Quantitative Chiral Analysis by Molecular Rotational Spectroscopy

CHAPTER 17

Quantitative Chiral Analysis by Molecular Rotational Spectroscopy Brooks H. Pate*, Luca Evangelisti**, Walther Caminati**, Yunjie Xu†, Javix Thomas†, David Patterson‡, Cristobal Perez§ , Melanie Schnell§ *Department of Chemistry, University of Virginia, Charlottesville,VA, United States **Department of Chemistry “Giacomo Ciamician”,University of Bologna, Bologna, Italy † Department of Chemistry, University of Alberta, Edmonton, AB, Canada ‡ Department of Physics, University of California Santa Barbara, Santa Barbara, CA, United States § Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany

17.1  INTRODUCTION This chapter presents early results from the emerging field of quantitative chiral analysis by molecular rotational spectroscopy. The focus is on the development of measurement techniques to solve the challenging analytical chemistry problem of determining the ratios of all stereoisomers for a chiral molecule. This analysis becomes particularly challenging as the number of chiral centers in the molecule increases. Furthermore, this area of spectroscopy has the goal of creating measurement techniques that can be used directly on complex chemical mixtures to perform chiral analysis without the need of chemical separation by chromatography. Examples of chemical samples that fall into this category include natural products like essential oils from plants that are a rich mixture of volatile species and reaction flask samples where stereospecific chemical reactions are performed and which contain unreacted reagents, desired and undesired reaction products, and solvents in the mixture.

17.1.1  Challenges in quantitative chiral analysis An illustration of the analysis challenges is the synthesis of isopulegol from citronellal in the commercial production of menthol shown in Fig. 17.1 [1–3]. Two new stereocenters are produced in the cyclization reaction that generates isopulegol. Subsequent hydrogenation of the olefin produces the final menthol product. The goal in menthol production is to generate only the isopulegol diastereomer because the other isomers have bad taste. The Chiral Analysis. http://dx.doi.org/10.1016/B978-0-444-64027-7.00019-7 Copyright © 2018 Elsevier B.V. All rights reserved.

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Figure 17.1  The cyclization of citronellal is shown as an illustration of the challenges for chiral analysis of molecules with multiple stereocenters. Chiral catalysts are designed to optimize the production of isopulegol. The cyclization sets two new chiral centers producing a product with 23 = 8 possible stereoisomers. If the reaction proceeds without racemization, then the stereochemistry at one site is fixed by the citronellal reagent. In this case, the reaction can produce the four diastereomer products shown on the right. Racemization, or a starting material with low enantiopurity, can produce the enantiomers of each of these products with all eight stereoisomers possibly present in the reaction mixture.

development of asymmetric catalysts for this process by Noyori was recognized with the 2001 Nobel Prize in Chemistry [4]. The reaction intermediate has three chiral centers and can exist in 23 = 8 stereoisomers. Four of these stereoisomers are diastereomers and have distinct molecular geometries. Traditional spectroscopy methods can distinguish these isomers. Each diastereomer exists in two nonsuperimposable mirror image forms—the enantiomers—to complete the full set of eight stereoisomers. The measurement challenge is to determine the fractional composition of stereoisomers produced in the reaction.This includes both the analysis of the diastereomer ratio and the enantiomer ratio for each diastereomer. In practical applications, there are two additional challenges: (1) The analysis should be possible without the use of any reference samples. For example, if the molecule is newly created in the lab, there will be no sample of known absolute configuration (e.g., useful to determine the order of elution in chromatography) and no sample of known enantiomeric excess (EE) (to

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calibrate measurements such as optical rotation or vibrational circular dichroism (VCD)). (2) The technique needs to have a large dynamic range so that minor stereoisomer impurities—or even chiral impurities produced by unexpected side reactions [5]—can be detected. The ability to perform the analysis without the need to develop a chromatographic chiral separation protocol would be a significant strength.

17.1.2  Rotational spectroscopy for chemical analysis Rotational spectroscopy measures a high-resolution spectrum where the spectral pattern is determined by the three-dimensional structure of the molecule [6]. The quantized energy levels for the spectroscopy come from the overall rotational motion of the molecule. The rotational kinetic energy is determined by the three moments-of-inertia in the principal axis system. Any changes in the mass distribution will produce a different energy level structure and spectroscopic transition frequencies. Therefore, structural isomers have distinct rotational spectra but enantiomers, which have the same set of bond lengths and bond angles, have identical rotational spectra. In order for the rotational motion of the molecule to couple with light, it is necessary for the molecule to have a permanent dipole moment. Although there are special cases of chiral molecules with elements of molecular symmetry, they generally have C1-symmetry and are polar. The important feature of molecular rotational spectroscopy for chemical analysis is that the resolution of the spectral transitions is sufficiently high that the spectra of isomers with only small changes in mass distribution can be measured without spectral overlap. For example, the 13C- isotopologues of molecules, isomers created when a single carbon atom is isotopically substituted, are routinely resolved in the instruments used for rotational spectroscopy [7].The extreme sensitivity to changes in the mass distribution make rotational spectroscopy well-suited to distinguishing diastereomers of molecules with multiple chiral centers. A second advantage of the high-resolution of the spectrometers is that complex sample mixtures can be analyzed directly without spectral overlap. An example of the rotational spectrum from the vapor head space of an essential oil will be presented later to illustrate this capability.

17.1.3  Bringing enantiomer-specific measurement capabilities to rotational spectroscopy Until recently, there has been limited application of molecular rotational spectroscopy to the study of chiral molecules. One impediment to the use of the technique was the inability to differentiate enantiomers with high sensitivity. The common spectroscopic approach to enantiomer-specific

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spectroscopy is to use circular dichroism. However, circular dichroism becomes weaker as the wavelength of the resonant radiation gets longer [8– 10]. The rotational circular dichroism properties of propylene oxide have been calculated and show that the fractional differential absorption of left and right circularly polarized light is more than an order-of-magnitude weaker than for VCD and is probably below the sensitivity of spectrometers used in the field [9,10]. The two approaches described here adapt other strategies for enantiomer analysis that have been used for vibrational and nuclear magnetic resonance (NMR) spectroscopy. The major breakthrough in rotational spectroscopy applications in chiral analysis occurred in 2013 with the demonstration of enantiomer-specific detection using three-wave mixing methods [11,12]. These methods are based on the realization that a gas sample with an EE lacks a center of symmetry and, therefore, can support sum and difference frequency generation [13].Three-wave mixing can be observed using pulses of light with orthogonal polarizations and in these experiments the phase of the coherent emission signal contains information about the absolute configuration. This concept had previously been demonstrated using infrared laser spectroscopy [14–16]. The advantages of performing rotational spectroscopy three-wave mixing measurements for quantitative chiral analysis will be described in this chapter [17]. The second approach to enantiomer analysis is to convert the enantiomers into spectroscopically distinct species using a chiral resolving agent. This method has been developed extensively for NMR spectroscopy using both chemical derivatization, with reagents such as Mosher's ester, and molecular complexation [18–21]. The rotational spectroscopy version of this enantiomers-to-diastereomers strategy uses noncovalent interactions to form a weakly bound complex between the molecule of interest and a small, enantiopure tag molecule in a pulsed jet expansion. This measurement approach is an extension of pioneering studies of the structures of complexes of small chiral molecules from the field of rotational spectroscopy [22–26].

17.2  BASIC PRINCIPLES OF MOLECULAR ROTATIONAL SPECTROSCOPY 17.2.1  Molecular rotational spectroscopy The theory for molecular rotational spectroscopy is highly developed and there are several excellent texts [6,27–29] on the topic with the work by Gordy and Cook [6] being the most frequently cited reference. In this

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s­ection, the theoretical principles of rotation spectroscopy are presented at minimum level required to understand the spectral observations. The fundamental challenges for performing rotational spectroscopy on large molecules are also discussed. The first consideration is the energy levels for molecular rotation. These energy levels come from the kinetic energy of rotation for the free molecule. As a result, molecular rotational spectroscopy requires the molecule to be in the gas phase and at low enough pressure so that molecular collisions do not produce significant line broadening. Because angular momentum is quantized, the allowed energies for molecular rotation are also quantized. They are obtained from the eigenvalues of the Hamiltonian operator for rotational kinetic energy. For a rigid rotor where the geometry is fixed as a function of the rotational energy, the Hamiltonian is: 

Hrot = A Pa2 + BPb2 + C Pc2

(17.1)

In this expression, Pa, Pb, and Pc are the angular momentum operators for rotational motion about the three principal axes of rotation. There are three molecular parameters in the Hamiltonian (A, B, C), and these are called the rotational constants. The constants are ordered in terms of their magnitudes: A > B > C. For a spherical top, all three constants are identical. For a symmetric top, two of the constants are equal (giving either a prolate symmetric top with (A, B = C) or an oblate top symmetric top with (A = B, C)). Except for a few special cases, chiral molecules have C1symmetry and are asymmetric tops with three distinct rotational constants. The rotational constants are inversely related to the principal moments-ofinertia (Ia, Ib, and Ic) that characterize the three-dimensional mass distribution of the molecule: 

A=  2 2Ia

(17.2)

with Ia the moment-of-inertia for the a-principal axis and with similar expressions for B and C. It is common in rotational spectroscopy to work with the Hamiltonian in frequency instead of energy units (through the relation ∆E = hν) and the rotational constants are commonly reported in MHz units. The rigid rotor Hamiltonian involves only angular momentum operators and can, therefore, be calculated exactly using computers. The resulting energy levels are labeled with three quantum numbers as JKaKc. Here, J is the usual quantum number related to the square of the length of the angular momentum vector. For a closed shell molecule, J is quantized and takes

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integer values starting from zero. The other two quantum numbers, Ka and Kc, describe the orientation of the angular momentum vector with respect to the molecular principal axis system. They are actually pseudo quantum numbers and give the projection of the angular momentum vector on the rotational axes in the two symmetric top limits: the one associated with the smallest moment-of-inertia (Ka) for prolate tops and the one associated with the largest moment-of-inertia (Kc) for oblate tops. Since these are projections, they must take integer values between –J..0..J.They are reported as unsigned quantities using the magnitude of the projection. For any value of J, there are (2J + 1) possible orientations of the angular momentum in the molecular principal axis system. As an example, for total rotational angular momentum quantum number J = 1, the labelling for the three energy levels in JKaKc notation is: 111, 101, and 110. Because these correspond to different amounts of angular momentum about the stable rotational axes, they will correspond to different allowed rotational kinetic energies for an asymmetric top. There is an additional (2J + 1)-degeneracy of the rotational energy levels that comes from the different projections of the total angular momentum in a space-fixed axis (the quantum number is MJ = −J..0..J). This orientation does not affect the rotational kinetic energy giving rise to the (2J + 1)-spatial degeneracy for each energy level. Although this degeneracy affects the transition intensities (since a single transition frequency has a series of exactly overlapping transitions in field-free space), it is not important to the interpretation of molecular rotational spectra in the absence of an external electric field. For large, rigid molecules at the low temperatures of a pulsed jet expansion it is often possible to obtain a quantitative fit of the experimental spectrum using just the rigid rotor Hamiltonian of Eq. (17.1). In rotational spectroscopy, a spectrum “fit” generally reproduces the transition frequencies to the experimental accuracy. For example, the root-mean-squared frequency error in an analysis is often on the order of 10 kHz and is significantly less than the experimental line width of the transitions at about 70 kHz in broadband rotational spectrometers. To achieve this level of accuracy, it is often necessary to include additional terms in the rotational kinetic energy Hamiltonian that account for distortion of the geometry as a function of the rotational kinetic energy. In this case, the Hamiltonian for rotational spectroscopy is the Watson Hamiltonian [30] and with the first correction for distortable rotation contains five experimentally determinable quartic centrifugal distortion terms:

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(

)

∆



(

4 2 2 4 2 2 2 J P − ∆ JK P Pa − ∆ K Pa − 2 δ J P Pb − Pc  − δ K Pa2 Pb2 − Pc2 + Pb2 − Pc2 Pa2

2 2 2 H A-reduction = A Pa + B Pb + C Pc + 

( (

) (

) )

) 

(17.3)

where P2 is the square of the total angular momentum: P  = Pa2 + Pb2 + Pc2 [6]. In most cases, the Hamiltonian uses the so-called A-reduction that is given above. In the case where the molecule is very close to a symmetric top, there is an alternative form of the Hamiltonian known as the S-reduction that gives a more suitable treatment of centrifugal distortion [6]. The Watson Hamiltonian still uses only angular momentum operators and parameters that are constants and, therefore, can be solved exactly. There are two other additions to the molecular rotational Hamiltonian that are encountered in the field of molecular rotational spectroscopy. For molecules that contain atoms with nuclear quadrupole moments (e.g., 14N with nuclear spin quantum number I = 1), the nuclear quadrupole hyperfine coupling must be included [6]. This Hamiltonian also includes only angular momentum operators and can be solved exactly. The second effect, that is, common comes from internal rotation of “tops” attached to the molecule—like methyl groups. The theory of internal rotation effects on molecular rotational spectra is also a well-developed topic and methods to include these effects are known [6,31]. However, for larger molecules the observation of “splitting” of the rotational transitions due to an internally rotating functional group is rare. The prediction of the rotational spectrum requires the calculation of the intensities for the allowed transitions between quantized energy levels. The coupling of light to the molecular rotation occurs through the permanent dipole moment of the molecule (and, as a result, rotational spectroscopy requires polar molecules). The torque on the molecule through the interaction of the electric field of the light source and electric dipole moment can change the kinetic energy of rotation around any of the three principal axes. As a result, there are three different rotational spectra that come from the interaction of light with the dipole moment vector components in the principal axis system where µ = (µa, µb, µc). Each of these three spectra, known as the a-type, b-type, and c-type spectra, have their own selection rules. The relative intensities of the three spectra are proportional to the squares of the dipole moment components. In this way, the relative intensities of the a-, b-, and c-type spectra give information about the direction of 2

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the dipole moment in the principal axis system. The theory for calculating the transition intensities in the rotational spectrum is known and described in the texts for this field of spectroscopy [6].

17.2.2  Challenges for large molecule rotational spectroscopy As the size of the molecule, as characterized by the principal moments-ofinertia, increases, it becomes more challenging to measure the spectrum at high sensitivity.The main issue is the size of the rotational partition function: Q rot ( T ) ≈ ( kT )

32



12

( ABC )

(17.4)

where A, B, and C are the rotational constants for the molecule.The sensitivity also depends on the population difference between energy levels of the rotational transition and the Boltzmann distribution adds an additional linear dependence bringing the overall temperature dependence of the signals to T−5/2. There are two important points in these results. First, for any measurement the sensitivity is improved by lowering the temperature of the gas sample. As a result, molecular rotational spectroscopy is most commonly performed on gas samples cooled in a pulsed molecular beam—an approach pioneered in the Balle-Flygare cavity-enhanced Fourier transform microwave spectrometer [32]. By seeding the molecule of interest in an inert gas, the rotational temperature of the sample in the pulsed jet expansion is typically 1–10 K. The pulsed jet expansion also effectively cools the vibrational excitation of the molecule. For larger molecules like those presented in this work, the population of vibrational excited states is generally <1%. This vibrational cooling further increases the measurement sensitivity by reducing the size of the vibrational partition function. Vibrational cooling also provides spectral simplification because each vibrational excited state has its own characteristic rotational spectrum and depopulating these states removes these transitions from the measurement. One important point is that the population of higher energy conformational isomers are not cooled as efficiently and it is common to see rotational spectra from several lowenergy conformations of the molecule [33]. The emerging technique of buffer gas cooling cells is seeing increased adoption in rotational spectroscopy measurements and offers similar gains in sensitivity due to the ability to produce low temperature gas conditions [34–36]. The second important result is that even with a low temperature gas, the sensitivity will be lower for larger molecules due to an increase in the partition functions from ever smaller values of the rotational constants.

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S­ imulations of the a-type rotational spectrum with a temperature of 1 K are shown for a series of progressively larger molecules in Fig. 17.2. The dipole moment component is the same in all three simulations so the reduction in transition intensity, that is, observed comes from the increase in the partition function. In general, the expected peak signal strength in the rotational spectrum is reduced by almost a factor of 10 when the size of the molecule is doubled. Despite these challenges, the size range for molecules that can be studied using molecular rotational spectroscopy has continued to increase. For example, the rotational spectrum of a molecular motor molecular system with molecular formula C27H20 (344 Da) was recently reported using simple heating of the sample to volatilize the molecule [37]. Other techniques for sample volatilization for molecular rotational spectroscopy have been developed, such as laser ablation sources [38–40], that have the potential to expand the types of molecules amenable to study using rotational spectroscopy.

17.2.3  Molecular structure from rotational spectroscopy Molecular rotational spectroscopy measurements are used to gain information about the structure of molecules. The rotational spectrum itself provides a somewhat coarse characterization of the structure since only three structure parameters, the moments-of-inertia in the principal axis system via the rotational constants, Eq. (17.2), are determined. The utility of the technique depends on how diagnostic these three parameters are for identifying molecular structures. This assessment is strongly connected to the ability of quantum chemistry to calculate the spectroscopic parameters of rotational spectroscopy [41]. These parameters include both the principal moments-of-inertia from the optimized geometry and the dipole moment. The dipole moment direction determines the relative intensities of the a-, b-, and c-type spectra and, alternatively, can be measured using the molecular Stark effect [6]. In cases where there is nuclear quadrupole hyperfine structure, the analysis of these patterns can supply crucial additional information about the molecular structure [42]. The major strength of rotational spectroscopy for structure determination is the use of isotopic substitution to determine the positions of individual atoms in the principal axis system.This method was first described by Kraitchman [43]. The analysis is based on the Born-Oppenheimer approximation that the atom positions in the molecular structure are isotope independent. By making a single isotopic substitution, the mass distribution will be changed in a characteristic way for each different atom. By ­measuring

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Figure 17.2  This figure shows spectrum simulations for molecules with different numbers of heavy atoms (C, N, O, etc.—hydrogen atoms make small contributions to the moments-of-inertia and have less influence on determining the size of the rotational constants). The simulations show only the spectra for a-type transitions and in each simulation the dipole moment component is 1D. The temperature for the simulations is 1 K and is typical for pulsed jet cooled samples. As the molecular size increases three things occur: (1) The number of transitions in the spectrum increases significantly, (2) the peak intensity of any single transition decreases significantly, and (3) the frequency where the strongest transitions occur moves to lower frequency. There is approximately an order-of-magnitude decrease in the peak signal intensity when the size of the molecule doubles.

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the change in the rotational constants upon single isotopic ­substitution, the changes in the three moments-of-inertia can be converted to the atom position in the principal axis system. Because the moments-of-inertia depend on the squares of distances from the principal axes, the sign of the atom coordinates cannot be determined directly. However, the sign ambiguity can usually be resolved easily using a candidate theoretical structure. For each isotopologue spectrum analyzed, a new atom position is obtained making it possible to build up the three dimensional structure of the molecule atom-by-atom. When sufficient instrument sensitivity is available, the atom positions of nuclei with relatively abundant stable isotopes—including carbon atom positions using the 13C isotope—can be obtained from the isotopologues present at natural abundance. In other cases, like the study of water cluster structures, isotope spiking strategies can be used to artificially increase the isotopic abundance [44,45]. Detailed discussion of molecular structure determination from isotopic substitution, including the effects of zero-point vibrational motion, can be found in Gordy and Cook [6]. This text also describes other structure analysis approaches that uses the isotopic changes in the rotational constants to determine the molecular structure. In general, carbon atom framework geometries obtained from Kraitchman analysis are expected to be accurate to 0.01 Å or better (expect for special cases where the atom lies very close to a principal axis and vibrational effects can make a large contribution).

17.2.4  Advances in rotational spectroscopy for chemical analysis There have been three important advances in the field of molecular rotational spectroscopy that make these measurements more suitable for applications in analytical chemistry: (1) The Development of Broadband Spectrometers for Molecular Rotational Spectroscopy The major recent advance in instrumentation for molecular rotational spectroscopy is the introduction of chirped-pulse Fourier transform spectrometers that enable broadband spectrum acquisitions [46–49]. Prior to this instrument design, the dominant instrument for pulsed jet rotational spectroscopy was the Balle-Flygare design that used a cavity resonator to enhance the electric field of the free induction decay [32,50]. The use of high reflectance mirrors to give a cavity with high quality factor, Q, results in a narrow measurement bandwidth of about 1 MHz. As seen in Fig. 17.2, the rotational spectrum of a molecule spans

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a frequency range of several GHz. As a result, the use of cavity-enhanced Fourier transform spectrometers requires a large series of measurements in ∼1 MHz steps to obtain the spectrum for analysis. This approach leads to long measurement times and high sample consumption. Chirped-pulse Fourier transform microwave spectrometers polarize the sample of a large bandwidth on each excitation pulse so that a spectrum covering the full spectrometer operating range is obtained on each measurement cycle [47]. A schematic diagram of the instrument is shown in Fig. 17.3 [48]. A key to the sensitivity gains in this spectrometer design is that high-power microwave amplifiers can be used to give efficient sample polarization over the large bandwidth. The excitation pulse is a short, linear frequency sweep, or chirp, that covers the full spectrometer frequency range in a time on the order of 1–4 µs. The time duration of the excitation pulse is determined by the dephasing time of the broadband free-induction decay signal. The main cause of the dephasing is residual Doppler broadening in the pulsed jet expansion. The important feature of the chirped pulse is that it is not a transform limited pulse shape and, instead, allows the pulse bandwidth and pulse duration to be chosen independently. As a result, the excitation pulse with about 10 GHz of spectral bandwidth can be “stretched” to the optimum excitation time (1–4 µs) making it possible to deliver the maximum amount of pulse energy to the sample from the microwave amplifier. A second technical advantage of chirped-pulse compared to cavity-enhanced spectrometers is that the instrument can be designed to operate over a wide range of frequencies with only small changes to the instrument physical dimensions. This feature is important for extending rotational spectroscopy to the study of larger molecules because larger molecules have pulsed jet rotational spectra that have peak intensity at progressively lower frequency (see Fig. 17.2). In contrast, the mirror size in a cavity-enhanced spectrometer must scale with the excitation wavelength to maintain the high quality factor of the resonator where diffraction losses become the main loss mechanism on the lower frequency end of the spectrometer [51]. One of the applications that chirped-pulse Fourier transform rotational spectroscopy instruments enabled is the determination of molecular structures using the natural abundance of isotopes (mainly 13C for organic molecules, but also 15N and 18O that are above 0.1%) [7]. The sensitivity advantages of the chirped-pulse instruments meant that the isotopologue spectra could be obtained through deep signal averaging without unfeasible sample consumption levels. This capability made it possible to explore the structures of larger molecules where

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Figure 17.3  A schematic diagram of a low-frequency (2–8 GHz operating frequency range) chirped-pulse Fourier transform microwave spectrometer is shown. The components in section (1) are for generation of the chirped excitation pulse. This pulse is digitally created using a high-speed (24 Gs/s) arbitrary waveform generator. The excitation pulse is a 2–8 GHz linear frequency sweep in 4 µs and there are eight excitation pulses in the pulse train. This pulse is amplified by a 300 W traveling wave tube amplifier. The components in box (2) are located in the vacuum chamber of the spectrometer. These include high-gain rectangular microwave horn antennas to broadcast the pulse across the sample and to receive the broadband coherent emission signal. Sample is injected using solenoid pulsed valves. Up to five pulsed valve sources can be used to optimally fill the active volume of the spectrometer to maximize spectrometer sensitivity. The signal detection components are shown in box (3). The receiver includes a PIN diode limiter and microwave switch to protect the electronics from the high-power excitation pulse. After the excitation pulse power has decayed, the receiver switch is closed and the molecular emission signal is amplified by a broadband, low-noise microwave amplifier and digitized on a high-speed digital oscilloscope. To increase measurement sensitivity, subsequent measurements are accumulated in the time-domain. The broadband rotational spectrum is finally produced by a fast Fourier transform of the time-domain signal.

i­ntramolecular ­dispersion interactions play a significant role in determining the molecular structure. The technique has also been widely applied to the determination of the structures of molecular clusters held together by noncovalent interactions [52–54].

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(2) The Development of Accurate Quantum Chemistry Methods For applications in analytical chemistry, it is necessary to identify the molecular rotational spectrum for the molecule of interest in the broadband spectrum that contains the spectra of all polar molecular components of the sample mixture. These spectral patterns are determined by a small set of molecular parameters (for a rigid molecule only the three rotational constants from the molecular geometry and the dipole moment vector represented in the principal axis system are required) and can be calculated exactly from the Hamiltonian. Although there are simple quantum mechanical rules for calculating the rotational ­spectrum, this ­Hamiltonian and the transition selection rules can produce somewhat complicated patterns that can be difficult to identify by inspection—especially in a complex sample mixture where these patterns are interspersed. Quantum chemistry can provide the spectral parameters to generate estimated spectral patterns. The rigid rotor Hamiltonian spectral parameters can be obtained from a geometry optimization. As is usual, there is a trade off in accuracy and computation time in the use of quantum chemistry for analytical chemistry applications.The development of dispersion corrected density functional (DFT) methods has significantly improved the accuracy of quantum chemistry predictions of the rotational spectroscopy parameters with time requirements compatible with analytical chemistry (where answers are needed on the time scale of about 1 day). Grimme recently performed a series of benchmark calculations for molecular rotational spectroscopy [41]. This study showed that dispersion corrected DFT using medium sized basis sets (e.g., 6–311++G(d,p) or the def2TZVP basis set) could estimate rotational constants of molecular monomers to better than 1% accuracy. Significantly higher accuracy, on the order of 0.1%, can be achieved using the B2PLYP method, but with a time cost, that is, closer to MP2 calculations. For analytical chemistry applications, this means that high confidence identifications of molecules can be performed without the need for a previously measured reference sample. This “library free” identification capability is especially useful for the identification of diastereomers in molecules with multiple chiral centers where samples with high stereoisomer purity are rarely available. There has been less benchmark analysis for molecular clusters, which are important to the chiral tag methodology discussed in this article. Similarly, accuracy for larger molecules where intramolecular noncovalent

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interactions are likely worse than for simple, rigid monomers and understanding the limits of quantum chemistry for these challenging systems is a topic of current research. However, the experience in the chiral tag work is that dispersion corrected DFT methods provide rotational constant estimates with accuracy of about 3% or better. The methods have also successfully identified the lowest energy isomers of the chiral tag complex.With this level of accuracy, it is generally straightforward to identify the spectrum of a candidate molecule or tag complex starting with the quantum chemistry estimates. (3) The Development of Software for Spectrum Analysis The final advance in the field of rotational spectroscopy is the development of software by the research community to perform spectrum analysis (called the “assignment” of the spectrum where the spectral pattern is matched to a candidate molecule and the “fitting” of the spectrum where the rotational constants are refined in a least squares fitting process using the measured transition frequencies). A general purpose fitting program, called SPFIT, has been developed by Pickett and the spectroscopy group at NASA JPL [55,56]. There is also a companion spectrum prediction program called SPCAT. This program has become the standard for spectrum fitting in molecular rotational spectroscopy. As noted by Kisiel, the error estimates of the rotational constants returned by SPFIT are not the usual definition and there is a reformatting program, PIFORM, that converts SPFIT output files to the more usual format. This program, and several other useful utilities for rotational spectroscopy are available on Kisiel’s Programs for Rotational Spectroscopy (PROSPE) website [57]. Graphical spectrum analysis programs are also available that make it easier to identify the spectrum of a molecule from the initial estimates from quantum chemistry.There are four commonly used programs: JB95 [58], PGOPHER [59], AABS [57], and the recently released VMS ROT [60]. The last three use the SPFIT spectral fitting engine. In addition, the commercial Gaussian quantum chemistry distribution has an option that converts the quantum chemistry results into the spectrum parameters for rotational spectroscopy and generates a summary file with the format required in the SPFIT and SPCAT programs [61]. This capability includes the estimate of the centrifugal distortion parameters in the Watson Hamiltonian. These parameters require the harmonic vibrational force constants and frequencies for evaluation. Therefore, a frequency calculation must be performed in addition to the geometry o ­ ptimization

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if these corrections to the rigid rotor Hamiltonian are desired. Recent results from the field of rotational spectroscopy suggest that quantum chemistry estimates of the centrifugal distortion parameters also have high accuracy [62,63]. Finally, there has been recent work to develop automated fitting routines to identify the spectra of candidate molecules using quantum chemistry estimates of the spectral parameters [64,65]. These methods make use of three characteristics of rotational spectroscopy: (1) the Hamiltonian is known, (2) the Hamiltonian determines the rotational spectrum transition frequencies to experimental accuracy, and (3) accurate estimates of the spectroscopic parameters are available from quantum chemistry. The AUTOFIT program uses the quantum chemistry parameters and estimates of their errors to identify a likely set of transitions that could form the spectral pattern. These sets are fit to the Watson Hamiltonian and the predictions of additional transitions form the Hamiltonian are tested against the measured set of transitions. As a result, the computer algorithm will identify any pattern of transitions, that is, consistent with the structure of the Hamiltonian and the estimates of the spectral parameters from a quantum chemistry optimized geometry. This automated analysis capability has recently been included in the PGOPHER graphical spectrum analysis package [66]. In summary, advances in the field of rotational spectroscopy over past decade have moved this measurement technology towards applications in analytical chemistry. Improvements in instrument design have made it possible to acquire the spectra of larger, more chemically relevant molecules with reduced sample consumption [67]. The combination of advances in quantum chemistry methods and spectrum analysis software has significantly reduced the time required to analyze the rotational spectrum of a complex chemical mixture. The traditional bottleneck of spectrum assignment has been greatly reduced—if not eliminated— making it possible to focus on applications of rotational spectroscopy to quantitative chemical analysis.

17.2.5  An example—diastereomer identification in fenchyl alcohol The analysis of a molecular rotational spectrum, with a focus on quantitative determination of the diastereomer ratio, is illustrated using fenchyl alcohol ((1R,2R,4S)-1,3,3-trimethyl-bicyclo[2.2.1]heptan-2-ol). Although this molecule has three asymmetric carbons, the relative stereochemistry of the

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two bridgehead carbons is fixed. Therefore, this molecule can exist in two diastereomer forms: fenchyl alcohol and its epimer ((1R,2S,4S)-1,3,3-trimethyl-bicyclo[2.2.1]heptan-2-ol). These structures are shown in Fig. 17.4. These stereoisomers have distinct geometries and can, therefore, be distinguished by traditional rotational spectroscopy. The ability to analyze the enantiomer ratio for a given diastereomer is discussed in the next section. Fenchyl alcohol has one conformational isomerization coordinate—the hydroxyl torsion. A relaxed potential energy surface for torsion is shown in Fig. 17.5 and shows three distinct minima.These minima have relatively low barriers to interconversion. The experimental spectrum of a commercial sample of Fenchyl alcohol is shown in Fig. 17.6. In this measurement, the fenchyl alcohol is heated in a reservoir nozzle to 50oC to give maximum signal intensities. Neon is used as the carrier gas at a total pressure of 2 atm. The spectrum is obtained using 1000 averages of the time-domain free induction decay. The spectrometer acquires 8 time-domain measurements for each sample injection using the General Valve Series 9 solenoid nozzles. Calibration of the sample injection indicates that 10,000 averages uses 2 mg of sample—so the spectrum in Fig. 17.6 was acquired with approximately 200 µg of sample and requires about 40 s of measurement time. The measurement is dominated by a single spectrum—not the three spectra that might have been expected based on the isomerization potential. In this case, where the barriers to isomerization are relatively low, there is strong cooling of the conformational population into the lowest energy isomer [33,68,69].

Figure 17.4  The two diastereomers of fenchyl alcohol are shown. The structure on the left is fenchyl alcohol ((1R,2R,4S)-1,3,3-trimethyl-bicyclo[2.2.1]heptan-2-ol, also known as (+)-fenchol and (1R)-endo-(+)-fenchyl alcohol). The structure on the right is the hydroxyl epimer of fenchyl alcohol ((1R,2S,4S)-1,3,3-trimethyl-bicyclo[2.2.1]heptan-2-ol).

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Figure 17.5  A relaxed potential energy surface for hydroxyl internal rotation of fenchyl alcohol is shown. There are two nearly isoenergetic conformational minima with a low barrier to interconversion of about 2–3 kJ/mol. The third conformational isomer lies only about 1 kJ/mol higher in energy with about a 5–6 kJ/mol barrier to convert to one of the lower energy forms. In the pulsed jet expansion using neon as the carrier gas, there is extensive conformational cooling and the lowest energy conformational isomer dominates the population of fenchyl alcohol.

In the top panel of the figure, the measured rotational spectrum is compared to the simulated spectrum using the rigid rotor Hamiltonian and estimates of the rotational constants from the optimized geometry calculated using Grimme’s dispersion corrected DFT theory (B3LYP D3BJ 6–311++G(d,p)) [70]. This example shows the close agreement between theoretical predictions of the spectrum and the measurement that are routinely achieved. The bottom panel of the figure shows the “fit” of the spectrum to the experiment, that is, achieved by fitting the rotational constants to the experimental transition frequencies. The spectrum simulation uses a temperature of 1 K. Quantitative agreement between the fit Hamiltonian and experimental transition frequencies is achieved. Qualitative agreement in the intensities of these transitions is observed using the chirped-pulse spectrometers.

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Figure 17.6  The spectrum of fenchyl alcohol acquired using 1000 averages of the timedomain signal is shown in both the top and bottom panels (black curve). The top panel illustrates the accuracy of quantum chemistry predictions of parameters for the molecular rotational spectrum. The negative going spectrum (blue) in the top panel is the theoretical simulation of the rotational spectrum for the lowest energy conformer of

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fenchyl alcohol. The close correspondence to the experimental spectrum makes assignment and fitting of the spectrum straightforward. The bottom panel compares the experimental spectrum of fenchyl alcohol (black) to the spectrum simulations of fenchyl alcohol and its epimer that are calculated using the fitted rotational constants reported in Table 17.1. The blue spectrum is for fenchyl alcohol and the red spectrum is assigned to fenchyl epimer based on the close agreement between the experimental and theoretical rotational constants. The simulation of the epimer spectrum is shown for a 2.8% abundance in the commercial fenchyl alcohol sample. The inset shows transitions of the epimer on an expanded scale.

From a chiral analysis perspective, the challenge is to quantify the amount of the fenchyl alcohol epimer in the sample. This analysis needs to be performed without the availability of a reference sample of the stereoisomer. The close agreement between theoretical estimates of the rotational constants from an optimized geometry and the experimental values gives high confidence in these “library-free” identifications. For the epimer, a spectrum consistent with the theoretical rotational constants and dipole moments was observed. The strongest transitions of the epimer are detectable in the spectrum shown in Fig. 17.6 where they are observed at a signal-to-noise ratio of 3:1. The comparison between theoretical and experimental rotational constants for fenchyl alcohol and its epimer is given in Table 17.1. Using spectrum simulations with the dipole moments from quantum chemistry, the epimer impurity is estimated to be 2%–3%.This example shows that the combination of high spectral resolution and measurement dynamic range makes it possible to identify low abundance chiral impurities in the sample without the need for separation by chromatography.

17.3  CHIRAL TAG ROTATIONAL SPECTROSCOPY FOR ENANTIOMER ANALYSIS The new capabilities that have been developed for quantitative chiral analysis by molecular rotational spectroscopy focus on enantiomer analysis. This section illustrates the use of noncovalently attached chiral tags to convert enantiomers into diastereomers so that they can be analyzed using standard methods of rotational spectroscopy. The complex of the analyte molecule with the small, chiral tag is formed in the pulsed jet expansion. This method has the potential for general application since cluster formation is almost always observed in these sources.The groundwork for this technique comes from pioneering studies of chiral recognition in molecular clusters starting with the rotational spectroscopy study of the dimer of butan-2-ol

Percent error for quantum chemistry estimates

A B C

−0.16 −0.21 −0.19

1520.225 (5) 1097.365 (3) 983.704 (3)

1521.4 1091.6 985.0

0.08 −0.53 0.13

A B C

1494.883 (6) 1201.811 (4) 901.905 (2)

1492.4 1199.3 900.2

a Quantum chemistry estimates of the rotational constants from the optimized geometry of the minimum energy conformer using dispersion corrected DFT theory: B3LYP D3BJ 6–311++G(d,p).

Quantitative Chiral Analysis by Molecular Rotational Spectroscopy

Table 17.1  Comparison of experimental and theoretical rotational constants for fenchyl alcohol and its epimer Rotational Experimental Quantum Percent error Rotational Experimental Quantum constants for constants (MHz) chemistry con- for quantum constants for constants chemistry confenchyl alcohol stantsa (MHz) chemistry fenchyl alco- (MHz) stantsa (MHz) estimates hol epimer

699

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alcohol by King and Howard [22]. More recent studies have addressed issues of fundamental physical chemistry importance in chiral recognition and transient chirality [21–23]. In this article, the discussion focuses on analytical chemistry applications. There are two chiral analysis measurements where chiral tag rotational spectroscopy has unique advantages. The first is the determination of the absolute configuration of a chiral molecule. In this case, the sample for the analysis is most likely chemically pure including having high enantiopurity. The measurement goal is to determine the absolute configuration with a high degree of confidence. The second application, that is, discussed here is the determination of EE. For this analysis, the strength of chiral tag spectroscopy is the potential for accurate determination of the EE without the need for a reference sample of known EE for instrument calibration.

17.3.1  Determination of absolute configuration The strategy of using chiral tags in rotational spectroscopy is similar to the use of chiral resolving agents in NMR spectroscopy [18–21]. For rotational spectroscopy, the idea is to add a new chiral center to the molecule through noncovalent interactions by forming a molecular complex with an enantiopure tag molecule. The addition of the asymmetric carbon with known configuration converts the enantiomers, with identical rotational spectra, into diastereomers. The ability of rotational spectroscopy to differentiate molecules with small differences in their mass distribution then makes it possible analyze these diastereomer complexes separately. At the basic level, the determination of the absolute configuration of the molecule rests on the ability to make a high-confidence attribution of a specific complex geometry to the experimental observation. In this way, the analysis of absolute configuration is similar to VCD spectroscopy where quantum chemistry interpretation of the experimental measurement is used to make the determination [71–75]. For chiral tag rotational spectroscopy, quantum chemistry must be able to predict the lowest energy isomer of the weakly bound complex and obtain an accurate structure of this complex for comparison between experimental and theoretical rotational constants.The dipole moment properties can also be useful in some cases for bolstering the attribution of a theoretical structure to an observed spectrum. Improved confidence in the absolute configuration determination can be gained if the rotational spectra for both diastereomer complexes are available. In this case, the differences in rotational constants for homochiral and heterochiral diastereomer complexes can be used in the comparison to theoretical structures instead of the absolute constants. This allows for

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c­ ancellation of correlated errors for any variations in the theoretical structures that show up in both diastereomer complexes. In addition, in measurements performed to date there have usually been multiple isomers present with comparable signal levels. Having a family of homochiral and heterochiral structures can provide further support for the absolute configuration. In practice, the measurement is performed in two steps. The first measurement uses a chiral tag of high enantiopurity. This chiral tag is mixed in with the neon carrier gas at a typical concentration of 0.1%. If the analyte is also of high enantiopurity, then either the homochiral or heterochiral complexes will dominate the measured spectrum. Following this measurement, the enantiopure tag is purged from the system using a pure neon carrier and then the spectrum is acquired using a racemic sample of the chiral tag (also at about 0.1% in neon). By using the racemic tag, both homochiral and heterochiral complexes are generated regardless of the enantiopurity of the analyte.The new spectra that appear in this measurement provide the complementary set of diastereomer chiral tag complexes. The rotational constants and dipole moment properties for the set of measurement are compared with quantum chemistry calculations of the lowest energy isomers for the complex to make a determination of the analyte stereochemistry. In some cases, exceptionally high confidence for the absolute configuration determination is desired and this can be provided if there is enough sample to perform a deep average spectrum to reach 13C-sensitivity in natural abundance so that a carbon framework substitution structure can be produced. Isotopic measurements cannot distinguish between the structure of the complex and its enantiomer. However, the enantiomers of the complex have different absolute configuration of the tag and since the configuration of the enantiopure tag is known, a structure of the analyte with correct stereochemistry can be determined.This measurement idea is analogous to internal chiral reference X-ray diffraction, which also determines a structure of a complex using a known, enantiopure complexation partner [76,77]. Chiral tag rotational spectroscopy provides a general method for creating these complexes that may have wider applicability than the corresponding X-ray diffraction approach that needs a crystal of a well-defined complex.

17.3.2  An example—the absolute configuration of 3-methylcyclohexanone These measurement principles are illustrated by the determination of the absolute configuration of 3-methlycyclohexanone.The commercially available sample used in the experiments is (R)-(+)-3-methylcyclohexanone with an EE of 99.6. The chiral tag molecule is 3-butyn-2-ol, which can

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hydrogen bond to the carbonyl oxygen of the analyte. The tag molecule is commercially available in both high enantiopurity and racemic forms. This molecule was chosen as a simple test case, in part, because it is a benchmark system in VCD spectroscopy [78–81]. One issue, that is, important for rotational spectroscopy is determining the conformer populations for the monomer. 3-methylcyclohexanone can exist in two conformations where the methyl group is either equatorial (lower energy) or axial. In a measurement of the spectrum of 3-methylcyclohexanone without the chiral tag, both conformers were identified using quantum chemistry estimates of the rotational constants and dipole moment with theoretical calculations using the B3LYP D3BJ 6–311++G(d,p) model chemistry. A summary of the results is shown in Table 17.2.The axial conformer is present at about 3% relative abundance. The energy difference from the quantum chemistry calculations (3.7 kJ/mol) implies a conformer ratio of 82:18 at 298 K.This ratio is in very good agreement with the 89:11 ratio obtained from analysis of the VCD spectrum of 3-methylcyclohexanone in CCl4 solvent [78]. The lower abundance in the pulsed molecular beam sample suggests that there is partial conformational cooling of the population. However, the cooling is not as effective as observed in fenchyl alcohol where there are low barriers to conformational interconversion. The measurement strategy discussed above is illustrated for 3-methylcyclohexanone in Fig. 17.7. The goal is to determine whether the sample is (R)-(+)-3-methylcyclohexanone or (S)-(+)-3-methylcyclohexanone. These enantiomers can’t be distinguished by rotational spectroscopy. A second chiral center of known configuration attached to the analyte through the hydrogen bond formation in the pulsed jet expansion and produces diastereomer complexes with the two different analyte enantiomers. By performing a measurement using both enantiopure tag and racemic tag it is possible to identify the spectra of both diastereomer complexes. The rotational spectra of the complexes observed in this measurement are shown in Fig. 17.8. The spectra are dominated by two isomers of both diastereomer complexes. By comparison of signal levels, it is estimated that about 10% of the 3-methylcyclohexanone forms a 1:1 complex with the butynol tag. The rotational constants obtained from the spectrum assignment and fitting procedure are given in Table 17.3. The theoretical estimates of the rotational constants for the two lowest energy isomers of both the homochiral and heterochiral complexes are also given in Table 17.3. The isomers result from the butynol hydroxyl group hydrogen bonding to the two different lone pair positions on the carbonyl oxygen atom. The

A B C Relative value of the dipole components squared (µa2:µb2:µc2)b Experiment

3091.525 (1) 1720.955 (1) 1204.695 (1)

3086.1 1716.9 1200.7

−0.18 −0.24 −0.33

A B C

2728.428 (1) 1998.623 (1) 1476.144 (1)

2731.2 1985.6 1465.2

0.10 −0.65 −0.74

1:0.44:0.08

Theory

1:0.48:0.09

Experiment

1:0.28:0.17

Theory

1:0.25:0.18

a Quantum chemistry estimates of the rotational constants from the optimized geometry of the minimum energy conformer using dispersion corrected DFT theory: B3LYP D3BJ 6–311++G(d,p). b Experimental values for the dipole component squared ratios are obtained using the adjustable intensity functionality for the a-type, b-type, and c-type spectra in JB95. These are adjusted to give the best approximation of the observed spectrum to the spectrum simulation at T = 1 K.

Quantitative Chiral Analysis by Molecular Rotational Spectroscopy

Table 17.2  Comparison of experimental and theoretical rotational constants for the equatorial and axial conformations of 3-methylcyclohexanone Rotational Experimental Quantum Percent error Rotational Experimental Quantum Percent error constants for constants chemistry for quantum constants for constants (MHz) chemistry for quantum equatorial 3-meth- (MHz) constantsa ­chemistry axial 3-methconstantsa chemistry ylcyclohexanone (MHz) estimates ylcyclohexa(MHz) ­estimates none

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Figure 17.7  The concept of chiral tag rotational spectroscopy to determine absolute configuration is illustrated. The top of the figure shows (R)-3-methylcyclohexanone and its mirror image (i.e., enantiomer)—(S)-3-methylcyclohexanone. Because these two structures have the same bond lengths and bond angles (i.e., the same mass distribution) they will have identical molecular rotational spectra. The bottom part of the figure shows the theoretical predictions for the structures of the lowest energy complexes of the 3-methylcyclohexanone enantiomers with enantiopure (R)-3-butyn-2-ol. With the addition of a second chiral center via the tag molecule, these complexes are diastereomers and have distinct molecular rotational spectra. In fact, in this case there is evidence for chiral recognition between these two molecules where the lowest energy isomers involve hydrogen bonding of the tag molecule hydroxyl group to different electron lone pair positions on the carbonyl oxygen of 3-methylcyclohexanone. The spectral analysis confirms that these theoretical geometries are the lowest energy structures for the diastereomer complexes.

a­greement between theoretical and experimental rotational constants for these four species supports the assignment of (R)-methylcyclohexanone as the absolute configuration of the analyte (in agreement with the known absolute configuration of the commercial sample). The spectrum of the complexes with enantiopure tag can be measured with sufficient sensitivity to identify the eleven different singly substituted

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Figure 17.8  The isolated spectra for the complexes of the enantiopure (R)-3-methylcyclohexanone commercial sample with enantiopure (R)-3-butyn-2-ol (top panel) and (S)3-butyn-2-ol (bottom panel) are shown (black). These spectra are dominated by two isomers for the 3-methylcyclohexanone-butynol complex in both cases. The ­spectrum simulations for these complexes using the fitted rotational constants reported in Table 17.3 are shown in both cases.

Rotational constants for lowest energy isomer

Quantum chemistry Experimental constantsa constants (MHz) (MHz)

Percent error for quantum chemistry estimates

Rotational constants for second lowest isomer

Experimental constants (MHz)

Quantum chemistry constantsa (MHz)

706

Table 17.3  Comparison of experimental and theoretical rotational constants for the isomers of the two diastereomer complexes of 3-methylcyclohexanone with the 3-butyn-2-ol chiral tag Percent error for quantum chemistry estimates

(A) Complexes formed when (R)-3-butyn-2-ol is used as the chiral tag compared to the quantum chemistry results for the two lowest energy isomers of the homochiral (R)-3-methylcyclohexanone/(R)-3-butyn-2-ol complex A

1185.843 (1)

1186.8

0.1

A

1243.868 (1)

1238.2

−0.5

B

420.130 (1)

430.1

2.4

B

410.994 (1)

425.0

3.4

C

350.173 (1)

357.7

2.1

C

399.300 (1)

412.0

3.2

Experiment

1:0.07:0

Theory

1:0.09:0.00

Relative value of the dipole components squared (µa :µb :µ ) 2

Experiment

1:0.14:0.06

Theory

2

2 b c

1:0.15:0.05

(B) Complexes formed when (S)-3-butyn-2-ol is used as the chiral tag compared to the quantum chemistry results for the two lowest energy isomers of the heterochiral (R)-3-methylcyclohexanone/(S)-3-butyn-2-ol complex A

1094.350 (1)

1096.1

0.2

A

1363.810 (1)

1351.0

−0.9

B

460.801 (1)

470.4

2.1

B

381.870 (1)

395.6

3.6

C

380.164 (1)

386.3

1.6

C

362.157 (1)

373.8

3.2

Experiment

1:0.06:0.16

Theory

1:0.05:0.14

Experiment

1:0.21:0.05

Theory

1:0.18:0.05

a Quantum chemistry estimates of the rotational constants from the optimized geometry of the minimum energy conformer using dispersion corrected DFT theory: B3LYP D3BJ def2TZVP. b Experimental values for the dipole component squared ratios are obtained using the adjustable intensity functionality for the a-type, b-type, and c-type spectra in JB95. These are adjusted to give the best approximation of the observed spectrum to the spectrum simulation at T = 1K.

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Relative value of the dipole components squared (µa2:µb2:µc2)b

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C-isotopologues in natural abundance. This measurement provides an extremely high confidence determination of the stereochemistry as illustrated in Fig. 17.9. 13

17.3.3  Measurement of the EE The same measurement procedure described for the absolute configuration measurement can be used to measure the EE of the sample.This application is also analogous to approaches in NMR spectroscopy where the chiral resolving agent is used to “split” the NMR transition so that the enantiomers can be detected at separate measurement frequencies [18–21]. The relative heights of the two peaks can then be used to determine the enantiopurity in the same way that chiral chromatography is used. For chiral tag rotational spectroscopy, the exceptionally high spectral resolution of the measurement produces a separation in the peak positions associated with different enantiomers that far exceeds what is possible by NMR or even chiral chromatography. This characteristic of the measurement holds the potential to develop measurement techniques for quantitative analysis of very high enantiopure samples. However, there are some important differences in the use of chiral tag rotational spectroscopy for EE measurements. The most important is that in the presence of the chiral tag resolving agent, the peak intensities corresponding to different analyte enantiomers will not be the same for a racemic sample.These differences are caused by the potential for different isomer populations for homochiral and heterochiral complexes, different dipole moment and rotational constants for the complexes that affect the intrinsic intensity of the rotational transitions, and frequency-dependent sensitivity variations in the instrument. Therefore, it is necessary to normalize for these factors before making an EE measurement. The procedure for EE measurements is illustrated in Fig. 17.10. The measurement with racemic tag is used to normalize two rotational transitions assigned to different diastereomer chiral tag complexes. The normalization constant simply makes these transitions equal intensity. The normalization factor is then applied to the same two transitions in the case where the enantiopure tag is used. If the sample being analyzed has an EE one of the two normalized peaks will gain intensity and the other will have reduced intensity. The ratio of the peaks, following application of the normalization constants obtained in the measurement using the racemic tag, is called R and is used for the EE determination.

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Figure 17.9  A very high confidence method for establishing the absolute configuration of a molecule using chiral tag rotational spectroscopy is illustrated. The rotational spectrum of the commercial (R)-3-methylcyclohexanone sample tagged with high enantiopurity (R)-3-butyn-2-ol was measured with 1 million averages to reach about 400:1 sensitivity on the rotational spectrum of the lowest energy isomer of the tag complex. At that sensitivity it is possible to assign the 11 singly-substituted 13C-isotopologues in natural abundance and derive a substitution structure for the carbon framework of the complex. The top panel shows the two possible “homochiral” complexes that are enantiomers. The substitution structure is consistent with either form. The experimental carbon atom positions, represented by the smaller blue spheres, are shown superimposed on the theoretical structures of the complex in the middle panel. Because it is known than the experiment used (R)-3-butyn-2-ol as the tag, the structure on the right can be ruled out. The noncovalent tag can be removed from the figure leaving the carbon atom substitution structure of the 3-methylcyclohexanone sample with correct absolute configuration. The experiment confirms that the commercial sample was the R-enantiomer.

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Figure 17.10  The concept for measuring enantiomeric excess for the ratio of the intensity of rotational transitions of tag complexes associated with different enantiomers of the analyte is illustrated. A racemic sample of the tag is used to provide a measurement that can normalize the intrinsic spectroscopic and instrumental difference in the transition line strengths. When an enantiopure tag is used in the measurement, one of these transitions will increase in intensity at the expense of the other if the sample has an enantiomeric excess. The ratio, R, of the transition intensity for the pair of transitions following application of the normalization constant is used via Eq. (17.6) to determine the sample enantiomeric excess.

Under the assumption that the abundance of heterochiral and homochiral complexes formed in the pulsed jet expansion are linear in the number density of the analyte and tag enantiomers:

(

)

Signal HOMO = CHOMO * [ Tag ( − )][ Analyte ( − )] + [ Tag (+)][ Analyte (+)]

(

)

Signal HETERO = CHETERO * [ Tag ( − ) ][ Analyte ( +) ] + [ Tag ( +) ][ Analyte ( − ) ]  (17.5) it can be shown that the normalized transition intensity ratio, R, is ­related to the EE of the analyte as



(1 − R ) = ( ee Tag )( ee Analyte ) (1 + R )

(17.6)

In this expression, ee denotes the fractional EE. Using the usual definition, the EE is 

EE = 100*ee

(17.7)

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Note that correct determination of the analyte EE requires knowledge of the EE of the tag. This value, eeTAG, is generally close to 1 for commercially available enantiopure tag samples, but would need to be calibrated for accurate measurements of high enantiopurity analytes. Using this approach, the analyte EE can be determined for any pair of transitions known to come from the different diastereomer complexes. Because the broadband rotational spectrum contains many rotational transitions for each complex, it is possible to improve the accuracy of the determination using a large number of individual transition pairs. Work is currently in progress to test the accuracy and linearity of this approach to EE determination.

17.3.4  An example—EE in fenchyl alcohol The use of chiral tag rotational spectroscopy to determine the analyte EE is illustrated using fenchyl alcohol—the molecule presented above where diastereomer detection was described. In this case, the chiral tag is chosen to be propylene oxide which can act as a hydrogen bond acceptor to the hydroxyl group of fenchyl alcohol. The spectrum of fenchyl alcohol without and with the racemic chiral tag present is shown in Fig. 17.11. Like the case of 3-methylcyclohexanone, there are two isomers for each diastereomer chiral tag complex that dominate the spectrum and the simulations of these spectra using the fit rotational constants are shown. When comparing the spectra with racemic and enantiopure tags, Fig. 17.12, it is seen that some transitions increase when the enantiopure tag is added while others decrease. This indicates that the fenchyl alcohol sample is nonracemic. Any pair of transitions from the different diastereomer complexes can be used to determine the EE of fenchyl alcohol. As an illustration, the ten strongest transitions for each diastereomer complex were used in the analysis. A histogram of the EE determinations (assuming that the tag EE is 100) is shown in Fig. 17.13. The average EE determination is 83 and the standard deviation over the 100 different pair combinations gives an uncertainty estimate: 83 ± 1 (1σ). There was no EE determination on the certificate of analysis of this sample so it is not possible to assess the accuracy of this technique by comparing it to other established methods. Benchmarking measurements of this type are currently underway. However, in a previously reported measurement of the EE for verbenone using chiral tag rotational spectroscopy, the EE was in agreement with the chiral GC value reported on the certificate of analysis within the measurement error estimated from the distribution of transition pair values [82].

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Figure 17.11  An enantiomeric excess measurement on a commercial sample of (1S,2S,4R)-1,3,3-trimethyl-bicyclo[2.2.1]heptan-2-ol (fenchyl alcohol) is shown. Note that this sample is the enantiomer of the more common (+)-fenchol shown in Fig. 17.6 and was sold as an unverified reaction product with unknown purity. It is found (but not

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shown here) that this enantiomer sample also has about a 3% impurity of the fenchyl alcohol epimer. The top panel shows the spectrum of the fenchyl alcohol sample before adding the tag molecule. The negative going blue spectrum shows the spectrum with racemic propylene oxide tag added. A new, dense set of transitions for the tag complexes is evident along with a decrease in the intensity of the fenchyl alcohol monomer spectrum. The tag complex spectrum is dominated by four complexes and the bottom panel compares the experiment to simulations of these fitted spectra. Two of the spectra (dark and light blue) come from complexes with (S)-propylene oxide and the other two (dark green and light green) are from complexes with (R)-propylene oxide.

Figure 17.12  An expanded frequency region of the spectrum of fenchyl alcohol with the propylene oxide tag is shown. The black spectrum uses racemic propylene oxide where both homochiral and heterochiral complexes are made in high abundance. Transitions marled with an asterisk are assigned to the stronger isomers of the homochiral and heterochiral complexes. The transition intensities in this racemic measurement are used to normalize the enantiomeric excess measurement. The negative going spectrum (blue) shows the spectrum when high enantiopurity (S)-propylene oxide is used as the tag. One set of transitions (red asterisk) increase their intensity by about a factor of two while the other set (green) are significantly reduced in intensity. These changes reflect the enantiomer ratio of the fenchyl alcohol. For these measurements, the racemic tag spectrum acquisition is 100 kavg for an estimated sample consumption of 20 mg. The measurement with enantiopure (S)-propylene oxide has 40 kavg and consumes approximately 8 mg of fenchyl alcohol.

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Figure 17.13  The results for 100 different enantiomeric excess (EE) determinations, using all pair combinations of the 10 strongest transitions of homochiral and heterochiral complexes of fenchyl alcohol with propylene oxide, are shown. The results are shown as a histogram of the different enantiomeric excess values. The average enantiomeric excess over all 100 measurements is 83 (assuming the EE of the tag is 100). An estimate of the measurement uncertainty is derived from the standard deviation of the 100 EE determinations: 83 ± 1 (1σ).

17.3.5  Challenges and the future for chiral tag rotational spectroscopy The two molecules that have been used in chiral tag experiments to this point, propylene oxide and 3-butyn-2-ol, were selected based on cost and availability in enantiopure form. More careful design of the chiral tag could improve the performance of the technique. For example, both of these tag can produce a relatively large number of isomers for the complex with the analyte and this adds spectral complexity while reducing the peak signal strengths.Tags that have less conformational freedom in the complex would be a key improvement. Another design consideration is the selection of tag molecules that give large discrimination of the diastereomer complexes based on rotational constant. This feature would improve the confidence in absolute configuration determinations based solely on the spectroscopy. Other strategies for increasing the confidence of the absolute configuration determination without the need to pursue a full substitution structure,

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which requires a significant increase in sample consumption to reach 13Csensitivity in natural abundance, are needed. The performance of the chiral tag approach in molecules with multiple functional groups that can provide docking sites with strong interactions needs to be tested to see if molecules of this type suffer from the formation of a very large number of isomers for the complex. Finally, there remains significant validation work for this method for quantitative EE determinations.

17.4  THREE-WAVE MIXING ROTATIONAL SPECTROSCOPY FOR ENANTIOMER ANALYSIS The introduction in 2013 by Patterson, Schnell, and Doyle of a new three-wave mixing method to perform enantiomer-specific molecular rotational spectroscopy catalyzed the recent efforts to use rotational spectroscopy for chiral analysis [11]. Soon after the initial report which used a DCfield based measurement methodology, a doubly-resonant pulse sequence approach was demonstrated [12].The double-resonance nature of this measurement method, coupled with the high-spectral resolution and chemical selectivity of molecular rotational spectroscopy, holds significant promise for the development of a method that can perform absolute configuration and EE measurements on individual molecular species in complex chemical mixtures without the need for chemical separations. There are two recent reviews of the progress in this field that offer detailed descriptions of the measurement theory and instrument design [17,83]. The basic principles and an example application of the technique to a complex chemical mixture are presented in this chapter. Microwave three-wave mixing (M3WM) is a nonlinear, resonant, and coherent approach. The measurement principle of M3WM is based on the fact that the two enantiomers and thus also their dipole moments are mirror images of each other as illustrated in Fig. 17.14. This results in an opposite sign for the product of the three dipole-moment components with respect to the molecule-fixed principal axis system where µ = (µa, µb, µc). That is, the sign of (µaµbµc) uniquely specifies the enantiomer. The threewave mixing experiment uses a special cycle of rotational transitions, where the three separate transitions between the set of energy levels have an a-, b-, and c-type transition, to generate a molecular emission signal, that is, proportional to the product of the three-dipole moment components represented in the principal axis system. As a result, the different enantiomers have opposite phase for the time-domain free induction decay signal. There

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Figure 17.14  The basic principle of enantiomer-specific molecular rotational spectroscopy is illustrated in this figure. The figure shows two enantiomers of 1,2-propanediol as nonsuperimposable mirror images. In the context of molecular rotational spectroscopy, the molecular geometry is equivalent to a three-dimensional solid with three distinct principal moments of inertia—depicted under the molecule. The molecule also has a dipole moment that can be represented in the principal axis system as depicted by the a-, b-, and c-dipole components. In this case, the mirror image enantiomer will have a sign change for only the c-dipole moment component. As a result, the sign of the products of the components of the dipole moment represented in the principal axis system for molecular rotation is a unique characteristic of the enantiomer. In this particular example is the c-component which inverts its sign, but the results can be generalized and the sign of the dipole moment components product is characteristic of the enantiomer. The three-wave mixing rotational spectroscopy technique generates molecular emission signal proportional to the dipole moment components and, therefore, the phase of this signal is enantiomer-specific.

is an additional requirement that the electric fields of the three light waves must be mutually orthogonal and this condition influences the design of spectrometers for three-wave mixing [84,85]. M3WM can be applied to any molecule with three nonzero electric dipole moment components, µa, µb, and µc.These conditions are typically met by molecules of C1-symmetry, which includes the vast majority of chiral molecules. An example M3WM cycle and measurement for (−)-menthone from Ref. [86] is shown in Fig. 17.15. The rotational kinetic energy levels are labeled using the JKaKc nomenclature discussed earlier. Quantum chemistry calculations for the lowest energy conformation of (−)-menthone estimate the dipole moment vector in the principal axis as µ = (1.3, 2.7, 0.5 D) [65]. A description of the M3WM experiment in the language of NMR spectroscopy has been presented by Grabow and is useful for understanding the optimum experimental set up [87]. In the M3WM experiment,

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Figure 17.15  An example measurement of three-wave mixing on menthone from Ref. [86] is shown. The level diagram for the three-wave mixing cycle used in the measurement is shown as an inset. A section of the coherent emission signal is shown for enantiopure (−)-menthone (cyan) and (+)-menthone (green) and demonstrates the enantiomer-selective phase. A commercial sample of unspecified enantiomer content is measured (magenta) and is found to be dominated by (−)–menthone based on the phase of the chiral signal.

two resonant excitation pulses are applied to the sample. These have been called the drive and twist pulses [17,83]. The result of these two pulses is the creation of a polarization for the third transition that coherently emits radiation at the sum or difference frequency (depending on the level diagram structure)—the so-called listen transition. It is the phase of this signal that contains information about the enantiomer. If the absolute phase of the emitted signal can be measured, then the absolute configuration can be determined. This phase calibration poses several experimental challenges and, to this point, there has not been an instrument design that can assign the absolute configuration with high-confidence based on the phase of the detected signal in the M3WM experiment.

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To make the detection signal as large as possible, this transition should have selection rules for the largest dipole moment component. For the menthone cycle, a b-type transition (212−101) is selected for detection (µb has the largest dipole moment component: 2.7 D). The coherence, that is, detected at the listen frequency originates from the excitation with the first pulse. This pulse converts the population difference of the drive transition into a coherence and to make this coherence as large as possible it is desired to have a high-frequency drive transition and to apply a π/2-pulse. For the menthone cycle, this is a c-type transition (211–101). The second applied pulse is used to transfer the coherence created by the drive excitation and this effect is optimum for a π-pulse, which is an a-type transition (211–212). The pulse propagation directions of the drive and twist pulses are generally chosen to be orthogonal (and, in addition, the electric field polarizations are orthogonal). In this case, the enantiomer-sensitive signal propagates in the same direction as the drive pulse, but with orthogonal electric polarization. There is also a phase matching requirement for three-wave mixing experiments. The use of a low-frequency pulse for the twist excitation improves the phase matching and helps maximize the detected single amplitude [85]. The enantiomer-specific coherent emission signals are shown in Fig. 17.15 for commercial samples of (−)–menthone and (+)-menthone with high enantiopurity.The 180 degrees phase relation between the threewave emission signal for these enantiomers is demonstrated. Once the cycle is calibrated, it can be used to determine the dominant enantiomer in an unknown sample—in this case the magenta trace is for a commercial sample with unspecified EE which is seen to be dominated by (−)–menthone. Because the two enantiomers emit signals that are 180 degrees out-ofphase, there will be no detected signal for a racemic sample because the enantiomer emission will exactly cancel through destructive interference. This result is just reflection of the fact that a sample with center of symmetry cannot produce sum and difference frequency generation [13]. This gives microwave three-wave mixing the feature that it is background-free at zero EE and provides a technique with the potential for quantitative measurement on low EE samples [88]. As the sample acquires an EE, the emission of one or the other enantiomer will dominate the emission giving rise to a coherent signal. It is evident that the amplitude of this signal must be proportional to the EE. As a result, the M3WM approach is expected to provide EE determinations that are linear over the full EE scale. There are potential complications related to the use of pulsed jet sources, for example,

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cluster formation may introduce nonlinearities, and work is currently underway to assess the accuracy of three-wave mixing EE determinations. Only moderate modifications to an existing Fourier transform microwave spectrometer are required to allow for M3WM, using either the DCswitching or the fully resonant M3WM approach. In the Hamburg COMPACT spectrometer, for example, a set of radiofrequency (RF) electrodes were integrated into the existing setup to enable excitation in a second direction of the laboratory [49]. Furthermore, one of the two horn antennas was exchanged by a dual-polarization horn to record the chiral signal in the third direction. In this setup, the frequency range that can be covered by the RF electrodes is from DC up to about 1 GHz. Larger frequency ranges for the twist transitions can be covered by integrating a horn antenna into the setup, as described in Ref. [85] and as also recently accomplished/done in the COMPACT spectrometer.

17.4.1  An example—the predominant enantiomer of menthone in buchu oil The potential for chiral analysis by rotational spectroscopy performed directly on complex chemical mixtures is illustrated by the determination of the dominant configuration of menthone in a commercial sample of buchu oil (betulina). The rotational spectrum of the volatile species in buchu oil is obtained using a head space sampling technique where the buchu oil is heated to 65oC and the vapor over the sample is entrained in the neon gas flow for injection into the spectrometer.The broadband rotational spectrum of the vapor over the buchu oil is shown in Fig. 17.16. The expanded scale section of the spectrum shows the instrument noise level and gives an idea of the transition line density in the measurement. The rotational spectra of 15 different known components of buchu oil have been identified in this spectrum. Using the results from GC–MS analysis of buchu oil samples, these species have 0.06%–22% relative abundance in the oil [89,90]. Given the transition density of the spectrum, a chiral tag approach to sample analysis would seem impossible. A major advantage of three-wave mixing approaches is that they can be applied without increasing the spectral complexity. The component of interest in this example is menthone which makes up 10% of the buchu oil. The rotational spectrum of menthone has been previously analyzed and it is known to exist in three conformational isomers in the pulsed jet expansion.The simulated spectra of these three isomers using the reported fitted rotational constants [65] are shown in Fig. 17.17 to

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Figure 17.16  The extension of three-wave mixing measurements to complex chemical mixtures is illustrated using buchu oil as the sample. The broadband spectrum of the head space vapor over the oil sample is shown. Fifteen different molecular components of the oil are detected from this spectrum. The bottom panel shows an expanded scale of the spectrum to show the instrument noise floor (red line) and to show that the measured spectrum is still completely spectrally resolved.

indicate the presence and transition intensity of menthone in the head space measurement. The determination of the dominant enantiomer of menthone is made using three-wave mixing rotational spectroscopy. The spectrometer used in this measurement is described in Ref. [91]. The transition cycle used in the measurement is shown in Fig. 17.18.The phase of the chiral three-wave signal is calibrated using a commercial sample of (−)-menthone with 98.8 EE. The three-wave pulse sequence is then applied to head space sample and the results are shown in Fig. 17.18. The first pulse of the cycle (5059.36 MHz) uses an a-type transition to create the initial sample polarization. The

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Figure 17.17  Menthone is one of the components of buchu oil and makes up about 10% of the mixture of volatiles. This figure shows spectral simulations of three conformers (A, B, and C) of menthone compared to the buchu oil broadband rotational spectrum. The spectrum simulations used the experimental fitted constants from Ref. [65]. This comparison illustrates an important feature of rotational spectroscopy. Instruments all use a high-accuracy time standard (Rb-disciplined quartz oscillators and the 1 pps GPS reference are the most common time base references) so that the measured transition frequencies reproduce from instrument-to-instrument to very high accuracy. This feature makes the use of previously measured library spectra very powerful in the analysis of complex chemical mixtures by rotational spectroscopy.

Figure 17.18  This figure shows the three-wave mixing measurement performed on the buchu oil sample. The level diagram for the measurement cycle is shown on the left. The middle panel shows the spectrum of buchu oil after application of the first drive pulse of the three-wave mixing sequence. In this case, several nearby peaks are observed in addition to the menthone peak (indicated with the asterisk). These transitions fall within the spectral bandwidth of the drive pulse. The spectrum in the region of the chiral sumfrequency transition after the application of the low frequency coherence transfer pulse is shown on the right. In this case, the double-resonance nature of the measurement has provided full chemical selectivity and only the chiral sum-frequency signal is observed.

s­ pectrum observed after application of just this pulse is compared to the full broadband spectrum in the top of Fig. 17.18. Several transitions, including the one for the menthone measurement cycle, are observed. These additional transitions are excited by the bandwidth of the first excitation pulse.

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The enantiomer-sensitive three-wave measurement is completed by applying the low-frequency pulse (854.69 MHz) using a c-type transition to transfer the initial coherence into the detected transition (at the sum frequency: 5914.05 MHz). The spectrum in the region of the detected sum frequency signal at 5914.05 MHz, a strong b-type transition, is shown in the bottom panel where it is also compared to the full spectrum from the buchu oil head space vapor. The ability of the doubly-resonant three-wave mixing pulse sequence to isolate the chiral response for a single component (menthone) in a complex mixture is demonstrated. The determination of the dominant enantiomer of menthone present in buchu oil is obtained from the phase of the chiral signal at 5914.05 MHz.The digitally filtered FID signal in a 1 MHz bandwidth around 5914.05 MHz is shown in Fig. 17.19. The bottom panel shows an expanded scale where the digitized signal can be clearly seen. There are three phase measurements shown here. Two of them are from the (−)–menthone commercial reference sample and were taken before (red) and after (green) the buchu oil measurement. These show that there is long term phase stability in the instrument. The measurement of the phase of the menthone chiral signal in buchu oil (blue) is out-of-phase with the reference measurement and indicates that the sample has (+)-menthone as the dominant enantiomer— as is known for this essential oil [91]. Note that these time-domain signals have been renormalized so that they can be compared and that the buchu oil measurement has lower signal-to-noise ratio than the reference sample measurements due to its 10% abundance in the oil.

17.4.2  Challenges and the future for three-wave mixing rotational spectroscopy The power of three-wave mixing for chiral analysis on complex mixtures is suggested by this example. The development of instruments for three-wave mixing rotational spectroscopy is still progressing and there remain significant challenges. At present, it has not been possible to perform absolute phase calibration of the chiral signal directly on the instrument. Once this problem is solved, it will be possible to determine the absolute configuration of the dominant enantiomer in a sample with minimal requirements from quantum chemistry—only an accurate dipole moment orientation in the principal axis system is needed. It is worth noting that there is a second experimental approach for M3WM that uses a DC-field [12]. It is possible that the difficulties in absolute configuration determination via M3WM can be solved using this method. In particular, robust absolute configuration

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Figure 17.19  The absolute configuration of the higher-abundance enantiomer of menthone in buchu oil is determined by comparison of the phase of the three-wave mixing signal to a reference measurement using a commercial sample of (−)-menthone with high enantiopurity. In this case, the signal from the menthone in buchu oil is found to be out-of-phase with respect to the reference measurement showing that (+)-menthone is the dominant enantiomer in the essential oil.

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assignment using the M3WM method requires accurate characterization of the phase difference between the two applied fields which are at distinct frequencies. In contrast, the DC switching method applies only a single frequency, substantially reducing the experiment’s sensitivity to dispersion. The amplitude of the chiral signal is proportional to the EE. Like VCD spectroscopy, the fact that the EE measurement is given by a single signal amplitude, instead of the ratio of enantiomer-specific signals in chromatography and chiral tag rotational spectroscopy, means that a reference sample is needed to calibrate the instrument response [92]. It may be possible that the signals can be modeled to reasonable accuracy so that approximate EE values can be obtained. However, this requires detailed knowledge of the molecule distribution in the pulsed jet and has been difficult to model. The development of buffer gas cooled gas cells for rotational spectroscopy may offer better characterized samples that make the modeling of the signals quantitative, thereby, removing the need for reference sample calibration [34–36]. In many applications, including high-throughput screening of chiral catalyst performance [93], only a relative value of the EE is needed and in these applications three-wave mixing may offer a high-speed analysis method with general applicability and limited requirements for sample purification.

17.5  CONCLUSIONS This chapter has focused on applications of molecular rotational spectroscopy to the quantitative analysis of the stereoisomers of chiral molecules. The strengths of the method to analyze stereoisomer composition of molecules with multiple chiral centers has been illustrated with some simple examples. The field is still in its infancy and there is need for more validation measurements and studies to determine the scope of application. In particular, there are challenges to performing rotational spectroscopy on larger molecules that come from both the difficulty in volatilizing the sample without decomposition and from the intrinsically lower detection sensitivity associated with the strong increase in molecular partition function with molecular size. The challenge of developing a generally applicable chiral analysis technique will hopefully drive future advances in the design of pulsed molecular beam sources and fundamental developments in spectrometer design to increase measurement sensitivity for molecular rotation spectroscopy. New ways of using the core techniques described in this chapter to probe the chirality of molecules

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are likely to emerge as the community gains experience with these tools. New approaches to the analytical chemistry of larger molecules, such as chiral analysis of fragmented molecules to reconstruct the stereochemistry of the full chemical system, may be developed that greatly extend the capabilities of chiral rotational spectroscopy beyond the simple examples presented here. It is also expected that rotational spectroscopy will have an increased role in more fundamental studies of chirality. The ability to determine the structures of molecular complexes with high confidence could be an important advance in physical chemistry studies of chiral recognition [94–96]. The three-wave mixing measurement methodology implicitly involves the quantum-state-specific manipulation of enantiomer-specific level populations. This is potentially an important chemistry tool since it makes it possible to study chiral effects in chemistry without the need to develop synthetic chemistry or chemical separations protocols to create enantiomerically enriched samples. The ability to generate state-specific EE from racemic samples using the phase properties of light pulses opens the possibility of enantiomer-specific cold molecule studies of molecular interactions and chemical reactivity [97–99]. Laser-microwave doubleresonance spectroscopy techniques will make it possible to transfer EE created by manipulation of the rotational quantum states to higher energy regions where photochemistry occurs and tests of chemical principles such as retention of stereochemistry upon reaction and dissociation can be performed. This chapter has described the advances in the field of molecule rotational spectroscopy in the past few years that have expanded the range of chirality studies possible using this technique. The key advances have been the development of three-wave mixing and chiral tag rotational spectroscopy to enable determination of the enantiomeric structure of molecules. Combined with the well-known advantages of rotational spectroscopy for the study of molecular structure, there is now a new set of experimental tools to perform quantitative analysis of the stereoisomers of molecules with multiple chiral centers.

ACKNOWLEDGEMENTS This work was supported by the National Science Foundation (CHE-153193) and the Virginia Biosciences Health Research Corporation. This work was also funded by the Natural Sciences and Engineering Research Council of Canada, Canada Foundation for Innovation, Alberta Enterprise and Advanced Education, and by the University of Alberta.

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We gratefully acknowledge access to the computing facilities by the Shared Hierarchical Academic Research Computing Network, the Western Canada Research Grid (Westgrid), and Compute/Calcul Canada. YX is a Tier I Canada Research Chair in Chirality and Chirality Recognition. Additional support was provided by the Sonderforschungsbereich 1319 “Extreme light for sensing and driving molecular chirality (ELCH)” of the Deutsche Forschungsgemeinschaft.

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