Infrared Spectroscopy of the Tropyl Radical in Helium Droplets - The

Aug 16, 2016 - The infrared spectrum of the X̃2E 2 ″ tropyl radical has been recorded in the range of the CH-stretch vibrational modes using the he...
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Infrared Spectroscopy of the Tropyl Radical in Helium Droplets Matin Kaufmann,† Daniel Leicht,† Martina Havenith,† Bernadette M. Broderick,‡ and Gary E. Douberly*,‡ †

Department of Physical Chemistry II, Ruhr-University Bochum, 44801 Bochum, Germany Department of Chemistry, University of Georgia, Athens, Georgia 30602-2556, United States

‡

S Supporting Information *

ABSTRACT: The infrared spectrum of the X̃ 2E″2 tropyl radical has been recorded in the range of the CH-stretch vibrational modes using the helium droplet isolation technique. Two bands are observed at 3053 and 3058 cm−1. The electronic degeneracy of the ground state results in a Jahn− Teller interaction for two of the CH-stretch modes, i.e., firstorder interaction for E3′ symmetry modes and second-order interaction for E2′ symmetry modes. The experimentally observed bands are assigned to the E′1 and E′3 CH-stretch modes. The E′1 mode is infrared-active, whereas the E′3 mode is inactive in the absence of the Jahn−Teller interaction. The transition to the upper component of the Jahn−Teller split E′3 mode gains intensity via vibronic coupling, giving rise to the second experimentally observed band.

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INTRODUCTION Aromatic radicals such as cycloheptatrienyl (tropyl; C7H7), cyclopentadienyl, and benzyl are of particular interest as reaction intermediates in organic synthesis and in the formation of polycyclic aromatic hydrocarbons (PAHs). PAH formation mechanisms are relevant to many fields of chemistry, for instance, in the generation of soot during combustion processes.1,2 In the initial stages of soot formation, multistep reaction pathways producing the smallest PAHs involve complex, multiwell potential energy surfaces, and it is proposed that aromatic radicals play a major role as reaction intermediates. Three C7H7 radical isomers, including the tropyl radical, are proposed to be particularly stable intermediates.3 PAHs are also investigated in the context of astrochemistry; indeed, infrared (IR) absorption and emission features attributed to PAHs have been observed in planetary atmospheres, e.g., on Saturn’s moon Titan, and in numerous regions of the interstellar medium.4,5 Reactive aromatic hydrocarbon radicals are therefore implicated in the formation of PAHs over a broad range of environments and conditions. Rearrangement pathways interconverting benzyl and tropyl radicals have been considered in the context of radical formation in molecular beam discharge sources. For example, in toluene discharges, benzyl radicals are preferentially formed, and interconversion to tropyl is apparently quenched by collisional cooling in the supersonic expansion.6 Tropyl radicals were produced using cycloheptatriene as the discharge precursor, and the rearrangement of tropyl to benzyl was similarly not observed in molecular beam experiments.6,7 Therefore, the reaction barrier between these isomers must be sufficiently high to inhibit rearrangement, as has been † suggested by theory (ΔH0K ≈ 70 kcal/mol).3 Recent © XXXX American Chemical Society

experimental studies on the pyrolysis of benzyl and tropyl radicals in a heated microreactor found no interconversion in either direction before the radicals decomposed at high temperatures.8,9 Photoionization studies of the tropyl radical revealed an ionization energy of 6.23 eV,10,11 producing the tropylium cation. Whereas benzyl is predicted to be more stable than tropyl by 0.73 eV,7 the energetic ordering of the cationic species is reversed, with the tropylium cation being more stable than benzylium by 0.24 eV.7 Rearrangement pathways interconverting the cations have also been investigated, predicting a barrier of 65 kcal/mol.12 The tropyl radical is an open-shell system with an unpaired, delocalized pi-electron, and as a seven-membered ring, it has a high intrinsic symmetry (D7h). Due to the molecule’s symmetric configuration, the excess electron occupies a pair of degenerate orbitals (E2″ symmetry), and therefore, the molecule is subjected to a Jahn−Teller (JT) distortion that reduces its symmetry through an in-plane ring deformation (yielding a C2v symmetric structure). A precedent spectroscopic study employed electron spin resonance (ESR) to probe tropyl trapped in different crystalline environments. Seven equally spaced resonances were observed in spectra taken at room temperature and interpreted as a uniform spin density corresponding to a symmetric configuration. At lower temperatures (about 10−50 K), anisotropic spectra were observed and attributed to a crystal field induced distortion of the ring.13 Received: June 28, 2016 Revised: August 15, 2016

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Figure 1. Mass spectra of the droplets (mean size ∼5000 atoms) for different pyrolysis source conditions. For the cold source (no pyrolysis, upper trace), strong signals at m/z = 78 and 91 are highlighted; for the hot source (pyrolysis, lower trace), additional strong signals at m/z = 65 and 89 are highlighted.

In a combined experimental and theoretical effort, Miller and co-workers employed laser-induced fluorescence (LIF), laserexcited dispersed fluorescence (LEDF), and ab initio calculations to probe the vibronic dynamics of the tropyl radical.14,15 Vibronic transitions were observed up to 1700 cm−1 above the ground and first excited electronic states. First-order coupling constants were determined for many JT-active vibrational modes, and the JT stabilization energy was experimentally determined to be 1043 cm−1. As all JT-active modes have a linear JT constant D < 1, the distortion is dynamic, and therefore, vibronic coupling is non-negligible.16 In another study, von Helden and co-workers measured the molecular beam IR absorption spectrum of tropyl, which revealed vibronic transitions in the 400−1800 cm−1 range;7 however, the spectra were not analyzed in the context of the JT effect. An IR absorption spectrum of tropyl in the range of the CH-stretch vibrations has not been reported. Spectroscopic data for tropyl are consistent with the spectroscopy of other symmetric aromatic radicals (cyclopentadienyl, benzene cation), also reported by Miller and coworkers.17−19 All of these radicals exhibit a dynamic JT distortion. The framework for the theoretical treatment of the JT effect has been discussed in detail by Barckholtz and Miller.16 A more recent computational study of these radicals employed multideterminantal DFT.20 Comparable results were obtained for the JT stabilization energy, and employing a multimode approach, the contribution of different vibrational modes to the JT distortion was analyzed in depth. While the CH-stretch vibrations are not expected to contribute significantly to the JT distortion, the splitting of these degenerate vibrational modes induced by vibronic coupling necessitates a detailed analysis of the JT effect to properly account for the CH-stretch region of the IR absorption spectrum. Herein we report the application of helium droplet spectroscopy to probe the CH stretch region of the tropyl radical’s IR absorption spectrum. This technique has been shown to perform well for the acquisition of mid-IR spectra of radicals produced via pyrolysis of organic precursors.21−28

Moreover, the helium solvent−solute interaction has been shown to be almost negligible with respect to its effect on vibrational band origins.29 We investigate the IR absorptions in the 2940−3140 cm−1 range. Two distinct CH stretch bands are observed, one of which cannot be accounted for in the absence of vibronic coupling.

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EXPERIMENTAL METHODS Measurements were carried out using the helium droplet apparatus at the University of Georgia. A comparable setup has been described in detail previously;22,23 therefore, only a brief review of the technique is given. Helium droplets are produced in a continuous expansion of pressurized (35 bar) and precooled (17 K) helium through a 5 μm diameter nozzle. This produces droplets with a mean size of about 5000 helium atoms.30,31 The droplets are skimmed into a beam and passed through a pickup chamber, where approximately 20% of them are doped with a single tropyl radical. Tropyl radicals were produced via the flash vacuum pyrolysis of bitropyl, using the pyrolysis source design described previously.23 Bitropyl (SigmaAldrich) was sublimated at room temperature and passed through a quartz tube. The tip of the quartz tube was wrapped with a few coils of tantalum wire and heated to ∼900 K. Upon collision with the hot quartz tube, bitropyl fragments into two tropyl radicals. The density of gas-phase radicals in the quartz furnace is sufficiently low such that bimolecular recombination reactions are negligible. The droplet beam passes immediately in front of the effusive output of the quartz tube, and the radicals are picked up by the droplets and cooled to ∼0.4 K.32−34 The doped droplets travel through a laser interaction zone prior to being ionized by electron impact. A continuous wave optical parametric oscillator (Lockheed Martin Aculight ARGOS 2400) was used as a tunable radiation source in the range 2940−3140 cm−1. The tuning and calibration of the laser is described elsewhere.35 The IR radiation counter-propagates the droplet beam. Upon exciting a vibrational transition of the embedded solute, the absorbed energy is dissipated via He atom evaporation. This reduces both the droplet size and cross B

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than both the expected rotational contour and the inhomogeneous width typical of small molecules in helium droplets. No other bands were observed for the radical in the range 2940− 3140 cm−1. An analysis of these transitions in the context of the JT effect is provided below. Spectroscopic Analysis. Tropyl vibrational modes in the symmetric configuration can be treated in the framework of the D7h symmetry group. The seven CH-stretch normal modes span A′1 ⊕ E′1 ⊕ E′2 ⊕ E′3. Of these, the nth order JT-active modes can be found from the following symmetry analysis

section for ionization, reducing the ion current measured with a quadrupole mass spectrometer. Photoinduced ion signal depletion is detected phase-sensitively, employing a lock-in amplifier, as the laser is tuned with ∼20 MHz resolution.

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RESULTS Experimental Section. It is well-known that electron impact ionization of doped He droplets leads to the production of dopant ions through a He+ + M → He + M+ charge-transfer ionization mechanism.29,36 Because the ionization potential of M differs substantially from He, this process often leads to the fragmentation of M+. Mass spectra for different pyrolysis source conditions were taken to optimize for the pickup of single tropyl radicals. Figure 1 shows a comparison between the mass spectra recorded under cold pyrolysis source conditions (black trace) and with conditions optimized for tropyl production (red trace). Without pyrolysis, the mass spectrum is that of a mixture of neat droplets and droplets containing bitropyl, with strong peaks appearing at m/z = 78 and 91. These peaks are due to the aforementioned charge transfer ionization of bitropyl, which generates the fragments (C6H6)+ and (C7H7)+, respectively. Under high-temperature pyrolysis source conditions, signals at m/z = 65 and 89−91 dominate the mass spectrum, corresponding to (C5H5)+ and (C7H5−7)+. The signal at m/z = 78 is significantly decreased upon heating the source, indicating a highly reduced probability for bitropyl pickup. The qualitative change in the mass spectrum upon heating the pyrolysis source is taken as initial evidence of the production of the tropyl radical. Mass channel m/z = 89 was determined to be the most selective channel for detecting the laser-induced cross section reduction of droplets containing the tropyl radical. Infrared spectra of bitropyl and tropyl were recorded as depletion in mass channels m/z = 91 and m/z = 89, respectively. Figure 2 shows both spectra in the 2990−3100

Γe ⊗ Γe ⊇ [Γv]n

(1)

where Γe is the symmetry of the electronic state and Γv the symmetry of the vibrational state. For the X̃ 2E″2 electronic ground state, the E′3 mode is linearly JT-active and the E′2 mode is quadratically JT-active. The Γe ⊗ Γv vibronic symmetries of the CH stretch modes are A1′ ⊗ E2″ = E2″

(2a)

E1′ ⊗ E2″ = E1″ ⊕ E3″

(2b)

E2′ ⊗ E2″ = A1″ ⊕ A 2″ ⊕ E3″

(2c)

E3′ ⊗ E2″ = E1″ ⊕ E2″

(2d)

From the E″2 vibronic ground state, transitions accessing E″1 , E″3 , or E′2 vibronic levels will have nonzero transition dipole moments (on the basis of the vanishing integral rule: Γe′ ⊗ Γv′ ⊗ Γx,y,z ⊗ Γe″ ⊗ Γv″ ⊇ Γs). Therefore, both the linearly (E3′ ) and quadratically (E2′ ) JT-active modes are expected to contribute one IR-active band in the CH stretch region. Moreover, the non-JT-active E1′ vibrational mode is IR-active, and therefore, a total of three IR-active CH stretching bands are predicted by symmetry. To model the JT splittings, we utilize the previously reported calculations of Miller and co-workers.14 These authors computed the geometry and normal modes for the tropylium cation at the RHF/6-31G** level and the linear JT coupling constants for the tropyl radical at the EOMEA-CCSD/TZ2P level. Because they did not predict a quadratic JT constant, we used a value of K = 0.01 to qualitatively model the splitting. Table 1 shows the harmonic frequencies of the fundamental CH modes and their corresponding linear and quadratic JT constants. Table 1. Harmonic Frequencies and Jahn−Teller Coupling Constants

Figure 2. Infrared spectra of bitropyl, measured as depletion on mass channel m/z = 91 (upper trace), and tropyl, measured on mass channel m/z = 89 (lower trace), with a mean droplet size of ∼5000 helium atoms. Two features at 3053 and 3058 cm−1 are observed in the radical spectrum.

symmetry

A1′

E1′

E2′

E3′

energy (cm−1) D (lin. JT) K (quad. JT)

3383a 0 0

3378a 0 0

3366a 0 0.01b

3356a 0.002a 0

a

The RHF/6-31G** harmonic frequencies for the tropylium cation and the predicted linear Jahn−Teller coupling constants for the tropyl radical at the EOMEA-CCSD/TZ2P level of theory.14 bEstimated quadratic JT constant used for a qualitative analysis.

cm−1 range. Two partially resolved features are observed at 3053 and 3058 cm−1 in the tropyl radical spectrum (red). Both bands have an approximately 4 cm−1 line width and are not observed in the bitropyl precursor spectrum. The line width most likely derives from a homogeneous mechanism associated with vibrational dephasing/relaxation, as the width is broader

The JT splittings are calculated according to the procedure outlined in the electronic Supporting Information, which follows ref 16. The results of these calculations are shown schematically in Figure 3. In the absence of vibronic coupling, the tropylium RHF harmonic frequencies of the E1′ and E2′ modes are separated by 12 cm−1, and the E2′ and E3′ modes are C

DOI: 10.1021/acs.jpca.6b06522 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A Ψ′L = −0.996|+, 1, −1⟩ + 0.088|− , 2, −2⟩

(3d)

ΨU = −0.996|−, 1, −1⟩ − 0.063|+ , 0, 0⟩ + 0.063|+ , 2, 0⟩

(3e)

Ψ′U = 0.996|+, 1, 1⟩ + 0.063|− , 0, 0⟩ − 0.063|− , 2, 0⟩ (3f)

with ΨG and Ψ′G the wave functions of the doubly degenerate vibronic ground state. The ΨL/Ψ′L and ΨU/Ψ′U wave functions are associated with the lower and upper components of the linearly split E3′ mode. For transitions between the ground vibronic state and these four possible excited states, the integrals ⟨Ψ′|μ̂ |Ψ″⟩ were evaluated. Disregarding the terms that violate selection rules (see eq 8 in the Supporting Information), we obtain ⟨ΨU|μ|̂ ΨG⟩ = 0.994⟨− 1, 1, −|μ|̂ +, 0, 0⟩ + 0.002⟨− 1, 1, −|μ|̂ + , 2, 0⟩ − 0.004⟨0, 0, +|μ|̂ −, 1, −1⟩ + 0.004⟨0, 2, +|μ|̂ −, 1, −1⟩

Figure 3. Schematic energy levels for the tropyl CH-stretch modes without and with the treatment of vibronic coupling. On the basis of the tropylium RHF/6-31G** harmonic frequencies (left), the E′2 mode is split by the quadratic Jahn−Teller constant K = 0.01 and the E′3 mode is split by the linear Jahn−Teller constant D = 0.002 (right). The red arrows indicate allowed infrared transitions from the ground vibronic state, with the solid arrows indicating our assignment of the experimentally observed transitions.

⟨ΨU|μ|̂ Ψ′G⟩ = 0 ⟨Ψ′U|μ|̂ ΨG⟩ = 0

⟨Ψ′U|μ|̂ Ψ′G⟩ = −0.994⟨1, 1, +|μ|̂ − , 0, 0⟩ − 0.002⟨1, 1, +|μ|̂ − , 2, 0⟩ + 0.004⟨0, 0, −|μ|̂ + , 1, 1⟩ − 0.004⟨0, 2, −|μ|̂ + , 1, 1⟩

separated by 10 cm−1. The nondegenerate A′1 mode is 5 cm−1 to the blue of the IR-active E′1 mode. As discussed above, the A′1 and E1′ modes are not JT-active. Vibronic coupling, however, splits the quadratically JT-active E2′ mode into A1″, A2″, and E3″ levels and the linearly JT-active E′3 mode into E″1 and E″2 levels. The calculation for the E′2 mode using K = 0.01 yields a doubly degenerate level, with a negligible shift from the uncoupled mode and two nondegenerate levels that are shifted by ±34 cm−1. The E″3 assignment is obvious, as it is assigned to the doubly degenerate level, while the assignment of the nondegenerate A1″ and A2″ modes remains unclear. The calculation for the linear JT-active E3′ mode using D = 0.002 yields two doubly degenerate levels (E″1 , E″2 ) that are shifted by ±13 cm−1 from the uncoupled mode. The upper component shifts into a position between the IR-active E1″ ⊕ E3″ (from which it now lies 9 cm−1 red) and the E3″ (from which it now lies 3 cm−1 blue) vibronic levels. This upper component is assigned E″1 on the basis of the magnitude of dipole matrix elements and the aforementioned symmetry arguments for IR activity (vide inf ra). The eigenfunctions for the ground and first excited states of the linearly split E′3 mode in terms of the vibronic Born− Oppenheimer basis functions (|Λ, v, j ⟩, where 1 j = l + ( −1)s1 2 Λ ; for more details, see the Supporting Information) up to a maximum of vmax = 2 are

⟨ΨL|μ|̂ ΨG⟩ = 0 ⟨ΨL|μ|̂ Ψ′G⟩ = 0 ⟨Ψ′L|μ|̂ ΨG⟩ = 0 ⟨Ψ′L|μ|̂ Ψ′G⟩ = 0

(3a)

Ψ′G = −0.998|−, 0, 0⟩ + 0.063|+, 1, 1⟩ − 0.002|− , 2, 0⟩ (3b)

ΨL = −0.996|−, 1, 1⟩ + 0.088|+ , 2, 2⟩

(4b)

Nonzero matrix elements occur for transitions between the ground state and the upper level; we therefore assign the upper component of the linearly split E′3 mode to the E″1 symmetry species, as shown in Figure 3 and noted above. We now determine the effect of the magnitude of JT coupling constants on the relative positions of IR-active transitions. The magnitude of the splitting of the linearly JTactive E3′ mode increases when the linear coupling constant D gets larger; therefore, the infrared-active E1″ component shifts to the blue. For the values D = 0.0025 and D = 0.004, the components of the E′3 mode are shifted by ±17 and ±27 cm−1, respectively. This places the upper component (i.e., E1″) 5 cm−1 to either the red or blue of the IR-active but JT-inactive E′1 mode. For the quadratically JT-active E′2 mode, the coupling constant K mainly determines the splitting between the nondegenerate components A1″ and A2″. In the case of large coupling constants, e.g., for K = 0.1, the degenerate and IRactive E″3 component shifts 6 cm−1 to the red, which shifts it further away from the E′1 mode. To summarize the theoretical analysis of the CH stretch region, there is one IR-active E1′ mode in the absence of vibronic coupling. On the basis of symmetry alone, two other bands might be expected to appear in the IR spectrum when vibronic coupling is included in the analysis. As shown in Figure 3, the upper component of the split E3′ mode (E1″ symmetry

ΨG = −0.998|+, 0, 0⟩ + 0.063|− , 1, −1⟩ − 0.002|+, 2, 0⟩

(4a)

(3c) D

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The Journal of Physical Chemistry A species) is predicted to lie 9 cm−1 below the E″1 ⊕ E″3 level, and the middle level of the split E′2 mode (E″3 symmetry species) lies another 3 cm−1 lower. Of the three potentially IR-active transitions, we have established definitive nonzero IR activity for the non-JT-active E1′ mode and the upper component of the linearly JT-active E′3 mode (E″1 symmetry species). The relative strength of the IR-active transition from the ground vibronic state to the middle component of the quadratically JT-active E′2 mode (E3″ symmetry species) has not yet been theoretically determined, as a procedure for this has not yet been reported, to the best of our knowledge.

reported here will greatly simplify efforts to locate the gas-phase band origins of tropyl radical in the CH stretch region.

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SUMMARY We employed the helium droplet isolation technique to measure the CH stretch spectrum of tropyl radical in the range 2940−3140 cm−1. Two partially resolved bands were observed at 3053 and 3058 cm−1 and assigned to two distinct CH stretch modes by taking into account vibronic coupling. These are the E1′ mode and the upper component of the E3′ mode (E″1 symmetry species), with no conclusive statement on the ordering of these. Due to the D7h symmetry, only one CH stretch mode (E1′ symmetry) has a transition dipole moment; however, first and second order vibronic coupling create two additional levels with dipole allowed transitions from the ground state. The E′2 mode is split by second order coupling into three levels (A1″ ⊕ A2″ ⊕ E3″) with the middle component (E3″) having a transition dipole moment that is nonzero by symmetry. This transition is not considered in the assignment, because the energy difference to the IR-active (and Jahn−Teller inactive) E1′ mode is too large (12 cm−1) compared to the experimental finding. The E3′ mode is split by first order coupling into two levels (E″1 ⊕ E″2 ) with the upper component (E″1 ) being IR-active. For linear coupling constants of D = 0.004 and D = 0.0025, the energy difference between the E1′ mode and the upper component of the E3′ mode is ±5 cm−1, respectively, i.e., the value determined experimentally. A value of D on the order of 10−3 is in reasonable agreement with previous theoretical predictions. Further work to confirm the assignment in the CH stretch region is necessary, including higher level computations to determine the Jahn−Teller coupling constants more precisely and experimental work, ideally, high-resolution gas-phase IR spectroscopy. To further probe the impact of the Jahn−Teller effect on the CH stretch region, measurements of the deuterated species and higher level computations of dipole matrix elements, including those for the quadratically split levels, should be considered. The helium droplet work reported here can serve as a starting point for future searches of the highresolution gas-phase spectrum, given the extremely weak solvent perturbation expected for the band origins.

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DISCUSSION The two experimentally observed bands are tentatively assigned to the nonsplit E′1 mode (E″1 ⊕ E″3 symmetry species) and the upper component of the linearly JT-active E3′ mode (E1″ symmetry species). This assignment is based on calculations of harmonic frequencies and the JT coupling constants to model the energy levels and their corresponding dipole matrix elements for transitions from the vibronic ground state. Stakhursky et al. reported harmonic frequencies for tropylium at the RHF, DFT, and MP2 levels of theory. While the unscaled frequencies differed significantly between the different methods, the energy spacing between the CH stretch modes roughly follows the same pattern of 5 cm−1 − 10 cm−1 − 10 cm−1. The JT coupling constant for the E3′ mode was predicted, depending on the level of theory (CASSCF(7,7) and EOMEA-CCSD), between D = 0.001 and D = 0.002.14 For the RHF harmonic frequencies, a value of D = 0.0025 would suffice to produce a 5 cm−1 spacing between the assigned IR-active modes, i.e., the value which corresponds to the experimentally observed difference. On the other hand, the energy difference between the E′1 mode (E″1 ⊕ E″3 symmetry species) and the middle component of the E2′ mode (E3″ symmetry species) is large (12 cm−1) and increases for a larger quadratic coupling constant K. It is important to note, however, the rather low level of theory for the harmonic frequencies and the neglect of anharmonicity in the determination of the energy levels. Nevertheless, even with these caveats, the assignment is motivated by the observation that the upper line of the split E′3 mode (E″1 symmetry species) has a non-negligible dipole matrix element and shifts into the correct region when using the estimated linear coupling constant, D = 0.002. Because small corrections to the coupling constant already have a relatively large impact on the splitting, a slightly larger D would make the energy difference between these bands closer to the experimental value. Because there is no gas-phase experimental value for the linear coupling constant, and the predictions vary for different levels of theory, values of D = 0.0025 and D = 0.004 are within reasonable agreement of the previously predicted value (D = 0.002). A more accurate calculation could resolve this residual discrepancy between prediction and experiment. We emphasize that we cannot rule out an alternative assignment of the observed spectrum to all three IR-active bands predicted by symmetry. Indeed, the bands are not completely resolved, and the presence of a third band in the 3050−3060 cm−1 region cannot be entirely ruled out. Finally, we note that we expect the helium solvent to have a minimal effect on the extent by which the tropyl radical is dynamically distorted by the JT effect. Indeed, the effect of the helium solvent on vibrational energy levels is typically between 0.1 and 1 cm−1. We therefore anticipate that the band origins

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b06522. An expanded discussion of the spectroscopic model used to predict the number and positions of IR-active lines in the mid-IR spectrum of the tropyl radical (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +01(706)542-3857. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS G.E.D. acknowledges support from the Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division of the US Department of Energy (DOE) under Contract No. DE-FG02-12ER16298. M.H. acknowledges support from the Cluster of Excellence E

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RESOLV (EXC 1069) funded by the Deutsche Forschungsgemeinschaft.

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DOI: 10.1021/acs.jpca.6b06522 J. Phys. Chem. A XXXX, XXX, XXX−XXX