The acetylenic CH stretch mode (ν_{1}) of propargyl (H_{2}CCCH) radical has been studied at sub-Doppler resolution (∼60 MHz) via infrared laser absorption spectroscopy in a supersonic slit-jet discharge expansion, where low rotational temperatures (T_{rot} = 13.5(4) K) and lack of spectral congestion permit improved determination of band origin and rotational constants for the excited state. For the lowest J states primarily populated in the slit jet cooled expansion, fine structure due to the unpaired electron spin is resolved completely, which permits accurate analysis of electron spin-rotation interactions in the vibrationally excited states (ε_{aa} = − 518.1(1.8), ε_{bb} = − 13.0(3), ε_{cc} = − 1.8(3) MHz). In addition, hyperfine broadening in substantial excess of the sub-Doppler experimental linewidths is observed due to nuclear spin–electron spin contributions at the methylenic (—CH_{2}) and acetylenic (—CH) positions, which permits detailed modeling of the fine/hyperfine structure line contours. The results are consistent with a delocalized 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.

## I. INTRODUCTION

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 (H_{2}CCCH) 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 C_{3} open shell species such as H_{2}CCCH 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, H_{2}CCCH 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 \u0307 \u2014C\u2261$ CH) or the nominally allenyl ($ H 2 C=C= C \u0307 H$) form, with the unpaired electron mainly localized at the methylenic $ ( \u2014 C \u0307 H 2 ) $ or acetylenic ($= C \u0307 H$) carbon atom, respectively. Indeed, microwave spectroscopic results have indicated that a more balanced resonance structure [$ H 2 C \u0307 \u2014C\u2261CH\u2194 H 2 C=C= C \u0307 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 Thistlethwaite^{26} 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 Krusic^{27} and Kasai^{28} 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 (*v*_{6}). Recent calculations by Botschwina *et al.*^{30} ascribed this band to the methylenic CH_{2}-*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 (CH_{2}CCD) 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 H_{2}CCCH and H_{2}CCCD species have been determined to be 3322.2929(20) and 2557.337 cm^{−1}, respectively.^{31–33} Strong rotational perturbations in H_{2}CCCH 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*= 0 or 1 manifold, which would correspond to the two uncoolable (

_{a}*ortho*and

*para*) nuclear spin states and thus the only

*K*levels populated significantly under slit supersonic expansion conditions.

_{a}In the lower frequency CH bending region, the fundamental ν_{6} 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 CH_{2}-wagging vibration and, furthermore, successfully analyzed interactions between *v*_{6} (CH_{2}-wagging) and *v*_{10} (CH_{2}-rocking) via *a*-type Coriolis coupling. At even lower frequencies, Tanaka *et al.*^{25} studied fine and hyperfine structures in the ground ^{2}*B*_{1} 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 (CH

_{2}) 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.

## II. EXPERIMENTAL

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 LiNbO_{3} (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 *μ*W. 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 *μ*m × 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 (H_{3}CCCH), propargyl chloride (ClH_{2}CCCH), and 1,3 butadiene (C_{4}H_{6}), 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 10^{12}–10^{13} radical/cm^{3} 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 (*v*_{3}) band of acetylene^{44} 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.

## III. RESULTS AND ANALYSIS

### A. Asymmetric top contributions

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 numbers^{46} (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*= 1←1 subband, in which the

_{a}*K*= 1 energy level splittings increase

_{a}*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*= 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

_{a}*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*= 0←0 and 1←1 manifolds, which therefore requires fitting to the complete line shape profiles in the least squares analysis.

_{a}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*= 1←1. Due to the indistinguishable methylenic hydrogens, the total wavefunction must be antisymmetric upon C

_{a}_{2}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*= even (odd) and

_{a}*K*= odd (even) sublevels, respectively. Note also that the linewidths for the

_{a}*K*= 0←0 manifold are qualitatively larger than for the

_{a}*K*= 1←1 subband. The splittings observed in the

_{a}^{q}

*R*

_{1}(

*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.

### B. Boltzmann analysis

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*= odd) levels, (ii) 2N + 1 (M

_{a}_{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*= 0 and 1 manifolds presented in Fig. 5. The discharge rotational temperature is estimated to be T

_{a}_{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*= 0 and 1 levels, which is in reasonable agreement with the 3:1 ortho/para values theoretically predicted for propargyl radical.

_{a}^{47}

### C. Spin-rotation and hyperfine contributions

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 (**I _{1}**,

**I**). To take these additional spin angular momenta into account, we construct an effective Hamiltonian

_{2} In this expression, H_{r} represents the Watson asymmetric top rotational Hamiltonian (A-reduction), which captures the rigid rotational and low order centrifugal distortion terms^{48}

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} = I_{1} = 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 I

_{1}= 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**, **F _{1}** =

**J**+

**I**,

_{1}**F**=

**F**+

_{1}**I**and calculate Hamiltonian matrix elements in a Hund’s case $ ( b ) \beta J N K S , J I 1 F 1 , F 1 I 2 F $ basis.

_{2}^{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, I

_{1}, and I

_{2}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 $, I

_{1}= I

_{2}= 0) in both

*K*= 0 and 1 manifolds yields two spin-rotation sublevels $N+ 1 2 $ and $N\u2212 1 2 $, with explicit predictions for 3

_{a}_{03}and 3

_{13}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 3

_{03}) than for K

_{a}= 1 (≈170 MHz for 3

_{13}). Furthermore, Pauli principle symmetry requires nuclear spin for methylenic H atoms in the

*para*K

_{a}= 1 levels to couple and form I

_{1}= 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*= 0 levels are necessarily coupled with a methylenic nuclear spin I

_{a}_{1}= 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*= 1 manifold are sensitive primarily to nuclear spin hyperfine interactions on the

_{a}*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 1_{10}←2_{11}, 1_{11}←2_{12}, 1_{01}←2_{02} 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 $) splits each rovibrational transition into three components (middle panel, Fig. 7(b)), with relative intensities that follow the simple Δ*J* = Δ*N* propensity rule. Inclusion of both methylenic (I_{1} = 0 and 1) and acetylenic ($ 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.

## IV. DISCUSSION

### A. Asymmetric top analysis

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 = I_{1} = I_{2} = 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 (Δ*K _{a}* = even and Δ

*K*= odd). Under supersonic expansion conditions, only the two lowest nuclear spin states (

_{c}*K*= 0 and

_{a}*K*= 1) are significantly populated, which introduces strong parameter correlation between ν

_{a}_{0},

*A*″, and Δ

_{K}. To break this parameter correlation, we therefore also include four

*Q*-branch transitions (1

_{10}←1

_{11}, 2

_{11}←2

_{12}, 1

_{11}←1

_{10}, and 2

_{12}←2

_{11}) observed in the band origin region (see arrow in Fig. 1), though with 10 × reduced weight. Furthermore,

*ab initio*calculations and microwave studies

^{25}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*, and

_{N}*δ*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.

_{K}^{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 ν_{0} = 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 ν_{0}, *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.

$ J K a \u2032 K c \u2032 \u2032 $–$ J K a \u2033 K c \u2033 \u2033 $ . | Observation (residual ×10^{4})
. | $ J K a \u2032 K c \u2032 \u2032 \u2212 J K a \u2033 K c \u2033 \u2033 $ . | Observation (residual ×10^{4})
. | ||
---|---|---|---|---|---|

R-branch | P-branch | ||||

1_{01} − 0_{00} | 3322.9180 | (0.8) | 0_{00} − 1_{01} | 3321.6698 | (−0.1) |

2_{12} − 1_{11} | 3323.5183 | (1.5) | 1_{11} − 2_{12} | 3321.0431 | (0.2) |

2_{02} − 1_{01} | 3323.5397 | (−0.7) | 1_{01} − 2_{02} | 3321.0436 | (0.2) |

2_{11} − 1_{10} | 3323.5393 | (2.6) | 1_{10} − 2_{11} | 3321.0219 | (−0.2) |

3_{13} − 2_{12} | 3324.1334 | (0.7) | 2_{12} − 3_{13} | 3320.4207 | (−0.4) |

3_{03} − 2_{02} | 3324.1602 | (0.6) | 2_{02} − 3_{03} | 3320.4159 | (−0.1) |

3_{12} − 2_{11} | 3324.1645 | (−0.6) | 2_{11} − 3_{12} | 3320.3890 | (1.0) |

4_{14} − 3_{13} | 3324.7472 | (1.4) | 3_{13} − 4_{14} | 3319.7964 | (−4.9) |

4_{04} − 3_{03} | 3324.7789 | (−1.1) | 3_{03} − 4_{04} | 3319.7867 | (−1.2) |

4_{13} − 3_{12} | 3324.7888 | (2.3) | 3_{12} − 4_{13} | 3319.7540 | (−4.0) |

5_{15} − 4_{14} | 3325.3594 | (0.7) | 4_{14} − 5_{15} | 3319.1717 | (−1.2) |

5_{05} − 4_{04} | 3325.3964 | (0.3) | 4_{04} − 5_{05} | 3319.1563 | (0.1) |

5_{14} − 4_{13} | 3325.4111 | (0.5) | 4_{13} − 5_{14} | 3319.1184 | (−0.2) |

6_{16} − 5_{15} | 3325.9702 | (0.5) | 5_{15} − 6_{16} | 3318.5454 | (1.5) |

6_{06} − 5_{05} | 3326.0123 | (0.9) | 5_{05} − 6_{06} | 3318.5245 | (1.1) |

6_{15} − 5_{14} | 3326.0321 | (0.9) | 5_{14} − 6_{15} | 3318.4811 | (1.3) |

7_{17} − 6_{16} | 3326.5797 | (1.9) | 6_{16} − 7_{17} | 3317.9172 | (−0.7) |

7_{07} − 6_{06} | 3326.6266 | (0.8) | 6_{06} − 7_{07} | 3317.8910 | (−0.9) |

7_{16} − 6_{15} | 3326.6516 | (1.6) | 6_{15} − 7_{16} | 3317.8418 | (−6.4) |

8_{18} − 7_{17} | 3327.1876 | (2.1) | 7_{17} − 8_{18} | 3317.2878 | (−0.9) |

8_{08} − 7_{07} | 3327.2393 | (0.1) | 7_{07} − 8_{08} | 3317.2565 | (0.9) |

8_{17} − 7_{16} | 3327.2694 | (0.7) | 7_{16} − 8_{17} | 3317.2017 | (0.5) |

8_{18} − 9_{19} | 3316.5598 | (−3.1) | |||

8_{08} − 9_{09} | 3316.6202 | (−1.5) | |||

8_{17} − 9_{18} | 3316.5598 | (0.0) | |||

Q-branch^{a} | |||||

1_{10} − 1_{11} | 3322.2929 | (3.7) | |||

2_{11} − 2_{12} | 3322.3107 | (0.8) | |||

1_{11} − 1_{10} | 3322.2717 | (1.9) | |||

2_{12} − 2_{11} | 3322.2478 | (2.5) |

$ J K a \u2032 K c \u2032 \u2032 $–$ J K a \u2033 K c \u2033 \u2033 $ . | Observation (residual ×10^{4})
. | $ J K a \u2032 K c \u2032 \u2032 \u2212 J K a \u2033 K c \u2033 \u2033 $ . | Observation (residual ×10^{4})
. | ||
---|---|---|---|---|---|

R-branch | P-branch | ||||

1_{01} − 0_{00} | 3322.9180 | (0.8) | 0_{00} − 1_{01} | 3321.6698 | (−0.1) |

2_{12} − 1_{11} | 3323.5183 | (1.5) | 1_{11} − 2_{12} | 3321.0431 | (0.2) |

2_{02} − 1_{01} | 3323.5397 | (−0.7) | 1_{01} − 2_{02} | 3321.0436 | (0.2) |

2_{11} − 1_{10} | 3323.5393 | (2.6) | 1_{10} − 2_{11} | 3321.0219 | (−0.2) |

3_{13} − 2_{12} | 3324.1334 | (0.7) | 2_{12} − 3_{13} | 3320.4207 | (−0.4) |

3_{03} − 2_{02} | 3324.1602 | (0.6) | 2_{02} − 3_{03} | 3320.4159 | (−0.1) |

3_{12} − 2_{11} | 3324.1645 | (−0.6) | 2_{11} − 3_{12} | 3320.3890 | (1.0) |

4_{14} − 3_{13} | 3324.7472 | (1.4) | 3_{13} − 4_{14} | 3319.7964 | (−4.9) |

4_{04} − 3_{03} | 3324.7789 | (−1.1) | 3_{03} − 4_{04} | 3319.7867 | (−1.2) |

4_{13} − 3_{12} | 3324.7888 | (2.3) | 3_{12} − 4_{13} | 3319.7540 | (−4.0) |

5_{15} − 4_{14} | 3325.3594 | (0.7) | 4_{14} − 5_{15} | 3319.1717 | (−1.2) |

5_{05} − 4_{04} | 3325.3964 | (0.3) | 4_{04} − 5_{05} | 3319.1563 | (0.1) |

5_{14} − 4_{13} | 3325.4111 | (0.5) | 4_{13} − 5_{14} | 3319.1184 | (−0.2) |

6_{16} − 5_{15} | 3325.9702 | (0.5) | 5_{15} − 6_{16} | 3318.5454 | (1.5) |

6_{06} − 5_{05} | 3326.0123 | (0.9) | 5_{05} − 6_{06} | 3318.5245 | (1.1) |

6_{15} − 5_{14} | 3326.0321 | (0.9) | 5_{14} − 6_{15} | 3318.4811 | (1.3) |

7_{17} − 6_{16} | 3326.5797 | (1.9) | 6_{16} − 7_{17} | 3317.9172 | (−0.7) |

7_{07} − 6_{06} | 3326.6266 | (0.8) | 6_{06} − 7_{07} | 3317.8910 | (−0.9) |

7_{16} − 6_{15} | 3326.6516 | (1.6) | 6_{15} − 7_{16} | 3317.8418 | (−6.4) |

8_{18} − 7_{17} | 3327.1876 | (2.1) | 7_{17} − 8_{18} | 3317.2878 | (−0.9) |

8_{08} − 7_{07} | 3327.2393 | (0.1) | 7_{07} − 8_{08} | 3317.2565 | (0.9) |

8_{17} − 7_{16} | 3327.2694 | (0.7) | 7_{16} − 8_{17} | 3317.2017 | (0.5) |

8_{18} − 9_{19} | 3316.5598 | (−3.1) | |||

8_{08} − 9_{09} | 3316.6202 | (−1.5) | |||

8_{17} − 9_{18} | 3316.5598 | (0.0) | |||

Q-branch^{a} | |||||

1_{10} − 1_{11} | 3322.2929 | (3.7) | |||

2_{11} − 2_{12} | 3322.3107 | (0.8) | |||

1_{11} − 1_{10} | 3322.2717 | (1.9) | |||

2_{12} − 2_{11} | 3322.2478 | (2.5) |

^{a}

*Q*-branch transitions are included in the least squares rotational fits with reduced weights (0.1) to break parameter correlation.

. | . | Ground state . | ν_{6}
. | ν_{1}
. | ||
---|---|---|---|---|---|---|

. | . | Tanaka et al.^{25}
. | Tanaka et al.^{35}
. | Morter et al.^{31}
. | Yuna et al.^{33}
. | This work^{b}
. |

A | 9.608 47(36)^{c} | 9.159 09(54) | … | 9.602 58(21) | 9.596 63(8)^{d} | |

B | 0.317 675 6(1) | 0.317 085 5(20) | 0.316 80(7) | 0.316 889(13) | 0.316 911(4) | |

C | 0.307 108 476(2) | 0.307 251 3(55) | 0.306 34(7) | 0.306 393(13) | 0.306 411(4) | |

Δ_{K} | ×10^{4} | 7.545 2 | −0.034 | 5.27(5) | 7.545 2^{e} | |

Δ_{NK} | ×10^{5} | 1.251 9(93) | 1.097(51) | 1.26(3) | 1.48(23) | |

Δ_{N} | ×10^{7} | 1.14(21) | 0.537(152) | 1.21(56) | ||

δ_{K} | ×10^{6} | 5.253 6 | 5.253 6^{e} | |||

δ_{N} | ×10^{9} | 3.435 7 | 3.435 7^{e} | |||

ε_{aa} | −529.386 | −518.1 | ||||

ε_{bb} | −11.524 | −13.0 | ||||

ε_{cc} | −0.52 | −1.8 | ||||

a _{F} | −36.323 | −36.323(24)^{e} | ||||

T _{aa} | 17.400(24) | 17.400(24)^{e} | ||||

T _{bb} | −17.220 | −17.220(37)^{e} | ||||

a _{F} | −54.21 | −54.21(11)^{e} | ||||

T _{aa} | −14.121 | −14.121(19)^{e} | ||||

T _{bb} | 12.88 | 12.88^{e} | ||||

ν_{0} | 687.176 03(62) | 3 322.287(2) | 3 322.292 9(20) | 3 322.294 60(7) | ||

σ^{f} | 0.002 8 | 0.000 17 |

. | . | Ground state . | ν_{6}
. | ν_{1}
. | ||
---|---|---|---|---|---|---|

. | . | Tanaka et al.^{25}
. | Tanaka et al.^{35}
. | Morter et al.^{31}
. | Yuna et al.^{33}
. | This work^{b}
. |

A | 9.608 47(36)^{c} | 9.159 09(54) | … | 9.602 58(21) | 9.596 63(8)^{d} | |

B | 0.317 675 6(1) | 0.317 085 5(20) | 0.316 80(7) | 0.316 889(13) | 0.316 911(4) | |

C | 0.307 108 476(2) | 0.307 251 3(55) | 0.306 34(7) | 0.306 393(13) | 0.306 411(4) | |

Δ_{K} | ×10^{4} | 7.545 2 | −0.034 | 5.27(5) | 7.545 2^{e} | |

Δ_{NK} | ×10^{5} | 1.251 9(93) | 1.097(51) | 1.26(3) | 1.48(23) | |

Δ_{N} | ×10^{7} | 1.14(21) | 0.537(152) | 1.21(56) | ||

δ_{K} | ×10^{6} | 5.253 6 | 5.253 6^{e} | |||

δ_{N} | ×10^{9} | 3.435 7 | 3.435 7^{e} | |||

ε_{aa} | −529.386 | −518.1 | ||||

ε_{bb} | −11.524 | −13.0 | ||||

ε_{cc} | −0.52 | −1.8 | ||||

a _{F} | −36.323 | −36.323(24)^{e} | ||||

T _{aa} | 17.400(24) | 17.400(24)^{e} | ||||

T _{bb} | −17.220 | −17.220(37)^{e} | ||||

a _{F} | −54.21 | −54.21(11)^{e} | ||||

T _{aa} | −14.121 | −14.121(19)^{e} | ||||

T _{bb} | 12.88 | 12.88^{e} | ||||

ν_{0} | 687.176 03(62) | 3 322.287(2) | 3 322.292 9(20) | 3 322.294 60(7) | ||

σ^{f} | 0.002 8 | 0.000 17 |

^{a}

Rovibrational and centrifugal distortion constants in cm^{−1}, and fine/hyperfine constants in MHz.

^{b}

The Watson-*A* reduced effective Hamiltonian based on the I^{r} representation.

^{c}

Held fixed at the ground state IR diode laser value of Tanaka *et al.*^{35}

^{d}

Parentheses represent one standard deviation.

^{e}

Upper states Δ_{K}, δ_{K}, δ_{N} and hyperfine parameters fixed at ground state values from microwave studies.^{25}

^{f}

Standard deviation for least squares fits to reported spin-rotation and hyperfine free line positions.

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 ν_{1} 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 CH_{2} bond displacement component activity at the methylenic CH_{2} 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 Morino^{58} 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 A^{2}, i.e., essentially the same (Δ = + 0.067 797(75) amu A^{2}) 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 B_{1} 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 \u0307 H$) and propargyl ($ H 2 C \u0307 \u2014C\u2261CH$) 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 CH_{2} wagging mode by Kanamori *et al.*^{59} as well as the CH_{2} 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}

### B. Electron spin-rotation interaction

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 ν_{1} 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*) and one electron operators (

_{q}*η*). 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 (

_{q}*a*

_{1}) of the

*C*

_{2v}group. Since the $ l 0 $ ground state electronic symmetry for propargyl radical is b

_{1}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

*b*

_{2},

*a*

_{1}, and

*a*

_{2}symmetry contribute via Coriolis mixing to ε

_{aa}, ε

_{bb}, and ε

_{cc}, respectively.

^{63}As no

*a*

_{2}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.

## V. SUMMARY

The work presents results from infrared study of the acetylenic CH stretch vibration (ν_{1}) 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 (CH_{2}) 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.

## Acknowledgments

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.

## REFERENCES

*ab initio*programs, 2009, see http://www.molpro.net.