Sub-Doppler infrared spectroscopy of propargyl radical (H₂CCCH) in a slit supersonic expansion

Hydrocarbon radical species play a crucial role in a wide range of extreme chemical environments, ranging from solar photochemistry in the upper atmosphere, to high temperature kinetics of combustion flames,¹ to synthesis of molecules in the interstellar medium.² It has been suggested, for example, that highly unsaturated radicals are responsible for the initial formation of polycyclic aromatic hydrocarbons (PAH) in astronomical contexts, as well as possible carriers of the diffuse interstellar bands (DIB).³ In a more terrestrial venue, complex reaction mechanisms have been proposed that suggest unsaturated reactive hydrocarbon radicals to be especially important intermediates in controlling combustion efficiency, as well as triggering the formation of large aromatic molecular structures that eventually result in macroscopic “soot” carbon particulate.^4–6 

The formation of large aromatic structures by sequential addition of acetylene and ethynyl radicals to smaller aromatic molecules has been well studied, with specific models, e.g., hydrogen abstraction acetylene addition (HACA) to existing aromatic ring structures, receiving strong support.^7–10 In light of the success of such models for predicting facile growth on aromatic species, it is therefore interesting to note that the detailed kinetics and dynamics for formation of even the simplest aromatic compounds from smaller non-aromatic radical species are still not well understood. One potential pathway toward aromatic ring formation has been a bimolecular reaction of two propargyl radicals (H₂CCCH) to form phenyl radical + H at low pressures or benzene at sufficiently high pressures. The removal kinetics due to the self reaction of propargyl + propargyl has been well studied, with the aromatically stabilized product species considered in the theoretical models.^11–19 In particular, such efforts are beginning to highlight the importance of highly unsaturated C₃ open shell species such as H₂CCCH in the early growth stages to form larger aromatic structures. This provides additional motivation for detailed high resolution spectroscopy and dynamics studies of jet cooled propargyl radical, in order to facilitate both laser based identification and absolute concentration measurements in further experimental studies of such aggregation processes.

From a fundamental perspective, H₂CCCH radical is also interesting in its own right, as a benchmark system for one of the simplest conjugated linear hydrocarbon radicals, with an unpaired electron nominally in the unfilled p molecular orbital perpendicular to the molecular plane (see Fig. 1). In particular, the extent of delocalization of this unpaired electron over the entire radical backbone proves to be an especially interesting issue, which has attracted much attention theoretically and experimentally.^20–24 This delocalization can arise from amplitude for electronic structures corresponding to either the propargyl (⁠$H 2 C ̇ —C≡$ CH) or the nominally allenyl (⁠$H 2 C=C= C ̇ H$⁠) form, with the unpaired electron mainly localized at the methylenic $( — C ̇ H 2 )$ or acetylenic (⁠$= C ̇ H$⁠) carbon atom, respectively. Indeed, microwave spectroscopic results have indicated that a more balanced resonance structure [$H 2 C ̇ —C≡CH↔ H 2 C=C= C ̇ H$] may be the most appropriate description for this system,²⁵ for which the probability density distribution of the unpaired electron can influence the nuclear geometry of the radical and vice versa. For a more planar structure, for example, radical hybridization tends to electronically favor the propargyl (i.e., acetylenic CH) form. However, as the radical is vibrationally distorted along the CCH out-of-plane or in-plane bending coordinate, the radical density shifts, and the hybridization tends to become more allenylic. In principle, vibrational excitation of the propargyl radical could therefore be expected to sample such geometries, for which mode specific effects could be revealed in both nuclear structure and electron spin delocalization from rovibrational and fine/hyperfine spectroscopies, respectively.

There have also been extensive experimental studies of propargyl radical in the literature. Ramsay and Thistlethwaite²⁶ first observed electronic absorption bands of propargyl radical in the region of 290–345 nm, for which they explained the diffuse structure resulting from predissociation in the upper electronic state. From electron spin resonance studies, Kochi and Krusic²⁷ and Kasai²⁸ concluded that propargyl radical exists in a planar C_2v equilibrium geometry. The infrared (IR) active vibrational modes of propargyl radical have been investigated in matrix isolation spectroscopy studies by Jacox and Milligan,²⁹ exploiting UV photolysis of methyl-acetylene and allene to form and trap propargyl in a low temperature argon matrix environment. Based upon isotopic substitution studies, the prominent absorptions at 3310 cm⁻¹ and 688 cm⁻¹ were assigned to the acetylenic C–H stretch and one of the two (in-plane or out-of-plane) ∠CCH-bending vibrations of propargyl radical, with other low frequency absorption features in the spectral region (548 cm⁻¹ and 484 cm⁻¹), however, left unassigned. Early ab initio calculations by Honjou et al.²⁰ predicted that the 688 cm⁻¹ frequency should be assigned to the out-of-plane ∠CCH-bending mode (v₆). Recent calculations by Botschwina et al.³⁰ ascribed this band to the methylenic CH₂-wag vibration. These efforts furthermore identified a large difference between the out-of-plane (476 cm⁻¹) and in-plane (621 cm⁻¹)∠CCH-bending vibrations, which could plausibly reflect strong allenyl contributions to the character of the radical electronic state.

In the gas phase, high resolution rotationally resolved spectra for the acetylenic stretching mode of the propargyl radical and isotopically substituted species (CH₂CCD) have been studied extensively by the Curl group, using 193 nm UV photolysis of a propargyl halide precursor (Br or Cl) and F-center flash kinetic spectroscopy at ambient room temperature. The band origins of the acetylenic stretching mode for H₂CCCH and H₂CCCD species have been determined to be 3322.2929(20) and 2557.337 cm⁻¹, respectively.^31–33 Strong rotational perturbations in H₂CCCH were observed in the K_a ≥ 2 sublevels of upper vibrational state, which were interpreted in the framework of a-type/c-type Coriolis and vibration (Fermi) coupling models. Interestingly, the spectral data revealed no rotational perturbations at low J for either of the K_a = 0 or 1 manifold, which would correspond to the two uncoolable (ortho and para) nuclear spin states and thus the only K_a levels populated significantly under slit supersonic expansion conditions.

In the lower frequency CH bending region, the fundamental ν₆ mode has been studied by Sumiyoshi et al.³⁴ and Tanaka et al.³⁵ using time-resolved diode laser flash kinetic spectroscopy. They confirmed the previous ambiguous spectral assignment to the CH₂-wagging vibration and, furthermore, successfully analyzed interactions between v₆ (CH₂-wagging) and v₁₀ (CH₂-rocking) via a-type Coriolis coupling. At even lower frequencies, Tanaka et al.²⁵ studied fine and hyperfine structures in the ground ²B₁ state of propargyl radical using pulsed discharged nozzle Fourier transform microwave spectroscopy. The unpaired electron distribution has been characterized by analysis of the Fermi contact interaction, from which electron spin density amplitudes are estimated to be ≈0.842 and ≈0.564 for the carbon atoms adjacent to the methylenic and acetylenic protons, respectively. Such measurements of a delocalized spin density confirm unambiguously that the electronic structure is best characterized as a resonance between both propargyl and allenyl forms. To the best of our knowledge, there have been no corresponding infrared spectroscopic studies for propargyl radical with fine and/or hyperfine resolution, with which the interesting effects of vibration on this hybridization and electron spin localization might be further elucidated.

In the present study, rovibrational transitions of the acetylenic CH stretching mode of propargyl radical in the vicinity of 3326 cm⁻¹ have been investigated in a discharge slit-jet expansion under supersonically cooled conditions and sub-Doppler resolution (60 MHz). The rovibrational transitions out of K_a = 0 (ortho) and 1 (para) are assigned and confirmed. Sub-Doppler resolution in the slit jet expansion geometry permits a detailed first glimpse into the fine-structure electron spin-rotation dynamics in propargyl radical for the CH stretching mode, with additional broadening due to hyperfine interactions on both the acetylenic (CCH) and methylenic (CH₂) radical centers analyzed and discussed.

The organization of present work is as follows. First, we provide a brief overview of the experimental methodology in Sec. II, which describes relevant details of sub-Doppler high resolution infrared spectrometer. In Sec. III, we address spectroscopic issues relevant to the rotational, fine and hyperfine structures, which is then followed with the experimental spectral fitting results and analysis in Sec. IV. Finally, Sec. V provides a brief discussion and analysis of the fully resolved fine structure at low J in the supersonic expansion as well as detailed fits in general to the high resolution absorption profiles due to incompletely resolved fine and hyperfine interactions.

The sub-Doppler resolution infrared spectrometer had been described elsewhere^36,37 with its performance demonstrated on a variety of jet cooled radicals and ions.^38–41 Consequently, only details specifically relevant to the present study will be summarized briefly. High resolution infrared radiation probing laser is generated via nonlinear difference-frequency generation (DFG) of a tunable single mode ring-dye laser (<1 MHz linewidth, Spectra-Physics 380D, operated with R6G dye) and a fixed-frequency single mode Ar⁺ laser (Spectra-Physics 2020, 488 nm) in a periodically poled LiNbO₃ (PPLN) crystal. Nonlinear subtraction of ring dye laser with either the green (514 nm) or blue (488 nm) lines of the Ar⁺ ion laser allows access to infrared frequencies in the 2600–4000 cm⁻¹ window region, which covers most fundamental CH, NH, and OH stretch modes of polyatomic hydrocarbon radicals. The infrared frequency is tuned by temperature control of a PPLN crystal (HC Photonics Corp.) to reach quasi-phase matching conditions.⁴² The IR radiation after PPLN is split via a beam splitter mirror into two components (hereafter referred to as signal and reference beams). The signal beam is sent into the chamber to probe transient absorption and imaged onto a liquid nitrogen cooled InSb detector (Infrared Associate, Inc., 50 KΩ load), with an estimated power of 5 μW. The reference beam is then monitored by a second InSb detector and serves to eliminate the common mode laser amplitude noise.⁴³ The absorption path length and sensitivity are further enhanced via 16-fold multi-pass of the infrared probe laser in a Herriot cell located at the downstream of the long axis of the slit jet expansion.

Jet-cooled propargyl radicals are generated by electrical discharge of a 0.1% mixture of propyne in 70:30 Ne-He buffer gas through a pulsed slit nozzle (300 μm × 4 cm), running at a 19 Hz repetition rate and 1 ms pulse duration. The radical species is formed via electron associative detachment of the neutral precursor in a 50 kHz modulated high voltage square wave (420 V, 200 mA) at the upper stream of the orifice. In initial trials, efficiency of propargyl radical generation has been tested for a variety of precursors such as propyne (H₃CCCH), propargyl chloride (ClH₂CCCH), and 1,3 butadiene (C₄H₆), which all provided nearly equivalent propargyl absorption signals. The backing pressure in the stagnation region is maintained at 230 Torr to optimize discharge stability, which results in 10¹²–10¹³ radical/cm³ concentrations in the laser probe region ∼1 cm downstream of slit. With both lock-in and time gated detection schemes operating simultaneously (as shown in Fig. 1), the absorption sensitivity is about ∼2.7 × 10⁻⁵ in a 10 kHz bandwidth, which is close to the quantum shot noise limit (1.88 pA/√Hz, or 1.7 × 10⁻⁵ in a 10 kHz bandwidth). These absorbances translate into signal to noise ratios (S/N) of ≈100:1 for the stronger sub-Doppler resolution lines in the absorption spectrum. Peak frequencies are determined from multiple scans of the same rovibrational line, and the standard deviation of the reported frequencies is estimated to be about ∼7 MHz via fringe interpolation of the optically stabilized marker cavity (free spectral range, FSR ∼ 220 MHz). To provide absolute frequency markers and spectral calibration, isolated sub-Doppler rovibational transitions in the antisymmetric C–H stretch (v₃) band of acetylene⁴⁴ at R(2) (3301.848 040 cm⁻¹), R(3) (304.166 740 cm⁻¹), and R(4) (3306.476 227 cm⁻¹) present in the jet cooled expansion are used.

The geometry of propargyl radical is shown in Fig. 1, with the principal axis definition based on the I^r representation and the c-axis orthogonal to molecular plane. Also shown in the Fig. 1 is the electron density distribution of the unpaired electron, based on calculations at the B3LYP/6-311+ + g(3df,3pd) level, which clearly indicates substantial unpaired electron delocalization between the methylenic and acetylenic radical C centers.⁴⁵ Rovibrational transitions of propargyl radical in the fundamental C–H stretching mode have been reported by Morter et al.³¹ under room temperature flash photolysis conditions in a flow cell and later in a pinhole supersonic expansion by Yuan et al.³³ However, the spectra under these conditions were substantially congested and dominated by high rotational levels due to inefficient internal cooling in the pinhole nozzle discharge source. Furthermore, considerable Doppler broadening in both the flash photolysis cell and pinhole expansion geometries limited spectral resolution of the fine/hyperfine structure on each individual rovibrational line. An intentionally low resolution overview of the high resolution slit jet direct absorption spectra of propargyl radical in this work is presented in Fig. 2. Extensive P and R branch rotational progressions for an a-type transition (ΔK_a = even and ΔK_c = odd) are clearly evident, as identified for the K_a = 0←0 sub-band at the top by end-over-end tumbling (N) and body fixed asymmetric top projection quantum numbers⁴⁶ (i.e., N_KaKc). In a more expanded spectral presentation (see Fig. 3), these P/R branch series of lines clearly break into a strong K_a = 0←0 sub-band flanked by K_a = 1←1 asymmetric split doublets and which reflects typical S/N levels of the propargyl radical spectrum.

At even higher resolution, however, these individual rovibrational lines begin to reveal spin-rotation fine structure for sufficiently low J, as well as partial broadening above the sub-Doppler limit due to nuclear hyperfine structure. This is nicely demonstrated in Fig. 4, which presents a systematic series of multiple high resolution scans in the R branch manifold at 2.5 MHz step size, with each scan registered with respect to the strong K_a = 0←0 line. Immediately evident is the asymmetry structure in the K_a = 1←1 subband, in which the K_a = 1 energy level splittings increase quadratically in N(N + 1) and thus result in spectral asymmetry doublet spacings increasing linearly with respect to the end-over-end angular momentum quantum number N. Second, these K_a = 1←1 transitions reveal clear spectral splittings due to spin-rotation interactions, which are quite noticeable at low N but merge quickly into a single broadened line as a function of rotational lower state. Indeed, such behavior explains why such spin-rotation dynamical information had proven challenging to obtain from previous IR efforts by Morter et al., taken under Doppler limited and much warmer rotational conditions.³¹ Finally, each transition line in Figs. 4(b) and 4(c) exhibits appreciable overlap between the K_a = 0←0 and 1←1 manifolds, which therefore requires fitting to the complete line shape profiles in the least squares analysis.

From Fig. 4, these rotational transitions are clearly dominated by progressions in the K_a = 0←0 manifold, with approximately 3-fold lower signals on the K_a = 1←1. Due to the indistinguishable methylenic hydrogens, the total wavefunction must be antisymmetric upon C₂ rotation around the a-axis,⁴⁷ which, in conjunction with the overall odd symmetry of the π radical electron, results in nuclear spin weights of 3:1 and 1:3 for the K_a = even (odd) and K_a = odd (even) sublevels, respectively. Note also that the linewidths for the K_a = 0←0 manifold are qualitatively larger than for the K_a = 1←1 subband. The splittings observed in the ^qR₁(N) component (guided by dashed lines in Fig. 4) are quite evident and this splitting merges quickly as the rotational state goes to high level. The observation of spin-rotation splitting effects comes from coupling of the unpaired electron spin (S) with the end-over end molecular rotation (N), which will be analyzed in detail below. Finally, the effect of further hyperfine coupling between electron spin (S) and nuclear spin (I) is also evident in the broadening substantially beyond the sub-Doppler resolution limit, which will be discussed in Sec. III C.

First of all, the N state dependent populations obtained from the spectral bands can be used to characterize the radical rotational temperature in the slit jet discharge expansion. Under the assumption of thermal equilibrium in the expansion environment, the intensity for a given individual transition can be expressed quantitatively by

Here, g_NS, g_N, and HL represent (i) nuclear spin statistical weights for the ortho (3, K_a = even) and para (1, K_a = odd) levels, (ii) 2N + 1 (M_N) degeneracy of a given rotational quantum state, and (iii) square of the transition dipole matrix element (Hönl-London factor), respectively, where E_rot and T_rot reflect the rotational energy and rotational temperature. The integrated signal strengths divided by rotational degeneracy and Hönl-London factor are plotted vs. the lower state rotational energy, which permits a relatively straightforward Boltzmann analysis for populations in the K_a = 0 and 1 manifolds presented in Fig. 5. The discharge rotational temperature is estimated to be T_rot ≈ 13.5(4) K, with the data constrained to match the two Boltzmann slopes for both K_a = 0 and 1. It is worth noting that the logarithmic difference in intercepts between these two plots should yield the total population ratio in the K_a = 1 and K_a = 0 manifolds, which can be rigorously tested against nuclear spin predictions. More quantitatively, these differential intercepts along y-axis correspond to a population ratio of 3.6(2):1 for K_a = 0 and 1 levels, which is in reasonable agreement with the 3:1 ortho/para values theoretically predicted for propargyl radical.⁴⁷ 

In order to analyze the inhomogeneous line profiles of each rotational line, it is necessary to consider the coupling between rotational angular momentum (N), electron spin (S), and nuclear spin (I₁, I₂). To take these additional spin angular momenta into account, we construct an effective Hamiltonian

In this expression, H_r represents the Watson asymmetric top rotational Hamiltonian (A-reduction), which captures the rigid rotational and low order centrifugal distortion terms⁴⁸ 

The parameters included in the least squares fits are three rotational constants (A, B, and C) along the principle axes plus five centrifugal distortion parameters (Δ_N, Δ_NK, Δ_K, δ_N, δ_K) up to the fourth order in the rotational angular momentum operator. The second term represents fine structure contributions arise from the coupling of the unpaired electron with the molecular rotation. For a molecule with orthorhombic symmetry, the spin-rotation Hamiltonian can be simply expressed as^49–51 

where ε_aa, ε_bb, and ε_cc represent the diagonal spin-rotation constants along the three principle axes. The final term in our effective Hamiltonian arises from hyperfine interactions, which for propargyl radical is dominated by (i) Fermi contact and (ii) electron spin-nuclear spin dipole-dipole interactions.^50,52

The two equivalent hydrogens at the methylenic position couple with each other to yield a resultant nuclear spin I_CH2 = I₁ = 0 and 1, while the lone hydrogen at the acetylenic position has nuclear spin $I CH = I 2 = 1 2$⁠. Due to Bose-Einstein statistics for integral nuclear spin, rotational levels with K_a = even (odd) will couple to I₁ = 1 ortho (0 para) levels, respectively. The most relevant parameters are the two isotropic Fermi contact constants, a_{F,acetylenic-H} and a_{F,methylenic-H}, which are sensitive to unpaired electron spin on the adjacent carbon atom, with smaller dipole–dipole terms from second rank tensors of the magnetic dipolar interaction. Though resolution of such contributions is ultimately limited by hyperfine spectral congestion even for low N, the spectra indeed show unambiguous evidence for hyperfine broadening well outside the instrumental sub-Doppler limit and therefore must be included.

In order to incorporate rotational, fine, and hyperfine terms into a least squares routine and thereby accurately fit the observed transition line profiles, we consider the coupling schemes J = N + S, F₁ = J + I₁, F = F₁ + I₂ and calculate Hamiltonian matrix elements in a Hund’s case $( b ) β J N K S , J I 1 F 1 , F 1 I 2 F$ basis.^50,53 This permits us to solve numerically for all relevant eigenvalues, eigenvectors, and dipole transition matrix elements corresponding to a given upper/lower total angular momentum F, F′ (with M_F = M_F′ = 0), which we can then convolve over an instrumental sub-Doppler linewidth to compare with experiment. By appropriate choice of S, I₁, and I₂ values, this also permits us to systematically predict spectral behavior associated with sequentially “turning on” fine and hyperfine structures for transitions out of both ortho (K_a = 0) and para (K_a = 1) manifolds. For example, inclusion of electron spin (⁠$S= 1 2$⁠, I₁ = I₂ = 0) in both K_a = 0 and 1 manifolds yields two spin-rotation sublevels $N+ 1 2$ and $N− 1 2$⁠, with explicit predictions for 3₀₃ and 3₁₃ multiplets shown in Figs. 6(a) and 6(b), respectively. Since fine structure in propargyl radical is dominated by A-axis rotation (ε_aa), the spin-rotation splittings are much smaller for K_a = 0 (≈20 MHz for 3₀₃) than for K_a = 1 (≈170 MHz for 3₁₃). Furthermore, Pauli principle symmetry requires nuclear spin for methylenic H atoms in the para K_a = 1 levels to couple and form I₁ = 0. As a result, all hyperfine contributions due to the methylenic spins vanish (Fig. 6(b)), thus reflecting only the terminal acetylene group and yielding overall narrower sub-Doppler line shapes. Conversely, the ortho K_a = 0 levels are necessarily coupled with a methylenic nuclear spin I₁ = 1 and thus yield much more significant contributions from hyperfine interactions (see Fig. 6(a)). As one experimental consequence, transitions out of the K_a = 0 manifold therefore prove more sensitive to methylenic Fermi contact hyperfine interactions (e.g., a_{F,methylenic-H}), while transitions out of the K_a = 1 manifold are sensitive primarily to nuclear spin hyperfine interactions on the acetylenic CH stretch proton (e.g., a_{F,acetylenic-H}).

Finally, these spectral predictions must be convolved over sub-Doppler instrumental broadening (Δν_Dopp ≈ 60 MHz) in the slit jet configuration to compare with the experimental absorption spectrum. Though such sub-Doppler capabilities permit full spectral resolution of the spin-rotation fine structure at low N, this residual instrumental broadening is in fact comparable with K_a-dependent hyperfine contributions due to methylenic and acetylenic H atoms at all N values, which requires inclusion of both fine and hyperfine effects in least squares fits to the observed line profiles. The combined effects of such spin-rotation and hyperfine interactions for the 1₁₀←2₁₁, 1₁₁←2₁₂, 1₀₁←2₀₂ rotational multiplets are illustrated in Fig. 7. In the absence of electron spin (S = 0), the asymmetric top transitions appear as asymmetry split rovibrational lines (bottom panel, Fig. 7(a)). Inclusion of spin-rotation interaction (⁠$S= 1 2$⁠) splits each rovibrational transition into three components (middle panel, Fig. 7(b)), with relative intensities that follow the simple ΔJ = ΔN propensity rule. Inclusion of both methylenic (I₁ = 0 and 1) and acetylenic (⁠$I 2 = 1 2$⁠) hyperfine interactions yields a rich manifold of transitions spread over a spectral window comparable to the sub-Doppler linewidths in the slit jet expansion (see upper panel, Fig. 7(c)). Finally, when convolved over the Δν_Dopp ≈ 60 MHz residual sub-Doppler broadening in the slit jet, the sample line profiles prove to be in excellent agreement with experimental observation, as demonstrated in the red simulation (top panel, Fig. 7(c)). The sample data in Fig. 7 make it clear why the hyperfine structure, even though unresolved, must be included in the Hamiltonian and analysis of the high resolution line shapes.

In order to extract and isolate information on the asymmetric top rotational structure, we fit the high resolution propargyl absorption line profiles as follows.⁵³ We first focus on the fine/hyperfine degrees of freedom and thereby obtain fine structure (ε_aa, ε_bb, ε_cc) and partial hyperfine structure (e.g., a_{F,acetylenic-H}, a_{F,methylenic-H}) information from simultaneous least squares fits to the complete set of line profiles. By explicit inclusion of these fine/hyperfine terms, the least squares fits therefore permit us to extract fine and hyperfine structure free (i.e., S = I₁ = I₂ = 0) center frequencies for each rovibrational line, which can then be fit separately to a Watson rotational Hamiltonian to determine the vibrational band origin and rotational/centrifugal distortion constants.⁵³ These rovibrational transitions for the acetylenic CH stretch follow the a-type selection rules (ΔK_a = even and ΔK_c = odd). Under supersonic expansion conditions, only the two lowest nuclear spin states (K_a = 0 and K_a = 1) are significantly populated, which introduces strong parameter correlation between ν₀, A″, and Δ_K. To break this parameter correlation, we therefore also include four Q-branch transitions (1₁₀←1₁₁, 2₁₁←2₁₂, 1₁₁←1₁₀, and 2₁₂←2₁₁) observed in the band origin region (see arrow in Fig. 1), though with 10 × reduced weight. Furthermore, ab initio calculations and microwave studies²⁵ indicate Δ_N and Δ_NK to be the only measurable centrifugal distortion parameters and thus allowed to float in the fits, with the much smaller Δ_K, δ_N, and δ_K centrifugal constants fixed to microwave values for the ground state. In all of these fits, the ground state parameters are constrained to the high precision values obtained from previous microwave studies.²⁵ The standard deviation of this rovibrational asymmetric top fit is σ ≈ 5 MHz, i.e., comparable to or less than experimental precision (≈7 MHz) of the frequency measurements. This confirms the absence of any local perturbations in the K_a = 0 and 1 manifolds for the N < 10 rotational levels populated under supersonic jet expansion conditions.

The molecular parameters obtained from such a fitting procedure are summarized in Table I, with the observed/calculated predictions for each rovibrational frequency listed in Table II. Table I also summarizes results from previous spectroscopic studies of the ground and vibrationally excited states. The rovibrational fits yield A′ = 9.596 63(8), B′ = 0.316 911(4), C′ = 0.306 411(4) cm⁻¹, and ν₀ = 3322.294 60(7) cm⁻¹, respectively, for the vibrationally excited upper state. These values are in very close agreement with the results reported by Curl and coworkers,^31,54 especially in light of the sub-Doppler resolution, colder rotational distributions, and reduced spectral congestion obtained in the current slit jet configuration. In particular, inclusion of the weak Q branch lines in the fitting process breaks parameter correlation and considerably improves the quality of the ν₀, A′, and Δ_K predictions. The differences in Δ_N values are also significant, limited by the lack of high rotational level under jet cooled conditions.

Partial geometric and dynamical information on propargyl radical can be inferred from the fitted rotational constants. The small but quite finite decrease in B and C rotational constants (ΔB/B ≈ − 0.24% and ΔC/C ≈ − 0.22%) with ν₁ vibrational excitation reports on geometric averaging over the anharmonic CH stretch, which on average increases these respective moments of inertia due to vibrational anharmonicity. In this context, therefore, it is particularly interesting to note a similar fractional decrease in the A rotational constant (ΔA/A ≈ − 0.12%). Based on the above arguments, one would expect only very small change in the A constant for pure collinear displacement of the acetylenic CH bond along the A axis. The presence of a sizable decrease in A instead confirms ab initio predictions of a significant symmetric CH₂ bond displacement component activity at the methylenic CH₂ radical center for what is nominally a CCH stretch.^55–57 Also of interest is the vibrationally averaged mass displacement away from the propargyl symmetry plane, which can be probed by the inertial defect (Δ ≡ I_c − I_a − I_b). This is zero for any rigid planar structure, with additional contributions from centrifugal distortion and finite electron mass considered by Oka and Morino⁵⁸ and thought to be minor. The inertial defect for propargyl radical in the CH stretch vibrationally excited state is Δ = + 0.066 20(3) amu A², i.e., essentially the same (Δ = + 0.067 797(75) amu A²) as obtained from ground state microwave data.²⁵ Such values of the inertial defect are therefore consistent with a planar equilibrium structure, with the small but finite positive deviations arising from zero point motion in out-of-plane vibrational coordinates. Indeed, ab initio MOLPRO calculations of propargyl radical at the coupled-cluster single doubles (perturbative triples) (CCSD(T))/avtz-f12 level identify two large amplitude B₁ symmetry modes that are likely candidates for such an effect, specifically out-of-plane CH bend (488 cm⁻¹) and CCC bend (382 cm⁻¹) vibrations, respectively.⁵⁵ 

Additional dynamical information for this radical arises from considering the resonance structure between the allenyl (⁠$H 2 C=C= C ̇ H$⁠) and propargyl (⁠$H 2 C ̇ —C≡CH$⁠) forms. As pointed out by Tanaka et al.,²⁵ if the allenyl form was the predominant structure, then the CCH moiety would acquire significant vinylic character, which, by analogy with vinyl radical, could imply a finite in-plane equilibrium bend angle with a finite in-plane barrier between the two equivalent minima. Indeed, the in-plane bending tunneling dynamics of vinyl radical has been studied extensively in the fundamental CH₂ wagging mode by Kanamori et al.⁵⁹ as well as the CH₂ symmetric stretch mode by Dong et al. and which reveals appreciable tunneling splittings (0.543 cm⁻¹) thermally populated and easily detected under low temperature, high resolution conditions.⁶⁰ The lack of such resolvable tunneling splittings in the sub-Doppler jet cooled propargyl radical spectrum at least rules out the possibility of a low barrier double minimum structure, which is again consistent with ab initio CCSD(T)/avtz-f12 predictions of a C_2v equilibrium geometry and a normal, acetylene-like frequency (610 cm⁻¹) for the in-plane C ≡ CH bend.^55–57 

As described in Sec. III, velocity collimation and sub-Doppler resolution in the slit jet expansion spectrometer prove sufficient to extract and analyze spin rotation structure even in the infrared region of the spectrum. This enables fine structure constants for many jet cooled hydrocarbon radicals to be determined for the first time in vibrationally excited states, with the results for ν₁ CH stretch excited propargyl radical summarized in Table I.³³ Specifically, the three non-vanishing spin-rotation constants are determined from least squares fits of the sub-Doppler line shapes to be ε_aa = − 518.1(1.8), ε_bb = − 13.0(3), and ε_cc = − 1.8(3) MHz, respectively. By way of comparison, spin rotation parameters for propargyl radical in the ground vibrational state have also been obtained via microwave spectroscopy by Tanaka et al.,²⁵ with corresponding results: ε_aa = − 529.386(60), ε_bb = − 11.524(30), and ε_cc = − 0.520(30) MHz. Consistency between microwave (ground state) and infrared (excited state) values is excellent, which both confirms the quality of the infrared line shape analysis as well as highlights the small but finite influence of vibration on the radical electron spin distributions.

The first-order contribution to spin rotation fine structure is often described by the semiclassical interaction between electron spin (S) and the body frame magnetic fields (B) generated by molecular rotation.⁵⁰ However, effects originating from second order mixing of excited electronic states often are found to dominate.^50,61,62 From second order perturbation theory, we can express the three diagonal components of the spin rotation tensor in a state $l 0$ as

where B_q is the rotational constant along the principle axis q, and $1$ is the set of intermediate states that contribute to spin rotation coupling by matrix elements of the electronic orbital angular momentum (L_q) and one electron operators (η_q). Though rigorous evaluation of this expression is limited by lack of excited state energies, simple symmetry arguments allow one to make some useful predictions. In order for a term to be non-zero for a given intermediate state $1$⁠, the integrands of both matrix elements must transform as the totally symmetric representation (a₁) of the C_2v group. Since the $l 0$ ground state electronic symmetry for propargyl radical is b₁ and the diagonal components of the spin rotation tensor require orbital angular momentum and one electron operator components with respect to the same principal axis, this implies that only electronic excited states with b₂, a₁, and a₂ symmetry contribute via Coriolis mixing to ε_aa, ε_bb, and ε_cc, respectively.⁶³ As no a₂ symmetry molecular orbital can be constructed from C and H atomic orbital basis sets for propargyl radical, this helps rationalize the nearly vanishing value for ε_cc observed experimentally.

The work presents results from infrared study of the acetylenic CH stretch vibration (ν₁) for propargyl radical, based on formation under high density discharge conditions and cooling down to low rotational temperatures in a slit supersonic expansion. The combination of high radical density, supersonic jet cooling, and sub-Doppler resolution permits high S/N detection and improved rovibrational spectroscopic analysis for this important combustion radical. As a result of low K_a populations and sub-Doppler velocity collimation along the slit expansion axis, electron spin-rotation fine structure is fully resolved, which, in conjunction with previous microwave studies in the ground vibrational state, permits the corresponding fine structure interaction in the vibrationally excited state to be observed and analyzed for the first time. Additional hyperfine broadening in excess of the sub-Doppler experimental linewidths is observed due to proton Fermi contact contributions at the methylenic (CH₂) and acetylenic (CH) positions, which both require and permit considerably detailed modeling of the complete fine/hyperfine structure line shapes. Vibrationally induced changes in the rotational constants support a picture of a delocalized CH stretch that involves substantial motion of both acetylenic and methylenic H atoms. Spin-rotation interactions in both the lower and upper vibrational levels appear to be dominated by a-axis Coriolis coupling, with vanishing contributions to c-axis coupling correctly predicted by symmetry analysis of the molecular orbitals. Finally, hyperfine broadening of the line profiles is consistent with radical spin density extending over both methylenic and acetylenic C atoms, in excellent agreement with simple resonance structures as well as ab initio theoretical calculations.

This work was supported by grants from the Department of Energy (Grant No. DE-FG02-09ER16021), with initial funds for construction of the slit-jet laser spectrometer provided by the National Science Foundation (Grant Nos. CHE1266416 and PHYS1125844). Dr. Chih-Hsuan Chang would like to acknowledge Dr. Melanie A. Roberts for programming assistance in the spectroscopic analysis codes.