected electrons per joule of exciting energy, are larger for the solutions prepared from the b form, indicating a higher concentration despite a shorter mixing time. The similarity Sab, eqn [5], of the spectra reaches 1.0 for Raman and 0.9 for ROA, deviating from 1 due to noise.
nI
(t = t0)
2395
R ()SCP
− nIL ()SCP
(103 e−/J)
−1.5 1.5 0.0
−1.5 1.5 0.0
(t = teq) (t = teq) (t = t0)
−1.5 9.0
nI
R ()SCP
+ nIL ()SCP
4.5 (106 e−/J )
(t = t0) 0.0 9.0 4.5
(t = teq)
0.0 9.0
(t = teq)
4.5
(t = t0)
0.0 1800
1600
1400
1200 1000 800 Wavenumber (cm−1)
600
400
200
Figure 9 Backscattering spectra of the two anomers of D-glucose measured in a cylindrical sample cell. Measurement time: 4 150 s with slices completed within 5 min of the start of the preparation of solutions (see the section on ‘a and b Anomers of Glucose’); laser power at sample: 940 mW for the a and 730 mW for the b anomer; exciting wavelength: 532 nm; resolution: 7 cm1. The curves are slightly smoothed with a third-order Savitzky–Golay procedure and represent detected photons per CCD column with one column covering approximately 2.4 cm1.
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Raman Optical Activity, Spectrometers
1
−RC(0)
0 −1
107 electrons
0.5
IRC()SCP − nIL()SCP
0.0
−0.5 1.0 1010 electrons
n
nI C() n SCP + IL()SCP R
0.5
0.0 1800 1600 1400 1200 1000 800 600 Wavenumber (cm−1)
400
200
Figure 10 Forward scattering spectra of ( ) b-pinene measured in a 1.4 mm ID capillary. Bottom curve: Raman; middle curve: ROA; top curve: degree of circularity inverted to correspond to backscattering convention. Sample size: 8.5 ml; exposure time: 20 min; laser power at sample: 250 mW; other parameters as in Figure 9.
Forward Scattering Measured in Capillaries ROA forward scattering has been considered difficult as it is generally smaller than backscattering. Figure 10 shows that it can readily be measured for small quantities in capillaries. Except for the higher precision, this recent spectrum of b-pinene agrees with earlier measurements. See also: Raman Optical Activity, Applications, Raman Optical Activity, Macromolecule and Biological Molecule Applications, Raman Optical Activity, Small Molecule Applications, Raman Optical Activity, Theory, Raman Spectrometers, Vibrational CD, Applications, Vibrational CD Spectrometers, Vibrational CD, Theory and Application to Determination of Absolute Configuration.
Further Reading Barron LD and Hecht L (1994) Recent developments in Raman optical activity instrumentation. Faraday Discussions 99: 35--47. Barron LD and Hecht L (1996) Recent developments in Raman optical activity of biopolymers. Applied Spectroscopy 50: 619--629.
Greulich KO and Monajembashi S (1996) Laser microbeams and optical tweezers: How they work and why they work. In: Optical and Imaging Techniques for Biomonitoring, vol. 2628 of Proceedings of SPIE – International Society of Optical Engineering, pp. 116–127. Bellingham: SPIE Press. Haesler J (2006) Construction of a new forward and backward scattering Raman optical activity spectrometer and graphical analysis of measured and calculated spectra of (R)-[2H1,2H2,2H3]neopentane. Thesis, University of Fribourg, Switzerland. Haesler J, Schindelholz I, Riguet E, Bochet CG, and Hug W (2007) Absolute configuration of chirally deuterated neopentane. Nature 446: 526--529. Hug W (1981) Optical artefacts and their control in Raman circular difference measurements. Applied Spectroscopy 35: 115--124. Hug W (2003) Virtual enantiomers as the solution of optical activity’s deterministic offset problem. Applied Spectroscopy 57: 1--13. Hug W and Hangartner G (1999) A novel high-throughput Raman spectrometer for polarization difference measurements. Journal of Raman Spectroscopy 30: 841--852. James JF and Sternenberg RS (1969) The Design of Optical Spectrometers. London: Chapman Hall. Nafie LA (1996) Vibrational optical activity. Applied Spectroscopy 50: 14A--26A. Vargek M, Freedman TB, and Nafie LA (1997) Improved backscattering dual circular polarization Raman optical activity spectrometer with enhanced performance for biomolecular applications. Journal of Raman Spectroscopy 28: 627--633.
Symbols 2
a b2 aG0 2 bG2 0 ¼ c b2A ¼ d
2
K ¼ Kp n
drp(h)
Dndrp(h)
Dp(h) Sab
isotropic Raman invariant anisotropic Raman invariant isotropic ROA invariant anisotropic ROA invariant due to the optical activity tensor anisotropic ROA invariant due to the quadrupole tensor (if specified for a particular vibration p) defined by Equation [3] differential scattering cross section for Raman scattering into an element of solid angle O under the angle y difference of differential scattering cross sections for left and right circularly polarized light ratio of ROA to Raman scattering similarity of two spectra, defined by Equation [5]
Abbreviations CCDs ICP ROA SCP VCD
charge-coupled devices incident circular polarization Raman optical activity scattered circular polarization vibrational circular dichroism
Raman optical activity (ROA) or, more precisely, spontaneous vibrational ROA scattering is, like vibrational circular dichroism (VCD), a spectroscopic method that directly probes the handedness, or chirality, of molecular vibrations. ROA of molecular origin was the first of the two phenomena to be measured, though not by much, in 1973. The decisive technologies that enabled the experimental demonstration of ROA were the invention of the argon ion laser, the availability of KD*P electrooptic modulators developed for laser Q-switching, and singlephoton counting. Decisive progress on the reliable collection of ROA data has been made since, and commercial spectrometers have made their appearance. Most present instruments use a backscattering configuration first described at the beginning of the 1980s rather than the earlier right angle configuration. Backscattering is expected to remain the preferred arrangement for biological samples, but for analytic purposes, right angle scattering retains the advantage of requiring smaller samples.
The advances in the measurement of ROA over the past three decades fall into three categories. The first reflects the progress in general Raman instrumentation: multichannel detection with backthinned charge-coupled devices (CCDs) combined with high-luminosity spectrographs based on holographic grating technology, and solid state lasers replacing gas lasers. The second is the conceptual solution of the offset problem ubiquitous in optical activity and the scourge of early ROA measurements. The third are improvements in light collection, sample cell, and handling techniques that have led to a reduction in the amount of the sample required by an order of magnitude, to less than a microliter, and also in backscattering.
ROA Variants There is a wide variety of scattering geometries and polarization schemes that can be used for ROA measurements. Some instrumental parts are common to all, such as lasers, spectrographs, and detectors, but light collection optics and offset reduction schemes may differ. This article will concentrate on the practically relevant or promising arrangements and merely point out others. It will discuss neither the potential use of Fourier transform Raman spectroscopy for ROA nor nonlinear ROA, as no experiments have been demonstrated. Basic Measurement Arrangements The scattering geometries of practical importance are right angle (901), backward (1801), and forward (01) scattering. The 01 and 1801 scattering geometries yield different ROA information, in contrast to ordinary Raman scattering where the signals are identical. ROA intensities are, in general, largest for 1801 and smallest for 01 scattering, with 901 somewhere in between, but details depend on the particular Raman band one observes. For any chosen scattering angle, ROA can be observed either by modulating the incident light between right and left circular (ICP, incident circular polarization) or by analyzing the content of the right and left circular component in the scattered light (SCP, scattered circular polarization). This analysis can be done either by separately measuring the intensity of each circular component or by determining the ellipticity of the scattered light, but only the first method has so far found practical application. The simultaneous modulation of the circularity of the incident light and of the analysis of the
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2388
Raman Optical Activity, Spectrometers
Table 1 Invariant combinations of SCP scattering cross sections for different geometries. ICP cross sections are a factor of 2 larger because they apply to the combined results of a distinct right and left modulation period Scattering angle
Incident polarization
Difference 4ðK =cÞ
Sum K
01 1801 901
Unpolarized Unpolarized Polarized Depolarized Unpolarized
90aG 0 þ 2b2G 2b2A 12b2G þ 4b2A 45aG 0 þ 7b2G þ b2A 6b2G 2b2A 2p 0 2 3 ð180aG þ 40bG Þ
90a2 þ 14b2 90a2 þ 14b2 90a2 þ 14b2 12b2
Integral
4p 2 3 ð180a
þ 40b 2 Þ
aG0 , isotropic ROA invariant due to the optical activity tensor; b2, anisotropic Raman invariant; c, speed of light.
circular polarization of the scattered light yields two dual circular polarization schemes, namely, DCPI for in-phase and DCPII for out-of-phase modulation and detection, where in-phase means the detection of the right circular content when the incident light is also right circularly polarized. The information provided by the two schemes differs and DPII only is of stereochemical interest. In an ICP experiment, the scattered light may or may not be polarization analyzed with a linear polarizer, and in an SCP experiment the exciting light can be linearly or naturally (n) polarized. In right angle scattering this allows the determination of a polarized and a depolarized ROA component, depending on whether the orientation of a linear polarizer is chosen perpendicular or parallel to the scattering plane, respectively. Of the multitude of experimental configurations ensuing from the combination of different geometries and polarization schemes, those of practical relevance are collected in Table 1. Included is the theoretically important cross section for scattering into a solid angle of 4p as its combination of tensor invariants is devoid of quadrupole contributions, and as it can readily be obtained from a polarized and a depolarized right angle ROA measurement.
on the dimensionless ratio D of ROA to Raman scattering, which is independent of many instrumental parameters. For SCP backscattering (scattering angle y ¼ p) with naturally (n) polarized exciting light one has for the average value, and the difference, respectively, of the differential scattering cross sections n dspL and n dspR , for vibration p for left (L) and right (R) circularly polarized light n
1 dsp ðpÞSCP ¼ ðn dspR þn d spL Þ 2 ¼ K p ð90a 2p þ 14b2p Þ dO
½1
D n dsp ðpÞSCP ¼ ðn dspL n dspR Þ ¼ Kp ¼
4K p ð12b2Gp þ 4b2Ap Þ dO c
1 m0 2 o0 o3p 90 4p
½2 ½3
The minus sign for Dds renders the standard definition of molecular quantities as left minus right in optical activity compatible with the ROA convention to represent scattering intensities as right minus left. o0 and op are the pulsations of the exciting and the scattered light, respectively, c the speed of light, and m0 is the permeability of the vacuum. D values follow from eqns [1] and [2] as
The Comparison of Experimental Data Except for band positions, measurements that yield different combinations of invariants of the scattering tensors according to Table 1 are not comparable. The ratio of the five Raman and ROA invariants of the scattering tensor can be extracted from three separate measurements, but this has been done only once. A qualitative comparison of backscattering with depolarized right angle ROA spectra can be meaningful if both are determined by the anisotropic invariant b2G . The quantitative comparison of ROA data with the same invariant combination is possible, in the form of recorded photons per joule of exciting energy, if the data have been recorded under identical conditions. Absolute scattering cross sections have so far not been measured in ROA. A better than merely qualitative comparison of ROA spectra measured under different conditions can be based
n
Dp ðpÞSCP ¼ n n
¼n ¼
dI pR ðpÞ n dI pL ðpÞ dI pR ðpÞ þn dI pL ðpÞ dspR ðpÞ n dspL ðpÞ dspR ðpÞ þn dspL ðpÞ
2 2 2 12bGp þ 4bAp c 90a2p þ 14b2p
½4
where n dI pR and n dI pL are the scattering intensities for right and left circularly polarized light, respectively, for scattering into an infinitesimal element of the solid angle O. ds measures the rate at which energy is removed from the incident beam by scattering, relative to the rate at which energy crosses a unit area perpendicular to the direction of propagation of the incident beam. ds/dO relates to the power scattered into a given element of
Raman Optical Activity, Spectrometers
solid angle dO, and dI is therefore proportional to it. Expressions for other scattering geometries follow from the invariant combinations in Table 1. In an actual measurement, a substantial solid angle is used for collecting light, and measured D values depend on this light collection angle. They depend further on the resolution of the instrument because isotropic and anisotropic invariants of the scattering tensor lead to bands of different width. D also depends on the exciting wavelength l as 1/l. This dependence is not explicit in eqn [4] but follows from the frequency dependence of the invariants. A second way to compare two experimental ROA spectra a and b can be based on their similarity Sab defined as: Pn˜2 n˜ ¼n˜1 I a;n˜ I b;n˜ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Sab ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn˜2 Pn˜2 ˜n¼n˜1 I a;n˜ I a;n˜ ˜n¼n˜1 I b;n˜ I b;n˜
½5
The summation is over discrete wavenumbers n˜ between the limits n˜1 and n˜2 . The similarity of spectra with the same intensity ratio of bands has a value of 1. Spectra recorded in a flat window sample cell and a capillary yielding lower scattering intensities will retain this value, except for the influence of a different light collection angle. Sab and D are useful for identifying instrumental artifacts.
Noise and Its Reduction in ROA Measurements ROA is a small difference of two already small quantities, with values of |D| rarely exceeding 103. Noise therefore sets the limits to the measurement of ROA. There are three noise components that can be distinguished: shot noise, flicker noise, and deterministic offset. They affect spectra differently, and their reduction requires distinct approaches. Shot Noise In the shot noise limited case, where the Raman intensity I is represented by N events, in our case detected scattered photons, the statistics of a Poisson distribution hold. With IREILEI, the rms pffiffiffiffiffiffi ffi deviation of DN corresponding to DI ¼ IR IL is 2N : Thus, to recover DN ¼ jDj N with a signal-to-noise ratio of Z, the number of detected photons needs to be pffiffiffiffiffiffiffi Z2 DN ¼ jDj N ¼ Z 2N ; N¯ ¼ 2 2 D
½6
For a typical value of |D| ¼ 5 104 and a desired minimal rms signal-to-noise ratio of Z ¼ 10, one needs to detect close to 109 photons per spectral element of
2389
resolution. This number is put into perspective by comparing it to the value of 5.5 104 detected photons per second obtained in backscattering at 4 cm1 resolution with a modern commercial Raman instrument, equipped with a CCD detector and a 15 mW He–Ne laser, for the peak height of the exceptionally strong 992 cm1 band of benzene. In comparison to shot noise, in view of the large number of photons needed in ROA, readout noise is negligible for modern slow-scan CCD detectors. The recipes for the reduction in shot noise are simple: an exciting laser with sufficient power, efficient collection of the scattered light, spectrographs with a large e´tendue (the amount of light that an optical system is capable of collecting), and multichannel detectors with a high quantum efficiency. Shot noise reduction has reached limits that cannot easily be pushed much further. It is the one area where ROA has profited most from the general advances in Raman instrumentation. Flicker Noise While shot noise, which follows a Gaussian distribution, increases as the square root of the measurement time, with the signal-to-noise ratio improving at the same rate, the cumulative error due to flicker noise tends to increase faster than shot noise. The improvement in the flicker signal-to-noise ratio with measurement time can therefore be slow or nonexistent. In clocks, for example, after the elimination of all systematic drifts, there remains an error due to flicker noise that is known to increase at least linearly with time. No analysis of flicker noise sources in ROA has been published. The influence of dust in the sample, which tends to get trapped by the optical tweezer effect in the waist of the focused laser beam, is well known, as is the influence of optical schlieren through local heating. Flicker noise in ROA does not seem to follow the 1/f behavior often observed for electronic circuitry, with f being the frequency, but it is prominent at low frequencies. Reducing it requires high modulation rates in ICP, or a switch to SCP where it can be reduced by the simultaneous detection of right and left circularly polarized scattered light. Deterministic Offset Spurious signals due to systematic instrumental offset are akin to deterministic drift in a clockwork. Such artifacts neither are reduced by an increase in observation time, nor they can be detected by the comparison of subsequent measurements done with the same instrument under identical conditions. Deterministic offset is at the root of early erroneous reports of measured vibrational optical activity. The mechanisms leading to spurious signals can have their root in timing errors, electrical and mechanical
2390
Raman Optical Activity, Spectrometers
perturbations synchronized with the data acquisition cycle, or optical errors leading to unequal intensities for right and left circular light unrelated to the sample’s ROA properties. The sample itself might exhibit undesirable characteristics such as turbidity, an optically active fluorescent background, or differential absorption for right and left circularly polarized light. From the point of view of optical offset, depolarized right angle ICP is the easiest ROA measurement as imprecisions in the circular polarization of the exciting light do not produce artificial scattering differences. This is true for small light collection angles. The reliable recording with large collection angles requires optics such as the dual-lens light collection system used for the first recording of polarized right angle ICP ROA. The successful measurement of ICP backscattering depends, in turn, on the depolarization of the scattered light because dispersive systems and detectors are polarization sensitive. SCP backscattering is highly sensitive to a component of circularly polarized light in the exciting light, as it will show up, depending on the polarization of Raman bands, as a spurious ROA signal. With linearly polarized exciting light, optical birefringences in the focusing lens and the scattering cell, even with otherwise perfect optics, tend to render the light in the scattering zone elliptical. Routine SCP measurements therefore require depolarized exciting light. An often overlooked problem are reflections of the exciting and the scattered light on optical surfaces, including the walls of the scattering cell.
Instrument Building Blocks Figure 1 gives an overview of the major functional parts of a backscattering SCP ROA spectrometer. In an ICP instrument, a circular polarization modulator in the incident light would replace the circular polarization analyzer in the scattered light. A DCP instrument would be obtained by combining the SCP and ICP building blocks. A dual-arm system is not mandatory for ICP and DCP, but switching the scattered light between two arms, synchronized with a rapid modulation of the exciting light, is a way to reduce flicker noise. Lasers Except for sufficient power, no particular requirements exist for the exciting laser. The tiny ROA effects of chirally deuterated neopentane were measured in backscattering with a frequency-doubled Yb:YAG thin-disk laser intended for display and machining purposes. Such lasers have no longitudinal coherence and are not transverse single mode. A laser’s transverse mode properties can matter in right angle scattering where the waist of the focused beam is imaged onto the entrance slit of the spectrograph.
The choice of exciting wavelengths in ROA has followed the availability of sufficiently reliable and powerful lasers: the 488 and 514.5 nm lines of the argon ion laser were initially used, but now the 532 nm line of the frequency-doubled YAG is common. Excitation in the red or near-infrared region would be preferable for reducing Raman spectroscopy’s ubiquitous fluorescence problem. The 1/l dependence of D, in addition to the fourth power 1/l dependence of Raman scattering, and the lack of sufficiently powerful and reliable continuous wave lasers in the 650–800 nm range, have hampered ROA at these longer wavelengths. CW laser powers of tens of watts are easily available at 1.06 mm, the wavelength of the nondoubled YAG, but problems with sample heating by the absorption of vibrational overtones, and the lack of suitable multichannel detectors, render 1.06 mm excitation unattractive. With green exciting light, 100–400 mW of laser power at the sample is typical for measurements of organic liquids, but 1000 mW can be desirable for aqueous solutions of proteins. Focusing and Light Collection Optics Figure 2 shows the focusing and light collection optics of an SCP instrument capable of measuring forward and backward scattering. A single Gradium lens is often used for focusing and collecting the backscattered light, but separate lenses as depicted in the figure allow for a softer focusing of the laser in the sample, and they eliminate stray light from fluorescence and Raman scattering produced inside a focusing lens also used for light collection. The nonimaging optics collect the light from a 2–3 mm long segment of the focused beam in the sample, as discussed in the context of sample cells (‘see Sample Cells’). This length is determined by the focal length of 30 mm of the light collection lens, 100 mm of the lens focusing light onto the fiber optics, and the diameter of approximately 1.56 mm of each of the two circular entrance ends of the fiber optics cross section transformer. Its two branches guide the light due to the right and left circular component of the scattered light into the spectrograph, as shown in Figure 1. Figure 3 shows a light collection optics capable of filling, also in right angle scattering, the e´tendue of a modern holographic planar grating spectrograph. In ICP, the dual-lens system also suppresses offsets otherwise caused by a deviation from circular of the polarization of the exciting light. Throughput can exceed that achievable with fiber optics in backscattering. Polarization Conditioning and Polarization Analyzing Optics Precise polarization control is quintessential to the elimination of offset in all but depolarized ICP right
Raman Optical Activity, Spectrometers
2391
Laser
Mechanical shutter
Polarization conditioner
Polarizing beam splitting cube
Sample cell
Fiber optics cross section transformer
Gradium lens Notch filter
Liquid crystal retarder
Spectrograph
Instrument control, data acquisition, and treatment Figure 1
CCD detector
Building blocks of an SCP ROA backscattering spectrometer.
angle scattering. The decisive advance that makes the recording of ROA routine and advantageous for other arrangements is the optical creation of a virtual enantiomer, combined with scrambling of linearly polarized components in the exciting and the scattered light. Figure 4 shows the optical arrangement used in a modern SCP backscattering instrument. A detailed analysis requires the Stokes–Mu¨ller formalism, but the principle can be understood without it. There are two related properties of half-wave plates that are exploited. The first is the interconversion of right
and left circular light passing through them, and the second is the rotation of the plane of polarization of linear incident light by twice the angle it makes with a wave plate’s fast optical axis. As a consequence, all chiroptical properties of a molecule, as observed from the outside, correspond to those of its enantiomer if the molecule is placed between half-wave plates with aligned axes. The circularity converters CC1 and CC2 in Figure 4, which are moved into and out of the exciting and scattered light, respectively, serve the purpose of forming a half-wave cage about the sample. Two measurements are made, one
2392
Raman Optical Activity, Spectrometers
M1 L1 S
M3
M2
L2
L3
BD
Figure 2 Focusing and light collection optics for backward and forward scattering. L1: 100 mm focusing lens; L2 and L3: 30 mm f/1.1 Gradium light collection lenses; M1, M2, and M3: beam deviation mirrors; BD: beam dump; S: sample. The actual orientation of M1 and M2 is at 901 to each other so that their polarizing properties cancel.
S
L4
L1 M1
L2
L3
I1 P
M2 Figure 3 Offset compensating dual-lens light collection optics for right angle scattering with less than 0.5 ml samples. L1 and L2 form the intermediate image I1, which is projected by L4 onto the spectrograph entrance slit S. L3 is a field lens.
without and one with the half-wave plates in place. The second measurement is treated as if it had been performed for a real enantiomer. Subtracting it from the first one yields twice the value of a single measurement. The sequence of four measurements used in practice is more complicated but based on this idea. Offsets other than those that depend on the chiroptical properties of the sample, and on imperfections of the optics between the circularity converters CC1 and CC2, are eliminated. The linear rotators LR1 and LR2 linearly depolarize the exciting light, and LR3 the scattered light. This cancels the effect optical rotation and stray birefringences may have, and it obviates the need to orient the axes of CC1 and CC2. Counter-rotating halfwave plates in the incident light increases the speed of rotation of the plane of polarization to over 50 000 rpm, and their relative rate of rotation of 29:33 reduces the influence of their imperfections. Spectrographs and Detectors
LR1 M1
LR2 CC1
S L M2 LR3 CC2 Figure 4 Offset elimination optics for collinear scattering. LR1, LR2, and LR3: rotating half-wave plates; CC1 and CC2: half-wave plates moved into the optical train for creating a virtual enantiomer. The mirrors M1 and M2 provide polarization neutral beam deflection.
Spectrographs with planar holographic transmission gratings have become the norm in ROA spectroscopy. The high-speed entrance optics of commercial spectrographs is ill-suited for coupling with the fiber optics of the dual-arm SCP backscattering arrangement of Figure 1. The 2 31 fibers with a 215 mm core and a 245 mm overall diameter have a low f-ratio degradation and accept light in an approximately f/2.2 cone. The length of the curved output surface of the cross section transformer, which directly substitutes for the entrance slit of the spectrograph, amounts to 15.5 mm and requires large diameter optics in order to avoid vignetting. The speed of the light coupled into the fiber optics is f/3.65. Aberration correction can thus be modest, and a single achromatic lens with 76 mm diameter and 200 mm focal length suffices as entrance optics. The modified spectrograph, based on a Kaiser Optical Systems HoloSpec, is shown in Figure 5. Efficiencies of holographic transmission gratings for s and p polarization (perpendicular and parallel to the plane of incidence of the grating) is claimed to be close to
Raman Optical Activity, Spectrometers L1
2393
G
S
L2
FP Figure 5 Holographic plane transmission grating spectrograph with an e´tendue of 1.6 mm2 sr (steradian) and an f/3.3 entrance speed for fiber optics coupling. S: curved entrance slit formed by fiber optics on a 217 mm diameter circle, length 15.5 mm, average optical width 0.169 mm; curvature is determined by f ¼ 401 and y ¼ 501 and is the same with 532 nm excitation for a 0–2400 and a 1555– 3825 cm1 grating G; L1: achromat, f ¼ 200 mm, + ¼ 75 mm; L2: photographic lens, f ¼ 85 mm, f/1.4; FP: focal plane with 6.6 27 mm2 (256 1024 pixel) backthinned CCD detector. Average optical resolution is 7 cm1, and one column of the detector covers a spectral interval of approximately 2.4 cm1.
100 and 60%, respectively. Owing to right angle bends in perpendicular planes, the output light of the fiber optics is partially depolarized, and the efficiency for light coming from the s and p arm of the polarization analyzer is similar. The two halves of the fiber optics are each imaged onto a 128-pixel-wide strip of a backthinned CCD with 256 1024 pixels. The curvature of the slitlike part of the fiber optics corresponds to a circle with a 217 mm diameter fitted to the central segment of a parabola. It leads to a straight line image on the detector so that binning can be used when the CCD is read.
Four dual acquisition cycles +45° LCR −45° On Illumination Off
Figure 6 SCP acquisition cycle for a single fixed position of the circularity converters CC1 and CC2. The CCD detector is read, and the liquid crystal retarder (LCR) is switched, when illumination of the sample is off. The circularity converters are moved to the next of four relative positions during the last dark interval.
Data Acquisition Logic A basic acquisition cycle of a circular intensity difference measurement consists in measuring and subtracting the Raman intensity for right and left circular polarization. Synchronization is required for the illumination of the sample, for reading the detector while illumination is switched off, and in ICP for switching the circular polarization of the exciting light. The basic cycle is complicated by the need to synchronize the motion of the optical elements that create the virtual enantiomer and that scramble components of linear polarization. The timing diagram of Figure 6 summarizes important aspects for the SCP instrument of Figure 1. The two arms of the instrument each measure the intensity of either the right or the left circular component of the scattered light, depending on the switching state of the liquid crystal quarter-wave retarder of the circular polarization analyzer. The sum for two switching states, a dual acquisition cycle, has a vastly increased precision as differences in the arms’ transmissions are eliminated. The polarization scramblers LR1 and LR2 rotate the plane of polarization of the exciting light by an integral number of turns during an illumination window. A trick
to reduce the required high timing precision is to consider not individual dual acquisition cycles but rather blocks of four of them, and to start consecutive dual cycles with the plane rotated by 451, by slightly extending every second dark period. Synchronization of the polarization scrambler LR3 in the scattered light is not needed for long acquisition times, but it is important for short acquisitions, such as the recording of the spectra of the anomers of glucose discussed in the section entitled ‘Experiment ROA Data’. The two half-wave plates used to create the virtual enantiomer are moved into and out of the optical train after four dual acquisition cycles. It is more effective to move them individually instead of together, resulting in four different relative positions. The shortest complete ROA data acquisition cycle then comprises 4 4 2 individual illuminations of the sample. Sample Cells The amount of substance required is a decisive characteristic of any analytical method. Early right angle
2394
Raman Optical Activity, Spectrometers
Figure 7 Quartz (35 ml) and black Teflon (22 ml) cylindrical sample cells. The inlets are shaped to fit standard 100 ml polypropylene pipette tips. O-joints are made from Kalrez. (DuPont Performance Elastomers L.L.C.).
1.566
0.462 n2
n1
n2
n1
Figure 8 Light collection zone of the nonimaging optics for a sample with an index of refraction n2 ¼ 1.47 (fused quartz) and a cell with flat windows. The curved surface of capillaries increases the internal light collection angle and shortens the zone of light collection.
measurements with micro-capillaries proved that ROA can be determined with less than 1 ml of sample, but sample volumes of more than 100 ml were standard. Rectangular cells requiring 100 ml are still common today in backscattering, even though cylindrical cells with less than a quarter of this volume yield data of the same quality. Figure 7 shows a cylindrical quartz cell for backscattering with a volume of 35 ml and a cell fabricated from black Teflon with a pathlength of only 3 mm and a volume of 22 ml. Small microscope cover glasses are used as its windows. Their thickness of only 0.15 mm reduces collection of Raman light from glass, and they can be replaced should material get burned to their surface. The shape of the zone from which light can be collected by the optics matters for the design of sample cells. The nonimaging optics in Figures 1 and 2 collect light
from a volume situated within a double-sided cone as shown in Figure 8. For a central diamond-shaped zone, light with a solid angle filling the f/1.1 Gradium lens is collected, with efficiency falling off outside this boundary. This makes for efficient light collection from the 50–100 mm diameter waist of a multimode laser beam focused by a 100 mm lens at the center of the light collection zone. The curved surface of a capillary shortens the light collection volume, similar to a reduction in the value of n2, for light scattered in a plane perpendicular to the capillary’s axis. This explains why the loss of Raman intensity amounts to 40% only for capillaries with an inner diameter (ID) of 1.4 mm, as compared to larger flat window cells. The loss increases for 0.56 mm ID capillaries required for sample volumes of 1 ml or less. For organic liquids, the collection of Raman scattered light
Raman Optical Activity, Spectrometers
from a capillary’s thin glass envelope (p0.15 mm) is negligible. It is comparable to that of water when measured in a 1.4 mm ID capillary. For all types of cells, it is of utmost importance to avoid the collection of Raman light reflected under oblique angles from walls. For capillaries, experience indicates that the scattering zone needs to be situated at a distance of about twice the capillary’s ID from either end of the column formed by the sample. For cylindrical cells that are longer than wide, the focus of the light collection optics needs to be placed deep enough into the sample.
Experimental ROA Data a and b Anomers of Glucose Depending on the conditions under which it is crystallized, solid D-glucose consists of the a-pyranose or the b-pyranose form of the molecule. On dissolution in water, the initial value of the specific angle of rotation is 112.21 for the a form and 18.71 for the b form. The two anomers interconvert in solution, and the measured
1.5 0.0
angles converge to a common value of 52.71 over a duration of approximately 3 h. Until about a decade ago, ROA measurements took far too long for determining the spectra of individual anomers, but recent instrumentation has changed this. Figure 9 displays spectra of the a and b forms of glucose, each measured with a total exposure time of 600 s with an SCP instrument based on the schematic of Figure 1. Recording was done in four slices completed within 5 min of the start of the preparation of fresh solutions by the vigorous shaking of powdered a- and b-glucose for 60 and 30 s, respectively, in distilled water. Each slice comprises only two of the acquisition cycles of 32 exposures discussed in the section ‘Data acquisition logic.’ Also shown are the spectra of the same solutions after their equilibration for 3 h. The Raman and ROA intensities, expressed in detected electrons per joule of exciting energy, are larger for the solutions prepared from the b form, indicating a higher concentration despite a shorter mixing time. The similarity Sab, eqn [5], of the spectra reaches 1.0 for Raman and 0.9 for ROA, deviating from 1 due to noise.
nI
(t = t0)
2395
R ()SCP
− nIL ()SCP
(103 e−/J)
−1.5 1.5 0.0
−1.5 1.5 0.0
(t = teq) (t = teq) (t = t0)
−1.5 9.0
nI
R ()SCP
+ nIL ()SCP
4.5 (106 e−/J )
(t = t0) 0.0 9.0 4.5
(t = teq)
0.0 9.0
(t = teq)
4.5
(t = t0)
0.0 1800
1600
1400
1200 1000 800 Wavenumber (cm−1)
600
400
200
Figure 9 Backscattering spectra of the two anomers of D-glucose measured in a cylindrical sample cell. Measurement time: 4 150 s with slices completed within 5 min of the start of the preparation of solutions (see the section on ‘a and b Anomers of Glucose’); laser power at sample: 940 mW for the a and 730 mW for the b anomer; exciting wavelength: 532 nm; resolution: 7 cm1. The curves are slightly smoothed with a third-order Savitzky–Golay procedure and represent detected photons per CCD column with one column covering approximately 2.4 cm1.
2396
Raman Optical Activity, Spectrometers
1
−RC(0)
0 −1
107 electrons
0.5
IRC()SCP − nIL()SCP
0.0
−0.5 1.0 1010 electrons
n
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Figure 10 Forward scattering spectra of ( ) b-pinene measured in a 1.4 mm ID capillary. Bottom curve: Raman; middle curve: ROA; top curve: degree of circularity inverted to correspond to backscattering convention. Sample size: 8.5 ml; exposure time: 20 min; laser power at sample: 250 mW; other parameters as in Figure 9.
Forward Scattering Measured in Capillaries ROA forward scattering has been considered difficult as it is generally smaller than backscattering. Figure 10 shows that it can readily be measured for small quantities in capillaries. Except for the higher precision, this recent spectrum of b-pinene agrees with earlier measurements. See also: Raman Optical Activity, Applications, Raman Optical Activity, Macromolecule and Biological Molecule Applications, Raman Optical Activity, Small Molecule Applications, Raman Optical Activity, Theory, Raman Spectrometers, Vibrational CD, Applications, Vibrational CD Spectrometers, Vibrational CD, Theory and Application to Determination of Absolute Configuration.
Further Reading Barron LD and Hecht L (1994) Recent developments in Raman optical activity instrumentation. Faraday Discussions 99: 35--47. Barron LD and Hecht L (1996) Recent developments in Raman optical activity of biopolymers. Applied Spectroscopy 50: 619--629.
Greulich KO and Monajembashi S (1996) Laser microbeams and optical tweezers: How they work and why they work. In: Optical and Imaging Techniques for Biomonitoring, vol. 2628 of Proceedings of SPIE – International Society of Optical Engineering, pp. 116–127. Bellingham: SPIE Press. Haesler J (2006) Construction of a new forward and backward scattering Raman optical activity spectrometer and graphical analysis of measured and calculated spectra of (R)-[2H1,2H2,2H3]neopentane. Thesis, University of Fribourg, Switzerland. Haesler J, Schindelholz I, Riguet E, Bochet CG, and Hug W (2007) Absolute configuration of chirally deuterated neopentane. Nature 446: 526--529. Hug W (1981) Optical artefacts and their control in Raman circular difference measurements. Applied Spectroscopy 35: 115--124. Hug W (2003) Virtual enantiomers as the solution of optical activity’s deterministic offset problem. Applied Spectroscopy 57: 1--13. Hug W and Hangartner G (1999) A novel high-throughput Raman spectrometer for polarization difference measurements. Journal of Raman Spectroscopy 30: 841--852. James JF and Sternenberg RS (1969) The Design of Optical Spectrometers. London: Chapman Hall. Nafie LA (1996) Vibrational optical activity. Applied Spectroscopy 50: 14A--26A. Vargek M, Freedman TB, and Nafie LA (1997) Improved backscattering dual circular polarization Raman optical activity spectrometer with enhanced performance for biomolecular applications. Journal of Raman Spectroscopy 28: 627--633.