INTRODUCTION

Resonance-stabilized radicals (RSRs) are profoundly important intermediates in combustion and pyrolysis. They are formed preferentially during thermal decomposition of hydrocarbons 1,2 and are slow to further decompose or react with oxygen, 3 allowing their accumulation in flames. Recombination reactions involving propargyl (C 3 H 3 ), [4][5][6] cyclopentadienyl (C 5 H 5 ), 7,8 and benzyl (C 7 H 7 ) [9][10][11] are considered the major pathways to benzene and naphthalene under combustion conditions. Similar chemistry is invoked in stellar outflows to explain the formation of polycyclic aromatic hydrocarbons, 12,13 the presumed carriers of infrared emission observed in diverse astrophysical environments. 14 Recent ground-breaking work by Johansson et al. has shown that extension of radical delocalization through covalent clustering reactions of RSRs is a key driver of the transition from molecular to particulate material during soot formation. 15 To unravel molecular growth and decomposition pathways in energetic environments, diagnostic gas-phase spectroscopic data on putative reactive intermediates is essential. The D 0 -D 1 electronic transitions of RSR chromophores generally appear in the optical band and often submit to interrogation by fluorescence and mass-resolved spectroscopies. In the past ∼15 years in particular, a slew of previously unknown RSRs of interest to combustion and astrochemistry have been characterized by these means, as reviewed recently. 16 Still, many more important radicals await spectroscopic observation. For a given molecular formula, a daunting variety of isomers are energetically accessible under combustion conditions. The C 7 H 7 surface, for example, harbors at least 10 resonancestabilized minima within 300 kJ/mol of the global minimum. 17,18 With increasing molecular mass, isomer-specific product identification by photoionization mass spectrometry, as in ref 15, can become intractable, highlighting a need for complementary optical assays.

To this end, we have set out to optically detect new RSRs under jet-cooled conditions by laser-induced fluorescence (LIF) and resonant two-color two-photon ionization (R2C2PI). Recently, in discharges of various precursors including toluene, we identified 3-ethynylcyclopentenyl, a C 7 H 7 RSR bearing the 1-vinylpropargyl chromophore. 23 Here, we focus on the less-explored C 9 H 9 surface. Figure 1 shows the low-lying phenyl-containing C 9 H 9 RSRs discussed in this work, with relative energies compiled from refs 19-22. The 1-indanyl radical was the first isomer to be observed under jet-cooled conditions, 19 followed shortly afterward by trans-1phenylallyl. 20,21 The former system is π-isoelectronic with benzyl, reflected in the small red shift of its D 0 -D 1 origin (near 472.6 nm) relative to benzyl (near 454.4 nm). The 1-phenylallyl and benzyl radicals have the same highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap at the Huckel level (β), but depression of the lowest excited state of 1-phenylallyl by configuration interaction shifts its D 0 -D 1 origin substantially, to 521 nm. The 2-phenylallyl radical probably absorbs modestly to the red of allyl (408 nm), but it has a lower resonance-stabilization energy, 20 and remains undiscovered.

No other C 9 H 9 RSR has been conclusively identified, but other C 9 H 9 band systems have been reported. In a discharge of 1,6-heptadiyne (C 7 H 8 ), Steglich et al. observed an unknown number of C 9 H 9 isomers in the region 630-550 nm by R2C2PI. 22 Intriguingly, several features were observed near diffuse interstellar band wavelengths (though near coincidences are not unlikely owing to the high spectral density of the DIBs). Because of their low ionization potentials (generally <8 eV), it would seem unlikely that neutral RSRs can survive in diffuse clouds (wherein 98% of C 60 , with an IP near 7.6 eV, is ionized 24 ); nevertheless, the authors suggested that neutral species derived from recombination of electrons with small cations may be of relevance to the DIB conundrum. An IP of 7.3 ± 0.1 eV was recorded for the carrier of an origin band near 629 nm. From this information and TD-B3LYP calculations, o-, p-, and m-vinylbenzyl radicals were suggested as the most plausible carriers.

The vinylbenzyl systems should be generously resonancestabilized and readily produced by cleavage of the weakest C-H bond in the parent vinyltoluenes. Herein, we describe the first observation, and a quite comprehensive isomer-specific assignment, of the cis-and trans-vinylbenzyl D 0 -D 1 transition. A Franck-Condon description of band intensities is rendered largely inutile by pronounced Herzberg-Teller activity in most totally symmetric vibrations. It emerges that probably no vinylbenzyl radical carries the 630-500 nm bands; promising candidates bearing cyclopentenyl groups are briefly discussed.

EXPERIMENTAL SECTION

MVB was produced using a pulsed discharge nozzle, 25 comprising a series of annular electrodes and Teflon insulators affixed to a pulsed valve with a 0.5 mm orifice. The precursor, meta-vinyltoluene, was stored behind the nozzle and heated to 60 °C, and the vapor entrained in Ar at 3 atm. A high-voltage pulse (typically 600-1000 V, 50 μs, 50 kΩ ballast resistance) was applied across the electrodes in synchronization with the leading edge of the gas pulse. The products were cooled to ∼15 K by supersonic expansion into vacuum.

Two vacuum chambers were used for this work: one for R2C2PI and one for LIF/DF (dispersed fluorescence). In R2C2PI, jet-cooled MVB radicals were admitted through a 2 mm skimmer into the extraction region of a time-of-flight mass spectrometer. There, they were exposed to tunable radiation (535-480 nm, 10 mJ/pulse) from a Nd:YAG-pumped pulsed dye laser, followed ∼10 ns afterward by UV radiation from a frequency-quadrupled Nd:YAG beam (266 nm, 0.5 mJ/pulse) or a KrF excimer (248 nm, 5 mJ/pulse). The nascent ions were extracted into a 1 m field-free drift tube and detected with a tandem microchannel plate. For adiabatic ionization energy (AIE) measurements, one dye laser was tuned to the origin transition of one or other MVB conformer, while the UV frequency-doubled output (250-270 nm, 0.5 mJ/pulse) of a second dye laser was scanned through the ionization threshold. Ion signal at m/z = 117 was averaged over 64 shots and integrated as a function of the scanned wavelength, yielding an optical excitation spectrum or a resonant two-color ion-yield curve. The laser wavelength was calibrated with a wavemeter of absolute accuracy 0.2 cm -1 .

Mass-resolved optical-optical hole-burning scans were recorded in a four-beam experiment. The fundamental and frequency-doubled beams from one dye laser (the burn) were simultaneously copropagated to excite and ionize one conformer via its origin transition, the notion being that immediate removal of excited-state population by ionization might mitigate saturation. Approximately 500 ns afterward, the visible probe beam and a subsequent ionizing pulse (248 m or 266 nm) entered the chamber, both beams counter-propagated to the burn using a dichroic mirror. The probe was operated at 10 Hz and the burn at 5 Hz. By toggling the output polarity of a boxcar integrator gated over probe signal at m/z = 117, the 5 Hz signal was actively subtracted from the 10 Hz signal, yielding a difference in the probe spectrum when probe and Figure 1. Low-lying resonance-stabilized radical isomers of C 9 H 9 . A red circle indicates the radical site in one of the multiple resonance structures that can be drawn for each isomer. Energies are reported in kJ/mol relative to 1-indanyl, the global minimum. [19][20][21][22] Only 1-indanyl and 1phenylallyl have been observed spectroscopically. 20,21 The Journal of Physical Chemistry A burn interrogated transitions originating from the vibrationless level of the same conformer.

The LIF chamber is adapted from one first described in ref 26. Jet-cooled MVB radicals were exposed to tunable dye laser output approximately 25 mm downstream of the discharge aperture. Laser-induced emission was detected with a photomultiplier tube after being imaged through a small (0.14 m focal length) or a large (1 m focal length) monochromator. The small monochromator serves as a broad-bandpass filter in excitation scans; the large monochromator is equipped with a 1200 lines/mm grating and is used for DF spectroscopy. The latter instrument was operated with 0.6 mm slits, corresponding to a bandpass of ∼20 cm -1 . In DF scans, typically 64 fluorescence decay profiles were averaged and integrated over three temporal gates: one for scattered laser light, and the others for prompt (100 ns) and for slower (2 μs) decay, to identify possible contaminant features from species with significantly different fluorescence lifetimes.

COMPUTATIONAL DETAILS

Optimized geometries and harmonic vibrational frequencies of the neutral ground (D 0 ) and first excited (D 1 ) states of cis-and trans-MVB, as well as their cation singlet ground states, were obtained from density functional theory (DFT) and timedependent density functional theory (TDDFT) calculations using the B3LYP functional with 6-311G++(d,p) basis set. The results were used to predict AIEs and D 0 -D 1 transition energies, simulate rotational contours, and calculate Duschinsky matrices and band intensities in the Franck-Condon (FC) and Franck-Condon-Herzberg-Teller (FCHT) approximations. The FC factors and HT (i.e., linear) transition moments were computed by the procedure of Barone et al. 27 as implemented in Gaussian 09. 28 The effects of Duschinsky rotation are included. AIEs were also predicted from CBS-QB3 calculations for the D 0 and S 0 states of the neutral and the cation, respectively, to help confirm the identification of MVB. It has been shown that the B3LYP/6-311G++(d,p) 20 (respectively, CBS-QB3 23 ) AIEs of hydrocarbon RSRs are, on average, ∼0.1 eV lower (respectively, higher) than observation, on which basis our calculations should bracket experiment.

Ground-and excited-state vinyl torsion (ν 48 ) potentials were obtained from relaxed B3LYP/TD-B3LYP scans of the vinylphenyl dihedral angle. The calculation of torsional eigenvalues and eigenfunctions from Fourier series fits to the B3LYP potentials is described in Section 4.2 and the Supporting Information, Section S2. In Franck-Condon simulations, the B3LYP D 0 frequencies of 47 small-amplitude modes were scaled by 0.97, in accordance with usual practice for hydrocarbon RSRs. 20,29,30 While various scaling factors in the range 0.95-0.97 have previously been used 20,21,31,32 for excited states, we have left all D 1 frequencies unscaled. All calculations were performed with the Gaussian 09 suite of electronic structure programs. 28 Figure 2. Upper trace: mass-selected R2C2PI spectrum of jet-cooled m-vinylbenzyl radical, produced in a jet-cooled m-vinyltoluene discharge. Reflected: optical-optical hole-burning spectrum recorded with the burn laser fixed to the origin transition of the cis-conformer. Vibronic band positions are reported relative to the trans and cis origin transitions, located at 18 939 and 19 037 cm -1 , respectively. Band assignments are given in Tables 1 and2 and discussed in detail in Section 5.

The Journal of Physical Chemistry A 4. RESULTS 4.1. Identification of m-Vinylbenzyl Radical. The top trace of Figure 2 is the m/z = 117 R2C2PI spectrum of the mvinyltoluene discharge in the region 18 900-20 600 cm -1 (ca. 530-485 nm); reflected is the m/z = 117 hole-burning spectrum recorded with the burn laser at 19 037 cm -1 . Part of the spectrum was also measured with the burn at 18 939 cm -1 (see the Supporting Information, Figure S1), but the weaker trans transition makes for relatively inefficient population depletion. The assignments for cis-and trans-MVB are given in Tables 1 and2, respectively; they are discussed in detail in Section 5. Because substituted benzyl radicals can undergo facile configurational isomerization in discharges, 33 we first prove the chemical identities and conformations of the carriers. There is little doubt that every feature in the spectrum arises from a conformer of MVB. One, indanyl absorbs much further to the blue, with an origin near 21 159 cm -1 , 19 and we find no evidence near 19 208 cm -1 of the phenylallyl D 0 -D 1 origin, which dominates the phenylallyl spectrum. 20,21 Second, the features in Figure 2 are absent or greatly diminished when other C 9 H 10 precursors are used.

Third, the AIEs of the carriers of the bands at 19 037 and 18 939 cm -1 (7.168 and 7.165 eV, respectively, with uncertainties of 2.5 meV) are both close to 7.17 eV (Figure 3). The two-color ion-yield scans were recorded with an electric field of 200 V/cm in the extraction region of the ToF spectrometer; the field-free AIEs are at most 0.01 eV higher 34 than the indicated thresholds. They are thus consistent with MVB AIEs from B3LYP/6-311++G(d,p) (7.12 eV) and CBS-QB3 (7.22 eV) calculations (Table 3), which tend to bracket experiment by ca. 0.1 eV, 20,23 while calculated AIEs of o-and pvinylbenzyl are below 7.1 eV, and that of 2-phenylallyl is above 7.7 eV. 22 Finally, MVB is the only isomer in Figure 1 for which the calculated AIE and D 0 -D 1 transition energy are both close to the experiment (Table 3). For both conformers, T e is 2.48 eV; inclusion of ZPE gives T 0 = 2.42 eV for cis (cf. 2.36 eV observed), and T 0 = 2.35 eV for trans (cf. 2.35 eV observed). In fact, an excellent estimate for T 0 can be obtained without resorting to theory. As suggested in Figure 1, and in contrast to ortho-and para-MVB, the vinyl group does not participate in radical delocalization, in the sense that no reasonable Lewis structure can be drawn with a vinyl carbon hosting an unpaired The shaded regions represent confidence intervals of 2.5 meV for experimental thresholds. The field-free AIEs are at most 0.01 eV higher than the vertical dashed lines.

The Journal of Physical Chemistry A electron. From this viewpoint, MVB can be described as containing a vinyl-substituted benzyl chromophore, and it is illuminating to compare the benzene/benzyl system to its vinyl-substituted equivalent, styrene/m-vinylbenzyl. The benzyl D 0 -D 1 origin is at 22 002 cm -1 and the S 0 -S 1 band-gap of benzene, neglecting the ∼600 cm -1 inducing mode ν 6 , is ca. 38 000 cm -1 , giving an electronic red shift from benzene to benzyl of approximately 16 000 cm -1 . Application of this red shift to the styrene S 0 -S 1 transition, with origin at 34 760 cm -1 , yields a prediction of ca. 18 800 cm -1 for the MVB D 0 -D 1 origin, in remarkable accord with the observed trans-MVB origin at 18 939 cm -1 (Tables 4).

While it is thus clear that MVB is responsible for the m/z = 117 R2C2PI spectrum, it is far from obvious which conformer carries which band system. The carrier AIEs differ by at most a few meV, which margin cannot be captured by any practicable calculation. The cation S 0 state is predicted to be planar for trans; for cis, the calculated vinyl-phenyl dihedral angle in S 0 is ca. 158°. One might therefore expect a relatively gradual onset in the cis-2-color ion-yield curve due to off-diagonal Franck-Condon activity in the vinyl torsion, an interpretation that appears to be at least qualitatively correct (see FC simulations, based on S 0 ← D 1 FC factors calculated using FCLab II, 35,36 in the Supporting Information, Section S4). The TD-B3LYP results imply cis-MVB absorbs to the blue of trans-MVB, consistent with our analysis, but again the difference is marginal, and the similar closed-shell systems m-fluorostyrene, 37,38 m-chlorostyrene, 39 and m-methylstyrene 40 show the opposite trend. Simulated origin band envelopes using calculated rotational constants and transition moments (Figure 4) are not inconsistent with our assignmentbut nor, at our resolution, are they conclusive.

Moreover, B3LYP cis and trans D 1 frequencies (Table 5; see Section 5) do not, unsurprisingly, differ considerably, and thus compare nearly equally well with both band systems. The D 0 -D 1 transition also engenders comparable Franck-Condon activity in the two conformers (Section 5), but curiously, only the 19 037 cm -1 band system is origin-dominated. In short, it is difficult to make unambiguous isomer-specific assignments from R2C2PI alone. On the other hand, inspection of the calculated properties in Tables 3 and5 reveals the D 0 vinyl torsion frequency to present a major point of difference. Indeed, relaxed scans (Figure 5) of the vinyl-phenyl dihedral angle suggest that while both D 1 wells and the D 0 trans well are roughly harmonic at low energies, the D 0 cis well is relatively flat-bottomed. To exploit the conformational specificity of the D 0 vinyl torsion, we turn to dispersed fluorescence spectroscopy.

4.2. Distinguishing the cisand trans-MVB Band Systems. Figure 6 shows the DF spectrum of the 19 037 cm -1 band. Its full assignment and the simulations beneath are discussed in Section 5. For now, we focus on the strong band at 73 cm -1 . It can have no assignment other than 48 2 0 , with ν 48 being the vinyl torsion, which is of a″ symmetry and governed by the selection rule Δv = ±2. How does this compare with theory? For trans-MVB, the B3LYP D 0 ν 48 frequency is 51 cm -1 using the 6-311++G(d,p) and cc-PVTZ basis sets, yielding a harmonic prediction of 102 cm -1 for 2ν 48 ; for cis, we obtain 15 cm -1 (6-311++G(d,p)) and 35 cm -1 (cc-PVTZ), giving predictions of 30 and 70 cm -1 . Allowing for the negative anharmonicity expected for a flat-bottomed potential, the cis isomer is perhaps the better candidate; but to allay doubt, the eigenvalues of the torsional potentials in Figure 5 should be calculated.

The Schrodinger equation for internal rotation of a rigid top attached to a rigid frame is The Journal of Physical Chemistry A

For vinyl torsion in MVB, ϕ is the dihedral angle between the vinyl and phenyl groups and B is the reduced rotational constant 42 of the vinyl top. To compute vibrational intervals for comparison with DF spectra, the potential of interest V(ϕ) is the relaxed D 0 vinyl-phenyl dihedral scan in Figure 5, which was fit, as is customary, 43 to a Fourier series of the form

Because the cis and trans wells are not equivalent, it is necessary to admit an angular dependence of B. The D 0 and D 1 geometries obtained at each point of the relaxed scans (i.e., 5°i ncrements from 0 to 180°) were used to calculate the reduced moment of inertia and internal rotation constant of the vinyl top as a function of ϕ by the procedure of Wong. 44 The resulting function was fit to a six-term cosine expansion

Following Laane, 45 the Hamiltonian matrix for the hindered rotor problem was set up in terms of the free rotor (i.e., V(ϕ) = All frequencies are unscaled. Mode descriptions are based on the D 0 normal coordinates. "ϕ" denotes the phenyl ring. D 0 mode numbers follow the Mulliken convention, and D 1 modes are numbered in terms of the D 0 basis, according to the diagonal elements of the Duschinsky matrices in Figure 9. Experimental frequencies determined in this work are in italics; square brackets enclose frequencies from tentative assignments. b 0.5 × 48 2 ; the anharmonic value (Figure 7) is ca. 33 cm -1 . c 0.5 × 48 2 ; the anharmonic value is ca. 89 cm -1 (see the Supporting Information, Section S2 and Figure S2). d Assumes anharmonic values for ν 48 (see note b), and no anharmonic cross-terms (see also the Supporting Information, Section S2).

The Journal of Physical Chemistry A 0) basis functions Φ m (ϕ) = (2π) -1/2 e imϕ , which have eigenvalues E m = m 2 B, m = 0, ±1, ±2, etc. The symmetry properties of trigonometric functions admit a decomposition of the Hamiltonian matrix into an even (cosine) block and an odd (sine) block. The matrix was diagonalized to give the eigenvalues E k and eigenfunctions Ψ k = ∑ m c mk Φ m . Fifty basis functions were more than sufficient to achieve satisfactory convergence of the eigenvalues.

Figure 7 shows the main results for the ground state (see also Figure S2 and Table S1); torsional intensities and D 1 eigenvalues are discussed in the Supporting Information, Section S2. The 73 cm -1 feature in the 19 037 cm -1 DF spectrum should be compared to the calculated ν 48 0-2 interval: 73 cm -1 for cis-MVB and 105 cm -1 for trans-MVB. The agreement is vastly superior for the cis-conformer, and further, the weak DF feature at 170 cm -1 accords with the calculated cis-MVB 0-4 interval (169 cm -1 ). The low signalto-noise ratio of the DF spectrum for the weaker origin at 18 939 cm -1 (Supporting Information, Figure S3) prevents us from identifying trans torsional transitions with confidence. Nevertheless, it exhibits no distinct reproducible features below 200 cm -1 , and the few bands observed are consistent The Journal of Physical Chemistry A with trans D 0 frequencies, notably ν 32 near 345 cm -1 . We therefore consider that the cis and trans band systems have been distinguished beyond doubt.

DETAILED ASSIGNMENTS AND DISCUSSION

5.1. Geometries, Frequencies, and Duschinsky Matrices. Figure 8 shows the optimized structures of the D 0 and D 1 states. The electronic transition is assigned as A″-A″, and as is typical for odd-alternant π-radical chromophores, 46,47 the D 1 state can be described as a superposition of nearly degenerate configurations derived from one-electron excitations into and out of the singly occupied orbital. The result of this configuration interaction is to diminish the D 0 -D 1 transition moment, consistent with the small predicted fvalues: 8 × 10 -4 for cis-MVB and 3 × 10 -4 for trans-MVB. For cis, the transition is mostly polarized along the x-axis (or aaxis), while for trans, the two in-plane components of μ are of similar size. The structural changes caused by electronic excitation involve lengthening of all C-C bonds by 0.01-0.04 Å, except for the C3′C3 and C1C1′ bonds, which are commensurately shortened. Both conformers are predicted to be planar in both states, and the only bond angle that changes significantly is ∠C1C1′C2, connecting vinyl and phenyl groups.

On these premises, a′ modes involving the carbon framework are expected to be Franck-Condon-active, particularly C-C stretch and ring-deforming modes, as well as the in-plane vinyl wag (ν 33 ). Neglecting anharmonic resonances, FC activity in a″ modes derives from changes in their force constants and is thus only expected to be noticeable for the vinyl torsion, ν 48 , and modes with which it is Duschinsky-mixed (vide infra). The C1C1′ bond, connecting the vinyl group to the phenyl ring, shortens markedly (0.04-0.05 Å) upon excitation, causing the vinyl torsion frequencies and cis-trans isomerization barrier (Figure 5) to increase by a factor of several (though the true D 0 and D 1 barriers are probably smaller than theory indicates 48 ).

Table 5 contains all unscaled D 0 and D 1 B3LYP/6-311G+ +(d,p) vibrational frequencies, neglecting the nine FC-inactive CH-stretch modes. We emphasize that while the D 0 mode labels follow the Mulliken convention, D 1 modes are numbered according to the Duschinsky matrices in Figure 9. To wit, for small displacements, the normal coordinates Q″ and Q′ of different electronic states can be related by the linear transformation 49

where K is a (3N -6)-dimensional vector of displacements along the normal coordinates and J is the (3N -6) × (3N -6)-dimensional Duschinsky (or rotation) matrix. Because MVB has C s symmetry in both electronic states, the elements of K are necessarily zero for all a″ modes and J is block-diagonal with respect to symmetry species. Figure 9 shows the Duschinsky matrices for MVB, separated into a′ and a″ blocks. For all but the cis a″ matrix, extensive mixing precludes a reordering of the columns such that the largest element is always on the diagonal. We have therefore arranged the columns to maximize the trace of each matrix and renumbered the D 1 modes in terms of the D 0 basis. The use of a single set of mode labels for both states in this manner greatly simplifies the discussion of spectral assignments. 29,31 One important manifestation of Duschinsky mixing is the appearance of "forbidden" transitions involving nontotally symmetric modes (see, e.g., 29,50,51 ). If X and Y are mutually rotated a″ modes, the level X 1 Y 1 contains the character of X 2 and Y 2 in terms of the ground-state basis, and the overlap integral for the otherwise forbidden transition X 0 1 Y 0 1 can be significant. This is a well-known feature of electronic spectra of styrene 52,53 and substituted styrenes, 37,38,54,55 whereby electronic excitation mixes the vinyl torsion with low-frequency out-of-plane bending modes, allowing transitions of the type X 0 n Y 0 m , where n, m are odd. The a″ matrices in Figure 9 imply that this effect should be in play for modes 46-48.

5.2. Franck-Condon Analysis. Franck-Condon simulations comprise the bottom traces ("FC") in Figure 6 (cis-MVB DF), Figure 11 (cis-MVB R2C2PI), and Figure 13 (trans-MVB R2C2PI). Herzberg-Teller effects will be discussed in the following section. Because B3LYP groundstate frequencies scaled by 0.97 56 agree reliably well with experiment, 20,29,30 it is simplest to assign the cis-MVB origin DF spectrum first (Figure 6). To begin, we note a recurring motif: every sufficiently strong featurefor example, at 535 cm -1 (presumably a blend, because of its width), 732, and 1643 cm -1 has a weaker consort ca. 75 cm -1 to the blue. Further, the bands at 1310 and 1643 cm -1 are relatively broad, probably owing to overlap with +75 cm -1 satellites of strong bands at 1250 and 1569 cm -1 . Because the 48 2 0 band at 73 cm -1 dominates the spectrum, we interpret that the +75 cm -1 satellites are combinations of 2ν 48 with a′ fundamentals. Calculated band intensities involving ν 48 are not expected to be highly accurate because of anharmonicity and normal coordinate rotation (see further comments in Section 5.3 and the Supporting Information, Section S2). However, we note that the observed intensities of the satellites relative to the putative fundamentals are ∼0.2 to 0.3. To guide the eye, we have thus scaled combination bands of the form X 1 0 48 2 0 to have The Journal of Physical Chemistry A 25% of the intensity of the related X 1 0 false origins in the FC and FCHT simulations (this factor is similar to that observed for styrene, for which the vinyl torsion frequency is similarly affected by electronic excitation 57 ). The assignment of the major features is subsequently quite straightforwardon the basis of calculated a′ frequencies, at least. The observed and scaled B3LYP frequencies of the a′ modes assigned in Figure 6 agree to within ∼1.5%, on average, and the mean absolute deviation is 13.0 cm -1 (see also the Supporting Information, Section S6).

Although experience with similar RSRs causes us to be confident in these assignments, the FC simulation is obviously grossly inaccurate throughout ca. 200-1000 cm -1 . The ν 28 -ν 32 fundamentals are expected to be weaker than 33 1 0 , which is absent; the strongest observed a′ fundamental, 28 1 0 at 732 cm -1 , has little FC intensity; and whereas the simulation implies a prominent 25 1 0 band (the ring-breathe) near 990 cm -1 , the observed feature is weak. The last point is surprising insofar as ring-breathe modes are often strongly FC-active in phenyl-containing chromophores. More curiously still the cis-MVB R2C2PI spectrum (Figure 11) is in several ways the reverse of the DF spectrum. For example, 25 0 1 is observed (at 963 cm -1 ), but not predicted, to be the strongest band after the origin; similarly, 33 0 1 should be below the noise floor, but is detected readily at 201 cm -1 ; and the most intense a′ feature in emission, 28 1 0 , has no counterpart in excitation. Nor do the FC simulations capture significant qualitative differences between the cis-MVB and trans-MVB R2C2PI spectra (cf. Figures 11 and13). For instance, while both conformers are predicted to have vastly origin-dominated The Journal of Physical Chemistry A transitions, several trans features rival or surpass the origin. Furthermore, for trans-MVB, the ring-breathe (ν 26 in the trans excited state) has the strongest predicted FC activity, but is weak in the trans-MVB excitation spectrumessentially the same trend observed for the analogous mode (ν 25 ) in emission for cis-MVB, but the opposite of its behavior in the cis-MVB excitation spectrum.

Most of the vibronic structure for both conformers unequivocally arises from a′ fundamentals and not from vinyl torsion transitions (see the trans-MVB 0 0 + 210 cm -1 DF spectrum Figure S3 in the Supporting Information). The unusually comprehensive failure of the FC approximation, particularly below 1000 cm -1 , implies that the D 0 -D 1 transition moment is strongly modulated by in-plane deformations of the carbon skeleton. The low symmetry of the molecule is of some import in this context. Distortion along a vibrational coordinate of symmetry Γ vib can enhance the transition moment to an electronic state of symmetry Γ elec if the product Γ elec × Γ vib contains the irrep of a bright state lying not too distant in energy. In relatively symmetric molecules, such as benzene (D 6h ) and the para-dihalobenzenes (D 2h ), this condition is not met readily. While vibronically induced transitions are of course well known in the S 0 -S 1 spectra of these species (see, e.g., refs 58 and 59), they manifest for only a small handful of modes, being in-plane deformations of symmetries e 2g in benzene and b 3g in the paradihalobenzenes (and correlating with a′ symmetry in a planar C s molecule).

For the D 0 -D 1 transition of MVB, the symmetry constraints for the vibronic acquisition of transition moment are much less onerous. Because the transition is dipole-allowed, a′ modes can contribute additional oscillator strength. We calculate that four 2 A″ excited states lie vertically within 2 eV of D 1 (Table 6); their f-values for excitation from D 0 all exceed the D 0 -D 1 fvalue, some by orders of magnitude. At least in principle, distortions along the 33 a′ modes can mix D 1 with one or more of these states and impart intensity to the D 0 -D 1 transition. To gain some heuristic sense of this possibility, approximate transition moment functions for selected a′ modes were obtained from TD-B3LYP calculations at a series of normal coordinate displacements Q-Q 0 (Figure 10). Indeed, vibronic activity is implied to be rampant among a′ modes, with one or both of the in-plane components of μ growing substantially away from Q 0 , plainly accounting for the inutility of purely FC simulations.

5.3. Herzberg-Teller Analysis. To accommodate the dependence of μ on nuclear motion, the transition dipole moment connecting lower and upper vibronic states v″ and v′ is expanded about Q 0 as a Taylor series in the normal coordinates {Q i } for each polarization direction, that is, i k j j j j j y { z z z z z i k j j j j j j j y

The zeroth-order (i.e., Condon) term represents the formally allowed v′ ←v″ transition moment at Q 0 ; higher-order terms describe Herzberg-Teller activity (but many authors refer strictly to the linear term as the HT moment). The D 0 -D 1 Condon term is small for MVB, but crucially, not zero, meaning that a′ modes can induce additional vibronic intensity. If, in addition to being vibronically active, a totally symmetric mode is also FC-active because of a displacement along Q, none of the integrals in HT and higher terms are necessarily zero for transitions involving that mode. Further, for weakly allowed transitions, the Condon and higher moments may be similar in magnitude, making for nonintuitive intensity patterns in progressions and combination bands, and causing a breakdown of mirror symmetry between excitation and emission (vide infra). Only the first derivatives of the transition moment surface are computed in the available implementation of the FCHT procedure used for this work; 27 as such, rigorous agreement with experiment is not expected of calculated FCHT intensities. Nevertheless, they are instrumental in securing vibronic assignments. 5.3.1. cis-MVB. FCHT simulations comprise the middle traces of Figure 6 (cis-MVB DF) and Figure 11 (cis-MVB R2C2PI). The reference geometry Q 0 and normal coordinates {Q i } are those of the final state, i.e., D 1 for excitation and D 0 for emission. 27 With the exception of ν 30 (and to a lesser extent ν 15 ), the inclusion of HT moments admits a mostly qualitatively correct description of the D 0 -D 1 transition. Beginning with the 0 0 DF spectrum, it is predicted that modes 32-28 dominate the region 200-1000 cm -1 ; that 25 1 0 (the ring-breathe) should be one of the weaker a′ fundamentals; and that 33 1 0 should be relatively insignificant. These predictions are borne out in the experimental DF spectrum, and with 2ν 48 (73 cm -1 ) built onto each a′ false origin as described in Section 5.2, essentially all of the observed features below 1800 cm -1 are accounted for.

Likewise, turning to the cis-MVB excitation spectrum, the FCHT simulation (again neglecting ν 30 ) compares respectably with observation (Figure 11). HT terms account for much of the transition moment for a′ modes, as for the cis origin DF spectrum. The transitions 33 0 1 and 32 0 1 are enhanced by a factor of ∼5, and 31 0 1 and 25 0 1 increase 2-fold. For 33 0 1 , 32 0 1 , and 25 0 1 , experimental intensities still exceed those of theory, but that could partly be a consequence that 412, 486, and 963 cm -1 , which are broader than the origin band, all comprise more than one transition.

From the assignments in Figure 11, we determine a scaling factor of 0.958 for the calculated cis-MVB D 1 frequencies The Journal of Physical Chemistry A (Supporting Information, Section S6); this is consistent with results for similar systems, 20,21,31,32 giving us confidence in our analysis. Nevertheless, several assignments must be closely reasoned. The clearest discrepancy is that ν 30 should be prominent in both emission and excitation spectra, but it exhibits middling strength in the former, and is apparently absent from the latter. While there is no plausible alternative assignment for the 525 cm -1 feature in DF, one might conjecture that the strong R2C2PI band at 282 cm -1 , which we assign as 46 0 . This would require, however, that the calculated ν 30 frequency is too high by ca. 18%. 60 It would furthermore imply the absence of 46 0 1 48 0 1 , unless the feature at 233 cm -1 has been misassigned; but then, the calculated ν 46 frequency would be in error by ca. 40%. In contrast, our assignments for 46 0 1 48 0 1 and 47 0 1 48 0 1 yield D 1 ν 46 and ν 47 frequencies within ca. 4 and 7% of theory, respectively; further, they suggest 46 0 2 might appear near 380 cm -1 , where indeed at least one plausible candidate can be found nearby.

Moreover, transitions such as 46 0 1 48 0 1 , which engage the vinyl torsion and an out-of-plane bend, are commonplace in the S 0 -S 1 spectra of styrene and its derivatives. 37,38,[52][53][54][55] They are forbidden in the independent normal mode approximation but become allowed by Duschinsky rotation (as described in Section 5.1), often overshadowing the related FC-allowed overtones, and having intensities comparable to low-frequency totally symmetric fundamentals. 57 For styrene, where the lowest-frequency a″ modes undergo similar changes upon excitation to those of MVB, the total intensity carried by analogous transitions (involving modes 40-42) amounts to more than half of the origin intensity, 61 which is consistent with our assignments. That 46 0 1 48 0 1 is stronger than predicted implies the mutual rotation of low-frequency modes has not been well described by theory, 62 which is hardly surprising given that ν 48 ″ is obviously highly anharmonic. In MVB, as in styrene, Duschinsky mixing involving the vinyl torsion is electronic in origin. The C1-C1′ bond attains significant double-bond character upon electronic excitation; the vinyl torsion frequency thus increases dramatically, becoming less disparate from other a″ modes, and causing strong modemixing. 51 Such coupling is much weaker in the ground state, as the vinyl torsion has a vastly lower frequency than any other a″ mode; the corresponding transition in emission (46 1 0 48 1 0 , in our example) is thus weak (perhaps responsible for signal near 235 cm -1 ), but the "pure" vinyl torsion overtone, 48 2 0 , is prominent. The Journal of Physical Chemistry A This is also consistent with the S 0 -S 1 origin DF spectrum of styrene, in which 42 2 0 and 42 4 0 have roughly 20 and 2.5% of the origin intensity, respectively, while the cross-sequence bands are relatively weak. 57 We are thus confident in our assignment of 0 0 + 282 cm -1 as 46 0 1 48 0 1 and conclude that the calculated intensity of ν 30 is erroneously high. It is perhaps no coincidence that the transition moment function for ν 30 is highly nonlinear (Figure 10). To the extent that the above Taylor series expansion of μ(Q) provides a useful description of vibronic intensities, the more stark disagreements between experiment and FCHT simulations owe in some measure to the neglect of higherorder terms. The calculation of such terms is relatively nontrivial, particularly if Duschinsky mixing is important; nevertheless, some inferences can be drawn from the signs of the diagonal contributions (i.e., of the form ( )

). If the ath totally symmetric mode is HT-active and modestly displaced along the coordinate Q a upon excitation, the integrals ⟨1 a ′|Q a |0″⟩ and ⟨1 a ′|Q a 3 |0″⟩ are similar in magnitude and carry the same sign, and likewise for the analogous transition in emission. On the other hand, the cis-MVB ν 30 transition moment function (Figure 10) is dominated by the Q 30 and Q 30 3 terms, which have coefficients of similar magnitude but opposite sign. Thus, the linear and cubic diagonal moments for 30 0 1 and 30 1 0 interfere destructively. Without wanting to belabor this argument, it is possible that lesser discrepancies (e.g., the FCHT relative intensities of 33 0 1 and 32 0 1 are roughly the inverse of the experiment) can be similarly explained, at least in part. For the S 1 -S 0 spectrum of phenylacetylene, for example, it has been shown that all moments up to second order must be included to satisfactorily describe intensities in several a 1 modes. 63

Asymmetry of Excitation and Emission Spectra.

A striking feature of the cis-MVB excitation and emission spectra is an absence of mirror symmetry in the intensities of several a′ modes. Most notably, the ν 25 and ν 33 fundamentals are conspicuous in excitation, but absent or weak in emission; and conversely, ν 28 is the brightest a′ mode in emission but is undetectable in excitation. The asymmetry is not due to Duschinsky rotation (as in fluorobenzene, for example 50 ) because the three modes exhibit no significant off-diagonal matrix elements (Figure 9). It owes instead to interference between Franck-Condon and Herzberg-Teller (and possibly higher-order) moments, an effect first described by Craig and Small in connection with the 340 nm transition of phenanthrene. 64 Its origin is explained in Figure 12, adapted from ref 65. An electronic transition displaces the equilibrium geometry of the molecule along the normal coordinate Q of a totally symmetric mode. For the fundamental transitions of that mode, the integrands for the FC term are of opposite sign in excitation vs emission, but there is no change in the sign for the HT integrands. Thus, if the FC and HT moments reinforce for one process, they will cancel for the other. Because the intensity of a transition depends on the square of the transition moment, the asymmetry can be pronounced when the two moments have similar magnitudes. A comparison of the FC and FCHT simulations shows that for ν 25 and ν 33 , the FC and HT terms interfere constructively for excitation and destructively for emission, and vice versa for ν 28 , which should be negligible in excitation. These predictions correspond well with experiment.

5.3.3. trans-MVB. Figure 13 shows the MVB R2C2PI spectrum with trans FC and FCHT simulations. Known features of cis-MVB are shown in reduced opacity. 66 In the FCHT simulation, intensities of all transitions appearing Figure 11. Optical-optical hole-burning spectrum obtained with the burn laser fixed to the cis origin transition, and beneath, simulations of the cism-vinylbenzyl electronic spectrum in the Franck-Condon Herzberg-Teller (FCHT) and Franck-Condon (FC) approximations, respectively. Each spectrum is intensity-normalized relative to its origin band.

The Journal of Physical Chemistry A between 33 0 1 and 18 0 1 have been scaled (×2) to facilitate comparison with experiment. While many observed and calculated intensities still differ considerably, the FCHT simulation provides crucial qualitative guidance for securing assignments. Significant strength is implied in several a′ modesnotably 33, 29, 28, and 18that carry relatively modest FC intensity; and the ring-breathe (ν 26 ) is correctly predicted to be weak because of destructive FC-HT interference. It is clear why the trans spectrum, in contrast to the cis spectrum, is not origin-dominated, even though the two conformers should exhibit similar FC activity: the transition moment gradients for a′ modes are of similar magnitude for both conformers (Figure 10), but trans-MVB has a roughly 3fold smaller Condon moment. The origin (indeed, any transition) is enhanced (or diminished) by HT moments of all FCHT-active a′ modes, but the size of the effect can be small relative to certain Δv = 1 transitions. By way of heuristic explanation, the HT terms for the origin 0′ ← 0″, and for one quantum of excitation 1 a ′ ← 0″ in a totally symmetric mode, FCHT-active mode a can be written as

where ⟨0′|0″⟩ = ∏ j=1 3N-6 ⟨0 j ′|0 j ″⟩ for independent normal modes in the absence of Duschinsky rotation, and the inequalities hold if normal coordinate displacements and changes in vibrational frequencies between the two electronic states are small, as is generally true of extended π-chromophores. The origin may thus be relieved of its dominance.

When scaled by 0.967, TD-B3LYP frequencies agree quite well with the experiment (Supporting Information, Section . R2C2PI spectrum of m-vinylbenzyl, and beneath, simulations of the trans-m-vinylbenzyl electronic spectrum in the Franck-Condon Herzberg-Teller (FCHT) and Franck-Condon (FC) approximations, respectively. Light gray bands in the experimental spectrum are features of the cis isomer, identified by hole-burning spectroscopy. Each spectrum is intensity-normalized relative to its origin band. In the FCHT simulation, all transitions to levels between 33 1 and 18 1 have been scaled (×2) to facilitate comparison with the experiment.

The Journal of Physical Chemistry A S6). Some frequencies derive from tentative assignments, particularly for weak bands in congested regions. Nevertheless, the scaling factor is again consistent with other RSRs 20,21,31,32 and is not dissimilar to that found for cis-MVB (0.958), which was determined from relatively few assignments. Still, a number of clearly discrepant FCHT intensities warrant further discussion. Some experimental bands may appear relatively strong simply because they comprise multiple transitionsfor example, the relatively broad 1346 cm -1 band may contain both 18 0 1 and 16 0 1 . The justification for several other assignments is rather more nuancedparticularly for modes 10 and 32. The assignment of 33 0 1 was confirmed by DF, which leaves no reasonable alternatives for 48 0 2 and 46 0 1 48 0 1 . However, there are several possibilities for the bands at 306 and 337 cm -1 . The simulation implicates 32 0 1 and 10 0 1 as the strongest features nearby, while 47 0 1 48 0 1 , which might be expected close to 32 0 1 , is predicted as the strongest of the vinyl torsion cross-sequence transitions. Again, we argue that the mutual rotation of modes 46-48 has been mischaracterized by theory. The observed 46 0 1 48 0 1 intensity exceeds prediction by at least an order of magnitude. A Fermi-resonance with 33 0 1 is a possible cause, but the 33 0 1 DF spectrum (Supporting Information, Figure S3) shows no evidence of emission to 46 1 48 1 . If 47 0 1 48 0 1 were identified with either the 306 cm -1 or the 337 cm -1 band, the total intensity in the transitions 48 0 2 , 46 0 1 48 0 1 , and 47 0 1 48 0 1 would amount to either at least 50% or more than 100% of the origin intensity. It would thus follow that FC activity in the vinyl torsion and its Duschinsky-mixed cohorts for trans is similar to or stronger than that for cis. However, it is clear that electronic excitation affects a much greater change in the cis vinyl torsion potential than for trans, thereby engendering stronger FC activity: for example, the torsional overtone cannot be identified in the trans 0 0 DF spectrum (Supporting Information, Figure S3), but it dominates the cis DF spectrum at 73 cm -1 (Figure 6).

It thus seems more reasonable to assign the features at 306 and 337 cm -1 as 32 0 1 and 10 0 1 , respectively. The D 1 "mode 10" is so labeled largely as a matter of convenience, according to the trans a′ Duschinsky matrix in Figure 9. In terms of the D 0 basis, it mostly contains the character of modes 32 and 31, both evident in the trans 0 0 DF spectrum (Supporting Information, Figure S3). These modes derive most of their intensity from HT activity and can thus be observed in excitation and emission. In contrast we note, as for cis, pronounced intensity asymmetry for modes 33 and 28, for which the FC factors are relatively significant: both are bright in excitation, but weak or absent in emission.

Neglect of higher moments may, as for cis, account for some of the disagreement between observed and FCHT intensities. For phenylacetylene, the inclusion of second-order terms produces a nearly 2-fold enhancement in several a′ modes. 63 The effect may be particularly substantial for overtones involving FCHT-active a′ modes even if the higher derivatives of μ(Q) are small, because the integrals ⟨n a ′|Q a n |0″⟩, for an upper level with n quanta in the ath mode, will be significant for small displacements. For example, the strong, broad 418 cm -1 band, which clearly involves at least two levels, could derive much of its intensity from the diagonal second-order contribution to 33 0 2 , expected near 420 cm -1 . The other component of the same band, assigned as 30 0 1 , could gain intensity both from higher moments and from an anharmonic resonance with 33 0

2

. Such resonances are probably common even at low energy owing to a mounting density of states of the same symmetry; more than one plausible zero-order assignment could have been suggested for almost every combination band above ca. 600 cm -1 . Our assignments for such combinations are based on the constituent frequencies, allowing for modest anharmonicities, but the intensities, which in addition to anharmonic coupling are sensitive to the mixed partial derivatives in μ(Q), do not follow expected patterns, insofar as no intense transition serves as a false origin. Several of the proposed assignments should be testable by single vibronic level DF, which we defer until we can produce cold MVB radicals in higher abundance.

5.4. Astrochemical Relevance and Other Isomers. In a jet-cooled discharge of 1,6-heptadiyne, Steglich et al. recently detected C 9 H 9 radicals in the region 630-550 nm by R2C2PI. 22 Several features were observed in close proximity to DIB wavelengths. The spectrum was tentatively ascribed to vinylbenzyl(s) from B3LYP/TD-B3LYP calculations and an AIE of 7.3 ± 0.1 eV measured for the carrier of an origin near 629 nm. It is now clear that MVB can be ruled out. Moreover, because their AIEs should be lower than that of MVB (7.17 eV), o-and p-vinylbenzyl can probably also be excluded. We have so far observed no optical absorption attributable to o-or p-vinylbenzyl in discharges of o-or p-vinyltoluene, under the same experimental conditions that yield MVB from mvinyltoluene. It could be that the ortho isomer rearranges to 1-indanyl in the discharge, while the para isomer appears to decompose efficiently to p-ethynylbenzyl (C 9 H 7 ), the identification of which we shall describe in detail elsewhere.

During recent work on the 1,6-heptadiyne discharge in our laboratory, we discovered 3-ethynylcyclopentenyl (c-C 5 H 6 -CCH) by R2C2PI near 459 nm. It is a highly resonancestabilized isomer of C 7 H 7 that contains a 1-vinylpropargyl chromophore. Its extension by vinyl substitution at the ethynyl terminus would yield an extensively delocalized C 9 H 9 radical with a red-shifted spectrum, but the likely size of the red shift is not intuitively obvious. Empirically, it has been observed that the extension of a linear π-chromophore by ethynyl substitution red-shifts its absorption by ca. 60 nm. 16 However, vinyl substitution of allyl 67 and propargyl 30 causes a red shift of roughly 110 nm, implying vinyl-substituted 3-ethynylcyclopentenyl motifs deserve consideration in connection with the laboratory 630-550 nm bands. If the carriers fluoresce, DF spectroscopy should permit their diagnosis.

CONCLUSIONS

We have observed both conformers of m-vinylbenzyl under jetcooled conditions by mass-resolved and fluorescence spectroscopies. Comparison of styrene/m-vinylbenzyl with the benzene/benzyl system gives a predicted D 0 -D 1 transition energy in excellent agreement with the experiment. Dispersed fluorescence, hole-burning measurements, and torsional eigenstate calculations admit a conformer-specific assignment of the major features. B3LYP vibrational frequencies agree tolerably well with observed band positions when appropriately scaled, but a Franck-Condon description of relative band intensities is almost wholly inaccurate. The transition can only be qualitatively understood by considering pervasive Herzberg-Teller activity in totally symmetric modes and its interplay with Franck-Condon contributions to the transition moment. The FC and HT moments are of similar magnitude for several a′ fundamentals but may have the same or opposite sign, causing some pronounced asymmetries between excitation and emission intensities. We have not yet optically

The Journal of Physical Chemistry A detected the ortho and para isomers; the former may isomerize to 1-indanyl, while in the p-vinyltoluene discharge, which should yield the latter, we find p-ethynylbenzyl (C 9 H 7 ). It would appear that no vinylbenzyl motif is responsible for C 9 H 9 absorption bands observed in a 1,6-heptadiyne discharge throughout 630-550 nm, the carriers of which thus remain unidentified. Chromophores derived from vinyl substitution of 3-ethynylcyclopentenyl (C 7 H 7 ), which is optically conspicuous in the heptadiyne discharge, may be plausible candidates.

■ ASSOCIATED CONTENT

* sı Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpca.1c04496.

Trans-MVB hole-burning scan and DF spectra from levels 0 0 and 33 1 (0 0 + 210 cm -1 ); D 0 and D 1 torsional potentials, eigenfunctions, eigenvalues, and discussion of Franck-Condon factors; simulated two-color ion-yield curves; optimized Cartesian coordinates and all calculated harmonic vibrational frequencies of D 0 and D 1 states of cis-and trans-MVB; and linear fits to observed vs calculated vibrational frequencies (PDF)

■ AUTHOR INFORMATION

Corresponding Author

Neil J. Reilly -Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, United States; orcid.org/0000-0001-5572-4784; Email: neil.reilly@umb.edu.