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Spectroscopy and Photochemistry; General Theory

Rotational Characterization of the Elusive Gauche-Isoprene Jessica P. Porterfield, John Harper Westerfield, Lincoln Satterthwaite, David Patterson, Bryan Changala, Joshua H. Baraban, and Michael C. McCarthy J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b00411 • Publication Date (Web): 21 Mar 2019 Downloaded from http://pubs.acs.org on March 22, 2019

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The Journal of Physical Chemistry Letters

Rotational Characterization of the Elusive Gauche-Isoprene Jessica P. Porterfield,∗,† J. H. Westerfield,‡ Lincoln Satterthwaite,¶ David Patterson,¶ P. Bryan Changala,§ Joshua H. Baraban,k and Michael C. McCarthy† †Harvard-Smithsonian Center for Astrophysics, Cambridge Massachusetts, USA ‡New College of Florida, Department of Chemistry, Sarasota, Florida, USA ¶Department of Physics, University of California, Santa Barbara, California, USA §Department of Physics, University of Colorado, Boulder, Colorado, USA kDepartment of Chemistry, Ben-Gurion University of the Negev, Beersheva, Israel E-mail: [email protected]

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The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Isoprene (2-methyl-1,3-butadiene) is highly abundant in the atmosphere, second only to methane in hydrocarbon emissions. In contrast to the most stable trans rotamer, structural characterization of gauche-isoprene has proven challenging: it is weakly polar, present at the level of only a few percent at room temperature, and structurally complex due to both torsional and methyl tunneling motions. Gauche-isoprene has been observed by two distinct but complementary experimental approaches: chirped-pulse Fourier transform microwave (CP-FTMW) spectroscopy coupled with cryogenic buffer gas cooling, and cavity enhanced FTMW spectroscopy with a pulsed discharge source. Thermal enhancement of the gauche population (from 1.7% up to 10.3%) was observed in the cryogenic buffer gas cell when the sample was pre-heated from 300 K to 450 K, demonstrating that high-energy rotamers can be efficiently isolated under our experimental conditions. Rotational parameters for the inversion states (0+ /0− ) have been determined for the first time, aided by calculations at increasing levels of theoretical sophistication. From this combined analysis, the inversion splitting ∆E and the Fbc Coriolis coupling constant between the two inversion states have been derived.

Table of Contents Graphic

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Isoprene and methane each comprise about one third of the total volatile organic compounds emitted into the atmosphere each year, with the remaining third being a sum of hundreds of other compounds. 1 Oxidation of atmospheric isoprene, mainly due to OH radical 2,3 and secondary organic aerosol formation, 4,5 has broad impacts on air quality. Isoprene is also a biomarker in human breath, serving as a diagnostic of overall health. 6–9 Despite the ubiquity of isoprene, the second of two stable conformers remains poorly characterized. 10 Evidence was only found for the trans rotamer when the microwave spectrum of isoprene was first recorded in 1964. 11 Despite more than 50 years since that original measurement, no rotational data is available for the higher energy rotamer until the present work. Recent experimental and theoretical investigations of the simplest diene, 1,3-butadiene, have established that destabilizing interactions in the cis rotamer 12 — likely antiaromaticity 13,14 — lead to torsion of the carbon backbone, and result in a gauche conformation. Thus for compounds such as isoprene, a methyl derivative of butadiene, the higher-energy rotamer in fact adopts a non-planar geometry. Figure 1 displays the relative energy of isoprene as a function of the torsional angle.

Figure 1: Relative energy of isoprene as a function of rotation about its central single C-C bond, in which the dihedral angle about the C=C-C=C bond is represented by τ in the Newman projections. The dihedral angle τ = 180◦ and 0◦ correspond to the trans and cis structures, respectively.

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At room temperature, the gauche rotamer accounts for roughly 3% of the total isoprene population, 10,15 a factor which has likely greatly hindered its detection and characterization. The first definitive spectroscopic evidence for the existence of this rotamer only occurred recently using infrared spectroscopy in a helium nanodroplet. 15 In addition to its low steady-state population, an additional challenge with respect to rotational spectroscopy is its vanishingly small dipole moment, with vibrationally-averaged components of only µa = 0.16 D, µb = 0.32 D, µc = 0.02 D calculated at the CCSD(T)/ANO1 level of theory. A further complication at high spectral resolution arises from additional line structure caused by: (1) tunneling motion through the cis barrier, which results in 0+ /0− inversion states that have transitions separated in frequency by approximately 1 MHz, and (2) three-fold methyl rotation, which results in closely-spaced (of order 0.1 MHz) A/E transitions. Despite these obstacles, gauche-isoprene has now been observed by two complementary Fourier transform microwave (FTMW) experiments: a cryogenic buffer gas cooling cell with continuous molecular input, and a Fabry-Pérot cavity with a pulsed discharge nozzle. The buffer gas cell proved highly adept in the initial detection (between 12-26 GHz), as the gauche conformer was observed with a neat sample of isoprene (at 1-2 sccm), i.e. without heating or application of an electrical discharge. The cavity experiment, requiring a gentle discharge 16 for observation (at roughly 30 sccm, 2.5 kTorr backing pressure, in 99.9% neon), provided complementary high accuracy measurements (± 2 kHz), as well as line frequencies over a wider spectral range (2-40 GHz) once an initial fit was achieved. On the basis of these measurements, rotational and quartic centrifugal distortion constants, the inversion splitting ∆E, and the Fbc Coriolis coupling constant between the 0+ and 0− states of gauche-isoprene have been determined. A complete line list, as well as the frequencies used in the leastsquares fits (in which splitting due to methyl rotation has been ignored), are summarized in the Supplemental Information. Isoprene was first introduced at room temperature into the cryogenic buffer gas cell and studied between 12 and 26 GHz. The prominent trans species and its singly-substituted 13 C

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isotopologues were identified 17 and subsequently removed from the spectrum. Many of the remaining unassigned lines appear as closely-spaced doublets, reminiscent of the gauche-1,3butadiene spectrum. 12 Rotational constants derived from high-level calculations were used as a starting point in assigning the 12-26 GHz spectrum. Following the analysis and assignment of this spectrum, line frequencies were re-measured between 12 and 26 GHz with the cavity spectrometer, and systematic searches for additional lines were performed in the frequency range of 2-40 GHz. Table 1: Best-fit spectroscopic constants (in MHz) of gauche-isoprene compared to those calculated theoretically. A total of 94 lines were used in the fit, with a root mean square error of 48 kHz.

+

A (MHz) B (MHz) C (MHz)

Calculateda 8800.581 3906.032 2849.458

−

A (MHz) B (MHz) C (MHz)

8795.043 3905.966 2849.526

0

0

DJ DJK DK d1 d2

a b

Best-fit 8820.2427(104) 3909.5178(50) 2850.04793(305) 8819.7131(107) 3909.5422(48) 2850.16885(312)

(kHz) (kHz) (kHz) (kHz) (kHz)

0.673 5.129 7.461 -0.160 -0.102

0.656(52) 3.57(37) 9.35(181) -0.107(38) -0.1189(184)

∆E (MHz) Fbc (MHz)

1010b ···

1457.8(44) -18.283(54)

Computed at the CCSD(T)/ANO1 level of theory. Computed at the CCSD(T)/ANO0 level of theory.

Experimentally-derived best-fit rotational constants were computed with the SPFIT/SPCAT package 18 (using S-reduced, Ir representation), and are compared to those calculated theoretically in Table 1. Three rotational constants are varied for each tunneling state, but to reduce the number of free parameters, only a single set of centrifugal distortion constants are used. At our highest spectral resolution, the closely-spaced methyl rotor splitting is readily observed (Figure 2). At this juncture of the analysis, the A/E splitting was 5



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Figure 2: Representative lines of gauche-isoprene observed in the buffer gas cell (black ), and in a supersonic jet expansion in the absence (green) and presence of an 850 V electrical discharge (DC) (red ). Closely-spaced structure arises from methyl rotor motion, while the larger, well-resolved splitting is a result of tunneling motion. Because the supersonic jet expands along the axis of the Fabry-Perot cavity, each line in these spectra is further split by Doppler doubling.

neglected because it is small in magnitude relative to the tunneling splitting, and instead a mean of this doublet structure was used in the 0+ and 0− fit. Overall, the agreement between the calculated and experimental values is excellent, particularly for B and C where differences amount to less than 0.09% and 0.01%, respectively. Although the Fac and Fbc Coriolis interaction parameters should be determinable from the present data set, the fit rms was only sensitive to Fbc ; as a consequence, Fac was constrained to zero. It is not possible from the present observations to directly determine the barrier height for 0+ /0− inversion, but the Coriolis interaction between the two states permitted a precise determination of the inversion splitting (Table 1). Its value of 1.45 GHz is significantly lower than the 55 GHz found in the parent molecule butadiene, 12 apparently due largely to the increased effective mass caused by the addition of the methyl group. The torsional angle of gauche-isoprene was estimated to be τ = 38 ± 1 6


◦

(Figure 1)

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on the basis of a calculation at the AE-CCSD(T)/cc-pCVQZ level of theory. This angle is roughly 4◦ larger than that of gauche-1,3-butadiene. The increase in the torsional angle upon backbone methylation is puzzling from the perspective of classical steric arguments, which predict that repulsion between the 1,4 endo hydrogens should destabilize the cis geometry. The angle increase, however, can instead be rationalized from the point of view of terminal overlap in the π system, 13,14 with which the 2-methyl group can interact. This effect is apparently the driving force for why these conformers adopt a non-planar geometry, and for why the torsional angle increases in isoprene relative to that in butadiene. As indicated in Figure 2, supersonic cooling in neon (at 0.1% dilution) results in efficient conformational relaxation from the gauche to the trans conformer, to the extent that observation was not possible in the cavity spectrometer without application of a low voltage electrical discharge (DC 850 V). The interested reader is directed to seeded supersonic jet studies 19,20 for further discussions of such conformational relaxation. Lines of the gauche were readily observed in the buffer gas cell, however, with direct sample injection at 1-2 sccm. Encouraged by this result, relative line intensities of the gauche and trans rotamers were subsequently measured in the cell as a function of inlet temperatures between 300 K and 450 K, see Figure 3. A determination of the gauche abundance relative to that of the ground state trans isomer has been made using the equilibrium relationship K = exp−∆G/RT , where ∆G at 298.15 K is calculated to be 10.2- 10.5 kJ/mol. 15,17 Accounting for the fact that there are two pathways of rotation which lead to the gauche configuration from trans, we estimate a gauche abundance in the range of 2.8-3.2% at room temperature. At elevated temperatures, values of ∆G are calculated assuming ∆H(0 K)=11.8 kJ/mol from Franke et al. 15 Additional temperature corrections are made that account for the rigid-rotor/harmonic-oscillator partition functions computed at the FC-CCSD(T)/ANO1 level of theory. Methods described in reference 17 were followed to calculate the observed experimental abundance of gauche-isoprene, and appear to match theoretical estimates (2.7%, 5.3%, 8.9%,

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and 13.2% at 300 K, 350 K, 400 K and 450 K, respectively) reasonably well, see Figure 3. An upper limit on ∆G can be derived from these abundances; for example the gauche population of 1.7% at 300 K corresponds to a ∆G upper limit of 11.9 kJ/mol. The experimental gauche population, however, is consistently lower than theoretical predictions, and this discrepancy increases with temperature. This is likely the result of inaccuracies in the underlying calculated thermodynamic values, or alternatively, the result of two experimental effects: 1) collisional cooling leading to conformational relaxation of some fraction of the gauche to the trans rotamer, and/or 2) incomplete thermalization of the sample at elevated temperatures prior to injection into the buffer gas cell. With slight modifications to the heated sample inlet (which would ensure proper thermalization), it may be possible to experimentally derive thermochemical quantities for isoprene and other molecules. Criegee intermediates from the ozonolysis of isoprene do not undergo rapid isomerization as a result of their Zwitterionic nature, 21 and thus their formation pathways may have a

Figure 3: A portion of the isoprene rotational spectrum near 12405 MHz, shown at inlet temperatures of 300-450 K. The more intense trans line (422 → 413 ) is normalized in each spectrum such that increase in gauche (413 → 404 ) is observed as a function of temperature.

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significant impact on their OH radical production rates in the atmosphere. 22–25 The relative reactivity of ozone with the gauche and trans conformers of isoprene has not been studied. 2,3,22,26–28 With over 5 × 1014 grams of isoprene emitted into the atmosphere each year, 1 a reasonable fraction of which is estimated to be consumed by ozone, 28,29 the atmospheric fate of its second stable conformer may not be negligible. Now that gauche-isoprene has been experimentally characterized, follow-up studies of its conformer specific reactivity may now be practical, an essential step towards improving the predictive power of atmospheric chemistry models. Using two powerful, but complementary microwave techniques, the rotational spectrum of the elusive gauche rotamer of isoprene has been characterized at high spectral resolution in the 2-40 GHz region. Additional investigations that delve deeper into the tunneling and methyl rotation of gauche isoprene are worth pursuing, as would be studies of other substituted derivatives of 1,3-butadiene. Of particular interest is developing a more complete picture of how the torsional angle changes with substitution, and the dominant factors that dictate the magnitude of this angle. Nevertheless, the present work is an important first step toward this goal; it provides a firm theoretical and experimental foundation for follow-up studies at millimeter wavelengths and in the infrared, which should enable the rovibronic spectrum of this conformer to be mapped out with confidence.

Experimental Methods Rotational parameters from theory were obtained by combining an optimized all-electron CCSD(T)/cc-pCVQZ equilibrium geometry with zero-point vibrational corrections. The mean zero-point correction for the 0+ and 0− states was calculated at the frozen-core CCSD(T)/ANO1 30 level of theory using second order vibrational perturbation theory, 31 which also furnished centrifugal distortion constants via the harmonic force constants. The differences in the 0+ and 0- energies and rotational constants were estimated by a reduced

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dimension rovibrational variational calculation treating only the methyl rotor and carbonbackbone torsion degrees of freedom. The 2D relaxed torsional potential energy surface for this calculation was constructed at the frozen-core CCSD(T)/ANO0 30 level of theory. The foregoing calculations were performed using the CFOUR and NITROGEN program systems. 32,33 The cryogenic buffer gas cell (12 - 26 GHz) has been described elsewhere, 34 but will be briefly described here. It is a 19 x 19 x 19 cm vessel anchored to the second stage of a helium cryostat (4 - 7 K). It has a 19 mm aperture for sample introduction, two sets of microwave horns (12 - 18 GHz and 18 - 26 GHz), and a continuous input of pre-cooled 4 K helium (roughly 1 x 1014 He atoms/cm3 ). As molecules enter the cloud of cryogenic He (at a rate of 1-2 sccm), they are collisionally cooled within roughly 1 ms, and 15-20 ms of observation time remain before molecules freeze out and stick to the walls of the cell. 17,35 Chirp-pulsed microwave electronics fire at a repetition rate of up to 50 kHz, depending on the pressure of He inside the cell and thus the collisional lifetime of the free induction decay (FID). 34 The FTMW cavity spectrometers employed between 2 - 40 GHz have also been described in detail, 16,36–38 but the pertinent information will be mentioned here. These experiments involve pulsed valve sample introduction, and rely upon a supersonic expansion for molecular cooling. Isoprene is blended with neon carrier gas (to roughly 0.1%) providing a backing pressure of 2.5 kTorr. Coupled to the output of the pulsed valve is a pulsed discharge source, which was employed at 850 V to enable detection of gauche-isoprene. As molecules expand into vacuum they are detected with a cavity enhanced measurement (to 2 kHz accuracy) or by CP-FTMW (to 60 kHz accuracy). In all experiments the emitted microwaves create a macroscopic polarization of the sample. The FID is detected and averaged in the time domain, and a Fourier-transform produces the detected frequencies. Analytical grade (≥ 99.5%) and stabilized (99%, 1000 ppm tert-butyl catechol) isoprene samples were compared to assure no false identifications of impurities were made. Additional tests to attenuation response in the cavity spectrometers validated that a weakly polar species gave rise to each

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rotational transition observed.

Acknowledgements The authors thank M.-A. Martin-Drumel and Z. Kisiel for many helpful discussions. This work was supported by the NSF grant CHE-1566266 and NSF Award DBI-1555781.

Supporting Information Available A complete list of experimental frequencies as well as those used in the best fit can be found in the Supplementary Material.

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Rotational Characterization of the Elusive Gauche-Isoprene - The

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