Infrared Spectroscopy of Molecular Radicals and Carbenes in Helium Droplets

Abstract

The helium droplet is an ideal environment to spectroscopically probe difficult to prepare molecular species, such as radicals, carbenes and ions. The quantum nature of helium at 0.4 K often results in molecular spectra that are sufficiently resolved to evoke an analysis of line shapes and fine-structure via rigorous “effective Hamiltonian” treatments. In this chapter, we will discuss general experimental methodologies and a few examples of successful attempts to efficiently dope helium droplets with organic molecular radicals or carbenes. In several cases, radical reactions have been carried out inside helium droplets via the sequential capture of reactive species, resulting in the kinetic trapping of reaction intermediates. Infrared laser spectroscopy has been used to probe the properties of these systems under either zero-field conditions or in the presence of externally applied, homogeneous electric or magnetic fields.

4.1 Infrared Spectroscopy of Molecular Radicals and Carbenes in Helium Droplets

The objective of our experimental research program is to isolate and stabilize transient intermediates and products of prototype gas-phase reactions relevant to both combustion and atmospheric chemistry. Helium Nanodroplet Isolation (HENDI) [1,2,3,4,5,6,7,8,9,10,11,12] is well-suited for this because liquid helium droplets have shown potential to freeze out high energy configurations of a reacting system, permitting infrared (IR) spectroscopic characterizations of reactive intermediates lying between the sequentially captured reactants and the various products associated with the potential energy surface. Hydrocarbon radical reactions with molecular oxygen or other small molecules relevant to combustion environments have been the focus of our recent work in this area (see Refs. [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] for our recent contributions applying this method). Here we describe a selection of the single and double [52,53,54,55,56,57] resonance IR laser spectroscopy techniques that are being used to probe the structural and dynamical properties of molecular radical and carbene systems solvated in helium droplets.

4.1.1 Experimental Methods

4.1.1.1 Droplet Production and Doping

A diagram of the HENDI apparatus is shown in Fig. 4.1. Helium droplets are formed (10$^{12}$ droplets per second) by the continuous expansion of He gas through a 5 micron diameter pin-hole nozzle (Fig. 4.1a). The average droplet size is controlled by changing the nozzle temperature, providing a dynamic range from $\sim$10$^{3}$ atoms at 24 K to $\sim$10$^{6}$ atoms at 8 K [58,59,60,61]. Upon leaving the high pressure region of the expansion, the droplets cool by evaporation to 0.4 K [62]. The droplet expansion is skimmed into a beam, which passes into the differentially pumped “pick-up” chamber (Fig. 4.1b). Here the droplets are doped by passing them through the vapor of the molecular species of interest (approximately 10$^{10}$ molecules/cm$^{3}$ over a 1 cm path length). The internal energy of the captured molecule is rapidly removed by He evaporation, which returns the system to 0.4 K [63]. Each evaporating He atom reduces the internal energy of the system by 5 cm$^{-1}$ (0.014 kcal mol$^{-1}$) [63]. The density of molecules in the “pick-up” region can be varied such that each droplet captures one (or more) molecules on average. Molecular species of differing composition can be added to the same droplet by implementing multiple “pick-up” zones. An effusive pyrolysis source (Fig. 4.2) has been successfully used to fragment precursor molecules and dope He droplets with halogen atoms and molecular radicals or carbenes [17, 18, 20,21,22,23, 25, 27, 29, 30, 34, 35, 37,38,39,40,41,42, 46, 50, 51].

Fig. 4.1

Schematic of the UGA HENDI spectrometer. The pyrolysis source for generating halogen atoms and molecular radicals or carbenes is load-locked into the vacuum chamber (section B). The laser excitation can be switched between a counter-propagating configuration to the laser-multipass/Stark/Zeeman cell configuration (section C). Detection of the droplet beam is achieved with a crossed-beam ionizer, quadrupole mass spectrometer (section D)

Fig. 4.2

A schematic drawing of our SiC high temperature pyrolysis source. The copper electrodes are water-cooled and the length of the hot zone can be adjusted

4.1.1.2 Droplet Detection via Mass Spectrometry

The droplet beam is detected with a quadrupole mass spectrometer (MS) (Fig. 4.1d). Electron impact ionization leads to the production of a He$^{+}$ cation within the droplet. The outcome of this ionization process is now well known to produce either a He$_{n}^{+}$ distribution or ions associated with the charge-transfer ionization and fragmentation of the molecular dopant [4, 6, 10]. The MS in Fig. 4.3a shows the He$_{n}^{+}$ ions associated with the electron impact ionization of a neat (dopant free) droplet beam. Figure 4.3b shows the MS of a droplet beam doped with n-butyl nitrite (one molecule is captured per droplet, on average; the energized molecular ion fragments predominately to C$_{3}$H$_{3}^{+}$, m/z=39). Thermal dissociation of n-butyl nitrite in a pyrolysis source leads to the production of the propargyl radical (C$_{3}$H$_{3}$), nitric acid (NO), and formaldehyde (CH$_{2}$O). The number density of molecules in the pyrolysate is sufficiently low such that droplets passing through it will capture either nothing or only one of the three fragment molecules. Multiple capture events by a single droplet occur with low probability due to the Poisson statistics associated with the capture process [4, 6]. Figure 4.3C shows the MS of the droplet beam after having passed through the pyrolysate associated with n-butyl nitrite pyrolysis. An intensity reduction is observed at m/z=39, along with intensity gains at m/z=29, 30, and 38. The peaks at m/z=29 and 30 are largely due to the ionization of droplets that have captured either NO or CH$_{2}$O. The peak at m/z=38 is a signature of the ionization and fragmentation of the He-solvated C$_{3}$H$_{3}$ radical.

Fig. 4.3

a MS of the neat droplet beam. b MS of droplets doped with single n-butyl nitrite molecules. c MS of droplets doped with single molecules, NO, formaldehyde, or the propargyl radical, C$_{3}$H$_{3}$

4.1.1.3 Infrared Laser Spectroscopy

After traversing the pick-up zones and prior to entering the mass spectrometer, the beam of droplets is irradiated with the idler output from a continuous-wave optical parametric oscillator (OPO) [24]. Survey spectra are recorded with the laser beam aligned counter-propagating to the droplet beam, whereas the laser is aligned into a two-mirror multipass cell for Zeeman, Stark or Polarization spectroscopy measurements. Vibrational excitation of He-solvated dopants leads to the evaporation of several hundred He atoms, which reduces both the geometric and ionization cross sections of the irradiated droplets. This photo-induced cross section reduction for electron impact ionization is measured as ion-signal depletion in selected mass channels. For example, the IR spectrum of n-butyl nitrite is measured as a depletion signal in mass channel m/z=39 (Fig. 4.4a; experimental conditions same as those in Fig. 4.3b), whereas the spectrum of the propargyl radical is measured in mass channel m/z=38 (Fig. 4.4b; experimental conditions same as those in Fig. 4.3c).

Along with the sharp acetylenic CH stretch band near 3333 cm$^{-1}$, the spectrum of n-butyl nitrite contains several bands below 3000 cm$^{-1}$ arising from the two CH$_{2}$ moieties. In comparison, the propargyl radical contains three sharp bands arising from the acetylenic CH stretch ($\nu _{1}$ at 3322 cm$^{-1}$), the symmetric CH$_{2}$ stretch ($\nu _{2}$ at 3039 cm$^{-1}$), and the antisymmetric CH$_{2}$ stretch ($\nu _{8}$ at 3130 cm$^{-1}$). The broader features in the precursor spectrum below 3000 cm$^{-1}$ are completely absent in the spectrum of the propargyl radical. For the acquisition of molecular radical spectra, as demonstrated in Fig. 4.4b, mass channels can usually be selected (judiciously) to discriminate against spectral features associated with droplets containing unpyrolyzed precursor molecules or other fragments in the pyrolysate.

The weakly perturbing, superfluid He solvent allows for highly resolved vibrational spectroscopy studies of these species, which can be compared directly to the predictions of quantum chemistry [4, 6]. Indeed, in the case of vibrational frequencies, when comparisons are available, the band origins of He-solvated molecules and molecular complexes differ little from those measured in the gas phase ($\sim$1 cm$^{-1}$ or less) [6]. For example, the acetylenic CH stretch of the propargyl radical is red shifted by only 0.14 cm$^{-1}$ upon solvation in a helium droplet [64].

Fig. 4.4

Infrared spectra of a n-butyl nitrite and b the propargyl radical measured as ion-signal depletion in mass channels 39 and 38 u, respectively

4.1.1.4 Spectra Exhibiting Rotational Fine Structure

For small molecules and molecular complexes assembled in He droplets, it is often the case that vibrational bands exhibit rotational fine structure. This fine structure results from the simultaneous change of vibrational and rotational quantum numbers upon vibrational excitation. The origin of resolved rotational fine structure has been discussed extensively in the helium droplet literature, [1, 3,4,5,6] and it may be thought of qualitatively as resulting from the fact that the rotational degrees of freedom of the embedded molecule are only weakly coupled to the helium bath; thereby, it is often the case that molecular rotations are sufficiently long-lived such that rovibrational bands are observed. This is readily apparent in the IR spectrum of the propargyl radical. Upon closer inspection of the $\nu _{1}$ and $\nu _{2}$ bands in Fig. 4.4b, the spectral patterns shown in Fig. 4.5 are revealed. For both of these rovibrational bands, the pattern of lines can be directly attributed to the orientation of the vibrational transition dipole moment in the molecular frame of reference.

Fig. 4.5

Higher resolution scans of the $\nu _{1}$ and $\nu _{2}$ acetylenic CH and symmetric CH$_{2}$ stretching bands for the propargyl radical. Both bands have $a_{1}$ symmetry and can be reproduced in simulations as a-type bands

Simulations of rotationally resolved spectra of helium-solvated molecules can be achieved by employing traditional effective Hamiltonian approaches, in which a gas-phase Hamiltonian is used with renormalized rotational constants. Moreover, Stark spectroscopy can be implemented and analyzed in the traditional sense, in which an external electric field perturbs the free-rotor behavior of the molecule or complex, and an additional term is appended to the zero-field effective Hamiltonian to account for the field-induced perturbation [41]. Our instrument is equipped with a laser multipass cell (Fig. 4.1c) that allows us to perform Stark spectroscopy measurements by applying a static electric field (0 to 80 kV/cm) to electrodes that surround the droplet beam/laser interaction region. The use of various Stark field strengths and laser polarization orientations (leading to different selection rules), allows us to accurately determine dipole moments of He-solvated species [21, 41, 44, 65, 66]. For example, the experimental (black) and simulated (red) Stark spectra of the linear OH-CO complex are shown in Fig. 4.6 [44]. The zero-field spectrum is shown along the bottom of the figure, and the Stark spectra recorded at three different field strengths provide the dipole moments of the complex in both the ground and excited OH stretch vibrational states.

Fig. 4.6

Reproduced with permission from Ref. [44]. $\copyright$ copyright American Institute of Physics. All rights reserved

Rovibrational spectra of the OH stretch band of the linear OH-CO hydrogen bonded complex. Individual transitions are labeled above the zero-field spectrum (bottom). Infrared Stark spectra were obtained with a perpendicular laser polarization configuration and three separate static field strengths, revealing the magnitude of the permanent dipole moments in both the ground and excited vibrational states. The red traces are simulations using an effective Hamiltonian model.

Upon replacing the two stainless steel Stark electrodes with Neodymium rare-earth permanent magnets, the laser multipass cell can be used to record IR Zeeman spectra. Again, the analysis of such spectra is carried out by appending an additional term to the zero-field effective Hamiltonian. The Zeeman term is parameterized by the permanent magnetic field strength and the various g-factors associated with the interaction of the molecular magnetic moments with the external field. Experimental (black) and simulated (red) Zeeman spectra of the linear OH-CO complex are shown in Fig. 4.7. Here we find that the g-factor of the electron is unchanged from the gas-phase value, indicating the absence of any significant solvent-induced quenching of the electron’s orbital angular momentum [44].

Fig. 4.7

Reproduced with permission from Ref. [44]. $\copyright$ copyright American Institute of Physics. All rights reserved

Infrared Zeeman spectra of the OH stretch band of the linear OH-CO hydrogen bonded complex. Zeeman spectra were obtained with both a perpendicular and b parallel laser polarization configurations. The red traces are simulations using an effective Hamiltonian model and a field strength of 0.425(2) Tesla.

4.1.1.5 Spectra Lacking Rotational Fine Structure

Often, the natural line width due to vibrational relaxation is broader than the rotational contour at 0.4 K ($\sim$1 cm$^{-1}$), precluding the determination of dipole moments via the aforementioned Stark measurements. This is a common feature for larger He-solvated systems that have a relatively high density of vibrational states, leading to more efficient coupling to the solvent and more rapid vibrational relaxation [6, 13, 14, 67, 68]. Nevertheless, by measuring the electric field dependence of the band intensity, it is possible to simultaneously obtain both the permanent electric dipole moment ($\mu _p$) and the vibrational transition moment angle (VTMA) [14, 67, 69] associated with each vibrational band [69, 70]. For any one normal mode vibration, the VTMA is defined as the angle $\mu _p$ makes with the transition dipole moment vector ($\mu _t$). Given a particular combination of VTMA and $\mu _p$ (obtained from ab initio calculations), this field dependence can be simulated and compared to the experiment [71,72,73]. Moreover, to make this comparison, the theoretical results do not require the scaling that often plagues the comparisons of experimental vibrational band origins to those obtained from ab initio harmonic frequency calculations [69]. Because dipole moments and VTMAs are accurately determined even at modest levels of ab initio theory, these Polarization Spectroscopy measurements provide key structural information that can be employed to assign vibrational spectra that contain contributions from multiple species or structural isomers [69]. An example of this is given in Fig. 4.8, where two closely spaced vibrational bands are attributed to two cyclic isomers of the OH-(D$_{2}$O)$_{2}$ trimer complex [38]. Being separated by only a few cm$^{-1}$, the two bands cannot be assigned to specific isomers on the basis of frequency computations alone. However, comparison of the experimental and computed VTMAs leads to a definitive assignment (see details in figure caption).

Fig. 4.8

Reproduced with permission from Ref. [38]. $\copyright$ copyright American Institute of Physics. All rights reserved

Vibrational transition moment angle analysis of the bands assigned to cyclic isomers of OH(D$_{2}$O)$_{2}$. The structures of the two cyclic trimers and the associated assignments are shown as insets. The middle frame contains the Lorentzians obtained from fitting the high-field spectra (31.0 kV/cm) obtained with parallel (red) and perpendicular (blue) polarization configurations. The Lorentzian areas are normalized to zero-field values obtained with an identical fitting procedure. The top frame shows the computed parallel to perpendicular intensity ratios expected at high-field versus VTMA for the ud/du (black) and uu/dd (red) cyclic trimers. Using the computed intensity ratio curve, the experimental intensity ratios are used to obtain semi-empirical VTMAs of 51(2) and 68(2)$^{\circ }$ for the 3377 and 3380 cm$^{-1}$ bands, respectively. These values compare favorably to the ab initio VTMAs computed for the OH stretch bands of the ud/du (48$^{\circ }$) and uu/dd (63$^{\circ }$) cyclic trimers.

4.1.1.6 Organic Pyrolysis Precursors

Efficient doping of He droplets is essential for the acquisition of high-quality IR spectra, which is one longstanding goal of our research program. Although this is trivially achieved for stable, closed-shell systems, much of the He droplet spectroscopy being carried out in our research group requires the clean, continuous generation of carbenes, hydrocarbon radicals, the hydroxyl radical, or halogen atoms. We find that this is most efficiently achieved via flash vacuum pyrolysis of organic precursors; photolysis and RF discharge sources have been explored with less success. Initial studies of He-solvated radicals employed a rather simple low-pressure, continuous, effusive pyrolysis source composed of a radiatively heated quartz tube. A tantalum filament connected to two water cooled electrodes heats the tip of the quartz tube, and radicals are produced by pyrolysis as precursor molecules collide with the walls of the heated tube. The effusive beam of radicals crosses the path of the droplet beam, and the concentration of radicals in this “pick-up” zone is controlled with a fine metering valve that is located between the heated output region and the precursor reservoir. The resulting pressure in the pyrolysis region is near 2$\times$10$^{-4}$ Torr (inside the quartz tube). Under these conditions, precursor molecules undergo only a few collisions with the walls of the heated tube; essentially no collisions occur in the gas phase, and the probability for radical recombination within the source is minimized. The maximum temperature achieved is $\sim$1400 K, which is the major drawback of this pyrolysis source. We have now expanded upon this original pyrolysis source design, increasing the upper temperature that can be achieved in our experiments. We incorporated a resistively heated silicon carbide (SiC) tube that can be heated up to $\sim$2100 K (Fig. 4.2). This new pyrolysis design was inspired by the pulsed pyrolysis sources originally reported by P. Chen and co-workers [74] and G. B. Ellison and co-workers [75]. At $\sim$2100 K, the range of precursor systems that can be pyrolyzed to create radicals is vastly expanded. A second-generation SiC pyrolysis source has now been designed to allow for the efficient use of solid organic precursors that have little vapor pressure at room temperature.

Fig. 4.9

Ethyl (CH$_{3}$CH$_{2}$) zero-field rovibrational spectra ($\nu _1$ CH$_{2}$ symmetric stretch). The radical is produced from the pyrolytic dissociation of three different organic precursors

Our spectroscopic studies of smaller hydrocarbon radicals have mostly employed halogenated, peroxide, or nitrite precursors [20, 23, 25, 27]. For example, Fig. 4.9 shows three rovibrational spectra of the ethyl radical obtained with various precursors. Halogenated pyrolysis precursors (RI) perform the poorest, because thermal decomposition branches significantly to alkene+HI products. We observe increased branching to closed-shell products upon increasing the size of the hydrocarbon group. Nitrite precursors (RCH$_{2}$ONO) are easy to synthesize and perform well for generating somewhat larger hydrocarbon radicals (e.g. propyl radicals; see Fig. 4.10). The drawback to nitrite precursors is the simultaneous production of formaldehyde and NO (i.e. in addition to R$^{\bullet }$). Because droplet doping is a statistical process, when three fragments are produced upon pyrolysis, only 12% of the droplet ensemble is doped with R$^{\bullet }$ (as an upper limit). Although largely commercially unavailable and difficult to synthesize, R(CH$_3$)$_2$COOC(CH$_3$)$_2$R, peroxide precursors exhibit the best performance, because thermal decomposition leads to 2R$^{\bullet }$ + 2(CH$_{3}$)$_{2}$CO, resulting in 18% of droplets being doped by R$^{\bullet }$. Evidence for this can be directly observed in the signal to noise ratios in the ethyl radical spectra (Fig. 4.9). Diazo, diazirine, and diacyl compounds are also well-known to be efficient pyrolysis precursors for carbenes and radicals, [76] although the synthesis of these is more complex, and the resulting compounds can be too unstable.

With the new SiC based pyrolysis source, we are now in a position to test the efficacy of alternative pyrolysis precursors. For example, production of the vinyl radical was achieved via the pyrolysis of di-vinyl sulfone (DVS), [30] which was obtained from a commercial vendor. Sulfone precursors decompose to give 2R$^{\bullet }$ + SO$_{2}$, which results in 24% of droplets being doped with the radical, although the temperature necessary to achieve efficient pyrolysis is somewhat larger than is possible with the quartz pyrolysis source used in our previous work. Future collaboration with synthetic groups will be aimed at the synthesis of novel sulfone systems, which may serve as high quality pyrolysis precursors.

4.1.2 Infrared Spectroscopy of Hydrocarbon Radicals

Thermal decomposition of organic precursors in a continuous, effusive pyrolysis source allows for the helium nanodroplet isolation and spectroscopic interrogation of a variety of hydrocarbon radicals (see Section 4.1.1 for a detailed description of the HENDI methodology). Many of these initial studies involved small radicals that had been spectroscopically probed in the gas phase. Nevertheless, as summarized here, the low temperature afforded by He droplets allows for a characterization of these systems beyond what has so far been achieved in the gas phase. More recent studies of larger radical systems that have yet to be spectroscopically probed in the gas phase are encouraging (e.g. propyl radicals), [45] as it seems the only limitation to the HENDI method is the availability of suitable pyrolysis precursors.

4.1.2.1 Helium-Mediated Tunneling Dynamics of the Vinyl Radical

The vinyl radical (H$_{2}$C$_{\beta } =$C$_{\alpha }$H) was trapped in liquid He droplets via the use of a di-vinyl sulfone pyrolysis precursor [30]. At 0.4 K, the entire population of nuclear spin isomers is cooled to either the 0$_{00}^{+}$ (ortho) or 0$_{00}^{-}$ (para) rotovibrational level. IR spectra in the fundamental CH stretch region revealed three bands that we assigned to the symmetric CH$_{2}$ ($\nu _{3}$), antisymmetric CH$_{2}$ ($\nu _{2}$) and lone $\alpha$–CH ($\nu _{1}$) stretch bands. The vinyl radical CH stretch band origins in He droplets differ from vibrational configuration interaction calculations [77] of J. Bowman and co-workers by $\sim$1, 2 and 10 cm$^{-1}$ for the $\nu _{3}$, $\nu _{2}$ and $\nu _{1}$ modes, respectively. Each band consists of a-type and b-type transitions from the 0$_{00}$ level, and each of these is split by either the difference in or sum of the $v=0$ and $v=1$ tunneling splittings. Comparing the He droplet spectra to previous high-resolution spectroscopy of the $\nu _{3}$ band (D.J. Nesbitt and co-workers), [78, 79] we found that the $A^{\prime }-B^{\prime }$ rotational constant for this mode is reduced to 89% of its gas-phase value, and the tunneling splittings (ground and $\nu _{3}$ excited states) are both reduced by $\sim$20%. In addition, the relative intensities of the $\nu _{3}$ transitions indicate 4:4 spin statistics for ortho and para nuclear spin isomers, suggesting a facile interchange mechanism [80] for all three H atoms within the $\sim$1200 K pyrolysis source, prior to the pick-up and cooling of the hot vinyl radical by the He droplet. The $\sim$20% reduction in the ground and $\nu _{3}$ excited state tunneling splittings is due to two contributing effects from the He solvent. The He droplet can modify both the tunneling barrier and the effective reduced mass for motion along this coordinate. We have estimated that either an $\sim$40 cm$^{-1}$ increase in the effective barrier height or an $\sim$5% increase in the effective mass of the tunneling particles (both as upper limits) is sufficient to account for the observed $\sim$20% tunneling splitting reduction. Future theoretical work will be required to assess the extent to which each of these effects contribute to the overall modification of the vinyl radical tunneling dynamics upon solvation in liquid He.

4.1.2.2 Methyl, Ethyl, Propargyl, Allyl, and Propyl Radicals

The methyl (CH$_{3}$) and ethyl (C$_{2}$H$_{5}$) radicals were produced via the pyrolysis of peroxide precursors and isolated and spectroscopically characterized in He droplets [25, 27]. The five fundamental CH stretch bands of C$_{2}$H$_{5}$ near 3 $\mu$m were each observed within 1 cm$^{-1}$ of the band origins reported for the gas phase species (D.J. Nesbitt and co-workers) [81, 82]. The symmetric CH$_{2}$ stretching band ($\nu _{1}$) is rotationally resolved, revealing nuclear spin statistical weights predicted by $G_{12}$ permutation-inversion group theory. The ethyl radical’s permanent electric dipole moment (0.28(2) D) was obtained via the Stark spectrum of the $\nu _{1}$ band. Three $a_{1}^{\prime }$ overtone/combination bands were also observed, each having resolved rotational substructure. These were assigned to 2$\nu _{12}$, $\nu _{4}$+$\nu _{6}$, and 2$\nu _{6}$ through comparisons to anharmonic frequency computations at the CCSD(T)/cc-pVTZ level of theory and via an analysis of the rotational substructure observed for each band.

Rotationally resolved IR spectra were obtained for the propargyl (C$_{3}$H$_{3}$) and allyl radicals (C$_{3}$H$_{5}$) [20, 23]. In the IR spectrum of He-solvated allyl, we observed rovibrational bands near the band origins previously reported in high resolution gas-phase studies carried out by D.J. Nesbitt and co-workers [83] and R. Curl and co-workers [84,85,86]. In addition to the fundamental CH stretching modes, four other bands were assigned to the allyl radical using a consistent set of rotational constants. Indeed, in the gas-phase studies, it was noted that the CH stretch bands are heavily perturbed, but no explanation was given as to the nature of the perturbations. Isolating the radical in He droplets greatly decreases the number of populated rovibrational levels, and aided by anharmonic frequency computations and the resolved rotational substructure, we assigned the $\nu _{1}$ ($a_{1}$), $\nu _{3}$ ($a_{1}$), $\nu _{13}$ ($b_{2}$) fundamentals and the $\nu _{14}$/($\nu _{15}$+2$\nu _{11}$) ($b_{2}$) and $\nu _{2}$/($\nu _{4}$+2$\nu _{11}$) ($a_{1}$) Fermi dyads, in addition to an unassigned resonant polyad near the $\nu _{1}$ mode.

Fig. 4.10

Reproduced with permission from Ref. [45]. $\copyright$ copyright American Institute of Physics. All rights reserved

Comparison of the IR spectra of n-propyl (top, red) and i-propyl radicals (bottom, black). All vibrational bands are broadened beyond the rotational contour expected at 0.4 K. Residual propene absorptions are marked by *.

In our most recent work, [45] gas-phase n-propyl and i-propyl radicals (C$_{3}$H$_{7}$) were generated via pyrolysis of n-butyl nitrite and i-butyl nitrite, respectively. An Ar-matrix isolation study from the late 1970s represents the only previous molecular spectroscopy of these radicals [76, 87]. Several previously unreported bands were observed in the IR spectrum between 2800 and 3150 cm$^{-1}$ (Fig. 4.10). The CH stretching modes observed above 2960 cm$^{-1}$ are in excellent agreement with anharmonic frequencies computed using second-order vibrational perturbation theory. However, between 2800 and 2960 cm$^{-1}$, the spectra of n- and i-propyl radicals become congested and difficult to assign due to the presence of multiple anharmonic resonances. Computations employing a local mode Hamiltonian reveal the origin of the spectral congestion to be strong coupling between the high frequency CH stretching modes and the lower frequency bending/scissoring motions. The most significant coupling is between stretches and bends localized on the same CH$_{2}$/CH$_{3}$ group. This work was carried out as a collaboration between the experiment/theory groups at the University of Georgia and Edwin L. Sibert at the University of Wisconsin-Madison.

4.1.2.3 Anharmonic Resonance Polyads in the Mid-IR Spectra of $^{\bullet }$C$_{n}$H$_{2n+1}$ Radicals: Vibrational Complexity in the CH Stretching Region

High-resolution, gas-phase, mid-IR spectra of alkyl radicals larger than ethyl are entirely missing from the spectroscopic literature. High-quality infrared spectra of n- and i-propyl radicals in the CH stretching region were recently obtained via the helium droplet isolation method [45]. In the limit of $3N-6$ uncoupled oscillators, one expects seven CH stretch vibrations for both n- and i-propyl. However, the resolution achieved in the experiment reveals a vibrational complexity that demands a treatment beyond the harmonic approximation (see Fig. 4.11 for the n- propyl example, black trace). Second-order vibrational perturbation theory, VPT2, accurately predicts the high-frequency stretching vibrations localized on the radical site ($\alpha$-CH$_{2}$ for n-propyl). The CH stretch vibrations localized on carbon atoms adjacent to the radical center are red shifted, due to a hyperconjugative stabilization of the system and concomitant softening of the CH oscillators ($\beta$-CH$_{2}$ for n-propyl) [45]. The associated red shifts drive these CH stretch modes into resonance with the overtones and combination tones of CH$_{n}$ bending modes. This effect contributes substantially to the spectral complexity observed between 2800 to 3000 cm$^{-1}$. Clearly, VPT2 alone cannot account for the complexity that emerges in this lower frequency region (see Fig. 4.11, red trace).

Fig. 4.11

Reproduced with permission from Ref. [45]. $\copyright$ copyright American Institute of Physics. All rights reserved

Comparison of the experimental n-propyl spectrum (top, black) to VPT2 simulated spectra. The bottom (red) trace represents a full VPT2 treatment with no resonance treatments whatsoever. The blue trace includes explicit treatment of Fermi and Darling-Dennison resonances. Labels correspond to the carbon atoms around which the vibrations are localized. The frequencies are the eigenvalues of a 22-dimensional effective Hamiltonian. Symmetry labels are included on the bottom trace; these are for the C$_{s}$ average structure (minimum energy structure on the zero-Kelvin enthalpic surface), although we note that the computation is carried out at the C$_{1}$ symmetry electronic global minimum structure.

Fig. 4.12

Reproduced with permission from Ref. [45]. $\copyright$ copyright American Institute of Physics. All rights reserved

Dipole decomposition of local mode Hamiltonian simulations (n-propyl). The experimental spectrum, the full model local mode simulation, and the dipole decomposed simulations are shown as black, blue, and red traces, respectively.

The pervasive anharmonic coupling and intensity borrowing evident in the CH stretch region was modeled with two separate effective Hamiltonian approaches [45]. (1) The VPT2+K approach treats Fermi and Darling-Dennison resonances explicitly via the diagonalization of an effective Hamiltonian matrix (see Fig. 4.11, blue trace). The matrix contains deperturbed diagonal elements and off-diagonal coupling terms derived from quartic force fields computed at the CCSD(T)/ANO0 level of theory. The effective Hamiltonian is represented in a normal mode basis consisting of CH$_{n}$ stretching fundamentals and CH$_{n}$ bending overtones/combinations. (2) The local mode effective Hamiltonian approach employs a localization scheme that takes as input a harmonic frequency computation at the B3LYP/6-311++G(d,p) level of theory (see Fig. 4.12, blue trace). The localized basis states correspond to CH stretching fundamentals and overtones/combinations of HCH scissor modes. Refined harmonic scale factors and anharmonic coupling terms are taken from previous studies of closed shell hydrocarbon CH stretch spectra and are transferred to the local mode model without modification [88]. Both approaches generate Hamiltonian matrices that are 22-dimensional for n-propyl. The computational cost of the local mode approach is far lower than the VPT2+K method, because it does not require a quartic force field as input.

Local mode predictions are generally in very good agreement with experiment, despite there being zero adjustable parameters in the model (see Fig. 4.12). The success of the local mode model indicates a rather robust transferability of the anharmonic coupling terms [88]. The presence of a radical center apparently does not significantly affect the cubic coupling between localized CH stretch and HCH scissor modes for the propyl radicals. On the other hand, the quadratic force field is strongly affected by the radical site. For example, the two $\alpha$-CH$_{2}$ stretches are shifted to higher energy and coupled more strongly by quadratic terms in the Hamiltonian. In contrast, the $\beta$-CH$_{2}$ stretches are largely decoupled from each other and shifted to lower energy. Both observations are consistent with the approximately sp$^{2}$ hybridization of the $\alpha$-CH$_{2}$ group and the hyperconjugative stabilization of the $\beta$-CH$_{2}$ group.

The choice of representation, local versus normal mode, appears to result in different convergence behavior. The coupling between basis states in the local mode model more accurately reflects the salient interactions responsible for the experimental spectral complexity (stretch-scissor coupling), and is therefore more easily converged. Because of its success in predicting the complexity associated with the propyl radical spectra, we expect the local mode model to accurately predict the CH stretch spectra of larger alkyl radical systems, and because of the low cost of such computations, this approach provides an excellent alternative to the more expensive VPT2+K method. The weakly interacting nature of superfluid helium allows for a direct comparison between experimental band origins and computed spectra using the local mode model. We propose to continue along this direction to explore the spectroscopy of larger alkyl radical systems that exhibit multiple conformations, such as the butyl radicals. Moreover, we plan to probe the CH stretch spectra of a series of cycloalkyl radicals. These studies will allow us to test/refine the local mode model and probe the anharmonic resonance polyads that emerge in the spectra of primary, secondary and tertiary alkyl and cycloalkyl radical systems. The spectra of these helium-solvated hydrocarbon radicals will provide a robust starting point for future high resolution gas-phase spectroscopic studies.

4.1.2.4 Infrared Spectroscopy of Cyclobutyl, Methylallyl, and Allylcarbinyl Radicals

Gas-phase cyclobutyl radical ($^{\bullet }$C$_{4}$H$_{7}$) was produced via pyrolysis of cyclobutylmethyl nitrite (C$_{4}$H$_{7}$(CH$_{2}$)ONO) [47]. Other $^{\bullet }$C$_{4}$H$_{7}$ radicals, such as 1-methylallyl and allylcarbinyl, were similarly produced from nitrite precursors. For the cyclobutyl and 1-methylallyl radicals, anharmonic frequencies were predicted by VPT2+K simulations based upon a hybrid CCSD(T) force field with quadratic (cubic and quartic) force constants computed using the ANO1 (ANO0) basis set. A density functional theoretical method was used to compute the force field for the allylcarbinyl radical. For all $^{\bullet }$C$_{4}$H$_{7}$ radicals, resonance polyads in the 2800-3000 cm$^{-1}$ region appear as a result of anharmonic coupling between the CH stretching fundamentals and CH$_{2}$ bend overtones and combinations. VPT2+K simulations are generally good at predicting the spectral complexity in the CH stretch region for the cyclobutyl radical; however, the predictions are less satisfactory for the 1-methylallyl and allylcarbinyl radicals. Upon pyrolysis of the cyclobutylmethyl nitrite precursor to produce the cyclobutyl radical, an approximately two-fold increase in the source temperature leads to the appearance of spectral signatures that can be assigned to 1-methylallyl and 1,3-butadiene. On the basis of a previously reported $^{\bullet }$C$_{4}$H$_{7}$ potential energy surface, this result is interpreted as evidence for the unimolecular decomposition of the cyclobutyl radical via ring opening, prior to it being captured by helium droplets. On the $^{\bullet }$C$_{4}$H$_{7}$ potential surface, 1,3-butadiene is formed from cyclobutyl ring opening and H atom loss, and the 1-methylallyl radical is the most energetically stable intermediate along the decomposition pathway. The allylcarbinyl radical is a higher energy $^{\bullet }$C$_{4}$H$_{7}$ intermediate along the ring opening path, and the spectral signatures of this radical are not observed under the same conditions that produce 1-methylallyl and 1,3-butadiene from the unimolecular decomposition of cyclobutyl.

4.1.3 R$\cdot$ + ($^{3}\Sigma _{g}^{-}$)O$_{2}$ Chemistry in Helium Droplets

4.1.3.1 Methyl Peroxy Radical

We have demonstrated that R$\cdot$ + ($^{3}\Sigma _{g}^{-}$)O$_{2}$ reactions can be carried out within the low temperature, He droplet environment. For example, the sequential addition of a methyl radical and molecular oxygen to He droplets leads to the barrierless reaction, CH$_{3}$ + O$_{2}$ $\rightarrow$ CH$_{3}$OO [17]. The reaction enthalpy is exothermic by $\sim$30 kcal mol$^{-1}$ and therefore requires the dissipation of $\sim$2000 He atoms to cool CH$_{3}$OO to 0.4 K. The CH$_{3}$OO radical remains in the droplet and is observed downstream with IR laser beam depletion spectroscopy. All three CH stretch bands are observed, and rotational fine structure is partially resolved for the $\nu _{2}$ totally symmetric CH stretch band, indicating complete internal cooling of the reaction product to the droplet temperature. Electron impact ionization of the droplets containing CH$_{3}$OO results in the charge transfer reaction He$^{+}$ + CH$_{3}$OO $\rightarrow$ CH$_{3}$O$_{2}^{+}$ + He, which is followed by the fragmentation of the CH$_{3}$O$_{2}^{+}$ ion. The major fragmentation channel is the production of HCO$^{+}$ and H$_{2}$O. The outcome of this work demonstrates that IR laser spectroscopy can be employed as a probe of the outcome of organic radical-radical reactions carried out in the dissipative environment of a He nanodroplet.

4.1.3.2 Propargyl and Allyl Peroxy Radicals

IR spectroscopy was used to probe the outcome of the reaction between the propargyl radical (C$_{3}$H$_{3}$) and ($^{3}\Sigma _{g}^{-}$)O$_{2}$ within He droplets [23]. Helium droplets doped with a propargyl radical (generated via pyrolysis of 1-butyn-4-nitrite) were subsequently doped with an O$_{2}$ molecule. The reaction carried out at 0.4 K resulted in the exclusive formation of the acetylenic-trans-propargyl peroxy radical (HC$\equiv$C–CH$_{2}$–OO$^{\bullet }$). This work helped to elucidate the shape of the entrance channel on the ground-state potential energy surface, as it was unclear whether or not there exists a small barrier to formation of the peroxy species. The rapid cooling afforded by the He droplets motivates the conclusion that if a barrier does indeed exist, it is too small to kinetically stabilize a van der Waals complex between C$_{3}$H$_{3}$ and O$_{2}$. MRCI computations carried out in collaboration with Stephen Klippenstein and co-workers indicate that the reaction is barrierless for O$_{2}$ addition to the –CH$_{2}$ “tail” group, similar to alkyl + O$_{2}$ reactions. Apparently, O$_{2}$ addition to the HC$\equiv$C– “head” group proceeds via a positive entrance channel barrier, consistent with the absence of allenic peroxy radicals in the He droplet IR spectra.

Five stable conformers were predicted for the allyl peroxy radical (H$_{2}$C$=$CHCH$_{2}$–OO$^{\bullet }$) [89]. A two-dimensional potential surface was computed for rotation about the CC–OO and CC–CO bonds, [20] revealing multiple isomerization barriers greater than $\sim$300 cm$^{-1}$. Nevertheless, the C-H stretch IR spectrum can be assigned assuming the presence of a single conformer following the allyl + O$_{2}$ reaction within He droplets [20]. This is similar to the observation for the propargyl peroxy system, and from this we can infer a cooling mechanism for the vibrationally hot reaction products (R–OO$^{\bullet }$) that is consistent with both sets of data. The mechanism assumes that the more closely spaced torsional levels (<100 cm$^{-1}$) are relaxed more efficiently by the He solvent in comparison to the higher frequency vibrations, allowing the system to funnel into the lowest energy conformational minimum as it cascades down the ladder of excited stretching/bending levels.

4.1.4 Infrared Spectroscopy of Hydroxycarbenes

4.1.4.1 Hydroxymethlyene, Dihydroxycarbene, Hydroxymethoxycarbene

Hydroxymethylene (HC̈OH) and its d$_{1}$-isotopologue (HC̈OD) were isolated in He droplets following the pyrolysis of glyoxylic acid [32]. Transitions identified in the IR spectrum were assigned exclusively to the trans-conformation based on previously reported anharmonic frequency computations [90, 91]. For the OH(D) and CH stretches, a- and b-type transitions were observed, and when taken in conjunction with CCSD(T)/cc-pVTZ computations, lower limits to the vibrational band origins were determined. The relative intensities of the a- and b-type transitions provide the orientation of the transition dipole moment in the inertial frame. The He droplet data are in excellent agreement with anharmonic frequency computations carried out in collaboration with John F. Stanton, confirming strong anharmonic resonance interactions in the high-frequency stretch regions of the mid-IR. Moreover, the He droplet spectra confirm appreciable Ar-matrix shifts of the OH and OD stretches, which were previously postulated by Schreiner and co-workers [90].

Dihydroxycarbene (HOC̈OH) was produced via pyrolytic decomposition of oxalic acid, captured by He droplets, and probed with IR laser Stark spectroscopy [35]. Rovibrational bands in the OH stretch region were assigned to either trans,trans- or trans,cis- rotamers on the basis of symmetry type, nuclear spin statistical weights, and comparisons to electronic structure theory calculations (Fig. 4.13). The inertial components of the permanent electric dipole moments for these rotamers were determined with Stark spectroscopy. The dipole components for trans,trans- and trans,cis- rotamers are ($\mu _a$, $\mu _b$) = (0.00, 0.68(6)) and (1.63(3), 1.50(5)), respectively. The IR spectra lack evidence for the higher energy cis,cis- rotamer, which is consistent with a previously proposed pyrolytic decomposition mechanism of oxalic acid [92,93,94,95] and computations of HOC̈OH torsional interconversion and tautomerization barriers [96].

Fig. 4.13

Reproduced with permission from Ref. [35]. $\copyright$ copyright American Institute of Physics. All rights reserved

Rovibrational spectrum of trans,trans- and cis,trans-HOC̈OH rotamers in the OH stretch region. A simulation (red) derived from an asymmetric top Hamiltonian is shown below the experimental (black) spectrum. Assignments are based on band-types and nuclear spin statistical weights. Pure b- and a-type bands are observed for the symmetric and antisymmetric OH stretching vibrations of the $C_{2v}$ trans,trans- rotamer, respectively. The a,b-hybrid band corresponds to the higher frequency OH stretch of the $C_s$ symmetry cis,trans- rotamer.

Hydroxymethoxycarbene (CH$_{3}$OC̈OH) was similarly produced via monomethyl oxalate pyrolysis [36]. Two rotationally resolved a,b- hybrid bands in the OH-stretch region were assigned to trans,trans- and cis,trans- rotamers. Stark spectroscopy of the trans,trans- OH stretch band provided the a-axis inertial component of the dipole moment, namely $\mu _a=$ 0.62(7) D. The computed equilibrium dipole moment agrees with the expectation value determined from experiment, consistent with a semi-rigid CH$_{3}$OC̈OH backbone computed via a potential energy scan at the B3LYP/cc-pVTZ level of theory, which reveals substantial conformer interconversion barriers of $\sim$17 kcal mol$^{-1}$.