Molecular Structure and Chirality Detection by Fourier Transform Microwave Spectroscopy

Efficient spatial separation for chiral molecules via optically induced forces

We investigate an efficient spatial enantioseparation method of chiral molecules in cyclic three-level systems coupled with three optical fields using optically induced forces. When the overall phase differs by π between two enantiomers, significant variations in the magnitude and direction of the optically induced forces are observed. The manipulation of the center of mass of chiral molecules in optical fields can be achieved through the induced gauge force, primarily generated from the variations in the chirality-dependent scalar potentials created by the three inhomogeneous laser fields. By appropriately configuring the system, we can completely separate the slow spatial and fast inner dynamics, making instantaneous eigenstates of the inner Hamiltonian independent of the transverse profiles of the laser beams. Compared to previous methods, which required adiabatic conditions to be satisfied, the proposed method overcomes the limitations of the adiabatic approximation by utilizing a specific system configuration. This allows for increased flexibility in the transverse profiles of the laser beams and relaxes the constraints on the velocity of chiral molecules, leading to significantly greater spatial separations achievable across a broader range of parameters.

Robust and high-efficiency dynamical method of enantio-specific state transfer

We propose a simple dynamical method to realize fast enantio-specific state transfer (ESST) of chiral molecules. Driven by three external electromagenetic fields, the chiral molecules are modeled as cyclic three-level systems, where the overall phase differs by π for the left- and right-handed chiral molecules. We unveil that the ESST is allowed when the amplitudes of three Rabi frequencies in the cyclic three-level systems are equal. Our method is robust and highly efficient in the sense that the external fields can have arbitrary waveforms. This thus provides the opportunity of simplifying the experimental implementations of ESST through pulse design.

Polarization-dependent intensity ratios in double resonance spectroscopy

Double Resonance is a powerful spectroscopic method that unambiguously assigns the rigorous quantum numbers of one state of a transition. However, there is often ambiguity as to the branch (ΔJ) of that transition. Spectroscopists have resolved this ambiguity by using the dependence of the double resonance intensity on the relative polarization directions of pump and probe radiation. However, published theoretical predictions for this ratio are based upon a weak (i.e., non-saturating) field approximation. This paper presents theoretical predictions for these intensity ratios for cases where the pump field is strongly saturating in the two limits of transitions dominated by homogeneous or of inhomogeneous broadening. Saturation reduces but does not eliminate the magnitude of the polarization effect (driving the intensity ratio closer to unity) even with strong pump saturation. For the case of an inhomogeneously broadened line, such as when Doppler broadened linewidth dominates over the power-broadened homogeneous line width, a large fraction of the low pump power polarization anisotropy remains. This paper reports predicted polarization ratios for both linear and circular pump and probe field polarizations. The present predictions are compared with experimental measurements on CH4 ground state → ν3 → 3ν3 transitions recently reported by de Oliveira et al.63 and these are in better agreement than with the weak field predictions.

Machine-Learning Enhanced Enantioselective Single-Shot-Single-Molecule ac Stark Spectroscopy

Enantiodiscrimination with single-molecule and single-shot resolution is fundamental for the understanding of the fate and behavior of two enantiomers in chemical reactions, biological activity, and the function of drugs. However, molecular decoherence gives rise to spectral broadening and random errors, offering major problems for most chiroptical methods in arriving at single-shot-single-molecule resolution. Here, we introduce a machine-learning strategy to solve these problems. Specifically, we focus on the task of single-shot measurement of single-molecule chirality based on enantioselective ac Stark spectroscopy. We find that, in the large-decoherence region, where the ac Stark spectroscopy without machine learning fails to distinguish molecular chirality, in contrast, the machine-learning-assisted strategy still holds a high correct rate of up to about 90%. Beyond this overwhelming superiority, the machine-learning strategy also has considerable robustness against variation of the decoherence rates between the training and testing sets.

Phase-matched locally chiral light for global control of chiral light-matter interaction

Locally chiral light is an emerging tool for probing and controlling molecular chirality. It can generate large and freely adjustable enantioselectivities in purely electric-dipole effects, offering its major advantages over traditional chiral light. However, the existing types of locally chiral light are phase-mismatched, and thus the global efficiencies are greatly reduced compared with the maximum single-point efficiencies or even vanish. Here, we propose a scheme to generate phase-matched locally chiral light. To confirm this advantage, we numerically show the robust highly efficient global control of enantiospecific electronic state transfer of methyloxirane at nanoseconds. Our work potentially constitutes the starting point for developing more efficient chiroptical techniques for the studies of chiral molecules.

Microwave Three-Wave Mixing Spectroscopy of Chiral Molecules in Weakly Bound Complexes

Since the first experimental implementation in 2013, microwave three-wave mixing has emerged as a robust spectroscopic approach for analyzing and controlling chiral molecules in the gas phase. This resonant, coherent, and nonlinear technique is based on the three-dimensional light-matter interaction in the electric dipole approximation, allowing for isomer- and conformer-selective chiral analysis with high resolution. Here we demonstrate the utility of microwave three-wave mixing for analyzing a molecular complex, limonene-H2O, which serves as a compelling example of addressing its potential to improve the chiral sensitivity for only weakly polar chiral molecules. The use of molecular complexes can also extend the applicability of microwave three-wave mixing to chiral systems that are not in the C1 point group.

Enantiomer detection via quantum Otto cycle

Enantiomers are chiral molecules that exist in right-handed and left-handed conformations. Optical techniques of enantiomers' detection are widely employed to discriminate between left- and right-handed molecules. However, identical spectra of enantiomers make enantiomer detection a very challenging task. Here, we investigate the possibility of exploiting thermodynamic processes for enantiomer detection. In particular, we employ a quantum Otto cycle in which a chiral molecule described by a three-level system with cyclic optical transitions is considered a working medium. Each energy transition of the three-level system is coupled with an external laser drive. We find that the left- and right-handed enantiomers operate as a quantum heat engine and a thermal accelerator, respectively, when the overall phase is the control parameter. In addition, both enantiomers act as heat engines by keeping the overall phase constant and using the laser drives' detuning as the control parameter during the cycle. However, the molecules can still be distinguished because both cases' extracted work and efficiency are quantitatively very different. Accordingly, the left- and right-handed molecules can be distinguished by evaluating the work distribution in the Otto cycle.

Enantiodetection of Chiral Molecules via Two-Dimensional Spectroscopy

Enantiodetection of chiral molecules is important to chemical reaction control and biological function designs. Traditional optical methods of enantiodetection rely on the weak magnetic-dipole or electric-quadrupole interactions, and in turn suffer from the weak signal and low sensitivity. We propose a new optical enantiodetection method to determine the enantiomeric excess via two-dimensional (2D) spectroscopy of the chiral mixture driven by three electromagnetic fields. The quantities of left- and right-handed chiral molecules are reflected by the intensities of different peaks on the 2D spectrum, separated by the chirality-dependent frequency shifts resulting from the relative strong electric-dipole interactions between the chiral molecules and the driving fields. Thus, the enantiomeric excess can be determined via the intensity ratio of the peaks for the two enantiomers.

Enantiodiscrimination of chiral molecules via quantum correlation function

We propose a method to realize enantiodiscrimination of chiral molecules based on quantum correlation function in a driven cavity-molecule system, where the chiral molecule is coupled with a quantized cavity field and two classical light fields to form a cyclic three-level model. According to the inherent properties of electric-dipole transition moments of chiral molecules, there is a π-phase difference in the overall phase of the cyclic three-level model for the left- and right-handed chiral molecules. Thus, the correlation function depends on this overall phase and is chirality-dependent. The analytical and numerical results indicate that the left- and right-handed chiral molecules can be discriminated by detecting quantum correlation function. Our work opens up a promising route to discriminate molecular chirality, which is an extremely important task in pharmacology and biochemistry.

Discrimination of enantiomers for chiral molecules using analytically designed microwave pulses

We perform a theoretical exploration of quantum coherent control of enantio-selective state transfer (ESST) of chiral molecules with three rotational states connected by the a-type, b-type, and c-type components of the transition dipole moments. A pulse-area theorem based on a closed-loop three-level system is derived without applying the rotating-wave approximation and used to analytically design three linearly polarized microwave pulses with optimal amplitudes and phases. By utilizing two optimized microwaves to mix two excited rotational states into the maximal coherence, we find that the discrimination of enantiomers via ESST for chiral molecules can be achieved by controlling the delay time of the third optimized microwave pulse. We examine the robustness of such control schemes against the Rabi frequency and detuning errors and the environment effect through pure dephasing processes for practical applications. This work provides an alternative approach to analytically designing optimal control fields for quantum control of ESST by using complex pulse areas.

A Scent of Peppermint—A Microwave Spectroscopy Analysis on the Composition of Peppermint Oil

Essential oils have a vast number of applications in different areas of our daily life. Detailed chiral analysis and structural characterization of their constituents remains an important subject in analytical chemistry. Here, we report on a broadband rotational spectroscopy study of peppermint oil in the frequency range 2–8 GHz. We focus on an unambiguous determination of the excess enantiomers of the oil constituents menthone and isomenthone in the oil by applying chirality-sensitive rotational spectroscopy, the so-called microwave three-wave mixing (M3WM) technique. Additionally, a new menthol conformer, not previously characterized, was experimentally observed, and the gas-phase structures of the two conformers of menthol and menthone were determined experimentally based on the assignment of their 13C-isotopologues in natural abundance.

Rational Pulse Design for Enantiomer-Selective Microwave Three-Wave Mixing

Microwave three-wave mixing allows for enantiomer-selective excitation of randomly oriented chiral molecules into rotational states with different energy. The random orientation of molecules is reflected in the degeneracy of the rotational spectrum with respect to the orientational quantum number M and reduces, if not accounted for, enantiomer-selectivity. Here, we show how to design pulse sequences with maximal enantiomer-selectivity from an analysis of the M-dependence of the Rabi frequencies associated with rotational transitions induced by resonant microwave drives. We compare different excitations schemes for rotational transitions and show that maximal enantiomer-selectivity at a given rotational temperature is achieved for synchronized three-wave mixing with circularly polarized fields.

Construction and Demonstration of a 6–18 GHz Microwave Three-Wave Mixing Experiment Using Multiple Synchronized Arbitrary Waveform Generators

This manuscript details the construction and demonstration of the first known microwave three-wave mixing (M3WM) experiment utilizing multiple arbitrary waveform generators (AWGs) completely operable in the 6–18 GHz frequency range for use in chirality determination and quantification. Many M3WM techniques, which involve two orthogonal, subsequent Rabi π/2 and π microwave pulses, suffer from flexibility in pulse types and timings as well as frequency due to most instruments only using one, one-channel AWG and the M3WM probability decreasing with an increasing quantum number, J. In this work, we presented an M3WM instrument that allows that flexibility by introducing multiple, synchronized AWGs and adheres to the high probability transition loop pathways in carvone. The functionality and reliability of the instrument were demonstrated using a series of experiments and mixtures of the R and S enantiomers and determined to be of similar accuracy to other reported M3WM setups with the additional benefit of flexibility in pulsing schemes.

Enantioselective Topological Frequency Conversion

Two molecules are enantiomers if they are nonsuperimposable mirror images of each other. Electric dipole-allowed cyclic transitions |1⟩ → |2⟩ → |3⟩ → |1⟩ obey the symmetry relation OR=-OS, where OR,S = (μ₂₁^R,SE₂₁)(μ₁₃^R,SE₁₃)(μ₃₂^R,SE₃₂) and R and S label the two enantiomers. Herein, we generalize the concept of topological frequency conversion to an ensemble of enantiomers. We show that, within a rotating-frame, the pumping power between fields of frequency ω₁ and ω₂ is sensitive to enantiomeric excess, P2→1 = ℏ[ω₁ω₂C_L^R/(2π)](N_R - N_S), where N_i is the number of enantiomers i and C_L^R is an enantiomer-dependent Chern number. Connections with chiroptical microwave spectroscopy are made. Our work provides an underexplored and fertile connection between topological physics and molecular chirality.

Assignment-free chirality detection in unknown samples via microwave three-wave mixing

Straightforward identification of chiral molecules in multi-component mixtures of unknown composition is extremely challenging. Current spectrometric and chromatographic methods cannot unambiguously identify components while the state of the art spectroscopic methods are limited by the difficult and time-consuming task of spectral assignment. Here, we introduce a highly sensitive generalized version of microwave three-wave mixing that uses broad-spectrum fields to detect chiral molecules in enantiomeric excess without any prior chemical knowledge of the sample. This method does not require spectral assignment as a necessary step to extract information out of a spectrum. We demonstrate our method by recording three-wave mixing spectra of multi-component samples that provide direct evidence of enantiomeric excess. Our method opens up new capabilities in ultrasensitive phase-coherent spectroscopic detection that can be applied for chiral detection in real-life mixtures, raw products of chemical reactions and difficult to assign novel exotic species.

Non-quantum chirality in a driven Brusselator

We report the discovery of non-quantum chirality in the a periodically driven Brusselator. In contrast to standard chirality from quantum contexts, this novel type of chirality is governed by rate equations, namely by purely classical equations of motion. The Brusselator chirality was found by computing high-resolution phase diagrams depicting the number of spikes, local maxima, observed in stable periodic oscillations of the Brusselator as a function of the frequency and amplitude of the external drive. We also discuss how to experimentally observe non-quantum chirality in generic oscillators governed by nonlinear sets of rate equations.

Enantio-detection via cavity-assisted three-photon processes

We propose a method for enantio-detection of chiral molecules based on a cavity-molecule system, where the left- and right-handed molecules are coupled with a cavity and two classical light fields to form cyclic three-level models. Via the cavity-assisted three-photon processes based on the cyclic three-level model, photons are generated continuously in the cavity even in the absence of external driving to the cavity. However, the photonic fields generated from the three-photon processes of left- and right-handed molecules differ with the phase difference π according to the inherent properties of electric-dipole transition moments of enantiomers. This provides a potential way to detect the enantiomeric excess of chiral mixture by monitoring the output field of the cavity.

Multiagent Consensus Equilibrium in Molecular Structure Determination

Multiagent consensus equilibrium (MACE) is demonstrated for the integration of experimental observables as constraints in molecular structure determination and for the systematic merging of multiple computational architectures. MACE is founded on simultaneously determining the equilibrium point between multiple experimental and/or computational agents; the returned state description (e.g., atomic coordinates for molecular structure) represents the intersection of each manifold and is not equivalent to the average optimum state for each agent. The moment of inertia, determined directly from microwave spectroscopy measurements, serves to illustrate the mechanism through which MACE evaluations merge experimental and quantum chemical modeling. MACE results reported combine gradient descent optimization of each ab initio agent with an agent that predicts the chemical structure based on root-mean-square deviation of the predicted inertia tensor with experimentally measured moments of inertia. Successful model fusion for several small molecules was achieved as well as the larger molecule solketal. Fusing a model of moment of inertia, an underdetermined predictor of structure, with low cost computational methods yielded structure determination performance comparable to standard computational methods such as MP2/cc-pVTZ and greater agreement with experimental observables.

Laboratory blueprints for interstellar searches of aromatic chiral molecules: rotational signatures of styrene oxide

The tracking of symmetry-breaking events in space is a long-lasting goal of astrochemists, aiming at an understanding of homochiral Earth chemistry. One current effort at this frontier aims at the detection of small chiral molecules in the interstellar medium. For that, high-resolution laboratory spectroscopy data is required, providing blueprints for the search and assignment of these molecules using radioastronomy. Here, we used chirped-pulse Fourier transform microwave and millimeter-wave spectroscopy and frequency modulation absorption spectroscopy to record and assign the rotational spectrum of the chiral aromatic molecule styrene oxide, C6H5C2H3O, a relevant candidate for future radioastronomy searches. Using experimental data from the 2-12, 75-110, 170-220, and 260-330 GHz regions, we performed a global spectral analysis, which was complemented by quantum chemistry calculations. A global fit of the ground state rotational spectrum was obtained, including rotational transitions from all four frequency regions. Primary rotational constants as well as quartic and sextic centrifugal distortion constants were determined. We also investigated vibrationally excited states of styrene oxide, and for the three lowest energy vibrational states, we determined rotational constants including centrifugal distortion corrections up to the sextic order. In addition, spectroscopic parameters for the singly-substituted 13C and 18O isotopologues were retrieved from the spectrum in natural abundance and used to determine the effective ground state structure of styrene oxide in the gas phase. The spectroscopic parameters and line lists of rotational transitions obtained here will assist future astrochemical studies of this class of chiral organic molecules.

Enantio-discrimination via light deflection effect

We propose a theoretical method for enantio-discrimination based on the light deflection effect in four-level models of chiral molecules. This four-level model consists of a cyclic three-level subsystem coupled by three strong driving fields and an auxiliary level connected to the cyclic three-level subsystem by a weak probe field. It is shown that the induced refractive index for the weak probe field is chirality-dependent. Thus, it will lead to chirality-dependent light deflection when the intensities of two of the three strong driving fields are spatially inhomogeneous. As a result, the deflection angle of the weak probe light can be utilized to detect the chirality of pure enantiomers and enantiomeric excess of the chiral mixture. Therefore, our method may act as a tool for enantio-discrimination.

Principal component analysis to enhance enantioselective Raman spectroscopy

Enantioselective Raman (esR) spectroscopy is an innovative technique with a high potential for online process monitoring in chiral media, e.g. in the pharmaceutical industry. A prerequisite for an effective application is to combine the experimental approach with suitable concepts for data analysis. In this work, we present a chemometric approach to analyze the esR spectra recorded in an automatized polarization-resolved Raman set-up. It is demonstrated that the proposed method is capable of distinguishing between the enantiomers of the chiral alcohol 4-methylpentan-2-ol in a fully unsupervised fashion. Furthermore, it is shown that the difficulty of facing only small intensity differences between the esR spectra of the enantiomers can be overcome by feeding difference spectra between the pure enantiomers and the racemate into the principal component analysis (PCA) algorithm. The enantiomers are clearly discriminable along the first principal component.

State-Specific Enrichment of Chiral Conformers with Microwave Spectroscopy

An interesting class of molecules is that in which the molecules do not possess a stereogenic center but can become chiral because of their spatial arrangement. These molecules can be seen as chiral conformers, whose two nonsuperimposable forms can interconvert from one to another by rotations about single bonds. Here, we show that an initially racemic mixture of chiral conformers, such as a sample of cyclohexylmethanol, C₇H₁₄O, can be enantiomerically enriched by performing the enantioselective process of coherent population transfer between rotational levels. By first performing a population transfer cycle, followed by a three-wave mixing experiment, we show that an enantiomeric excess in a rotational level of choice can be achieved. This represents the first experimental demonstration of such an effect in a chiral pair of conformers, and it showcases the broad applicability of three-wave mixing not only for analytical applications but also to a wide scope of experiments of fundamental interest.

Enantioselective Raman spectroscopy (esR) for distinguishing between the enantiomers of 2-butanol

The first experimental application of enantioselective Raman spectroscopy (esR) is demonstrated using the example of the chiral alcohol 2-butanol. Samples of the neat enantiomers and the racemic mixture were analyzed in a self-built Raman set-up. The Raman spectrum allows the discrimination of the chemical species. It is shown that the optical rotation of a Raman peak with a small depolarization ratio can be measured. In addition, without any sample modification, e.g. chiral solvent, the enantiomers are distinguishable at a suitable half-wave retarder angle detecting only the vertically polarized component of the Raman signal.

Sensing Chirality with Rotational Spectroscopy

Chiroptical spectroscopy techniques for the differentiation of enantiomers in the condensed phase are based on an established paradigm that relies on symmetry breaking using circularly polarized light. We review a novel approach for the study of chiral molecules in the gas phase using broadband rotational spectroscopy, namely microwave three-wave mixing, which is a coherent, nonlinear, and resonant process. This technique can be used to generate a coherent molecular rotational signal that can be detected in a manner similar to that in conventional Fourier transform microwave spectroscopy. The structure (and thermal distribution of conformations), handedness, and enantiomeric excess of gas-phase samples can be determined unambiguously by employing tailored microwave fields. We discuss the theoretical and experimental aspects of the method, the significance of the first demonstrations of the technique for enantiomer differentiation, and the method's rapid advance into a robust choice to study molecular chirality in the gas phase. Very recently, the microwave three-wave mixing approach was extended to enantiomer-selective population transfer, an important step toward spatial enantiomer separation on the fly.

Rotational Spectrum and Conformational Analysis of N-Methyl-2-Aminoethanol: Insights into the Shape of Adrenergic Neurotransmitters

We describe an experimental and quantum chemical study for the accurate determination of the conformational space of small molecular systems governed by intramolecular non-covalent interactions. The model systems investigated belong to the biological relevant aminoalcohol's family, and include 2-amino-1-phenylethanol, 2-methylamino-1-phenylethanol, noradrenaline, adrenaline 2-aminoethanol, and N-methyl-2-aminoethanol. For the latter molecule, the rotational spectrum in the 6–18 and 59.6–74.4 GHz ranges was recorded in the isolated conditions of a free jet expansion. Based on the analysis of the rotational spectra, two different conformational species and 11 isotopologues were observed and their spectroscopic constants, including ¹⁴N-nuclear hyperfine coupling constants and methyl internal rotation barriers, were determined. From the experimental data a structural determination was performed, which was also used to benchmark accurate quantum chemical calculations on the whole conformational space. Atom in molecules and non-covalent interactions theories allowed the characterization of the position of the intramolecular non-covalent interactions and the energies involved, highlighting the subtle balance responsible of the stabilization of all the molecular systems.

Theoretical Foundation for Electric-Dipole-Allowed Chiral-Specific Fluorescence Optical Rotary Dispersion (F-ORD) from Interfacial Assemblies

Fluorescence optical rotary dispersion (F-ORD) is proposed as a novel chiral-specific and interface-specific spectroscopic method. F-ORD measurements of uniaxial assemblies are predicted to be fully electric-dipole-allowed, with corresponding increases in sensitivity to chirality relative to chiral-specific measurements in isotropic assemblies that are commonly interpreted through coupling between electric and magnetic dynamic dipoles. Observations of strong chiral sensitivity in prior single-molecule fluorescence measurements of chiral interfacial molecules are in excellent qualitative agreement with the predictions of the F-ORD mechanism and challenging to otherwise explain. F-ORD may provide methods to suppress background fluorescence in studies of biological interfaces, as the detected signal requires both polar local order and interfacial chirality. In addition, the molecular-level descriptions of the mechanisms underpinning F-ORD may also potentially apply to aid in interpreting chiral-specific Raman and surface-enhanced Raman spectroscopy measurements of uniaxially oriented assemblies, opening up opportunities for chiral-specific and interface-specific vibrational spectroscopy.

Chiral Analysis Using Broadband Rotational Spectroscopy

broadband microwave spectroscopy is a proven tool to precisely determine molecular properties of gas-phase molecules. Recent developments make it applicable to investigate chiral molecules. Enantiomers can be differentiated, and the enantiomeric excess and, indirectly, the absolute configuration can be determined in a molecule-selective manner. The resonant character and high resolution of rotational spectroscopy provide a unique mixture compatibility. Future directions, such as extending the technique to chemical analysis, are discussed.

Phase Dependence of Double-Resonance Experiments in Rotational Spectroscopy

We here report on double-resonance experiments using broadband chirped pulse Fourier transform microwave spectroscopy that can facilitate spectral assignment and yield information about weak transitions with high resolution and sensitivity. Using the diastereomers menthone and isomenthone, we investigate the dependence of pumping a radio frequency transition on both the amplitude and phase of the signal from a microwave transition with which it shares a common rotational level. We observe a strong phase change when scanning the radio frequency through molecular resonance. The direction of the phase change depends on the energy level arrangement, that is, if it is progressive or regressive. The experimental results can be simulated using the three-level optical Bloch equations and described with the AC Stark effect, giving rise to an Autler-Townes splitting.