• transition state
• photolysis
• vibrational population distribution
• chirped-pulse millimeter-wave spectroscopy
• vibrational satellites

The primary objective of transition-state spectroscopy (1⇓⇓–4) is experimental observation of the most hidden aspect of a chemical reaction: the transition state (TS). Formally, the TS is a hypersurface in phase space that delineates reactants from products. Reactants that pass through this hypersurface in the forward direction proceed on to products, and vice versa. Since molecules are never stabilized on the TS dividing surface, one cannot directly observe the TS. Instead, with TS spectroscopy one aims to observe spectroscopic features of the structures surrounding this TS dividing surface. The 10- to 100-fs (5) duration passage through the neighborhood of the TS determines the reaction rate and molecular product ratios and is also a key determining factor in the nascent internal state content of each chemical species. The observed vibrational and rotational state distributions of the reaction products encode information about the structures of and relative fluxes through multiple TS regions, as well as the dynamics from the TS on to products. Acquisition of such information over a range of rotation–vibration quantum numbers is a nontrivial challenge that requires both high resolution and the ability to sample the populations of a wide range of quantum states* (6⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓–28).

Chirped-pulse Fourier transform millimeter-wave (CPmmW) spectroscopy (29⇓⇓⇓⇓⇓⇓⇓⇓–38) is capable of recording, in each chirp, a several-gigahertz spectral region at submegahertz resolution. The chirped-pulse technique was developed (29⇓–31) by Brooks Pate and coworkers at the University of Virginia for the microwave region and later extended to the millimeter-wave (mm-wave) region by Field and coworkers (35), in collaboration with the Pate group and, independently, by Plusquellic and coworkers (34). Rotational spectroscopy is unsurpassed in its precision of sampling molecular geometric structure in the gas phase and its ability to resolve and vibrationally assign transitions, “vibrational satellites,” that originate from different vibrational levels (39, 40). However, until the advent of CP techniques, it was only possible to exploit the high resolution and state specificity of microwave spectroscopy over sequential samples of few-megahertz spectral regions. Now, many new classes of rotational spectroscopy experiments are possible. For example, simultaneous broadband detection of isomerizing molecules enables “dynamic rotational spectroscopy” (31, 41). The relative transition intensities in CP experiments can be converted to branching ratios of multiple reaction products for chemical kinetics studies (42⇓⇓–45). A recent study of 193-nm photolysis of vinyl cyanide (VCN) in a room-temperature reactor revealed a new pathway to HCCCN by measuring the time evolution of the vibrational-level population distribution (VPD) in a CPmmW spectrum (43). Precise determination of (averaged) molecular structure remains at the core of these new directions, while broad spectral range and line intensities at ∼20% relative accuracy enable new chemical applications.

In this work, we utilize the VPD measured over several gigahertz of pure rotational CPmmW spectrum to sample the properties of TSs. We studied the 193-nm photolysis of VCN (acrylonitrile) in a supersonic jet and identified 2 distinct sets of VPDs of HCN reaction products. Both the structures of the TSs and the branching between the corresponding product channels are extracted from the VPDs.

Photolysis of ethylene (13) and its substituted analogs, VCN (12, 22, 46⇓⇓⇓⇓⇓–52), vinyl chloride (15, 23, 25, 26), vinyl bromide (17, 24, 53, 54), vinyl iodide (55), and propene (56), has been extensively studied during the last 4 decades. The 193-nm photolysis (57) of VCN has been observed (12, 22, 43, 47, 49) and calculated (43, 48, 50, 52) to take place via a dizzying array of reaction pathways. Since many of these pathways lead to difficult-to-distinguish final product channels, it has been challenging to obtain definitive experimental evidence in support of a particular model or theoretical description. We assume here that dissociation occurs on the ground electronic potential surface of VCN after rapid electronic relaxation and intramolecular redistribution of the photon energy (12, 58).

The present paper is primarily based on further analysis of measurements reported earlier (38), and the experimental details are available in SI Appendix, Experimental Details. and ref. 38. In particular, the spectrum of the VCN photolysis products, HCN and HNC, in the 86.5- to 93.0-GHz region is republished from ref. 38 in Fig. 1, now displaying assignments of multiple HCN and HNC J = 1–0 rotational transitions to various vibrational states of these isomers. The HCN and HNC transition frequencies are listed in SI Appendix, Table S1. In our previous work (38) we observed multiple HCN and HNC transitions that were attributed to the vibrationally excited molecules and assigned a few of them. We noticed (figure 15 of ref. 38) that deuteration to CH₂CDCN had a surprisingly modest effect on the observed total HCN vibrational population. We expected most of DCN to originate from the 3-center unimolecular elimination mechanism CH₂CDCN → CH₂C: + DCN and to replace the majority of HCN upon deuteration of the precursor. In this work we examine the CPmmW spectrum of DCN and investigate its VPD in comparison with that of HCN.

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Fig. 1.

CPmmW spectrum of the HCN and HNC photolysis products in the 86.5 to 93.0 GHz region with vibrationally assigned HCN and HNC rotational J = 1–0 transitions. The HCN and HNC transition frequencies are listed in SI Appendix, Table S1. The vibrational states (v₁ = C–H or N–H stretch, v₂ = bend, v₃ = C–N stretch) of HCN and HNC molecules are shown in round and square brackets, respectively, near their rotational lines. Two insets illustrate the electric quadrupole hyperfine (eQq)_N structure, with the assignments. The chirp covers the 84.5- to 97.0-GHz region, but only the region containing the observed HCN and HNC transitions is shown. The spectrum and the FID are available in Datasets S1 and S2, respectively. The laser-off background spectrum and FID are given in Datasets S3 and S4, respectively. arb. un., arbitrary units. Adapted from ref. 38 with permission from The Royal Society of Chemistry.

Vibrational excitations cause small changes in rotational constants, and thus pure rotation transitions associated with different vibrational levels are easily resolved and assigned in the CPmmW spectrum. In HCN and HNC, the vibrational quantum numbers are (v₁, v₂, v₃), where v₁ designates the number of quanta in the C–H stretch of HCN and N–H stretch for HNC, v₂ in the bend, and v₃ in the C–N stretch. Since only J = 1–0 transitions fall within the present spectral range of our CPmmW spectrometer, transitions involving vibrational angular momentum ℓ > 0 cannot be observed, and the corresponding quantum number label is omitted. This restriction to ℓ = 0 renders all odd-v₂ vibrational levels of HCN and HNC unobservable with our spectrometer. The vibrational state assignment procedure is described in SI Appendix. Apropos of v₂ and ℓ, it is important to note that even ∆ℓ relaxation within a given v₂ is expected to be fast, similar to rotational cooling; however, odd ∆ℓ changes are necessarily vibrational (Δv₂ ≠ 0) in nature, and therefore less efficient. The only ℓ = 0 states with bending excitation are (0, 0, 0), (0, 2, 0), (0, 4, 0), and so on, and their combinations with stretching vibrations.

We begin by analyzing the dynamical information encoded in the frequencies of the rotational transitions. An isomerization reaction may be enabled by high vibrational excitation and large amplitude motion in the parent molecule (4, 31, 59⇓–61). Because of the I = 1 nuclear spin of the ¹⁴N atom and its electric quadrupole interaction with the electric field of the electrons in the molecule, the electric quadrupole constant (eQq)_N is a sensitive diagnostic for HCN ↔ HNC isomerization dynamics. As the [H, C, N] molecule proceeds along the isomerization path via highly excited bending states, the evolution of the electronic configuration is probed by the strong vibrational-level dependence of the (eQq)_N constant (59, 61, 62). Previously observed (38) rotational transitions of the HCN and HNC products of VCN photolysis are assigned here to vibrational levels up to v₂ = 14 in HCN and v₂ = 8 in HNC, and the corresponding (eQq)_N constants are determined (see SI Appendix for details). Fig. 2 shows the dependence of the (eQq)_N constant on the bending vibrational quantum on both sides of the HCN/HNC barrier and at vibrational energies up to 9,488.5 cm⁻¹, measured from the HCN (0,0,0) ground state.

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Fig. 2.

Comparison of the (eQq)_N constants between the previous calculations by Wong (61), previous experiment by Bechtel et al. (59), and the present work. The details of the calculations are available in SI Appendix. In order to position the ladder of HNC vibrational levels opposite to the ladder of HCN levels across the HCN ↔ HNC isomerization barrier, we use the E_HNC[0,0,0] – E_HCN(0,0,0) = 5,212 cm⁻¹ value (68) for the energy difference between the 2 isomers. The HNC [0,6,0] (eQq)_N value measured in this work deviates from the prediction (61) toward the HCN (eQq)_N values and is in close resonance with the HCN (0,12,0) level. This may encode evidence of a resonant tunneling interaction between the HCN and HNC isomers.

Although the vibrational term energies of many HCN and HNC levels are separately known from Fourier transform infrared studies (63, 64) with a precision of 0.001 cm⁻¹ or better, the energy of the HNC levels relative to those of HCN is much less well characterized. The experimental value (65) of 14.8 ± 2 kcal/mol (5,176 ± 700 cm⁻¹) is too uncertain to draw conclusions about the relative energies of the HCN and HNC vibrational levels. Recently, the combination of high-accuracy HEAT-456QP calculations and the Active Thermochemical Tables (ATcT) approach (66, 67) produced (68) a recommended value of 5,212 ± 30 cm⁻¹ for the E_HNC[0,0,0] – E_HCN(0,0,0) energy difference, which we adopt in this study. Thus, the plot in Fig. 2 puts the (eQq)_N values of both isomers on a common energy scale.

The values of (eQq)_N in HCN (0, v₂, 0) states decrease nearly linearly with v₂ and in agreement with the calculation (61) up to 14 quanta of bending excitation. Eventually, at v₂ > 24, the (eQq)_N curve for HCN is predicted to converge with that for HNC (59). We observe that the calculated value of HNC [0,6,0] (eQq)_N is outside the 1σ but within the 2σ experimental uncertainty of the measured value. The accepted value (68) of E_HNC[0,0,0] – E_HCN(0,0,0) = 5,212 cm⁻¹ puts the HNC [0,6,0] level in near-resonance with the HCN (0,12,0) level across the isomerization barrier. Delocalization of the vibrational levels of the 2 isomers has been calculated (69, 70) for the near-transition-state energies of ∼15,000 cm⁻¹ and above, which lies at significantly higher energy than the EHCN(0,14,0) = 9,488.5 cm⁻¹ and EHNC[0,6,0] ∼ 8,021 cm⁻¹ energies that we reach in this work. In principle, accidental resonances are possible and those can lead to calculable mixing between HCN and HNC basis states at lower energies.

Because our current experiment is limited to J = 1–0 pure rotational transitions of H(D)CN, we cannot observe transitions between the states that possess nonzero vibrational angular momentum, ℓ. One might expect that the photodissociation of VCN is contained in the plane defined by the H, C, and N atoms, and therefore no HCN bending out of that plane would be allowed, and thus the vibrational angular momentum should be ℓ = 0 for all HCN and HNC products. However, quasi-classical trajectory calculations suggest that HCN elimination is not constrained in a plane and predict the average value of the vibrational angular momentum <ℓ> to be 2.8 and 2.5 for 3-center and 4-center mechanisms, respectively (52). For linear molecules, dynamics of the vibrational angular momentum defined by the TS properties and subsequent relaxation can affect the populations of rotational levels with specific symmetries. Future experimental observations of rotational transitions between J > 0 levels of HCN at higher mm-wave frequencies will reveal those ℓ-excitations.

We now turn to examination of the intensities of the spectral transitions, which encode important chemical information in addition to that obtained from transition frequencies. Specifically, the intensities of rotational transitions of molecules in vibrationally excited states are related to the VPD of those molecules, and a previously unobserved class of information about the 193-nm photolysis TS(s) of VCN is encoded in the VPDs of HCN and DCN.

Fitting the measured VPDs with a physically meaningful function can be a powerful tool in decoding the experimental data. Such VPDs depend on the vibrational wavefunctions of both the TS and photofragments and on the dynamics from the TS onward. Thus it seems appropriate to invoke generalized Franck–Condon overlap integrals of these vibrational wavefunctions for VPD analysis (71⇓–73). Franck–Condon overlaps of vibronic levels have been extensively analyzed and applied to extract vibrational populations (74⇓⇓⇓⇓⇓⇓⇓–82). Ruscic (81) has shown that the distribution of Franck–Condon overlap integrals in photoelectron spectra is well represented by the Poisson distribution if a harmonic potential approximation can be adopted. Klemperer and coworkers (82) have used Gaussian and Poisson functions to fit vibrationally resolved dispersed fluorescence spectra. The Poisson distribution had been invoked to describe the VPDs that result from electronic-to-vibrational collisional energy transfer (83, 84). On the other hand, theoretical (85⇓–87) and experimental (21) work has been done to extend the Franck–Condon principle beyond electronic transitions and into the realm of reaction dynamics. Here we propose use of the generalized Franck–Condon principle to analyze the TS properties by fitting the experimental VPDs to a Poisson-type function:P(n,λ)=Aλnn!,[1]where P(n) is the concentration of a product species with n vibrational quanta in a certain mode and A and λ are the adjustable parameters.

In an attempt to obtain more detailed information on the various channels leading to HCN products, we photodissociated deuterated VCN, CH₂CDCN. The corresponding spectra of HCN and DCN are shown in figure 15 of ref. 38 and in Fig. 3, respectively. In this test, we expected that unimolecular DCN elimination would proceed via the 3-center TS in which CN forms a bond with D, whereas the HCN would be formed by the 4-center unimolecular elimination TS. Most recent calculations predict dominance of the 3-center mechanism in HCN elimination from VCN over all other channels (43, 50, 52). As a consequence, in photolysis of a precursor that is singly deuterated near the cyano group, one would expect dominance of the DCN product accompanied by a 4-fold decrease in the HCN population. However, in figure 15 of ref. 38 we show that only an approximate 20% decrease in HCN signal is observed in our experiments as a result of deuteration of the VCN parent molecule. This suggests that DCN is formed with smaller branching ratio than HCN. In this work, we investigate the qualitative behavior of these HCN and DCN products’ VPDs.

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Fig. 3.

CPmmW spectrum of the singly deuterated isotopologue of VCN, CH₂CDCN, and its DCN and DNC photofragments in several vibrational states. The 2 strong transitions of the parent CH₂CDCN molecule are J_KaKc = 8₁₈ to 7₁₇ at 72.275 GHz and J_KaKc = 8₀₈ to 7₀₇ at 74.057 GHz. The DCN (0,6,0) lines are situated on the shoulder of the CH₂CDCN line. The DNC spectrum was obtained with a narrow chirp centered at the line. arb. un., arbitrary units. The DCN and DNC transition frequencies are listed in SI Appendix, Table S2. The laser-on and laser-off spectra are available in Datasets S5 and S6, respectively.

The VPDs of HCN and DCN, plotted as a function of bending mode population, are presented in Fig. 4, where 2 quanta of the HCN or DCN bend mode are the abscissa unit. The HCN VPD is from the line intensities published in figures 14 and 15 of ref. 38. We find that the DCN VPD can be well approximated by Eq. 1 with λ = 2 and also closely resembles the Vázquez and Martínez-Núñez results (52) of the trajectory calculations. The presumed 4-center TS-associated distribution of HCN vibrational population is better fit by an exponential rather than by a weighted Poisson distribution of Eq. 1 and qualitatively differs from the calculated (52) one. The observed non-Boltzmann DCN VPD shows that vibrational cooling does not erase the information encoded by TSs in the nascent vibrational state distributions.

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Fig. 4.

Poisson and exponential fits of the HCN and DCN data. The rotational line intensities of pure bending vibrational levels of the HCN and DCN product molecules that result from CH₂CDCN 193 nm photolysis are integrated over their hyperfine components and corrected for the frequency-dependent transmission curve of the CPmmW spectrometer. The relative intensities of the excitation chirp between the 68.7 ← 78.7 GHz and 84.4 → 97.0 GHz chirping regions for DCN, DNC, and HCN, HNC were independently verified to be comparable by referencing them to a T_rot = 6 ± 1 K PGOPHER (92) simulation of the parent CH₂CDCN transitions. No adjustment of intensities for the chirp direction (34) was made since the spectral regions of interest are significantly smaller than the chirp ranges (93). Data for the HCN plot from ref. 38. arb. un., arbitrary units.

The DCN VPD in Fig. 4 reaches a maximum at v₂ = 4 pure bending excitation, which is similar to the VPDs calculated for both the 3-center and newly discovered “CCdiss” elimination mechanisms (52). We therefore assign the DCN products to a combination of these 2 reaction pathways, with the 3-center pathway dominating. The exponentially decaying VPD of HCN in photodissociation of CH₂CDCN in Fig. 4 is maximum at v₂ = 0, suggesting that the geometry of H, C, and N atoms in that TS is near-linear. However, we cannot at this point relate that distribution and the associated TS properties to any HCN elimination mechanism that has been considered in the literature. The TS branching deduced from Fig. 4 is DCN: HCN = 1: 4, which is consistent with the previously observed depletion of the HCN signal upon deuteration of the precursor. Thus, while the 3-center mechanism is expected to be the dominant pathway to HCN, according to our results it accounts for only 20% of H(D)CN. The 80% majority of the H(D)CN observed in this work is associated with a presently unidentified reaction mechanism.

We estimated several possible ways in which the chemically unassigned part of the HCN VPD could stem from bimolecular reaction pathways in the collisional region of the slit jet expansion. The details are given in SI Appendix. We estimate that the branching ratio for a CH₂CCN + CH₂CHCN → C₅H₄N + HCN channel relative to that for the 3-center HCN elimination is <4 × 10⁻³ and thus exclude this possibility. For the CH₂CCN + CH₂CCN → C₅H₃N + HCN reaction the same branching ratio is estimated to be <3 × 10⁻². In that radical–radical self-reaction, the HCN photofragments are expected to be highly energized rotationally, and unlikely to be detectable. We evaluate the upper bound for the CN radical elimination channel CH₂CHCN → CH₂CH + CN branching to be 0.01 relative to the 3-center HCN channel. Although H-atom abstraction by CN is barrierless, the concomitant energy release will reduce the observable CPmmW signal unless perfect rotational cooling of HCN is achieved in the jet.

Finally, we consider a free H-atom attacking a CH₂CHCN molecule and eliminating HCN: H + CH₂CHCN → CH₂CH + HCN. Using the ATcT results from the SI appendix, table S5 of ref. 43, we find that this reaction is slightly endothermic: Δ_rH°(0K) = 5.01 kcal/mol. According to the photofragment translational spectroscopy study of Hall and coworkers (12), the average kinetic energy release in the CH₂CHCN → CH₂CCN + H reaction is near 4 kcal/mol, with its distribution extending to 10 kcal/mol. Most of it will be deposited in the kinetic energy of the light H-atom, which might then be able to surmount (or tunnel through) the barrier of 7.1 kcal/mol for its addition to CH₂CHCN. Decomposition of the adduct may potentially lead to colder HCN products. This decomposition has a relatively high barrier of 10.5 kcal/mol relative to the initial reactants but may still occur via tunneling. Note that these barriers are obtained here by CCSD(T)/CBS//CCSD(T)/cc-pVTZ calculations. We leave more detailed theoretical and experimental exploration of this possibility for future studies.

A fundamental difficulty in the use of CPmmW spectroscopy is understanding how the observed intensity of only one rotational transition relates to a vibrational population. The relevant equations require the existence and knowledge of the rotational temperature (43). The contribution to our measured VPD from TSs that release products with very high rotational excitation (23, 24, 26, 54), which are not thermalized to the ambient temperature in the detection volume, will be underestimated relative to nascent product populations in the low-J states (43). Even if more than one rotational transition for each vibrational level can be measured, the nascent rotational-level population distribution (RPD) may not be Boltzmann, in which case the rotational temperature that is needed for intensity calibration is undefined.

The RPD affects these CPmmW measurements of relative vibrational level populations in several ways. 1) It is necessary to assume that in the supersonic expansion rotational relaxation is much faster than vibrational relaxation; 2) rotational populations in every vibrational level are thermalized; 3) the rotational temperature in every vibrational level is the same; 4) the rotational temperature of the photofragment molecules (HCN, HNC) is the same as that of the parent molecule (VCN), which acts as a thermometer; and 5) there is no significant population in very-high-J, rotational levels which are too highly excited to be thermalized in the supersonic expansion.

Here we assume that the RPD in the mm-wave interaction region is the same for every vibrational level of a product molecule. That assumption relies on the effectiveness and uniformity of postphotolysis rotational cooling in the quasi-1-dimensional expansion from the slit-shaped nozzle (88), and on the trajectory calculations (52) of nascent HCN RPDs that predict similar rotational temperatures for HCN eliminated via 3-center, 4-center, and the newly discovered CCdiss mechanisms: 6725 K, 5372 K, and 3133 K, respectively. We also assume that for small linear molecules with sparse vibrational levels, like HCN, vibrational energy redistribution is slow (42, 89) compared to rotational cooling and the VPDs are not significantly altered. The highly nonthermal DCN VPD suggests that in this experiment vibrational cooling is incomplete and less effective than rotational cooling. If these assumptions are valid, which we presently have no independent way to confirm, then, for each product molecule formed via any TS the relative intensities in Fig. 4 would represent the nascent VPDs (23, 24, 26, 43, 52, 54). Hence, the origin of the strong HCN signal with an exponential VPD eludes definitive explanation. Although we considered various bimolecular possibilities for alternative sources of cold HCN, our calculations and estimations identified no plausible candidates, with the possible exception of translationally hot H-atoms reacting with VCN.

In summary, we have used CPmmW spectroscopy to investigate previously unknown chemical pathways to HCN following 193-nm photodissociation of VCN. The toolbox consists of measuring the vibrational population distribution of photolysis products and isotopic labeling of the precursor molecule: CH₂CDCN. The broadband and high-resolution features of CPmmW spectroscopy enable us to observe the HCN, HNC, DCN, and DNC products and their vibrational population distributions. The relative intensities of the CPmmW rotational transitions reveal the functional dependences of vibrational-mode populations in these products. A Poisson-like DCN VPD is consistent with the combination of the 3-center and CCdiss reaction channels in unimolecular photodissociation of CH₂CDCN. The exponential HCN VPD points to the existence of an unexpected reaction pathway likely outside of known unimolecular dissociation channels in VCN. The experimental evidence for this previously unknown reaction channel has directed us to consider bimolecular chemistry in the supersonic expansion. Our calculations suggest that a possible route is the H-atom addition/HCN elimination reaction H + CH₂CHCN → CH₂CH + HCN. This work demonstrates that the CPmmW technique has promise for characterization of TSs of chemical reactions. The ability to sample additional (higher-J) rotational transitions to better characterize the rotational temperatures of the photolysis products and the use of additional parent molecule isotopologues are desirable next steps, especially when complemented by rotationally and vibrationally level-resolved calculations of product yields.