Collisional Energy Transfer from Vibrationally Excited Hydrogen

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Collisional Energy Transfer from Vibrationally Excited Hydrogen Isocyanide Michael J. Wilhelm, and Hai-Lung Dai J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b07041 • Publication Date (Web): 24 Jul 2019 Downloaded from pubs.acs.org on July 27, 2019

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The Journal of Physical Chemistry

Collisional Energy Transfer from Vibrationally Excited Hydrogen Isocyanide Michael J. Wilhelm* and Hai-Lung Dai Department of Chemistry, Temple University, 1901 N. 13th Street, Philadelphia, PA 19122, USA

ABSTRACT Collisional deactivation of vibrationally excited hydrogen isocyanide (HNC) by inert gas atoms was characterized using nanosecond time-resolved Fourier transform infrared emission spectroscopy. HNC, with an average nascent internal energy of 25.91.4 kcal mole-1, was generated following the 193 nm photolysis of vinyl cyanide (CH2CHCN) and collisionally deactivated with the series of inert atomic gases: He, Ar, Kr, and Xe. Time-dependent IR emission allows simultaneous experimental observation of the 1 NH and 3 NC stretch emission from vibrationally excited HNC. Subsequent spectral fit analysis enables direct determination of the average energy of HNC in each spectrum and therefore a measure of the average energy lost per collision, E, as a function of internal energy. Collisional deactivation of excited HNC is shown to be relatively efficient, exhibiting E values more than an order of magnitude larger than comparably sized molecules at similar internal energies. Furthermore, the lighter inert gases are shown to be more efficient quenchers. Both observations can be qualitatively explained by the momentum gap law modeled through the repulsive force dominated vibration-to-translation energy transfer mechanism. The feasibility of efficient collisional deactivation as a contributing factor to the observed overabundance of astrophysical HNC is discussed.

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1. INTRODUCTION The simple geometric isomers, hydrogen cyanide (HCN) and hydrogen isocyanide (HNC), have been shown to exist in ratios well outside predicted thermodynamic equilibrium in numerous regions of the interstellar medium (ISM).1–3 HNC is a local minimum on the HCN potential energy surface and located roughly 5000 cm-1 above the global zero point energy. For typical ISM temperatures on the order of 100 K, the HNC:HCN equilibrium abundance ratio is predicted to be on the order of 10-33. In reality, however, HNC is often observed to be significantly more prevalent in the ISM with measured abundance ratios that are closer to unity.1–3 In an effort to reconcile this long standing puzzle, it has been hypothesized that UV induced photolysis of larger parent cyanides could account for the observed non-equilibrium abundance ratios.1 As a test of this hypothesis, we have investigated the photolysis reactions of representative parent cyanides. For instance, we have now demonstrated that vinyl cyanide (CH2CHCN), methyl cyanoformate (CH3O(O)CCN), and pyrazine (C4H2N) are all viable photolytic sources of both HCN and HNC.4–6 Our experimental results have consistently reveal nascent relative abundance ratios well above the thermodynamically predicted equilibrium ratio, similar to astrophysical observations.4–6 In our studies, time-resolved Fourier transform infrared (FTIR) emission spectroscopy was used to experimentally interrogate the photofragments generated following photolysis of a given precursor cyanide. Time-resolved FTIR emission, demonstrated on a nanosecond time scale by our laboratory,7 provides a sensitive measure of a molecule’s time-dependent internal energy and has previously been used to characterize photodissociation dynamics,8–16 the spectroscopy of radicals and transients,17–21 and energy transfer kinetics of highly excited molecules.22–26 In general, time-resolved FTIR emission is capable of simultaneously monitoring emission from all vibrationally excited reaction channel products. Any fragment that is produced vibrationally cold, however, will not produce IR emission and therefore cannot be detected with this method. In our prior examinations of the UV photolysis of parent cyanides, the resulting time-resolved spectra revealed emission assignable to the various IR active modes of HCN and HNC, indicating that both species are produced vibrationally excited.4–6 Consequently, if UV photolysis is indeed contributing to the overabundance of HNC in the ISM, this suggests that a portion of astrophysical HNC is being produced vibrationally hot. This conjecture in fact can be corroborated by prior experimental studies. For instance, Schilke et al. previously observed vibrationally excited HNC

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in the Westbrook Nebula (CRL 618).27 Vibrationally excited molecules eventually relax down the ro-vibrational manifold through a combination of radiative decay (with lifetimes of tens of milliseconds or longer) and collision deactivation. For ISM regions of higher gaseous density, including planetary atmospheres, comets, and dark molecular clouds, vibrational relaxation through collision-induced deactivation is particularly important. To better understand the fate of photolytically produced HNC in the ISM, we now quantify its collisional energy transfer properties. In this study, we experimentally study the collisional deactivation of vibrationally excited HNC produced following 193 nm excitation of vinyl cyanide. Specifically, time-resolved FTIR emission spectroscopy is used to monitor the internal energy of HNC as a function of time as it is collisionally quenched with the series of inert atomic colliders: helium (He), argon (Ar), krypton (Kr), and xenon (Xe). The HNC average energy lost per collision can be deduced and used as a measure to quantify the relative efficiency of vibrational-to-translational (V-T) energy transfer for each of the inert atomic colliders. Finally, we discuss the significance of efficient V-T energy transfer as a possible contributing factor to the origin of the known overabundance of HNC in the interstellar medium. 2. METHODS 2A. Time-Resolved Fourier Transformed IR Emission Spectroscopy A detailed description of our time-resolved IR emission experimental setup has been given elsewhere.7,28 Briefly, the output from an ArF excimer laser (Lambda Physik, LPX 200, =193nm, 20Hz repetition rate, >50 mJ/pulse) was lightly focused through a photolysis reaction cell mounted with two CaF2 salt windows. The sample consisted of a mixture of 10 mTorr vinyl cyanide in an inert collider gas of 4 Torr (either He, Ar, Kr, or Xe), under constant flow conditions. Pressure in the cell was monitored with a capacitance manometer (MKS Baratron, 0-10 Torr). Measurements of the laser pulse energy, before and after the photolysis cell, indicate that only ca. 10% of the vinyl cyanide undergoes photolysis. Emission in the mid-IR region after the photolysis laser pulse was collected perpendicular to the laser propagation axis by a set of gold-plated mirrors (in a Welsh cell arrangement), then collimated and focused into the FTIR spectrometer with a pair of KBr salt lenses. The spectrometer (Bruker, IFS 66/s) was equipped with an interferometer capable of time-resolved step-scan measurements and a mercury cadmium telluride (MCT) detector (EG&G Judson Technologies, HgCdTe J15D14, 500 ns time constant, ca. 1.1 s rise-time, 75010000 cm-1 spectral range). The sensitivity of the MCT detector is highly peaked with a 100% maximum near 900 cm-1, dropping to ca. 30% around 1500–2500 cm-1, then 99%) was processed with several freeze-pumpthaw cycles before use and purity checked with static IR absorption spectroscopy. He, Ar, Kr, and Xe gases were used directly as obtained from the supplier (Spectra Gas, research grade, 99.9%). Unphotolyzed vinyl cyanide was recollected after each experiment at liquid nitrogen temperature and purified for continued use. 2B. Spectral Reconstruction Analysis We recently developed an algorithm for improving the signal-to-noise ratio (S/N) in timeresolved spectra, called spectral reconstruction analysis (SRa).29,30 SRa is rooted in the idea that signal exhibits a specific time dependence, while noise is random. SRa has since been applied to a number of experimental studies, including spectroscopy of the Criegee intermediate31,32 and photolysis reactions of pyrazine6 and methyl cyanoformate.5 The working principles of SRa have been described before. Briefly, for a set of (n) time-resolved spectra, the time dependence of the measured signal is fit to an analytical function (using an iterative analysis) to characterize the temporal signature at each frequency. The (n) spectra can then be reconstructed, with improved S/N, by replacing the frequency-dependent measured curves with the resulting noiseless curves obtained from the fit analysis at each frequency. On average, this analysis has been demonstrated to yield a ca. 0.6 𝑛 enhancement in S/N. As compared to simply averaging the (n) spectra, in which the spectra are condensed into a singular spectrum with

𝑛 improved S/N

(whereby all time-dependent information is sacrificed), SRa concurrently improves the S/N in all

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(n) spectra and preserves the measured time dependence. For the set of vinyl cyanide spectra presented here, SRa employed a series of exponential functions and was performed using inhouse developed code implemented in MATLAB (Mathworks). 3. RESULTS & ANALYSIS 3A. Time-Resolved IR Emission Spectra Figure 1 depicts representative SRa-processed time-resolved emission spectra collected at 5, 10, and 15 s following the 193 nm photolysis of 10 mTorr vinyl cyanide embedded in 4 Torr Ar. As detailed previously, the measured spectra consist of five distinct emission bands which can be assigned as originating from the various IR active vibrational modes of HCN, HNC, acetylene (HCCH), cyanoacetylene (HCC-CN), and the cyanovinyl radical (H2CC-CN).4,33

Of key

importance for the current study, the transitions originating from HNC with fundamentals at 2023 cm-1 (3 NC stretch) and 3652 cm-1 (1 NH stretch), exhibit partial resolution of the rotational contour and are free of significant overlap with transitions from other photofragments. Note that the 3 CN stretch of HCN has a fundamental transition at 2097 cm-1, which is in partial overlap with the 3 NC stretch of HNC. Additionally, it has previously been shown that UV photolysis of vinyl cyanide produces more HCN than HNC, in an approximate (3:1) ratio.4,34 Still, the CN stretch of HCN has an insignificant transition dipole moment of only 0.001362 Debye, which is two orders of magnitude weaker than the 0.108 Debye moment of the NC stretch in HNC.35 Given that emission intensity scales as the square of the transition dipole moment, this suggests that the C-N stretch emission from HNC will be more than 6000 times stronger than that from HCN. Consequently, all emission from the 3 CN stretch of HCN should be buried in the noise of our spectra. Thus, despite the strong concurrent presence of HCN, our measured spectra contain a clean spectral view of vibrationally excited HNC. The two bands assignable to HNC exhibit sizable anharmonic shifts in frequency, which manifests as a time-dependent narrowing of the low energy side of the observed spectral bands. This indicates that the nascent HNC produced in the photolysis reaction is generated vibrationally hot. The time-dependent internal energy distribution of HNC can be deduced from analyzing the emission spectral bands. Importantly, the change in the internal energy content over time is a result of collisional energy transfer. Consequently, the energy transfer efficiency of a particular HNC / inert atom pair can be examined by varying the identity of the collider.

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In addition to Ar (Figure 1), we have also examined collisional deactivation of HNC with He, Kr, and Xe. As expected, the observed emission features following the photolysis reaction are qualitatively invariant with respect to the specific collider employed. That is, regardless of the specific collisional partner used, the resulting emission spectra show the same five main emission bands described above. It is only when one considers the time-dependence of the individual features that the influence of the atomic collider is revealed, as each atomic collider possesses a unique collisional frequency, which varies as a function of mass. The reaction cell contains a complex mixture of gases. In addition to the precursor and the inert atomic collider, various molecules and radicals are produced in the photolysis reaction. This warrants further consideration of the collisional partners and their collisional frequencies before we move forward. As outlined in the Methods section, the initial gas mixture in the reaction cell is composed of 4.0 Torr of the rare-gas collider and 10 mTorr of the molecular precursor. Laser power measurements before and after the gas cell suggest that only about 10% of the vinyl cyanide precursor undergoes photolysis (i.e., assuming a unit quantum yield for the photolysis reaction), yielding at most 1 mTorr of any photofragment. Furthermore, we have previously shown that the two dominant dissociation pathways yield HCN + H2CC: (77%) and HNC + HCCH (23%),4 suggesting that there is at most only 0.23 mTorr of HNC present in the photolysis cell (and less than 1 mTorr of acetylene and HCN at any given time). The partial pressure of the rare-gas atomic collider therefore dominates the gas mixture as it is more than 363 times greater than all other molecular species combined. Aside from the rare-gas atomic colliders, each experiment contains the same precursor and associated photolysis reaction products. If collisional deactivation was driven by something other than the atomic collider (e.g., unphotolyzed precursor), the deduced time-dependence of the series of spectra should be identical (within error). The fact that the timedependence of the HNC emission bands vary as a function of the inert atomic collider (Figure 2) further validates our assertion that deactivation is primarily driven by the inert gas. 3B Determination of Average Internal Energy and Average Energy Lost Per Collision Time-resolved IR emission is an effective means for monitoring the internal energy of vibrationally hot molecules.36–38 The corresponding spectral analysis has been described in great detail previously and will only be briefly reviewed here as it is applied to HNC.4–6 The photolysis reaction channel producing HNC and HCCH has an endothermicity of H = 56 kcal/mole, which suggests ca. 92 kcal/mole of available energy (𝐸𝑎𝑣𝑎𝑖𝑙) to be partitioned amongst the various degrees of freedom of the resulting photofragments.4 We have previously demonstrated that this

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energy is predominantly distributed in a statistical manner.4 Application of the information theoretic statistical prior method outlined by Muckerman39 predicts that (8 29)𝐸𝑎𝑣𝑎𝑖𝑙 will be partitioned into the vibrational degrees of freedom of HNC, which is roughly 9,000 cm-1. To simulate the emission from vibrationally excited HNC, We first calculate its ro-vibrational states up to 12,000 cm-1 above the zero-point energy by iterating over the standard expressions for vibrational, 𝐺(𝜐,𝓁), and rotational energy, 𝐹(𝜐,𝓁,𝐽), for which 𝜐 is the set of vibrational quantum numbers, 𝓁 is the vibrational angular momentum, and 𝐽 is the rotational quantum number. We purposely chose to include states above the statistically predicted energy upper bound to ensure the accuracy of the model simulation. The 1 NH and 3 NC bands of HNC were quantitatively modeled using the molecular constants deduced in Maki and Mellau’s high-temperature emission study.40 The calculated rovibrational states were then partitioned into 500 cm-1 wide energy bins. A representative emission spectrum was generated for each energy bin, where all levels within the bin were assumed to be equally populated. Allowed transitions within an energy bin were calculated using the rigid-rotor and harmonic oscillator selection rules (i.e., 1 and 3 = -1, J = 0, 1), convoluted with a Lorentzian line shape function to match the 12 cm-1 spectral resolution of the experiment, and then summed into a single representative bin spectrum. Emission intensity for each individual rovibrational transition was modeled as:

( )

𝐼𝜈′𝐽′ = 𝜔3𝜈′𝐽′|𝜇𝜈′′,𝜈′|2𝑆Δ𝐽 𝐽′ × 𝑒𝑥𝑝

―𝐸𝜈′𝐽′

𝑘𝐵𝑇𝑟𝑜𝑡

,

(1)

where |𝜇𝜈′′,𝜈′| are the vibrational transition dipole moments, which is calculated using the fundamental transition moment and the harmonic scaling rule, 𝜔𝜈′𝐽′ is the frequency of the transition, 𝑆Δ𝐽 𝐽′ are the Honl-London factors, 𝐸𝜈′𝐽′ is the energy of the emitting state, 𝑘𝐵 is Boltzmann’s constant, and 𝑇𝑟𝑜𝑡 is the rotational temperature. As discussed previously,41 the combination of high vibrational energies and lower spectral resolutions (12 cm-1) renders individual ro-vibrational transitions unresolvable. Nevertheless, as shown in Figure 1, the rotational contours of the 1 and 3 bands of HNC are partially resolved in nearly all of the measured spectra. As a linear molecule, HNC produces emission spectra with separate P and R branches, the maximum intensity of which reveals the rotational state with maximum probability, or Jmax. Of significance, the measured emission frequency of Jmax deduced for both the 1 and 3 bands are shown to be reasonably constant for t5 s. More importantly, fit

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analysis of the fundamental bands observed in the late time spectra (t>15 s) are well fit to a rotational temperature of 300 K. This suggests that collisions with 4 Torr of the inert gas, whose collisional frequencies span 30 to 43 collisions per s, are sufficient to thermalize the rotational distribution of HNC within a few microseconds. Comparable rotational quenching has been reported previously for ro-vibrationally hot photofragments, including HBr produced in a threecenter transition state following UV photolysis of vinyl bromide.42 As depicted in Figure 1, the time-resolved emission spectra were fit by imposing a timedependent population distribution over the calculated energy-dependent bin spectra, in which the distribution was defined by a vibrational temperature, Tvib: 𝑃𝑗(𝑡) =

𝛼𝑡 2𝜋

(

× 𝑒𝑥𝑝

―ℎ𝑐𝐸𝑗 𝑘𝐵𝑇𝑣𝑖𝑏

)

,

(2)

where 𝛼𝑡 is an intensity scaling factor and 𝐸𝑗 is the energy of the jth bin. Once the distribution has been determined, the time-dependent average internal energy, E, for each spectrum can be deduced directly as Tvib. This process was then repeated for all spectra collected using each of the four inert atomic colliders. We note that the 1 NH stretch is the most anharmonic active mode of HNC and is therefore the most sensitive indicator of E. In prior studies, in which the 3 NC band was obscured by overlapping bands from additional photoproducts,5,6 fit analysis was isolated solely to the 1 band. Nevertheless, for the current study, the NH and NC bands were both well resolved and were therefore fit simultaneously to obtain the most accurate determination of E. Figure 2 depicts the deduced average internal energy of HNC, collisionally quenched with He, Ar, Kr, and Xe, as a function of the number of rare-gas collisions, ZRg. It is observed that the E vs. ZRg trends can be well described by a single exponential decay function: 〈𝐸〉 = 𝛺0 + 𝛺1 × 𝑒𝑥𝑝( ― 𝑘𝑅𝑔𝑍𝑅𝑔),

(3)

where 0 is an energy offset, 1 a scaling factor, and 𝑘𝑅𝑔 a decay rate constant. For all atomic colliders considered, extrapolation of the deduced trend back to the zero-collision point (𝑍𝑅𝑔 = 0) yields a common HNC nascent internal energy of 25.91.4 kcal mole-1 (9060490 cm-1). This is in excellent agreement with the statistical partitioning of available energy following the photolysis reaction (25.4 kcal mole-1) as well as the ca. 24.07.0 kcal mole-1 value that can be estimated from the UV photoionization spectrum of Blank et al.43 It is also worth noting that this energy falls roughly 7 kcal mole-1 below the calculated barrier of isomerization to HCN.44 This suggests that it

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is unlikely that any of the nascent HNC population will be lost via isomerization to HCN. Altogether, the common nascent internal energy deduced for all atomic colliders examined, coupled with the close quantitative agreement with the photoionization derived value,43 illustrate the accuracy of our modeling of the HNC emission spectra. As described previously,41 the average energy lost per collision, E, can be deduced as the derivative of the average internal energy with respect to the number of rare-gas collisions, which can be evaluated using the analytical expression for E in equation 3 above: ∆E =

𝑑E = ― 𝑘𝑅𝑔𝛺1 × 𝑒𝑥𝑝( ― 𝑘𝑅𝑔𝑍𝑅𝑔). 𝑑𝑍𝑅𝑔

(4)

As shown in the inset of Figure 2, the deduced E trends are all observed to be linear functions of E and exhibit a well-behaved reduced-mass trend in which the lightest collider (He) exhibits the most efficient deactivation (followed by Ar, Kr, and finally the heaviest collider Xe). It is worth noting that the deduced E values for HNC are all relatively large (i.e., well in excess of 1 cm-1 for all average internal energies).41 As a comparison, Figure 3 shows experimentally deduced E trends for vibrationally excited populations of HNC and the comparably sized triatomic molecules: CS2, SO2,45 and NO2,46 as well as the slightly larger cyanide, nitrosyl cyanide (NC-N=O).47 These examples were specifically chosen for comparison as they have low energy bending modes similar to HNC (ca. 460±60 cm1)

and therefore have similar energy dependent density of state scaling. Importantly, all these

molecules exhibit the same reduced mass trend in which lighter colliders appear to induce more efficient quenching. Of significance, collisional deactivation of vibrationally excited HNC is shown to be at least an order-of-magnitude more effective than these similarly sized molecules, suggesting that vibrational energy transfer from HNC is a relatively more efficient process. It is also worth noting that these excited species were prepared in a slightly different manner compared to the HNC in the current study. Unlike HNC, the other molecules are stable at room temperature and can be produced in highly vibrationally excited states by optical electronic excitation followed by rapid internal conversion to the ground state surface. Conversely, HNC, at sufficiently high internal energy, can isomerize to the more stable HCN. Nevertheless, vibrationally excited HNC can be produced through photolysis as a product so long as the nascent energy is below the isomerization barrier. 4. DISCUSSION 9



The experimental observations presented here exhibit interesting properties that we will attempt to qualitatively justify through the classical collisional deactivation theories.48–51 Specifically, it is observed that the collisional deactivation of vibrationally excited HNC through V-T energy transfer exhibits a well-behaved inverse reduced-mass trend, in which the lightest collider exhibits the most efficient energy transfer. Additionally, as compared to prior V-T energy transfer studies of similarly sized vibrationally excited molecules,45,47,52 collisional deactivation of HNC is shown to be relatively efficient, though it is still much lower in scale in comparison with the so-called super-collisions, in which many thousands of wavenumbers of energy are transferred in a single collision.53–55 Rather, V-T collisional deactivation is often observed to be a relatively inefficient process that results in the transfer of less than one wavenumber of energy per collision. Conversely, our results here demonstrate that the transfer of many tens of wavenumbers of energy is feasible for HNC, even for comparably low internal energies. There are a number of known systems and interactions which have previously been shown to result in efficient V-T energy transfer, including: transition dipole mediated vibronic coupling, intramolecular vibrational redistribution (IVR) following formation of reactive collision complexes, and vibrationally highly excited polyatomic molecules exhibiting a high density of states. We will now briefly review these cases and show that they are not relevant to the behavior of HNC considered here. Previous studies have shown that V-T energy transfer, under certain conditions, can be induced through long-range attractive forces, rather than short-range repulsive forces.49,51 The long-range attractive interaction operates primarily through an interaction between the transition dipole of the energy donor and an induced-dipole in the collider. This interaction can be significantly enhanced when the vibrational energy of the donor is high enough to couple to excited electronic states. The vibronically coupled donor states result in stronger transition dipoles for inducing larger energy transfer encounters.38,45,56–58 For instance, experimentally deduced E vs. E trends for vibrationally highly excited NO2 revealed a characteristic elbow curve, in which enhanced energy transfer was observed for energies above the onset of the energetically 2 2 accessible 𝐴 𝐵2/𝐵 𝐵1 electronic states.38 For the HCN/HNC system, Herzberg showed that the

𝐴1𝐴′′ first excited electronic state is 6.5 eV (150 kcal mole-1) above the HCN minimum.59 This is well beyond the accessible energies of our system and hence excited electronic state coupling cannot be occurring here.

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Efficient V-T energy transfer has also been demonstrated for collisional partners capable of forming transient reactive collision complexes.60,61 We have previously demonstrated this mechanism through examining the collisions between hyperthermal hydrogen atoms and HCCH as well as sulfur dioxide (SO2).36,62 It was shown that H atoms prepared with roughly 60 kcal/mole of translational energy were able to transfer up to 70% of this energy into the internal degrees of freedom of HCCH with high probability.36 In general, any excited species capable of attractive interactions with the collisional quencher could form a transient collision complex and may therefore exhibit enhanced energy transfer via IVR prior to eventual dissociation of the complex. Highly reactive species such as radicals are also prone to such a mechanism. We recently characterized the V-T collisional deactivation of vibrationally highly excited ketenyl radical (HCCO), which exhibited E values on the order of 100 cm-1 per collision.41 Similar behavior has likewise been observed for the hydrogen containing iodomethyl (CH2I) and benzyl radicals (C6H5CH2).63,64 While HNC is an unstable isomer, it is not expected to generate long-lived collision complexes. Consequently, IVR in a transient collision complex is an unlikely origin for the efficient energy transfer from HNC reported here. There is a considerable body of knowledge focused on the collisional deactivation of vibrationally highly excited polyatomic molecules (N>3), in particular aromatic species. In general, comparatively efficient V-T energy transfer has been documented for numerous polyatomic species, including for example benzene (C6H6),65,66 toluene (C6H5CH3),66,67 pyrazine (C4H4N2),68,69 azulene (C10H8),70 and biphenylene (C12H8).71 Focusing specifically on V-T energy transfer with inert atomic colliders, E values of many tens to hundreds of wavenumbers per collision are consistently reported. Such a result is reasonable and actually fully expected based upon the energy gap law, which dictates that V-T energy transfer is most efficient when the quantity of energy to be transferred is small. The probability of V-T transfer scales as the negative exponential of the energy difference (or energy gap) of the vibrational states involved.51 This suggests that larger molecules with numerous vibrational modes at high internal energies should exhibit the most efficient V-T energy transfer as they will have the smallest energy gaps. It is important to note, for the polyatomic systems listed above, energy transfer was monitored for molecules containing many tens of thousands of wavenumbers (e.g., 30,000+ cm-1) of internal energy. This is significantly larger than the comparably modest ca. 9,000 cm-1 internal energy for HNC in the current study. Additionally, as compared to the polyatomic examples above, HNC has far fewer fundamental vibrational modes. Consequently, the HNC examined here is at significantly lower density of states and will therefore have comparatively large energy gaps.

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An important consideration for HNC is that it exists as a high energy minimum on the global potential energy surface of HCN. Therefore, we need to consider the possibility that HNC could couple to isoenergetic ro-vibrational states of HCN in the vicinity of the isomerization barrier, which would increase the vibrational density of states. However, as deduced in our spectral fit analysis (and in full agreement with the results inferred from Blank et al.43), UV photolysis of vinyl cyanide produces HNC with an average nascent internal energy of roughly 26 kcal mole-1. While substantial, this energy falls short of the predicted 33.1 kcal mole-1 isomerization barrier to HCN.44 Furthermore, it is worth noting that Christoffel and Bowman previously employed quantum scattering calculations to examine the complementary reverse process, namely translation-tovibration (T-V) energy transfer from kinetically excited (i.e., hyperthermal) Ar atoms to ambient HCN and HNC.72 Their calculations predicted that the collisional interaction potential only weakly coupled the localized HCN and HNC states. While the total internal energy in their calculations was more than sufficient to induce isomerization, the failure to produce delocalized states of mixed HCN and HNC character suggests that collision-induced isomerization is unlikely to explain the observed energy transfer efficiency of HNC. Figure 3 compares the energy transfer efficiency of HNC against other triatomic molecules, including CS2, NO2, and SO2, as well as NCNO. It is important to note that all of the triatomic molecules in this comparison have very similar low energy bending modes with fundamental transitions in the range of 460±60 cm-1. Consequently, if we only consider the influence of the energy gap, it would be expected that all of these molecules should exhibit very similar V-T energy transfer efficiencies. While this is certainly true of CS2, SO2, NO2, and NCNO, which exhibit E values around 1 cm-1, energy transfer from HNC is deduced to be at least an order of magnitude more efficient. One primary difference between HNC and the other molecules is that HNC contains a hydrogen atom which is capable of large amplitude displacements in a collision. Light atom effect The effect of a light atom in V-T transfer has been illustrated by the quantum scattering calculations of Christoffel and Bowman who examined collisions between HNC and hyperthermal Ar atoms.72 Specifically, their calculations predict that head-on collisions, in which Ar collides with the hydrogen end of the molecule, were far more efficient at promoting energy transfer compared to tail-on (i.e., carbon end of the molecule) or even perpendicular collisions.72 Consequently, we speculate that the observed efficient V-T transfer of HNC may in part originate from the existence

12


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of the light hydrogen atom in the energy donor. A potential experimental test of the propensity for such a mechanism would be to examine the effects of isotope substitution on energy transfer efficiency. For instance, replacing hydrogen with deuterium should result in a reduced energy transfer. In one example, Toselli and Barker examined the collisional deactivation of hydrogen containing vs fully deuterated toluene.66 Indeed, their results showed a measurable reduction in E following deuteration.66 Nevertheless, other studies have suggested that deuterium substitution yields either little change in energy transfer efficiency or that it can become even more pronounced.73,74 In the context of the energy gap law, deuterium exchange is not expected to induce a significant effect on energy transfer efficiency as isotope substitution primarily affects the high frequency stretching modes and only slightly changes the low frequency bending modes. Effect of the Mass of the Collisional Quenchers Apart from the relatively large E magnitudes, another interesting observation is the trend of the mass of the rare gas atoms. As revealed above, HNC exhibits a well behaved inverse reduced mass trend in which the lightest collider (He) exhibits the most efficient energy transfer. Conversely, for the vibrationally highly excited polyatomic examples, the exact opposite reduced mass trend is observed (i.e., He is the least efficient quencher). It should be noted that this is not the first such observation of an inverse reduced mass trend in V-T energy transfer. As depicted in Figure 3 and documented elsewhere, small molecules, such as CS2, SO2, NO2, and NCNO have also previously been shown to exhibit inverse reduced mass trends.45–47,75,76 We show here that the reduced mass trend can be qualitatively described by the momentum gap law. As formulated by Ewing, the momentum gap law can be illustrated by modelling the collisional interaction between a vibrationally excited molecular donor and a rare gas atomic quencher as vibrational predissociation of an excited van der Waals complex.77 In particular, the dissociation rate (Γ) of such a complex can be quantitatively described as:77,78

(

Γ = 𝜐 × 𝑒𝑥𝑝 ―

𝜋 2𝜇𝐸𝑡𝑟𝑎𝑛𝑠 , 𝛼ℏ

)

(5)

where 𝜐 is the vibrational quantum numbers of the decaying state, 𝛼 is a measure of the steepness of the repulsive portion of the interaction potential, 𝜇 is the reduced-mass of the complex, and 𝐸𝑡𝑟𝑎𝑛𝑠 is the translational energy which becomes available following dissociation of the complex. In the context of V-T transfer, 𝐸𝑡𝑟𝑎𝑛𝑠 is simply the fraction of the vibrational energy of the excited molecule transformed into translational energy of the atomic collider, hence 𝐸𝑡𝑟𝑎𝑛𝑠 = 〈Δ𝐸〉.

13



Equation 5 can therefore be rewritten to describe the average energy lost per collision as a function of the reduced-mass and dissociation rate of the transient collision complex: 〈Δ𝐸〉 = ―

[ ( )]

1 𝛼ℏ Γ 𝑙𝑛 𝜐 2𝜇 𝜋

2

.

(6)

When comparing collisional interactions across a series of atomic colliders, Equation 6 dictates that the amount of the energy lost per collision inversely depends on the reduced-mass of the complex. Ewing also showed that the E trend can be predicted based upon the well depth of the attractive interaction potential (De) of the excited molecular donor and the collisional quencher.77 Specifically, E scales as the difference of the vibrational frequency of the donor (𝜔𝐻𝑁𝐶) and the well depth of the interaction: 〈Δ𝐸〉~ 𝜔𝐻𝑁𝐶 ― 𝐷𝑒.

(7)

Given that 𝜔𝐻𝑁𝐶 is invariant with respect to the atomic collider considered, E simply varies as a function of De. In order to test this relation for HNC, we performed a series of ab initio calculations quantifying the interaction potential energy surfaces of HNC with the series of rare gas atoms (see Supporting Information, SI, for additional details). Briefly, our calculations focused solely on the linear approach of the atomic colliders with the hydrogen end of the molecule. Interaction energies were deduced at the MP4(full) level of theory using the aug-cc-pVTZ basis set, along with a supplemental (3s3p2s1f) set of bond functions centered on a ghost atom maintained midway between the rare gas atom and the hydrogen. The interaction well depth (De) was deduced relative to the energy of the complex at an approximate infinite separation (i.e., 2000 angstroms). As an initial test of the accuracy of our approach, we first calculated the interactions of the series of atomic colliders with HCN. The deduced interaction energies were within 6% of the previously reported high-level CCSD(T) values.79 The resulting basis-set superposition error corrected interaction energies for HNC with the rare gas atoms were deduced as: 43 cm-1 (He), 215 cm-1 (Ar), 266 cm-1 (Kr), and 527 cm-1 (Xe). Consequently, as De is shown to increase with the mass of the atomic collider, Equation 7 likewise predicts that E should follow an inverse reduced mass trend, favoring lighter colliders such as He. Astrophysical Significance

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The collisional deactivation of vibrationally excited HNC directly affects the stability of the HNC isomer and is therefore relevant to understanding the abnormally high HNC/HCN abundance ratios observed in various astrophysical environments. Collisions in the interstellar medium can be so infrequent that sequential collisions can be separated by months and even years depending upon regional molecular density.80 In this regard, efficient collision-induced energy transfer may initially seem irrelevant as relaxation in such environments is invariably dictated by radiative processes. Nevertheless, there are a variety of regions of increased molecular density (e.g., planetary atmospheres, comets, and dark molecular clouds) for which collisional frequencies are significantly larger and for which collisional deactivation must therefore be considered. For instance, we have previously demonstrated the propensity of larger parent cyanides to photolytically produce significant concentrations of vibrationally excited HCN and HNC.4–6 As has been noted previously, such photochemistry can certainly be induced by the UV flux of stars.5 Given the proven feasibility of such photochemistry, it is of interest to consider the influence of collisions on the resulting vibrationally excited reaction products. The current study revealed that deactivation of excited HNC follows a well-behaved reduced-mass trend in which lighter colliders exhibit the greatest propensity to transfer energy. It is noteworthy then that hydrogen is the most abundant atom (and molecule) in the ISM and is lighter than the lightest collider (He) considered here.81 Consequently, it is reasonable to speculate that collisions with atomic or molecular hydrogen may result in even more efficient deactivation of excited HNC. The persistence of HNC outside predicted thermodynamic equilibrium is influenced by two main processes, 1) the rate of production of HNC and 2) the kinetic competition between collisional deactivation and activation. In principle, our results showcasing the efficient deactivation of HNC should be useful for modeling the abundances of astrophysical cyanides but highlight the need for additional experimental measurements. 5. CONCLUSION We have experimentally examined the collisional deactivation of vibrationally excited HNC, produced following the 193 nm photolysis of vinyl cyanide, by the series of inert atomic colliders: He, Ar, Kr, and Xe. Spectral fit analysis of the time-resolved IR emission spectra enabled identification of the IR emission bands from HNC and determination of its internal energy as a function of the number of collisions with the inert gas atoms. The amount of V-T energy transfer per collision from vibrationally excited HNC revealed a well-behaved inverse reduced-mass trend, in which the lightest atoms resulted in the most efficient transfer of energy. Additionally, it is revealed that HNC exhibits relatively efficient V-T energy transfer in which many tens of

15



wavenumbers are transferred per collision. These trends can be qualitatively explained through the momentum gap law reflected in the repulsive force dominated V-T energy transfer mechanism. It is reasoned that the relatively efficient energy transfer is due to the presence of the light atom, H, in the energy donor. Finally, it is speculated that the efficient collisional deactivation (which suggests efficient collisional thermalization) is relevant to understanding the overabundance of HNC in the interstellar medium. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (M.J.W.). ORCID Michael J. Wilhelm: 0000-0002-4634-9561 Hai-Lung Dai: 0000-0001-6925-8075 Notes The authors declare no competing financial interest.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.______. Details regarding ab initio calculations of the interaction energies of HNC + the series of rare gas atoms: He, Ar, Kr, and Xe. ACKNOWLEDGEMENTS This work was supported in part by the Air Force Office for Scientific Research, under Grant Number FA9550-15-1-0213.

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Figure 1. Representative time-resolved IR emission spectra collected at 5 (blue trace), 10 (grey trace), and 15 s (red trace) following the 193 nm photolysis of 10 mTorr vinyl cyanide imbedded with 4 Torr Ar. Spectral fit analysis of the 1 NH and 3 NC stretch modes of HNC are shown overlaid as solid black lines.

17



Figure 2. Average internal energy of HNC plotted as a function of the number of rare-gas collisions with He (blue circles), Ar (black circles), Kr (green circles), and Xe (red circles). Black dashed lines represent fits to equation 3. Inset depicts E as a function of E, deduced with equation 4. The dashed lines in the inset represent a guide for the eye to highlight the linear trend.

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Figure 3. Representative trends of E for HNC, CS2,45 SO2,45 NO2,46 and NCNO47 collisionally deactivated with various rare-gas atoms, plotted as a function of E. Note that E is plotted on a logarithmic scale.

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