Spectroscopy and dynamics of A [²B₁] allyl radical

Abstract

The A [²B₁] ← X [²A₂] band system between 380 and 420 nm was observed in a supersonic jet expansion. The allyl radical was found to dissociate following electronic excitation, releasing a hydrogen atom. Monitoring the appearance of the hydrogen atom photoproduct as a function of the excitation laser wavelength, similar spectral features are observed as in earlier absorption experiments. Time- and frequency-resolved photoionization of the hydrogen atom product provides information on the unimolecular dissociation dynamics. The measured dissociation rates and kinetic energy releases of both allyl radical, C₃H₅, and partially deuterated allyl radical, C₃DH₄, suggest direct loss of the central hydrogen atom, leading to allene as the major product.

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1. Introduction

Allyl radical, C₃H₅, is presently one of the best understood polyatomic radicals. It is the simplest π-conjugated hydrocarbon radical, thus serving as a model system for a whole class of molecules.

Small hydrocarbon radicals play a key role in combustion chemistry, in hydrocarbon crackers and in certain regions of the atmosphere as well as in interstellar space. All hydrocarbons with a framework of three carbon atoms are assumed to be precursors in the formation of polycyclic aromatic hydrocarbons and soot.¹ Allyl is also an important intermediate in propane-, butane- and acetylene-rich flames.² Kinetic modelling of combustion processes is very sensitive to the rates of reactions that produce or consume hydrogen atoms.³ Thus, data on the unimolecular dissociation of allyl is important.

Spectroscopy and dynamics of allyl radical have been studied for many years. Numerous absorption measurements have been performed in the visible and ultraviolet region.^4–13 Whereas the spectroscopy of the B [²A₁], C [²B₁] and D [²B₂] electronically-excited states were studied in detail earlier in our group using resonance-enhanced multiphoton ionization (REMPI),^8,9 relatively little is known about the first electronically-excited A [²B₁] state.

Nearly 40 years ago, Ramsay and Currie observed a weak absorption in the spectral range between 370–410 nm, with a band origin at 408.3 nm, after flash photolysis of various allylic compounds in the gas phase. They assigned this to a transition between the ground state and first excited state of the allyl radical.¹¹ This was recently confirmed in two cavity ring-down experiments,⁴ as well as in a picosecond time-resolved experiment.¹⁴ Due to the diffuse nature of the observed bands, they were not assigned further and the homogenous broadening was attributed to either predissociation¹¹ or isomerization to cyclopropyl radical.^15,16

Although the allyl radical is stable in the electronic ground state, it becomes reactive following electronic excitation. Photodissociation studies of the B, C and D excited states performed in our group suggest rapid internal conversion to hot ground state allyl radicals, which eventually dissociate into a hydrogen atom and C₃H₄ on the ground state surface. Three main reaction channels were identified, which lead to a hydrogen atom and either allene, cyclopropene or propyne as photoproducts.^17,18 The lifetimes of these three excited states have been measured by time-resolved photoelectron spectroscopy (PES) and were found to be in the range of 10–20 ps.^14,19 In the same experiment, the authors found a resonant enhancement of the pump–probe signal upon excitation in the range between 400–410 nm. The observed signal decay, however, was limited by the instrument response function, thus a lifetime <5 ps of the A-state may be presumed.

The allyl B, C, and D excited states have a partially rotationally-resolved spectrum, which allowed the investigation of angular-momentum-selected dynamics.²⁰ An investigation of J-dependent dynamics was of interest since Szpunar et al. reported allyl radicals that were unusually stable towards dissociation.^21,22 They used photofragment translational spectroscopy to disperse rotationally and vibrationally energized radicals and found a considerable fraction with internal energies up to 15 kcal mol⁻¹ above the barrier but that did not dissociate. They attributed the increased stability of these radicals to a centrifugal barrier. In our earlier angular-momentum-selected experiment, we could not find any observable difference between the photodissociation dynamics of high- and low-J allyl radicals at 115 kcal mol⁻¹ total energy.²⁰ The A-state therefore offers a good opportunity to probe dissociation dynamics at energies closer to the barrier to unimolecular dissociation and in the same energy range as in the study of Szpunar et al.

2. Experimental

All experiments were carried out in a standard molecular beam apparatus, equipped with a time-of-flight mass spectrometer. The details were previously described in an earlier publication,¹⁷ and we will only give a brief summary. The signal-to-noise ratio was increased by modification of the ion source, ion optics and detector of the mass spectrometer and improved stability of the dye lasers.²⁰

We generated a clean pulsed beam of cold allyl radicals by supersonic jet flash pyrolysis²³ of allyl iodide, obtained from Aldrich and used without further purification, seeded in 1.6 bar of helium. Isotopically-labeled precursors were synthesized according to procedures given in the literature.⁸ The skimmed radical beam was crossed in the ionization chamber by two counter-propagating laser beams. Fig. 1 depicts the energetics of the pump–probe experiments. The two-fold expanded output of a Nd:YAG-pumped dye laser (Radiant Dyes Narrow Scan) was used for excitation. The 365 nm output of another dye laser was frequency tripled in a Kr-cell (220 mbar) to provide 121.6 nm VUV light for the 1s–2p transition in the hydrogen atom. The ²P-hydrogen atoms were ionized by the residual 365 nm light in the source of the time-of-flight mass spectrometer and detected on double channel plates. Two digital delay generators (Stanford Research DG 535) controlled the relative timing of the lasers and the valve with a resolution better than 2 ns. The data were recorded on a digital storage oscilloscope, averaged over typically 200 laser shots, and transferred to a computer.

Fig. 1 Schematic energy level diagram for the pump–probe experiments. After electronic excitation, the allyl radicals decay non-radiatively to form hot ground state radicals that dissociate into C₃H₄ and hydrogen. The hydrogen atoms are ionized by 1 + 1′ REMPI.

We performed the following three types of experiment: (1) The probe laser was held fixed at the Lyman-α wavelength while the excitation laser was scanned in frequency to obtain an action spectrum of the hydrogen atoms; (2) the excitation laser was held fixed at a selected band of the A-state allyl while the probe laser was scanned in frequency to record the Doppler profiles of the hydrogen atoms; and (3) the wavelength of both lasers was fixed while the relative timing between them was changed to acquire a transient spectrum. The pump–probe delay in experiments (1) and (2) was set to 100 ns.

3. Ab initio calculations

Equilibrium geometries for both the ground and excited state were optimized using the complete active space self-consistent field (CASSCF) method²⁴ with the cc-pVTZ, aug-cc-pVTZ, 6-311G(3df,3pd) and 6-311+G(3df,3pd) basis sets.^25–27 A proper analysis of orbital occupancy showed that a small active space consisting of three electrons distributed among the three π-orbitals (1b₁, 1a₂, 2b₁) is sufficient to account for the multireference character of the allyl radical. Harmonic frequency analysis in the first excited state was also performed at the CASSCF level. Energies were calculated using the multiconfiguration reference internally contracted configuration interaction (MRCI) method^28,29 and extrapolated to the basis set limit (cc-pVXZ, X = D,T,Q).

The geometries of stationary points on the C₃H₅ ground state surface and the possible dissociation products of allyl radical were optimized at the CCSD/cc-pVTZ level, whereas single-point energies were calculated including non-iterative triples excitation^30,31 and extrapolated to the basis set limit (cc-pVXZ, X = D,T,Q). Vibrational frequencies used for zero-point energy correction and RRKM calculations were obtained using an anharmonic frequency analysis³² at the HCTH147/TZ2P level.^33,34 All calculations were carried out using the MOLPRO³⁵ and Gaussian 03³⁶ packages.

4. Results and discussion

4.1 Vibrational structure of the A [²B₁] ← X [²A₂] band

Recording absorption spectra in a molecular beam was not feasible due to the inherently small number of radicals in the beam (∼10¹⁰ cm⁻³) and the low absorption cross section of the A [²B₁] ← X [²A₂] transition (∼2 × 10⁻¹⁹ cm² molecule⁻¹ at 402.9 nm).⁴ The oscillator strength associated with this transition (f_osc = 0.0013) is more than two orders of magnitude lower than that observed for the UV bands (f_osc = 0.26)⁷ and, combined with the presumed short lifetime of the A-state, also made resonance-enhanced multiphoton ionization (REMPI) spectroscopy impossible. Calculated reaction barriers for unimolecular reactions of the allyl radical suggest that the loss of hydrogen is possible at the energy of the A-state (∼70 kcal mol⁻¹). We therefore monitored the appearance of hydrogen atoms as a function of excitation laser wavelength and obtained the action spectrum shown in Fig. 2. This spectrum shows the same spectral features as in the earlier absorption experiments by Currie and Ramsay¹¹ and Tonokura and Koshi;⁴ a clear indication that these hydrogen atoms were released following excitation to the allyl A-state.

Fig. 2 Action spectrum obtained by monitoring the total flux of hydrogen atoms while scanning the excitation laser. The delay time between excitation and probe laser was 100 ns.

The excited states of the allyl radical have been the subject of numerous quantum chemical calculations.^37–40 Noteworthy is an early LCAO self-consistent orbitals calculation by Longuet-Higgins and Pople.⁴⁰ They calculated vertical excitation energies of 2.74 and 5.29 eV for the first two doublet excited valence states, and predicted a weak absorption for the transition in the visible region and a much stronger absorption in the UV. This has been experimentally confirmed and these two band systems correspond to transitions to the A- and C-excited states. We calculated a zero-point energy-corrected adiabatic excitation energy of the A [²B₁] ← X [²A₂] transition at the MRCI/CBS level of 3.04 eV, which is in quantitive agreement with the experiment. The configuration state function of the A-state can be described as a linear combination of the following two reference configurations: (1b₁)¹(1a₂)²(2b₁)⁰ and (1b₁)²(1a₂)⁰(2b₁)¹. This corresponds formally to either a π → n or a n → π* transition. It should be pointed out that the allyl C-state is a linear combination of the same reference configurations, but with different coefficients for each configuration.

The A [²B₁] ← X [²A₂] transition is allowed by electronic selection rules in both C_2v and C₂ symmetry. If a transition between states with different symmetry to the equilibrium conformation is considered, the selection rules must be applied to the common elements of symmetry, which is C₂ in this case. The dipole transition moment lies along the long axis of the molecule (y) if the transition is treated in C_2v symmetry, leading to an A-type band. Within C₂ symmetry, the transition dipole moment lies in the xy-plane, leading to an A,C-type hybrid band. Fig. 3 shows a simulation of the rotational contour performed using the AsyrotWin program.⁴¹ The rotational constants for the allyl A-state equilibrium geometry were taken from ab initio calculations at the CASSCF/6-311+(3df,3pd) level of theory. The rotational temperature was taken from a rotational contour analysis of a REMPI-spectrum of the partially rotationally-resolved C-state obtained under the same experimental conditions, and was found to be ∼100 K. The simulation of an A,C-type hybrid band with a line FWHM of 2 cm⁻¹ gave the best fit of the peak at 408.5 nm.⁴² The band origin is ∼10 cm⁻¹ red-shifted from the peak maximum. The intervals between this origin and the vibronic bands observed in the action spectrum are listed in Table 1.

Fig. 3 Simulation of the rotational contour in the A-state origin region as an A,C-type hybrid band. The rotational temperature was set to 100 K and a line FWHM of 2.0 cm⁻¹ was used.

Table 1 Vibrational frequencies (cm⁻¹) of A-state allyl

		Mode	CASSCF^a cc-pVTZ	CASSCF^b 6-311+G (3df,3pd)	Expt.^c
a Scaled by 0.910. b Scaled by 0.902. c Taken from the action spectrum depicted in Fig. 2, the uncertainty of the intervals is ≤ ± 10 cm^−1.
a	ν 1	As CH2 str (in phase)	3055	3029
	ν 2	CH str	3003	2976
	ν 3	Sym CH2 str (in phase)	2966	2939
	ν 4	Sym CH2 scis	1439	1425
	ν 5	Sym CH2 rock	1095	1082	1032
	ν 6	Sym CCC str CH2 rock	880	872	(934)
	ν 7	As CH2 wag	511	509	553
	ν 8	CCC bend	403	400	381
	ν 9	Sym CH2 twist	160	156	135
b	ν 10	As CH2 str	3055	3028
	ν 11	Sym CH2 str	2966	2939
	ν 12	As CCC str	1593	1572	1501
	ν 13	As CH2 scis	1394	1382
	ν 14	CH rock	1230	1215	1232
	ν 15	As CH2 rock	922	913	934
	ν 16	As CH2 twist CH wag	750	751	752
	ν 17	Sym CH2 wag	500	500
	ν 18	CH wag (in phase)	418	415

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Harmonic frequencies were calculated at the CASSCF level for the C₂ symmetric A-state equilibrium geometry. The frequency scaling factors were calculated by linear regression to experimental frequencies obtained from the tentatively assigned vibronic bands. The scaling factors are in the same range as derived from other calculations with these basis sets.⁴³ The root-mean-square error of the scaled harmonic frequencies is 30.8 cm⁻¹ for the 6-311+G(3df,3pd) basis set and 33.1 cm⁻¹ for the cc-pVTZ basis set, which is much lower than the rms errors reported for various Hartree–Fock (HF) methods by Scott and Radom.⁴³

Upon electronic excitation, the allyl radical undergoes significant changes in geometry. The C₂ symmetric A-state equilibrium geometry has a non-planar structure, with the two terminal CH₂ groups rotated out-of-plane by a dihedral angle of ∼40°. The CC bonds are substantially lengthened to 1.47 Å, while the remaining coordinates remain essentially unchanged. Both lengthening of the CC bond as well as the out-of-plane twisting of the CH₂ groups can be explained by the promotion of electrons from the bonding π orbital to the non-bonding n or anti-bonding π* orbital. The ν₉ asymmetric CH₂ twist frequency is lowered from 547 cm⁻¹ in the ground state to 135 cm⁻¹ in the excited state. As this twist is one of the major changes in equilibrium geometry upon excitation, the ν₉ mode is prominent in the spectrum and its first overtone also appears with about half of the intensity of the fundamental. Nearly all peaks observed in our action spectrum can be assigned to a vibrational mode of A-state allyl and tentative assignments are listed in Table 1. The nonplanar geometry results in a double-well potential for the ν₉ mode. Tonokura and Koshi⁴ calculated the height of the inversion barrier to be around 400 cm⁻¹, which is in agreement with our own calculations. This leads to an inversion doubling of levels at or below the top of the barrier, although the splittings are far too small to be observed in the experimental spectrum. The vibronic bands seem to broaden towards higher energy in the spectrum, possibly indicating a shortening of the lifetime.

4.2 Dissociation dynamics

As already discussed in the previous section, from the similarity between our observed action spectrum and earlier absorption spectra, as well as the agreement of experimental with calculated frequencies, it is evident that the observed hydrogen atoms originate from the A-state allyl. One question that may immediately arise is whether the dissociation occurs in the excited state or on the ground state surface. The photodissociation dynamics of the B, C, and D-states were examined in an earlier publication and it was found that dissociation occurred on the ground state surface after fast internal conversion.^17,18 There are clear indications that the lifetime of the A-state is extremely short, presumably <5 ps, and we would thus not expect a dissociation in the excited state to proceed on a ns time scale as depicted in Fig. 4. We obtained the appearance time of hydrogen atoms by monitoring the total flux of hydrogen atoms while varying the time delay between excitation and probe laser. The data points were fitted using the expression

S_H(t) = N(e^−k₁t − e^−k_Ht) (1)

which was convoluted with a 6 ns FWHM Gaussian function corresponding to the cross-correlation of the two laser pulses. S_H is the hydrogen atom signal, k_H the unimolecular rate constant and k₁ accounts for the decay of the signal at longer delay time due to hydrogen atoms moving out of the detection volume of the probe laser. Note that in contrast with earlier measurements in the C-state,^17,20 the signal rise can be fitted by one exponential without significant deviation from the experimental data points. This is a clear indication that we observe one unimolecular process and not competing reaction channels via different intermediates, as found at higher excitation energies.

Fig. 4 Appearance of the hydrogen atom signal as a function of the time delay between pump and probe laser for initial excitation to the A-state origin.

Fig. 5 shows calculated reaction channels for allyl radical unimolecular dissociation. The lowest barrier is for cyclization to cyclopropyl radical via transition state 5. At 70 kcal mol⁻¹ there is not enough energy available for allyl to dissociate to cyclopropene and a hydrogen atom. On the right hand side of the scheme, there is, in principle, enough energy available for any reaction to take place, leading to allene and propyne as final products. As TS 1 is more than 2 kcal mol⁻¹ lower in energy than TS 2, we expect mainly allene and hydrogen as products.

Fig. 5 Possible reaction pathways for allyl radical unimolecular dissociation. Cyclization to cyclopropyl and subsequent dissociation to cyclopropene is depicted on the left-hand side. Direct loss of hydrogen to form allene via TS 1, or 1,2-H-shift leading to 2-propenyl, which can then dissociate to either allene or propyne, are shown on the right-hand side. Given energies are zero-point energy corrected and are calculated at CSSD(T)/cc-pVXZ (X = D,T,Q, extrapolated to basis set limit) level of theory at CSSD/cc-pVTZ geometries of these stationary points.

The substitution of selected hydrogen atoms with deuterium allows an investigation of the site selectivity of the reaction. For the dissociation forming allene via TS 1, one would expect loss of the hydrogen connected to the central carbon atom in allyl. Upon cyclization to cyclopropyl on the other hand, one of the terminal C–H bonds should be cleaved. Finally, 2-propenyl formed by a 1,2-hydrogen shift can either dissociate to propyne or allene, giving rise to isotopic scrambling. In order to identify the dominant channel, 2-deuterioallyliodide (in which the central hydrogen atom is replaced by deuterium) was synthesized. We performed Doppler spectroscopy of the hydrogen and deuterium atom photofragments and obtained the spectrum depicted in Fig. 6. The 1s–2p Lyman-α transition in deuterium is blue-shifted only by 22.4 cm⁻¹ with respect to hydrogen, so that both transitions could be recorded in the same scan of the probe laser. Due to the proximity of the signals, we assume the efficiency of the non-resonant frequency tripling for the generation of VUV photons to be constant over the whole range. If it is also presumed that both absorption and ionization cross sections for hydrogen and deuterium are comparable, the area under the H and D peaks is directly proportional to the number of H and D atoms lost from the parent allyl radical.

Fig. 6 Doppler profiles for 2-deuterioallyl obtained from the A-state origin at a time delay of 100 ns between excitation and probe laser. The ratio between hydrogen (◇) and deuterium (○) is ∼1 ∶ 5.

If the bond between deuterium and the central carbon is broken, one has to consider a first order kinetic isotope effect. Substitution of hydrogen with deuterium leads to a decrease of zero-point energy and an increase in the density of states, caused by a lowering of the C–D frequency compared to C–H. As a result, reaction rates involving cleavage of a C–H bond will, in general, decrease upon deuteration up to one order of magnitude. From the ratio between the H- and D-signals obtained from the Doppler profiles in Fig. 6, we conclude that direct dissociation to allene from loss of the central deuterium atom is the dominant reaction channel. Note that the kinetic isotope effect works in favor of cleavage of the terminal C–H bonds. We also measured Doppler profiles at different pump–probe delays but did not observe a significant change in the H/D ratio, except for a moderate increase of the deuterium signal at longer pump–probe delays. This can easily be explained by the faster movement of the hydrogen atoms out of the probe laser detection volume, which becomes significant at longer delay times. The isotopic purity of the radical precursor 2-deuterioallyliodide was determined by NMR and is >95%. Hence, a significant fraction of the observed hydrogen atoms is due to isotopic impurity.

RRKM calculations for direct allene formation yielded a microcanonical rate constant of 1.96 × 10⁷ s⁻¹, which is in good agreement with our experimental unimolecular dissociation rate k_H(E) = 1.75 (± 0.47) × 10⁷ s⁻¹. We also measured the rates for the isotopically-labelled species and obtained k_D(E) = 1.09 (± 0.43) × 10⁷ s⁻¹, which is roughly two times slower as a consequence of the kinetic isotope effect. More dissociation constants obtained after excitation of allyl to different energies are listed in Table 2 together with the calculated RRKM values. The measured dissociation constants are in good agreement with the calculated RRKM values and, as expected, the reaction becomes faster with increasing excitation energy.

Table 2 Unimolecular dissociation rate constants (10⁷ s⁻¹)

Energy^a/kcal mol^−1		k H(E)^b	k D(E)^b	k H, RRKM(E)^c	k D, RRKM(E)^c
a Corresponding to excitation to indicated bands. b Obtained from time-dependent appearance of H/D atom signal as shown in Fig. 4. c RRKM calculations based on anharmonic frequencies at HCTH147/TZ2P level.
70.0	A^000	1.75	1.09	1.96	1.08
71.6	A^107	3.49	2.04	3.90	2.13
73.5	A^1014	6.58	3.89	7.78	4.24

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From frequency-resolved photoionization of the hydrogen atom photoproduct, we obtained the Doppler profile shown in Fig. 7. The profile is broadened by the VUV laser linewidth of 0.5 cm⁻¹ and a Gaussian FWHM of 2.67 cm⁻¹ resulted after proper deconvolution. The translational temperature of the hydrogen atom in the laboratory coordinate frame can be calculated using the expression

from which the translational energy 〈E_T〉 = (3/2)kT_T can be obtained, assuming a Boltzmann-like distribution of E_T. From our measured Doppler profiles, we derive a translational temperature of 2100 K and an expectation value for the translational energy of 6.2 ± 0.5 kcal mol⁻¹. Assuming allene as reaction product, 42% of the excess energy of 14.6 kcal mol⁻¹ would be released as translation. After excitation to the allyl C-state, 23% of the 59 kcal mol⁻¹ excess energy is released in translation.¹⁷ For hydrogen loss from unsaturated hydrocarbons, typical translational energy releases between 10% and 25% have been reported.^45–47 Obviously, the kinetic energy release of this reaction is exceptionally high. Already in our earlier experiments for dissociation following excitation to the C-state, the kinetic energy release was much higher than predicted by simple statistical models such as the prior distribution approach⁴⁸ or RRKM calculations.⁴⁹ These simple models, however, do not take into account the energy of a reverse barrier and are thus restricted to reactions with a loose transition state. The more recent statistical adiabatic impulsive model⁵⁰ is suitable for unimolecular dissociations with a reverse barrier. The total energy available to the products is divided into two reservoirs: the statistical reservoir containing the energy difference between total energy and zero point energy of the transition state; and the impulsive reservoir defined as the difference between zero point energies of the transition state and the products, which is the reverse activation barrier. The model predicts that most of the energy in the impulsive reservoir (60–80%) goes into translation whereas the product energy distribution of the statistical reservoir depends on the transition state geometry. Our ab initio calculations predict a reverse barrier for direct allene formation of 4.3 kcal mol⁻¹. If we assume that 70% of the impulsive reservoir (4.3 kcal mol⁻¹) goes into translation, 28% of the statistical reservoir (11.3 kcal mol⁻¹) must contribute to translation to get the measured expectation value of 6.2 kcal mol⁻¹ for the translational energy release. In the A-state with small excess energy, the reverse barrier has a larger influence on the kinetic energy release than in photodissociation at higher excess energy because the impulsive reservoir is independent of excitation energy, as the energy of this reservoir is defined by the constant energy of the transition state. The ratio of energy going from the statistical reservoir into translation corresponds well to values obtained for similar reactions.^{17–18,20,45–47}

Fig. 7 H-atom Doppler profile obtained following excitation into the A-state origin at 100 ns pump–probe delay.

The high-energy wings of the Doppler profile in Fig. 7 may indicate a small contribution of higher-order multiphoton processes. We have measured the H-atom signal intensity at different excitation laser energies and found a linear dependence on laser power, typical for a one-photon process. Doppler profiles recorded at different laser intensities showed no significant difference. Furthermore, two-photon processes would lead to resonant Rydberg states around 200 nm with sharp bands, which were not observed in the spectrum.

4.3 ² A ₂–²B₁ conical intersections and the fate of the electronically-excited allyl radical

The short lifetime of the A-state may be explained in terms of the flat character of the potential energy surface along several internal coordinates, in particular the CH₂-twist motion. An additional conrotatory 16° out-of-plane twisting of the terminal CH₂ groups and a substantial decrease of the CCC angle leads to a conical intersection with the ground state surface, as shown in Fig. 8a, which lies only 1.10 kcal mol⁻¹ higher in energy than the allyl A-state equilibrium geometry. Another conical intersection was located when the geometry was held in C_s symmetry and the CH₂ groups were rotated in a disrotatory fashion (Fig. 8b). It should also be mentioned that both the C₂ symmetric A-state equilibrium geometry and the minimum energy geometry at the conical intersection are chiral, and that there are two enantiomeric conformations with the terminal CH₂ groups simply twisted the other way round. Dynamic correlation included at the MRCI/CBS level of theory at the CASSCF geometries leads to a ∼3 kcal mol⁻¹ decrease in the minimum energy conical intersections relative to the A-state equilibrium geometry. These values should be considered with care, as one would expect different geometries of the minimum energy conical intersections at the MRCI level of theory. This is also reflected in the ∼0.5 kcal mol⁻¹ energy differences of the upper and lower states, which are energetically exactly the same at the CASSCF level of theory.

Fig. 8 Geometries at the conical intersections between the A-state and ground state, located using SA-CASSCF/6-311+G(3df,3pd).⁴⁴ The C₂ geometry (a) is 1.1 kcal mol⁻¹ higher and the C_s geometry (b) is 3.8 kcal mol⁻¹ lower in energy than the A-state equilibrium geometry.

An electrocyclic reaction between allyl and cyclopropyl radical has already been discussed when Woodward and Hoffmann introduced the concept of conservation of orbital symmetry.⁵¹ They suggested cyclization in a conrotatory fashion in the ground state and a disrotatory fashion in the excited state; however it was rapidly demonstrated by Longuet-Higgins that in both conrotatory and disrotatory modes the ground state of each radical is correlated to an excited state of the other using state correlation schemes,⁵² as depicted in Fig. 9. The issue of electrocyclic interconversion between allyl and cyclopropyl has been addressed by numerous theoretical studies. A quasi-classical trajectory study of the ring opening of cyclopropyl in the ground state via a highly asymmetric transition state resulted in nearly equal probability for conrotatory and disrotatory ring opening.⁵³ A CASSCF study of the photochemical cyclization found no barrier on the conrotatory pathway and a very small (<1.5 kcal mol⁻¹) barrier on the disrotatory pathway,¹⁶ which is in good agreement with the state correlation scheme in Fig. 9. Our own calculations show conical intersections along both pathways, and thus the excited allyl radical can either undergo cyclization leading to cyclopropyl or end up in the allyl ground state. Holtzhauer et al.¹⁵ found evidence for the formation of cyclopropyl after irradiation of allyl radicals in an argon matrix, which supports the picture of photochemical electrocyclization. The resulting cyclopropyl has enough internal energy to ring-open to allyl on the ground state surface again. This electrocyclic interconversion of allyl and cyclopropyl radical in the ground state is reversible and fast compared to the other unimolecular reactions shown in Fig. 5.

Fig. 9 State correlation scheme for conrotatory and disrotatory electrocyclic interconversion of cyclopropyl and allyl radical. Note that only valence excited states are considered in allyl, although there are some intruding low lying Rydberg states.

5. Conclusions

We have measured the action spectrum of the allyl radical in the range of 380–420 nm. The observed vibronic bands correspond to those obtained in earlier absorption experiments and were assigned with the help of calculated vibrational frequencies for the A [²B₁] electronically-excited state.

The primary photophysical and photochemical processes upon excitation are very intricate. The three conical intersections of the A-state and the ground state and the possibility of electrocyclic conversion to cyclopropyl radicals give rise to various mechanisms for non-radiative decay, and thus explain the short lifetime of the A-state. Whereas we have no experimental information on the primary photochemical processes leading to hot ground state radicals, the measured kinetics of the hydrogen atom loss and Doppler profiles suggests that dissociation to the primary photoproducts, allene and a hydrogen atom, must occur on the ground state surface.

The observed diffuse spectrum unfortunately has no rotational resolution and prevents investigation of J-dependent dynamics at energies close to the barrier to unimolecular dissociation. A further investigation of the primary photochemical processes would demand sophisticated experiments, with isotopically-labeled precursors combined with extensive computational studies of the non-adiabatic dynamics.

Acknowledgements

We appreciate assistance in the early stage of the project and help in the synthesis of the deuterated precursor by Didier Zurwerra and Daniel Meier. The support of this work by the Schweizerischer Nationalfonds and ETH Zürich is gratefully acknowledged.

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Footnote

† Electronic supplementary information (ESI) available: Geometries, frequencies and total energies of the ab initio calculations.. See DOI: 10.1039/b602412b

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