Chemical Physics Letters 642 (2015) 5–11
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Electronic emission spectroscopy of the 4-methyl-3-azabenzyl radical Johnny Lightcap, Joseph T. Butler, Daniel J. Goebbert ∗ Department of Chemistry, The University of Alabama, Tuscaloosa, AL 35487, United States
a r t i c l e
i n f o
Article history: Received 4 September 2015 In final form 31 October 2015 Available online 10 November 2015
a b s t r a c t The 4-methyl-3-azabenzyl radical was generated from 2,5-lutidine in a corona excited supersonic expansion, and its fluorescence emission spectrum was recorded. Two possible radical isomers could form by loss of an H atom from either methyl group in 2,5-lutidine. Theoretical studies of both isomers confirmed the only species observed was 4-methyl-3-azabenzyl. The emission spectrum corresponded to the D1 → D0 transition, with a strong origin peak and several vibronic bands. The origin transition is located at 21 401 cm−1 , in good agreement with a previous assignment, and calculated vibrational energies were in good agreement experimental vibrational energies. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Heavy fuels derived from coal are rich in heteroatom containing compounds, particularly nitrogen and sulfur. Combustion of compounds rich in nitrogen is thought to increase the formation of undesirable products such as NOx [1,2]. All combustion mechanisms invoke formation of radicals in early stages, thus the properties of organic radicals containing heteroatoms are important in combustion modeling. Coals are typically composed of aromatic oligomers or polymers, and combustion of these compounds yields aromatic radicals. The combustion of 2-picoline, a model compound for heteroatom compounds in coal combustion, has previously been investigated using pulse shock tube methods [3–5]. These kinetic studies suggested the 2-picolyl radical, a heteroatom substituted benzyl radical, is a key intermediate formed in the pyrolysis of 2-picoline. The properties of a few nitrogen heteroatom substituted benzyl radicals have been studied previously. The 3,5-dimethyl4-azabenzyl and 3-methyl-2-azabenzyl radicals were generated by photodissociation in a cryogenic matrix and low resolution absorption spectra of these species were recorded [6]. Lloyd and Wood [7] investigated a series of similar azabenzyl radicals by E.P.R. spectroscopy in an adamantane matrix. Several decades later, Bray and Bernstein recorded the absorption spectra of the 3-picolyl (3azabenzyl) and 2,5-lutidyl (4-methyl-3-azabenzyl) radicals in the gas phase using a pulsed molecular beam laser photolysis apparatus for radical generation and multiphoton ionization spectroscopy
∗ Corresponding author. Present address: The University of Alabama, Department of Chemistry, Box 870336, Tuscaloosa, AL 35487, United States. E-mail address:
[email protected] (D.J. Goebbert). http://dx.doi.org/10.1016/j.cplett.2015.10.076 0009-2614/© 2015 Elsevier B.V. All rights reserved.
[8,9]. The spectrum of 4-methyl-3-azabenzyl consisted of a strong origin band and several weak vibronic transitions. The researchers tried to study the absorption spectra of several other nitrogen atom substituted benzyl radicals, but they could not obtain a spectrum for any other species. Their study concluded the excited state lifetimes of nitrogen atom substituted benzyl radicals are much shorter than those of the corresponding hydrocarbon radicals. That work did not mention the other radical, 4-methyl-2-azabenzyl, that could also be formed by loss of an H atom from the 2,5-lutidine precursor. It is possible the other isomer was not detected due to a short excited state lifetime, absorption in a different spectral region, rearrangement, some other process. This Letter presents our study on the fluorescence emission of the 4-methyl-3-azabenzyl radical using a home-built corona excited supersonic expansion source for generation of radicals in electronic excited states. The 4-methyl-3-azabenzyl radical was chosen for this initial study because its previously reported absorption spectrum [8] provides useful reference for comparison with the emission spectrum. This study confirms the previously reported electronic origin energy. The emission spectrum also provides vibrational energies of the radical in the electronic ground state. Theoretical calculations were carried out to investigate the ground and excited states, and the vibrational energies of 4-methyl-3azabenzyl radical for comparison with experiment. 2. Experimental and theoretical methods All measurements were carried out using a newly designed and constructed corona excited supersonic expansion, CESE, source for radical generation based on previously published designs [10–13]. A tapered glass nozzle with a narrow pin-hole (ca. 0.20–0.50 mm diameter) was used to create a supersonic gas expansion. Analyte
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vapors from several milliliters of 2,5-lutidine were mixed with helium carrier gas in a 1 L glass bubbler at a pressure of 1–2 atm. The gas underwent expansion through the nozzle into a vacuum chamber. The vacuum chamber was continuously evacuated by a roots blower (Edwards EH-250) backed by a mechanical pump (Edwards E2M40). Typical pressure in the vacuum chamber during operation varied between 1 and 4 Torr depending on the orifice diameter and the backing pressure of the helium gas. A tungsten wire, 0.002 diameter, was inserted through the high pressure side of the nozzle with the wire tip located about 1 mm behind the nozzle orifice. Electrical discharge was initiated by application of a current limited high voltage, 1–2 kV, applied to the wire. A bluegreen emission was observed downstream from the nozzle orifice, the signature of benzyl-type radical emission. The emission signal was collected by a lens placed on the air side of a quartz window perpendicular to the nozzle expansion. The light was focused into a fiber optic cable connected to an Ocean Optics USB4000 CCD spectrometer recording signals between 350–1050 nm, with a resolution of about 1 nm. Composite spectra were generated by summing individual spectra. Experiments were repeated over multiple days to ensure reproducibility. The spectrum was calibrated using peaks from the background helium emission. 2.1. Theoretical studies Theoretical calculations were carried out using Gaussian 09 [14]. Geometries were optimized at the unrestricted (U)B3LYP level of theory with the aug-cc-pVDZ basis set. Vibrational frequencies are reported at the (U)B3LYP/aug-cc-pVDZ level of theory without anharmonic correction. Excited state geometries and vertical excitation energies were calculated using the time dependent (TD) formalism [15–20]. 3. Results and discussion 3.1. Emission spectrum A representative emission spectrum using 2,5-lutidine as a radical precursor is shown in Figure 1. The spectrum contains a number of sharp lines over a broad background located between 16 000 and 21 500 cm−1 . Several narrow peaks correspond to well-known He lines and these are indicated in the spectrum by asterisks. The electronic origin is assigned to the highest energy peak at 21 401 ± 11 cm−1 , in good agreement with the previously reported value of 21 395.0 cm−1 for the 4-methyl-3-azabenayl radical [8]. No hot bands were observed, suggesting the molecules were efficiently cooled during the supersonic expansion. No higher energy transitions were observed, indicating the molecule fluoresces from the first electronic excited state. The low intensity broad background is typical for our instrument and is attributed the resolution of the spectrometer. Survey spectra of the benzyl, and xylyl radicals using the nozzle source yielded sharp lines in agreement with previous spectra [21–26], but all spectra contained a broad low intensity background similar to that in Figure 1. Table 1 lists the absolute and relative energies of the major peaks in Figure 1. Peak assignments are discussed later in the text. The 2,5-lutidene precursor can lose an H atom from either methyl substituent resulting in two different radical isomers, 4methyl-2-azabenzyl and the 4-methyl-3-azabenzyl (see Figure 2 or Figure 4 for structures). The spectrum in Figure 1 does not show evidence for two isomers because a single set of lines was recorded. No other molecular bands were detected between 350 and 1050 nm. Spectral signatures from different benzylic radical isomers are often observed in CESE spectra [23,27], and the observation of a single set of lines corresponding to one isomer was not expected. This does
-1
Absolute Wavenumber (cm ) 15000
16000
17000
18000
19000
20000
21000
22000
*
*
*
000 *
* ‡
6000
5000
4000
3000
2000
1000
0
-1
Relative Wavenumber (cm ) Figure 1. Fluorescence emission spectrum of the 4-methyl-3-azabenzyl radical. The absolute energy scale is shown on the top of the spectrum, and the relative energy scale, with respect to the electronic origin, is shown on the bottom of the spectrum. The peaks labeled with an * are helium emission lines, and the sharp line with the ‡ label is detector noise. Several vibronic transitions are labeled, and progressions are designated by colored markers corresponding to each type of vibration. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
not eliminate the possibility that both isomers are generated in the discharge. Both species should have similar bond dissociation energies, and are expected to have similar number densities. The signal from the other isomer could overlap with the main set of transitions in Figure 1, the other isomer could have low number densities, and/or much shorter (or longer) excited state lifetimes. 3.2. Theoretical results Theoretical calculations were carried to confirm isomer and spectral assignments shown in Figure 1. The optimized geometries of the two possible isomers are similar in the ground state but show large differences in the first excited state. Figure 2 lists some of the calculated structural parameters for the two isomers. The angle vertices indicated in Figure 2 are measured with respect to atoms in the aromatic ring. The optimized geometries for 4-methyl3-azabenzyl in the ground and first excited state are similar. The bond lengths in the aromatic ring increase slightly, while the benzylic C C bond length decreases in the excited state. Bond angles in the aromatic ring or on the substituents show small changes. In contrast, the geometry for 4-methyl-2-azabenzyl shows major differences between the ground and first excited state. Bond lengths do not change substantially, but several bond angles undergo large changes. The two most significant changes involve the increase of the aromatic C N C bond angle from 118.2◦ to 133.2◦ , while the N C C bond angle (central carbon connected to the methylene group) decreases from 120.5◦ to 107.2◦ . The first excited and ground state geometries of the two isomers in Figure 2 suggest the emission spectra for each species should be different and distinguishable. The emission spectrum for the D1 → D0 transition in 4-methyl-3-azabenzyl is expected to have an intense origin band with a few vibronic transitions corresponding to aromatic ring vibrations because the optimized geometries for the ground and first excited state of the 4-methyl-3-azabenzyl
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Table 1 Experimental and theoretical D1 ← D0 vertical transition energies (TD-(U)B3LYP/aug-cc-pVDZ) for substituted benzyl type radicals. Radical
Experiment
Theory cm−1
Theory − experiment
Ref.
Benzyl p-Methylbenzyl o-Methylbenzyl m-Methylbenzyl 3,4-Dimethylbenzyl 2,4-Dimethylbenzyl 4-Methyl-3-azabenzyl (D1 ← D0 ) 4-Methyl-3-azabenzyl (D2 ← D0 )a 4-Methyl-2-azabenzyl (D1 ← D0 )a 4-Methyl-2-azabenzyl (D2 ← D0 )
22 002 21 700 21 346 21 487 21 592 21 306 21 401 Not obs. Not obs. Not obs.
25 364 25 089 24 163 24 248 24 656 24 393 24 556 26 230 22 631 25 526
3365 3389 2817 2761 3064 3024 3150
[22,32,33] [21,25,34] [21] [21,26] [23,27,35] [23,27,35] This work
a
Calculated oscillator strength, f = 0.000.
isomer are nearly identical. The geometries for the ground and first excited state of the 4-methyl-2-azabenzyl isomer require significant ring distortions. This should result in poor Franck–Condon overlap for the D1 → D0 origin transition and a broad band with a weak origin transition and a large number of vibronic transitions. The intense origin band in Figure 1 is consistent with the small geometry changes calculated for the 4-methyl-3-azabenzyl radical. We calculated the lowest energy vertical excitation energies, D1 ← D0 , and D2 ← D0 for both isomers from the optimized ground state geometries at the TD-(U)B3LYP/aug-cc-pVDZ level of theory, Table 1. Although we measured the emission spectrum in this experiment, relative excitation energies from theory should mirror the experimental emission energies. Calculations predict the 4-methyl-3-azabenzyl isomer has a D1 ← D0 vertical transition
energy of 24 556 cm−1 corresponding to promotion of the unpaired non-bonding electron, NB , into the lowest energy * orbital. Excited states of resonance stabilized radicals generally involve paired transitions [28]. Theory shows one of the excited configurations dominates. Therefore, the azabenzyl radical excited states are well-approximated as one-electron transitions, and this simplifies the description for both isomers. The optimized geometry in Figure 2 shows the effect of the D1 ← D0 excitation. Transfer of the non-bonding electron, localized on the methylene group, into a * orbital on the aromatic ring increases the antibonding character and results in slightly longer bond lengths in the ring. The vertical transition energy to the second electronic excited state of 4methyl-3-azabenzyl isomer, D2 ← D0 , corresponds to a NB ← NB transition involving promotion of one of the nitrogen lone pair
Figure 2. Optimized geometries for the 4-methyl-3-azabenzyl and 4-methyl-2-azabenzyl radicals in the ground electronic state, D0 , calculated at the (U)B3LYP/aug-cc-pVDZ level of theory, and first electronic excited state, D1 , calculated at the TD-(U)B3LYP/aug-cc-pVDZ level of theory. Bond angles are indicated for atoms in the aromatic ring (the vertex is indicated by arrow).
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electrons into the partially filled nonbonding orbital. The calculated vertical transition energy is 26 230 cm−1 . Theory predicts zero oscillator strength for the perpendicular D2 ← D0 excitation, and this transition would be a much weaker transition relative to the D1 ← D0 excitation. No higher energy signals corresponding to emission from the D2 state were observed. Higher excited states have not been observed for other benzyl type radicals in our experiment, indicating the excited species are efficiently cooled in the supersonic expansion to the first excited state. Calculations predict the D1 ← D0 vertical excitation energy for 4-methyl-2-azabenzyl is 22 631 cm−1 , considerably lower than the D1 ← D0 excitation energy calculated for the 4-methyl-3-azabenzyl isomer. Theory predicts this is a perpendicular NB ← NB transition with zero oscillator strength, thus the intensity of this transition should be significantly weaker compared to the other isomer. The optimized geometry for the D1 state of the 4-methyl2-azabenzyl isomer in Figure 2 shows the effect of the NB ← NB transition. The promotion of a NB electron on the nitrogen atom reduces electron repulsion at the nitrogen atom, allowing an increase in the C N C bond angle. Bond lengths show small changes because the transition involves non-bonding orbitals. The second excited state for the 4-methyl-2-azabenzyl isomer, D2 ← D0 , corresponds to an allowed * ← NB transition with an energy of 25 526 cm−1 . This energy is about 1000 cm−1 greater than the same * ← NB transition calculated for 4-methyl-3-azabenzyl. No higher energy emission signals attributed to relaxation from the D2 state of 4-methyl-2-azabenzyl were detected in this experiment. Theory suggests that if the 4-methyl-2-azabenzyl radicals are generated in the discharge, they are not detected because the radicals are cooled in the supersonic expansion to the D1 state. However, the D1 state of 4-methyl-2-azabenzyl results in a forbidden perpendicular transition, and does not generate a strong emission signal. Both isomers are expected to form in the discharge, but only one undergoes emission. Theoretical studies predict different electron configurations for the D1 and D2 states of 4-methyl-2-azabenzyl and 4-methyl-3azabenzyl, but the only difference between the two isomers is the relative position of the radical center and the nitrogen atom. It is interesting to understand why the electron configurations of the two isomers have a different ordering. The lowest energy NB ↔ NB and NB ↔ * one-electron transitions for both isomers are shown schematically in Figure 3. The diagrams indicate relative energies of the occupied spin-orbitals based on theoretical calculations. Figure 3 shows the lowest energy transition of the 4-methyl-3-azabenzyl isomer corresponds to the * ↔ NB transition, whereas the lowest energy transition of the 4-methyl2-azabenzyl isomer corresponds to the NB ↔ NB transition. The different first excited states for these radicals can be attributed to two primary effects. The first is stabilization of the NB orbital in the 4-methyl-2-azabenzyl radical due to partial density at the nitrogen atom position, Figure 3. In contrast, the heteroatom is located at a node for the NB orbital in the 4-methyl-3-azabenzyl radical. The second factor that contributes to the different excited state configurations is spin polarization [29]. The unpaired NB electron polarizes electron spins in the molecular framework through exchange interactions. The relative position of the nitrogen atom in 4-methyl-3-azabenzyl results in partial stabilization of the oneelectron spin-orbital for the  electron in the nitrogen lone pair. This increases the energy required for the NB ↔ NB transition relative to the * ↔ NB transition. In contrast, the relative position of the nitrogen atom in 4-methyl-2-azabenzyl results in a slightly higher relative energy of the  electron in the nitrogen lone pair. The higher energy of the  electron, combined with the lower relative energy of the NB orbital, explains why theory predicts a low energy for the NB ↔ NB transition relative to the * ↔ NB transition in 4-methyl-2-azabenzyl.
The theoretical vertical excitation energy for the 4-methyl-3azabenzyl radical is 24 556 cm−1 compared to the experimental origin at 21 401 cm−1 in Figure 1. Table 1 shows a comparison of theoretical vertical excitation energies for a series of similar methyl substituted benzyl radicals compared with experimental origin band energies. Theory systematically overestimates vertical excitation energies, and the average difference between theory and experiment is 3080 cm−1 . These differences in similar in magnitude to previously reported energies [30]. Figure 4 shows a plot of the theoretical vertical excitation energies for the benzyl radicals listed in Table 1 compared with their corresponding experimental origin bands. The general trend in this comparison is similar to those found in previous studies [28,30]. The calculated vertical excitation energies of the two isomers are also plotted against the experimental origin energy of 21 401 cm−1 in Figure 4. The 4-methyl-3-azabenzyl isomer fits the trend between experiment and theory for similar benzyl radicals, while both transitions for the 4-methyl-2-azabenzyl isomer lie well outside the trend. This helps confirm the emission spectrum in Figure 1 belongs to the 4-methyl-3-azabenzyl isomer. The electronic origin of the 4-methyl-3-azabenzyl radical shows the effect of heteroatom substitution on electronic energies in aromatic benzylic radicals. The origin band for the benzyl radical, Table 1, is located at 22 002 cm−1 [8,28]. Previous experiments have shown that methyl group substitution decreases the energy of the origin band, Table 1. The radical in this study is isoelectronic with, and structurally similar to, the well-known p-xylyl radical. The origin transition for p-xylyl has been reported at 21 700 cm−1 , indicating the methyl group results in a red-shift of about 299 cm−1 . Replacement of an aromatic C H group with a nitrogen atom results in a further red-shift of the origin band of about 304 cm−1 compared to p-xylyl. The nature of the additional red-shift can be attributed to the relative orbital energies shown in Figure 3. The relative energies of the orbitals in both p-xylyl and 4-methyl-3azabenayl should be similar (albeit in a crude one-electron Hückel approximation). However, the relative energy for the * orbital in 4-methyl-3-azabenyl is stabilized relative to p-xylyl due to partial electron density at the nitrogen atom. This accounts for the red-shift of the origin band in 4-methyl-3-azabenzyl relative to the benzyl and p-xylyl radicals.
3.3. Vibronic transitions The highest energy peak in Figure 1 is assigned as the origin for fluorescence emission from the 4-methyl-3-azabenzyl radical. The lower axis in Figure 1 shows the energy of the remaining peaks relative to the origin transition. The major peaks are located in the region from 500 to 1750 cm−1 relative to the origin and a long progression of weak bands continues to energies around 2600 cm−1 from the origin. Table 2 lists the experimental energies of the major peaks in Figure 1. Peak assignments were made with the assistance of calculated vibrational energies for the ground state of 4-methyl3-azabenzyl and are listed in Table 2. The three major peaks at low energy are assigned as the 6a, 6b and 1 vibrations [31], commonly observed in the spectra of benzyl type radicals. These assignments agree well with similar assignments of the excited state vibrational energies in the previous absorption study of 4-methyl-3-azabenzyl radical [8]. The experimental vibrational energy, 474 cm−1 , obtained from the peak assigned to the 6a01 transition agrees well with the calculated vibrational energy of 485 cm−1 . The energy of the 6a10 absorption transition is 406.5 cm−1 . The experimental vibrational energy obtained from the peak assigned to the 6b01 transition is 620 cm−1 , in agreement with the calculated vibrational energy of 647 cm−1 . The energy of the 6b10 absorption transition is 661.4 cm−1 . Finally,
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Figure 3. Schematic orbital energy diagram for the 4-methyl-3-azabenzyl and 4-methyl-2-azabenzyl radicals. The structures at the top of the figure indicate electron spin polarization (␣ or ) induced by the unpaired ␣ electron on the methylene group. The orbital diagram depicts the relative energies of the spin-orbitals for the non-boding electrons. Two possible one-electron transitions are indicated in the diagram, * ↔ NB and NB ↔ NB .
the experimental vibrational energy of 836 cm−1 obtained from the peak assigned to the 101 transition is in good agreement with the calculated vibrational energy, 854 cm−1 . The energy of the 110 absorption transition is 819.6 cm−1 . These three vibrations typically have strong Franck–Condon factors in the emission spectra of benzyl radicals because their motions map onto the major structural changes calculated for relaxation from the D1 to D0 state.
The remaining structure in Figure 1 is either due to other vibrations or overtone and combination bands. The resolution of the spectrometer results in a congested spectrum, and the following assignments are tentative. The weak peak at 951 cm−1 corresponds to the 6a02 overtone. The two peaks at 1254 cm−1 and 1306 cm−1 are assigned to the 6b02 overtone and 101 6a01 combination band respectively. The weak band at 1671 cm−1 is in good agreement with the
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26,000 4-methyl-2-azabenzyl (D2 → D0)
Theorecal Vercal Transion Energy (cm-1)
25,500 p-methylbenzyl 25,000
benzyl
2,4-dimethylbenzyl 4-methyl-3-azabenzyl
24,500
24,000
3,4-dimethylbenzyl m-methylbenzyl
o-methylbenzyl
23,500
23,000 4-methyl-2-azabenzyl (D1 → D0)
22,500
22,000 21,200
21,300
21,400
21,500 21,600 21,700 21,800 Experimental Origin Band Energy (cm-1)
21,900
22,000
22,100
Figure 4. Comparison of theoretical vertical transition energies (D1 ← D0 ) with experimental origin energies for several benzyl radicals calculated at the TD-(U)B3LYP/augcc-pVDZ level of theory. The trend line shows the fit between experiment and theory. The corresponding transitions for the 4-methyl-3-azabenzyl and 4-methyl-2-azabenzyl radicals are indicated using the origin energy assigned in Figure 1.
Table 2 List of vibronic transitions observed in this study and their assignments. Absolute peak position cm−1 21 401 21 218 21 011 20 927 20 781 20 565 20 450 20 319 20 147 20 095 19 944 19 854 19 813 19 730 19 674 19 617 19 505 19 371 19 324 19 262 19 018 18 891 18 839 a
Relative position cm−1 0
474 620 836 951 1254 1306 1547 1671 1727 1784 1896 2030 2077 2139 2383 2510 2562
Intensity
Assignment
s s vw s m s w vs m s vs m s w w w w w vw w w vw vw
Origin He 6a01 6b01 101 6a02 He 6b02 101 6a01 He
Theoretical vibrational energya cm−1
485 647 854
He 102 101 6a02
101 6b02 103
Unscaled harmonic frequencies for 4-methyl-3-azabenzyl radical in the ground electronic state at the (U)B3LYP/aug-cc-pVDZ level of theory.
102 overtone. Higher energy peaks are detected above the broad background signal, but have low intensity. The 101 6b01 combination band should be located near 1456 cm−1 , but this is in the region of a strong He line (1457 cm−1 on the relative scale). There are several groups of peaks located above 1500 cm−1 . Tentative assignments include 101 6a02 for the peak at 1784 cm−1 , 101 6b02 for the peak at 2139 cm−1 , and 103 for the peak at 2508 cm−1 .
4. Summary This study reports the first gas-phase emission spectrum of the 4-methyl-3-azabenzyl radical. Two possible benzyl radicals could be formed upon loss of an H atom from the 2,5-lutidine precursor, but only one species was detected from the CESE source. Theoretical studies of the two benzyl radicals reveal the first excited
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electronic states have different electron configurations, and these result in significant differences in relative energies, geometries, and oscillator strength. Theory predicts forbidden emission from the 4methyl-2-azabenzyl radical that would yield a broad band with a low intensity electronic origin due to poor Franck–Condon overlap. Emission for the 4-methyl-3-azazbenzyl radical is allowed, and the optimized geometries for the ground and first electronic excited states suggest a strong origin transition for this species. The experimental origin transition reported in this study is in good agreement with the previously reported value in an absorption spectroscopy study on 4-methyl-3-azabenzyl. The emission spectrum consisted of three primary vibronic transitions and a few short progressions. The experimental vibrational energies were in good agreement with theoretical predictions.
[11] [12] [13] [14]
[15] [16] [17]
Acknowledgements This project was supported by the University of Alabama and the UA Emerging Scholars Program. We would like to thank Mr. Rick Smith of the University of Alabama, Department of Chemistry for fabrication of the nozzles. J.L. would like to thank the UA National Alumni Tag Foundation for a fellowship. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
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