Automated microwave double resonance spectroscopy: A tool to identify and characterize chemical compounds Free

Rotational spectroscopy, a long-established analysis technique in physical chemistry, is now undergoing a rapid transformation, driven by technological advances in related disciplines.^1,2 It is a structure-based tool in which the frequencies of the many individual lines in the rotational spectrum of a polar molecule are largely determined by at most three free parameters: the moments of inertia along its three principal inertial axes. Despite this redundancy and underlying simplicity, rapidly decoding the spectrum of an asymmetric top molecule to yield rotational constants can prove challenging and tedious, and some a priori theoretical guidance of the predicted line pattern is frequently required for this process to be efficient.

With new broadband excitation and detection methods based on fast passage or chirped techniques,^1,3,4 it is now possible to acquire a classical one-dimensional (1D) rotational spectrum (frequency vs. intensity) of a molecule in a fraction of a second, with a wide instantaneous bandwidth, typically of order 10 GHz or more. The highest sensitivity is presently achieved in the cm-wave band owing to the availability of traveling wave tube amplifiers (TWTAs) that can generate high power over the short duration (∼1 μs) of a chirp. This type of Fourier transform microwave (FTMW) spectroscopy is routinely combined with a free jet nozzle source because the detection wavelength and very low rotational temperature (T_rot ∼ 2–5 K) of the molecules are well matched.⁵ Populated energy levels at these temperatures are minimally affected by centrifugal distortion, and consequently, the observed spectrum can often be fit to good precision using a simple rigid rotor Hamiltonian.

In contrast, cavity FTMW spectrometers⁶ operating in the same frequency bands possess considerably higher sensitivity per unit bandwidth and resolution (both by roughly a factor of 50, see Ref. 1) albeit at the expense of greatly reduced instantaneous bandwidth (∼1 MHz). Double resonance (DR) is often used in combination with these measurements, both to confirm assignments when lines fall within the range of the spectrometer and to extend the measurements to a higher frequencies.^7–9 Although automated multi-dimensional techniques^10–16 are widely used at other wavelengths (e.g., NMR and ESR), relatively little work has been done in the radio band since the late 1980s. This situation is surprising both because of the structural simplicity that underpins rotational spectroscopy and because the primary impediment does not appear fundamental, but rather technical in nature, requiring a sustained effort in software and hardware development. Previous studies^17,18 have demonstrated the fundamental principles of the technique and have frequently focused on two dimensional (2D) spectroscopy involving relatively closely spaced transitions.^19,20

We have recently developed a combined approach using chirped and cavity FTMW spectroscopies to detect, sort, and systematically identify individual chemical species in a gas mixture containing many compounds, a procedure referred to as “microwave spectral taxonomy.”²¹ We describe here an automated analysis capability to rapidly record and analyze rotational double resonance spectra of stable, polar molecules; a method we call “automated microwave double resonance” (AMDOR) spectroscopy. In this procedure, lines in the 1D chirped spectrum are screened against one another using cavity FTMW detection and DR to uniquely link only those lines that share a rotational energy level and thus arise from the same molecule. AMDOR spectra can be represented on a 2D plot displaying the frequencies of linked lines and yield a unique 2D “barcode” for a chemical species from which some of the rotational constants can be estimated by visual inspection. Using newly developed software, we show that in some cases a least-squares fit of a small subset of DR linkages can quickly determine all three rotational constants of a molecule even if its structure and composition are unknown. This entire procedure can now be performed in near real-time (i.e., of order a few hours for relatively large organic molecules) and requires no prior theoretical guidance, as demonstrated here for the study of three aroma compounds: trans-cinnamaldehyde and two violet ketones (α- and β-ionone), depicted in Fig. 1.

The first step in the AMDOR method is to rapidly record the 1D rotational spectrum over a sufficiently wide frequency range, whereby many successive rotational transitions of a molecule are observed, and to quickly identify these “bright” resolution elements. The spectrometer should also possess a relatively flat instrument response over the range of measurement. This task is ideally performed by chirped-pulse spectroscopy. In the 8–18 GHz frequency band, for example, typically of order 100 000 discrete resolution elements are simultaneously available. At a rotational temperature of 3 K, even a large organic molecule might give rise to at most ∼1000 transitions in this band, i.e., a filling factor of only 1%. For a stable molecule that can be seeded into a supersonic expansion at a modest vapor pressure, high signal-to-noise ratio (SNR) spectra can often be recorded in 30 min or less.

The second step is to automatically, exhaustively, and rapidly screen newly detected lines in the 1D spectrum by DR to establish which lines share a common quantum state. To perform these DR tests, a cavity FTMW spectrometer²³ is used in combination with radiation from a second source, normally a frequency synthesizer, which is introduced into the cavity via either the transmitting or the receiving horn antenna in the chirped experiment. In this step, a cavity spectrometer is sequentially tuned to the frequency of each rotational line in the 1D spectrum (hereafter the pump transition), and a series of DR tests are then performed in rapid succession using the frequencies of the other newly detected lines (the probe transitions). If the two transitions share a rotational energy level, the intensity of the pump line normally decreases; depletions of at least 50% are fairly routine because at high DR powers (>10 dBm) coherence dephasing between the linked transitions is significant.^7–9 

In the AMDOR experiments performed here, the chirped and cavity spectrometers are located in the same vacuum chamber, but aligned perpendicular to one another; the same free jet, located behind the fixed cavity mirror, serves as the molecule source for both spectrometers. By using a retractable curtain of highly absorbent material to suppress cavity ringing in chirped operation, it is possible to block or unblock the second, movable cavity mirror and therefore to quickly switch between the two spectrometers. A detailed description of this instrument is given elsewhere.^21,22 The chirped-pulse spectrometer presently operates in the 8–18 GHz range and is fully computer controlled. Radiation is amplified by a 200 W TWTA, and the free induction decay is directly digitized on a fast digital oscilloscope. At a sampling rate of 50 GSa/s, a 10 μs free induction decay (FID) spans 25 GHz and results in a resolution of 100 kHz. Using a peak finding algorithm, a line list is first generated and instrumental artifacts and lines from common contaminants [e.g., SO₂, OCS, and (H₂O)₂] are automatically removed. The resulting line list is used by the cavity spectrometer for DR studies.

Using powerful control software, the cavity spectrometer can reliably be tuned to any frequency in the 5–25 GHz range in a few seconds, and AMDOR measurements are then performed. Owing to the high sensitivity in cavity mode, most lines are observed with high SNR in a few seconds of integration, so that each DR test typically takes only 2–3 s. For two frequencies f₁ and f₂ in the 1D spectrum, the two (f_pump, f_probe) DR tests (f₁, f₂) and (f₂, f₁) should give the same binary result (linked or not), therefore only half of the possible DR tests are needed to fully determine the AMDOR spectrum (which is consequently symmetric along the diagonal).

Exhaustive DR tests can nevertheless be time consuming, as the number of tests scales as (n/2)(n − 1), where n is the number of lines. To reduce the integration time, the initial line list is sorted by decreasing intensity so that the greatest number of DR tests is performed on pump transitions requiring the least integration time. To further reduce the integration time, only a subset of the most intense lines can be included in the initial screening. Benchmark tests show that 50 lines can be screened in approximately 90 min, assuming 2 s of integration time per line. If necessary, larger screenings can subsequently be performed on a more complete line list. A portion of a typical DR sequence is shown in Fig. 2, and a flow chart summarizing the detection and analysis steps in our AMDOR experiments is presented in Fig. 3.

For the DR tests described here, a threshold of ≥50% depletion was required for lines to be considered positively linked. False positives occur occasionally in the DR measurements; they are almost always instrumental in origin, arising most frequently when the probe and pump radiations are very close in frequency, e.g., less than 50 MHz, owing to radio frequency interference. For this reason, matches between frequencies closer than this amount are usually disregarded. As a further check on the authenticity on a DR linkage, the pump and probe transitions are routinely reversed to confirm that a similar intensity decrease is observed. Although the false positive rate is approximately 1% at present, it could likely be lowered further by using a frequency synthesizer of very high spectral purity for the probe source.

Liquid samples of the three molecules studied, trans-cinnamaldehyde, α-, and β-ionone, were injected into a heated nozzle warmed to 80 °C (trans-cinnamaldehyde) or 120 °C (α- and β-ionone) to increase their vapor pressure. Neon was passed over the warm reservoir at a pressure ranging between 1.5 and 2.5 kTorr, and the resulting gas mixture was supersonically expanded into the large vacuum chamber. This production method was used in both the CP and the cavity FTMW experiments.

The broadband spectrum of each sample was first measured in the 8–18 GHz region using CP-FTMW spectroscopy. CP spectra accumulated over 50 000–200 000 individual gas pulses (see Table S1²⁶), each interrogated by 10 frequency chirps, were recorded for the three molecules, and the high SNR allowed a large number of transitions to be identified (see Table S2²⁶). For α- and β-ionone, a CP spectrum which is the result of only about 15 min integration (5000 gas pulses) was the basis for all subsequent cavity FTMW tests.

The visual appearance of an AMDOR spectrum and the patterns formed by the linkages sensitively depend on molecular structure, as defined by Ray’s asymmetry parameter κ²⁵ and the non-zero components of the dipole moment along the principal axes. An example of the AMDOR spectrum obtained for trans-cinnamaldehyde is presented in Fig. 4. To better understand possible trends, AMDOR spectra have been simulated for a variety of cases (see Figs. S1-S6²⁶). It is evident from these simulations that if enough DR measurements are made, qualitative information on κ and the projections of the dipole moments can be inferred by visual inspection.

A key advantage of AMDOR lies in the capability to rapidly construct an energy level diagram of a single molecule based solely on experimental observations. As a practical matter, the DR linkages within a-type ladders are often relatively easy to detect for large, near-prolate molecules like those studied here because they are often closely spaced and roughly harmonic in frequency. Once found, identification of one or more DR linkages between different K_a ladders can then be used to constrain the value of the A rotational constant. We have experimented with different search strategies, from exhaustive DR screening of all lines identified in the 1D spectrum to targeted DR measurements within subsets of data. We found that it is efficient to start by screening only the strongest ∼50 lines against one another. Once a pattern emerges from these tests, more exhaustive, but targeted, DR tests are performed between already linked transitions and a larger line list (∼250 lines) from the 1D spectrum. In this way, weaker cross-ladder transitions might be found. From a small subset of DR linkages, it is then possible to extract all three rotational constants, at least for molecules that have low-order symmetry (C₁, C_s, C₂, or C_i) and at least two nonzero dipole moment projections.

For the molecules investigated here, only four DR linkages were needed to uniquely determine their rotational constants. Exhaustive simulations and analyses have not yet been performed, but it appears that a similarly small number of linkages may be sufficient for the analysis of most molecules, even though more linkages are helpful to better constrain the fit. There are several ways to determine these constants, ranging from the assumption of some initial assignments from the plot to a purely brute-force least-squares optimization. Although a number of approaches may be worth pursuing, we have focused our initial efforts on fitting algorithms that only use a minimal number of DR linkages. Our present approach, detailed below, has been successful for the analysis of these aroma compounds which are rigid, near-prolate asymmetric tops, but further development is underway to broaden its applicability to a wider variety of molecules that have different structures and dipole projections.

Rotational constants are presently determined from DR matches using a script that has been written in Python and incorporates the SPFIT/SPCAT suite of programs,²⁴ which is particularly efficient for fitting rotational constants of rigid molecules. This script requires only 4 DR matches between 5 frequencies as input: those of four a-type transitions, two from each of two a-ladders, and one cross-ladder transition connecting these two a-ladders (see Fig. 5). An appropriate set is easily identified by selecting transitions from the red and green linkages indicated in Fig. 4. The relative K_a and J ordering between the two ladders is not known (only that they differ in magnitude by at most one), nor is the transition type (b- or c-) which connects the two a-ladders. For each possible value of J, K_a, and K_c in a given range (e.g., 0 ≤ K_a ≤ 5 and 5 ≤ J ≤ 15), each of four possible ways to connect the cross-ladder transition (linking the upper or lower energy level of each a-type transition), each possible selection rule (b- or c-type), and for the two possible ways the two a-ladders can be ordered in energy (the second ladder may lie below or above the first one), the program creates a line assignment file (.lin) and then calls a least-squares optimization program (SPFIT), assuming an initial set of rotational constants (.par file). These constants are estimated in the following manner: initial B and C values are roughly estimated from the observed rotational spacing between successive a-type transitions — approximately B + C — by naively assuming that C = 0.8B; the A value is then deduced on the assumption that the inertial defect is zero. For instance, with 0 ≤ K_a ≤ 5 and 5 ≤ J ≤ 15, 4470 different assignments are possible. Fits that do not converge or for which A≱B≱C are discarded. The remaining fits are rank ordered by the root-mean-square deviation of the calculated and measured frequencies. Despite the large number of possibilities, only 30 s were needed to test all possible assignments for each of the three molecules studied here. In all cases, the best fit was easily identified, as evidenced in Fig. 6, by its very low reduced standard deviation value. Additional details on the script and how it was used to determine the rotational constants of the three aroma compounds are presented in the supplementary material.²⁶ 

As a first illustration of this approach, the AMDOR spectrum of trans-cinnamaldehyde (C₉H₈O, Fig. 1), the major constituent in cinnamon oil and the compound responsible for its characteristic aroma, has been measured in the 8–18 GHz frequency range, as depicted in Fig. 4; the left panel shows the raw data, while the right panel shows the rotational assignments and transition type (a or b). In this example, exhaustive DR tests have been performed (for about 19 h).

Several distinctive features are evident in these AMDOR plots. The most obvious is the large number of points lying parallel to the diagonal (in red in the left panel). As indicated on the right panel, these DR linkages involve two R-branch, a-type lines; the vertical/horizontal distance of these series of points from the diagonal is approximately the rotational spacing, B + C. It is thus clear from the AMDOR spectrum alone that trans-cinnamaldehyde possesses both a- and b-type transitions, and B + C ∼ 1080 MHz.

Although not as obvious from the limited resolution of Fig. 4, further inspection of the points lying parallel to the diagonal reveals that there is a distinctive pattern among them, likely indicating that each probably arises from a different K_a ladder. The progressions that run nearly perpendicular to the diagonal are more subtle: a number of these linkages consist of a tightly spaced cluster of four points (left panel, green points). These linkages arise from the combination of a- and b-type transitions from the same lower J and appear to spread out away from the diagonal with decreasing J (making the visual appearance of “wings” on an airplane).

The rotational constants of trans-cinnamaldehyde, determined by the procedure described in Sec. III C, are summarized in Table I, along with those derived from comprehensive fits of the 1D data between 2–8 GHz²⁷ and 8–18 GHz (the complete fit is given in Table S1). The frequency accuracy is approximately 20–50 kHz (depending on the SNR) for the CP transitions and 2 kHz for lines measured in the cavity. Cavity frequencies, when available, were used in the final fit. We note that with only five lines, the rotational constants are determined to an accuracy of better than 0.001%.

As a second example, the AMDOR spectrum of α-ionone (C₁₃H₂₀O, Fig. 1), a common aroma compound found in a variety of essential oils, including violet, has been recorded following the Fig. 3 flowchart and is shown in Fig. 7. This plot was generated in approximately 4 h of acquisition time: 15 min for the chirped spectrum, approximately 2.5 h to screen the strongest 50 lines, and 1 h for follow-up DR tests. In this time, a-type transitions from more than 10 distinct K_a ladders were found, as were more than 20 b- or c-type transitions between these ladders. The rotational constants have initially been determined using our script (from four DR matches involving five transitions, see Figs. S11 and S17²⁶) and then refined in a more extensive fit (based on this initial assignment). In Table II, these rotational constants are compared to those obtained by density functional theory calculations for the lowest energy conformer of α-ionone.²⁸ An essentially identical experiment and analysis for another violet ketone, β-ionone (Figs. 1, S11, and S17²⁶), yields the rotational constants in Table III. Only the CP frequencies were included in the fits for both molecules because the presence of a –CH₃ group results in a complex line structure (of order 50 kHz) at high spectral resolution which was not resolved in CP spectrum.

The present work illustrates the potential for AMDOR as an analytical tool for rapid identification and characterization of volatile samples; a strength of this approach is that no a priori knowledge of the species or its structure is required. Indeed, while this analysis does not provide species identification directly, the resulting rotational constants shed much light on the qualitative structure of the molecule. The value of the asymmetry parameter indicates a linear, symmetric, or asymmetric molecule and gives an indication as to the degree of oblate or prolate character. The relative intensities of the a-, b-, and/or c-type transitions are related to the dipole moment projections, providing clues as to the distribution of the electronegative atoms or functional groups within the molecule. Furthermore, the magnitudes of the rotational constants themselves hint at the distribution of heavy atoms within the molecular network, and help to significantly narrow the parameter space to be explored when identifying an unknown molecule.

In the present version of the method, rotational constants are most easily determined for fairly rigid molecules where any additional structure (e.g., –CH₃ rotation and nuclear quadrupole) is small enough to allow each rotational energy level to be defined by three quantum numbers (J, K_a, and K_c). However, there is no fundamental obstacle to applying AMDOR to study a wider range of molecules, including non-rigid ones and those that might contain atoms with large nuclear quadrupole moments (e.g., Cl and I), as long as appropriate Hamiltonians to describe their energy level structures are used.

A more robust version of our current script is under development, in which no assumption of transition type (a, b, or c) for the DR matches is required. Because the transition type is now a free parameter, an even larger number (by a factor 10 or more) of possible assignments must be tested, but this approach has the significant advantage that as soon as one transition in the 1D spectrum is linked to at least three other ones, the algorithm is very likely to converge. However, more DR experiments may be necessary to increase the network of linked transitions if the solution is not unique. This approach should permit the study of molecules which have a weak, or nonexistent, a-type spectrum.

Although the focus of this paper is on rapid rotational analysis of a pure sample, AMDOR measurements inherently resolve mixtures into individual components by identifying distinct networks of linked lines prior to subsequent assignment. For this reason, species separation should be possible even when line densities are very high. Depending on the size of the initial line list, search algorithm employed, and the relative abundance of the various components, AMDOR measurements — in the absence of a library — could be used to quickly identify the most conspicuous chemical components in a mixture. Once their rotational constants are determined and their rotational lines identified in the 1D spectrum, searches for less obvious ones could be undertaken. For α-ionone, more than 250 lines were removed in this fashion, but about an equal number remain (∼300). Using either a sequential or simultaneous approach, AMDOR measurements and analyses should enable systematic identification of multi-component mixtures.

In addition to determining the composition of an unknown sample, the present methodology might be useful as a characterization technique for small molecules. For instance, NMR and mass spectroscopy are routinely used in organic chemistry to verify the existence and purity of a compound formed in a chemical reaction. With the AMDOR approach outlined here, determination of rotational constants could provide complementary evidence for compound characterization. One could envision coupling this type of spectrometer with electrospray, laser desorption, and other methods used in the mass spectrometry (MS) community to volatilize larger, more fragile samples. A real advantage of rotational spectroscopy relative to NMR and MS is its conformer and diastereomer selectivity,² which could prove useful for characterizing the performance of selective catalysis.

AMDOR method appears to be a powerful technique to rapidly characterize compounds because: (1) it is unbiased, requiring no a priori theoretical input; (2) it is unambiguous, because linkages between seemingly unrelated rotational lines can be established with confidence: a true DR effect can only occur if two lines arise from the same molecule, and if they have rotational energy level (lower or upper) in common; (3) it can be performed exhaustively, since every possible combination of rotational lines can in principle be tested; and (4) it is highly redundant since the three rotational constants primarily dictate the overall pattern of lines.

When viewed in the context of recent, related developments in the field, it is tempting to make comparisons to the early development of multi-dimensional NMR, where data processing and hardware limitations hindered the usefulness of this technique for structural determinations. To further improve the speed of AMDOR and achieve the goal of true real-time analysis, however, still more efficient search algorithms are needed, in which subsequent DR tests are conditioned by the outcome of prior DR tests. In this way, the fewest number of possible DR measurements are performed, so as to yield a set of linkages which are unique to the specific molecule(s) under study. Since this number appears quite small and can readily be verified and extended using the 1D spectrum, real-time analysis may well be possible; it does not appear to be limited by any obvious fundamental obstacle. Its utility can likely be enhanced further when used in combination with phase-sensitive detection²⁹ and complementary automated analysis tools such as AUTOFIT.³⁰ 

The authors thank E. S. Palmer and P. Antonucci for technical assistance. M.C.M. and M.A.M.-D. acknowledge support from NSF Grant No. CHE-1213200. B.A.M. thanks A. J. Remijan for his support.