Unraveling the Spectroscopy of the Phenalenyl Radical

Abstract

Jet-cooled excitation spectra of the phenalenyl radical are obtained using resonance enhanced multiphoton ionization. The excitation spectra reveal previously unobserved transitions, up to 17,000 cm^–1 above the D₁ origin, including transitions to electronically forbidden A₂ electronic states. A quasi-diabatic approach is applied to construct a vibronic Hamiltonian, including both Jahn–Teller and pseudo-Jahn–Teller interactions, between seven excited electronic surfaces. This is employed to calculate the electronic excitation spectrum of the phenalenyl radical in its entirety, providing vibronic assignments and spectral parameters to help decode the spectroscopy of this key radical.

Introduction

The phenalenyl radical (C₁₃H₉) possesses a high level of symmetry (D_3h) and is the smallest odd-carbon, open-shell radical, that consists of solely six-membered rings, as shown in Figure (a). As a 13-carbon conjugated species, the phenalenyl radical also exhibits significant resonance stabilization, which is strong enough to preserve the radical in solution at room temperature. − The combination of strong resonance-stabilization and high symmetry makes the phenalenyl radical an interesting prototype for many areas of chemistry. In combustion chemistry, the formation of the phenalenyl radical from acenaphthylene is believed to be a vital initial step of soot growth, that leads to the formation of polycyclic aromatic hydrocarbons (PAHs) with exclusively 6-membered rings. − Phenalenyl is also the smallest polycyclic odd alternant hydrocarbon (POAH), a class of molecules which have received widespread attention over the past 60 years due to the attractive properties of their nonbonding molecular orbitals , and ability to form multiple redox species. − In materials chemistry, these phenalenyl derivatives are known as open-shell graphene fragments, and have promising potential applications for quantum electronic devices ,,− and molecular organic conductors. ,− The phenalenyl radical is also a key intermediate species in astrochemical PAH growth mechanisms, that recycle carbon material between stellar death and stellar birth. Combined with the strong aromatic stabilization and the ability to form multiple redox states, this makes phenalenyl-like radicals and cations promising carriers for the enigmatic diffuse interstellar bands. ,

1.

(a) Depiction of the D_3h phenalenyl radical. (b) Corresponding molecular orbital diagram. The four single-electron transitions that give rise to the two pairs of degenerate E" states are shown in blue, while the transitions that give rise to the two A₂ states are shown in red. (c) Corresponding Jablonski diagram, showing the phenalenyl excited states and predicted transitions.

Despite the wide attention phenalenyl chemistry has received over the last 60 years, our understanding of the electronic structure and spectroscopy of the phenalenyl radical has remained sparse. , Early studies relied on magnetic resonance methods, with the radical prepared in deoxygenated solutions. Little was known about the optical spectroscopy of the radical until 1984, when the fluorescence excitation and emission spectra of phenalenyl were first observed, by isolating the radical within a cryogenic matrix at 20 K. This resolved many sharp features around 535 nm which were assigned to the D₁ → D₀ electronic transition. However, no satisfactory analysis could be obtained due to complications that arose from the Jahn–Teller effect, which distorts the D₁ surface. The first gas-phase spectrum of the phenalenyl radical was later reported by our group in 2011. The excitation spectrum of the radical was observed using 1 + 1′ resonance-enhanced multiphoton ionization (REMPI), which resolved many sharp vibronic features corresponding to the D₁ ← D₀ electronic transition. This work determined the origin to be at 18,800 cm^–1 (531.9 nm). However, attempts to decode the D₁ ← D₀ spectrum were again complicated by vibronic coupling effects. Consequently, apart from the origin, only the most intense feature occurring at 19,560 cm^–1 (511.0 nm) was able to be assigned to a vibronic transition. Confidently assigning any of the other spectral features was not possible without also considering the higher-lying excited states that influence the spectroscopy on the D₁ surface.

In this work, we report the first observation of three new excited states of the phenalenyl radical, up to 17,000 cm^–1 above the previously observed D₁ state. This includes transitions to electronic states with A₂ symmetry, which are electronically forbidden. We show that a vibronic Hamiltonian may be constructed by switching to a quasi-diabatic description, which allows for the vibronic spectrum of the phenalenyl radical to be simulated and assigned in its entirety, providing a benchmark for the calculation of other high-symmetry PAH radicals.

Experimental Details

The experimental apparatus used in this work to obtain jet-cooled excitation spectra has been described in detail in refs , . The D_3h phenalenyl radicals are generated via cycloaddition of CH radicals to acenaphthylene, as was demonstrated in ref . Briefly, a sample of acenaphthylene is heated to 90 °C and seeded in 5 bar of a methane/argon gas mixture (1% methane/99% argon). The seeded gas mixture then passes through a pulsed discharge nozzle, as it expands into a differentially pumped vacuum chamber. A voltage of −1.65 kV strikes the expanding gas pulse, generating CH radicals that can attach to isolated acenaphthylene molecules to initiate the formation of phenalenyl radicals. The discharge products are cooled through supersonic expansion with the argon buffer gas, and the central, coldest section of the molecular beam (∼ 10 K) passes through a 2 mm diameter skimmer into a second differentially pumped chamber.

Two Nd:YAG-pumped dye lasers may then be used to resonantly excite and/or deplete the jet-cooled phenalenyl radicals. In this work, excitation wavelengths were scanned across a broad energy range from 555 nm (18,000 cm^–1) to 285 nm (35,000 cm^–1). The excited radicals are then subsequently ionized, using the fourth harmonic (266 nm) of a third Nd:YAG laser. The resulting C₁₃H₉ cations are orthogonally accelerated up the length of a Time-of-Flight mass spectrometer, and strike a multichannel plate (MCP) detector. This produces an electronic signal that can be displayed on an oscilloscope. Custom-written LabView software allows for the mass-selective spectra to be recorded as the excitation/depletion lasers are scanned.

Computational Details

The quantum chemical calculations presented in this work were performed using the CFOUR computational package. The equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) level of theory with a correlation-consistent polarized basis set of double-ζ quality (cc-pVDZ) was used on a restricted open-shell reference to perform geometry optimizations and frequency calculations. The EOMEE-CC method is effective in describing several important types of open-shell wave functions, such as singly excited states, and many Jahn–Teller and pseudo-Jahn–Teller systems. , As the phenalenyl radical possess D_3h symmetry, the geometry may be represented by only seven unique parameters that were required to be optimized. This allowed for the robust and highly accurate EOM framework to be efficiently applied, despite the relatively large size of the radical. ,

The linear-diabatic coupling constants, required to describe the vibronic interactions, were calculated analytically at the EOMEE-CCSD/pVDZ level of theory, using the quasidiabatic ansatz of Ichino et al.

Results and Discussion

Predictions from the Coulson-Rushbrooke Theorem

Due to the unique electronic structure of the phenalenyl radical, its molecular orbital (MO) structure may be understood by considering the Hückel MO approximation and the Coulson–Rushbrooke theorem. − As an odd alternant hydrocarbon, phenalenyl possess a singly occupied nonbonding molecular orbital of a₁ symmetry. Immediately above and below this singly occupied molecular orbital (SOMO) are two pairs of degenerate e″ orbitals, which must be equally distributed around the SOMO energy level to satisfy the Coulson–Rushbrooke theorem. This gives rise to four single electron transitions which are equivalent in energy: two transitions into the a₁ orbital (a₁ ← e″) and two transitions out of the a₁ orbital (e″ ← a₁ ), as shown by the blue arrows in Figure (b).

These four single electron transitions generate two pairs of degenerate E″ states, which are not only equal in energy, but also in transition moment. However, mixing of the E″ wave functions breaks this degeneracy, causing the transitions to split. This wave function mixing also affects the transition moments involving each state. The lower energy transition, denoted 1E″ ← A₁ arises from destructive interference, resulting in a weak transition dipole moment. Conversely, the higher energy transition 2E″ ← A₁ arises from constructive interference, resulting in a significantly larger transition dipole moment.

This simple, “back-of-the-envelope” description is supported by the results obtained from high-level EOMEE-CCSD/pVDZ calculations, shown in Table . The vertical excitation energies and transition dipole moments for the first five excited states are reported, with the corresponding molecular orbitals shown in Figure (b). The calculations verify the description above, with a weak first excited state transition 1E″ ← A₁ and a much stronger transition into a higher lying state 2E″ ← A₁ . Additionally, transitions to two A₂ excited states are predicted, with energies that lie in between the two E″ state transitions, as shown by the red arrows in Figure (b) and (c). These excited states are derived as the in-phase and out-of-phase combination of single-electron transitions into and out of the two a ₂ molecular orbitals equally spaced about the a ₁ nonbonding molecular orbital. However, transitions from the ground A₁ state into these two A₂ states are electronically forbidden for the D_3h point group. The calculations also predict a fifth low lying excited state transition D₅ ← D₀. Therefore, there may be up to seven possible low-lying excited state surfaces to consider, as shown in the Jablonski diagram in Figure (c).

1. Vertical Excitation Energies (cm^–1) and Squared Transition Dipole Moments (Debye²) of Excited-State Transitions of the Phenalenyl Radical Calculated at the EOMEE-CCSD/pVDZ Level of Theory.

upper state	symmetry	T v	|μ|2	T v
D1	E″	21668.83	0.00016	18800.00
D2	A2	24386.22	0.00000	21157.62
D3	A2	30135.01	0.00000	26145.31
D4	E″	35042.57	0.24871	30403.13
D5	A2	38131.66	0.00000	33083.24

^aTransition dipole moments are calculated from the ground D₀ ²A₁ state.

^bA scaling factor of 0.87 may be applied to the transition energies to better compare to the experimentally observed transitions.

Spectroscopy of the Free Phenalenyl Radical

To examine the electronic structure predicted above, phenalenyl radicals were generated in the gas phase via cycloaddition of CH radicals to acenaphthylene. The phenalenyl radicals were cooled in a supersonic-jet expansion to ∼ 10 K, then interrogated using a 1 + 1′ REMPI scheme. The excitation laser was scanned across the range 18,000–35,000 cm^–1 (285–555 nm) to search for all of the calculated states in Table . The excited radicals were subsequently ionized using 266 nm light, with the resulting excitation spectrum presented in Figure .

2.

REMPI spectrum of the phenalenyl radical in the 18,350–35,000 cm^–1 energy range. Observed vibronic transitions are assigned to the D₁ ← D₀, D₃ ← D₀, D₄ ← D₀, and D₅ ← D₀ transitions. Inset: REMPI spectrum of the D₃ ← D₀ transition in the 26,500–29,500 cm^–1 energy range.

Multiple sharp features are observed between 18,350 and 22,000 cm^–1, which are assigned to the D₁ ← D₀ transition that has been reported earlier. Within this range, a previously unobserved feature is recorded at 21,838 cm^–1. Given that this band is ∼ 3000 cm^–1 above the D₁ origin (18,800 cm^–1), it may possibly be assigned to a cluster of C–H stretch normal modes. However, the features are noticeably broader than the rest of the D₁ ← D₀ spectrum, suggesting they may also be a signature of the D₂ (1A₂ ) electronic state, or another C₁₃H₉ isomer.

Although the entire vibronic spectrum shown in Figure was recorded by monitoring a single mass channel (m/z 165), it is possible that the observed spectral features originate from more than one isomer. To account for this possibility, hole-burning experiments were carried out across each electronic state. Briefly, a regular 1 + 1′ REMPI scheme was set up, with the excitation wavelength tuned to the dominant D₁ transition of the phenalenyl radical at 19,560 cm^–1. This was followed by a 266 nm ionization laser to produce a constant resonant ion signal on m/z 165. A third, hole-burning laser was then introduced, preceding the excitation laser, which is scanned across the spectrum of interest. If this hole-burn laser excites a transition from the same isomer as the excitation laser, a depletion of the resonant signal from the second laser may be observed. Conversely, if the lasers excite different isomers, the original REMPI signal will be unaffected. Therefore, any transition that results in depletion in the hole-burn spectrum must correspond to the same D_3h phenalenyl isomer.

The resulting hole-burning spectrum for the phenalenyl radical (blue) is presented in Figure , underneath the experimental REMPI spectrum (black). The lower inset shows the hole-burning comparison across the range of the D₃ ← D₀ spectrum, between 27,500 and 29,500 cm^–1. Here, it is seen that most peaks in this energy range have a counterpart in the hole-burn spectrum, and correlate exactly with their vibronic equivalent in both position and intensity. Hole-burning of the D₄ ← D₀ transition (30,000–33,000 cm^–1) produced a significantly broader and more intense depletion band, as expected. Due to the diffuse nature of this state it is more difficult to match equivalent structure to the 1 + 1′ REMPI spectrum. However, the shoulder band at ∼ 30,500 cm^–1 is observed, matching the vibronic counterpart. The doublet-like structure at ∼ 31,200 cm^–1 is missing from the hole-burning spectrum, however this is likely due to a saturation effect as the D₄ ← D₀ transition is much more intense than the D₁ ← D₀ baseline transition.

3.

Hole-burning (depletion) spectrum of the phenalenyl radical. The depletion spectrum was measured while monitoring the REMPI mass signal on m/z 165, when the excitation laser is fixed at 19,560 cm^–1. Lower inset: Hole-burning spectrum of the D₃ ← D₀ transition between 27,500 and 29,500 cm^–1. Upper inset: Hole-burning spectrum of significant peaks of the D₁ ← D₀ transition.

Hole-burning experiments were also carried out across the D₁ ← D₀ transition. However, as the lifetime of the 1E″ state is much longer than the other excited states, a different technique is required. Briefly, the hole-burn laser wavelength is fixed to the strongest resonant transition of the D₃ ← D₀ spectrum, at 28,370 cm^–1. The excitation laser is then set to a chosen transition of D₁ ← D₀, and a 3-laser depleted REMPI signal is recorded. The hole-burn laser is then turned off and the standard 2-laser ion signal is recorded. By switching between 2 lasers and 3 lasers each step as the laser is scanned across the D₁ ← D₀ region, a hole-burning spectrum may then be reproduced. Using this scheme, hole-burn spectra for the most intense vibronic transitions of the D₁ ← D₀ spectrum were recorded, as is shown in the upper inset in Figure . These scans reproduced a multiplet of peaks which line up exactly with the corresponding peaks in the D₁ ← D₀ spectrum, and so are conclusively assigned to the phenalenyl radical. Hence, the employment of the 3 laser hole-burn technique confirms that the entire vibronic spectrum in Figure may be assigned exclusively to the D_3h phenalenyl radical.

Following this spectroscopic assignment, the D₁ ← D₀ transition was used to determine the ionization energy of the phenalenyl radical. The excitation laser was fixed at the origin transition while the ionization laser wavelength was scanned. To ensure a field-free environment during ionization, the time-of-flight lens voltages were rapidly switched using a pulse generator prior to accelerating the resulting ions up the time-of-flight spectrometer. The resulting ionization curves (provided in the Supporting Information) yield a field-free ionization energy of 6.496(3) eV. This relatively low ionization energy reflects the intrinsic stability of the phenalenyl cation, and suggests that phenalenyl radicals are likely to exist predominantly in their cationic form in the interstellar medium.

Beyond the D₁ state, multiple new spectral features appear above 27,000 cm^–1 that have not been reported previously. Between 30,000 and 32,000 cm^–1 an intense broad peak (fwhm ∼ 200 cm^–1) is detected, which is assigned (based on the calculations in Table ) to the D₄ ← D₀ transition to the 2E″ state. While there are several distinguishable features, these bands are very diffuse in comparison to the D₁ ← D₀ spectrum, suggesting a shorter excited-state lifetime. To investigate this, lifetime scans were performed, in which the resonant ion signal was monitored as a function of the time delay between the excitation and ionization lasers. These measurements (provided in the Supporting Information) revealed a lifetime for the D₄ state of 108 ± 3 ns, notably shorter than the measured lifetime of the D₁ state of 341 ± 14 ns. However, this suggests there are other factors contributing to the observed broadening in Figure . The most obvious feature in this region is a strong doublet feature at 31,200 cm^–1. There also appears to be bands on either shoulder of the strong doublet, at 30,600 cm^–1 and 31,700 cm^–1.

Another excited state is observed around 27,000–29,500 cm^–1, with a first band at 27,380 cm^–1. The peaks in this region possess a fwhm of ∼ 50 cm^–1, in between the width of the bands of D₁ and D₄ states. Lifetime scans determined an excited state lifetime of 172 ± 5 ns. The excitation energies calculated in Table suggest these features may be assigned to the D₃ ← D₀ transition. A pure electronic transition from initial state (Γ _i ) A₁ to final state (Γ _j ) A₂ is forbidden for the D_3h point group. However, vibronic transitions to states with an odd quanta of e′ modes may become allowed if they are vibronically coupled to another E″ state as

$$\begin{array}{l}\hfill {\mathrm{\Gamma }}_i\otimes {\mathrm{\Gamma }}_{\mu }\otimes ({\mathrm{\Gamma }}_j\otimes {\mathrm{\Gamma }}_v)\subset {\mathrm{\Gamma }}_{\mathrm{tot}.\mathrm{sym}.}\hfill \\ \hfill {\mathrm{A}}_1^{″}\otimes {\mathrm{E}}^{\prime }\otimes ({\mathrm{A}}_2^{″}\otimes {\mathrm{e}}^{\prime })={\mathrm{A}}_1^{\prime }+{\mathrm{A}}_2^{\prime }+{\mathrm{E}}^{\prime }\hfill \\ \hfill \subset {\mathrm{A}}_1^{\prime }\hfill \end{array}$$ 1

where Γ_μ is the transition dipole operator. Therefore, the spectral features observed between 27,000 and 29,500 cm^–1 may be assigned to e′ vibronically coupled transitions involving the 2A₂ (D₃) state. A magnified view of the spectrum in this region is displayed in the inset in Figure . The spectrum is dominated by multiple doublet features at 28,000, 28,300, and 29,100 cm^–1.

Jahn–Teller and Pseudo-Jahn–Teller Couplings

In order to guide the spectral assignment of the phenalenyl radical in Figure , along with similar PAHs of astronomical interest, calculated spectroscopic parameters are required. However, due to the strong vibronic coupling that is prevalent in the excited states of high-symmetry PAH radicals, reliable transition intensities and line positions cannot be obtained via standard Franck–Condon calculations based on the usual quantum chemistry methods. ,,,

For the phenalenyl radical spectrum in Figure , this is further complicated as the 1E″ and 2E″ states represent degenerate Jahn–Teller (JT) surfaces. The JT effect causes the electronic states to undergo a geometric distortion along a nontotally symmetric mode (e′) to lift the degeneracy. This lowers the symmetry from D_3h, splitting the electronic states into two components of C_2v symmetry, stabilizing the molecule at a lower energy configuration. However, this generates a conical intersection at the equilibrium geometry, meaning the system can no longer be effectively described adiabatically. −

This may be overcome by converting to a diabatic representation through a unitary transformation, that decouples the electronic states with respect to the nuclear kinetic terms, at the expense of introducing coupling in the electronic components. In the diabatic electronic basis, the e′ JT active modes reduce the D_3h point group at the degeneracy point into two components of C_2v symmetry. These components are of a₁ and b₁ symmetry, and the normal mode coordinates are labeled here as Q _a and Q _b respectively. Harmonic diabatic frequencies may then be determined by using both components of the E″ states and calculating the adiabatic potentials separately. The diabatic potential is then produced from the average of the two adiabatic potentials. This results in a well-behaved unperturbed potential surface, upon which the JT coupling may be added in the absence of a conical intersection. ,−

The observation of Franck–Condon forbidden vibronic transitions in the REMPI spectrum in Figure suggests the presence of Herzberg–Teller (HT) coupling, where nontotally symmetric modes (e′) may gain intensity by vibronically coupling to higher excited states. − In the diabatic representation, the HT coupling is manifested as the pseudo-Jahn–Teller effect (pJT). The pJT effect is another source of structural distortions in highly symmetric molecules, that results in coupling between both degenerate and nondegenerate states. , The vibronic contribution of the pJT effect between an initial electronic state ψ _i and higher electronic state ψ _j may be described by the matrix element

$$h_{\mathit{ij}}=⟨{\psi }_i|\left({\frac{\mathrm{d}H}{\mathrm{d}Q}}_i\right)|{\psi }_j⟩·Q_i$$ 2

which correspond to off-diagonal vibronic coupling constants between the different electronic states. ,

Therefore, a vibronic Hamiltonian which describes the entire phenalenyl system may be constructed by transforming to a diabatic representation, then introducing JT coupling constants for the D₁ and D₄ surfaces as well as pJT coupling constants between the D₁, D₄, D₂, D₃, and D₅ surfaces. Following this procedure produces the vibronic Hamiltonian in eq , which includes the ground state D₀, two sets of degenerate E″ states D₁ and D₄, and the three A₂ states D₂, D₃, and D₅ from Table ,

3

The diagonal potential terms V_i = Δ _i + λρ² correspond to each electronic state, with V₁ being the ground state D₀, V₂ and V₃ representing the two components of the degenerate D₁ state, and so on. Δ _i represents the electronic energy of the ith state (relative to the ground state at the equilibrium geometry in Table ) and λρ² is the harmonic potential, where λ are the diabatic harmonic frequencies (ρ² = Q _a + Q _b ). Diabatic frequencies were calculated for the excited state of the phenalenyl radical at the EOMEE-CCSD/pVDZ level of theory, , using the CFOUR computational package and the method described above. The resulting frequencies for the D₁ state are provided in the Supporting Information.

The linear diabatic coupling constants f and g (inside the red box in eq ) represent the JT coupling within the D₁ and D₄ states, and correspond to the gradients of the conical intersections of the D₁ and D₄ surfaces, respectively. These constants were calculated analytically at the EOMEE-CCSD/pVDZ level of theory, , using the CFOUR computational package and the quasidiabatic ansatz of Ichino et al. Briefly, the EOMEE procedure is used to operationally define quasidiabatic states (those that relax according to a well-behaved reference state wave function) and the coupling constants are then evaluated as the first derivative of the off-diagonal elements of the electronic Hamiltonian in the basis defined by this representation. , JT coupling gradients were calculated for each normal coordinate Q _i (7 × a₁ + 14 × e′) and degenerate electronic state, and are provided in the Supporting Information.

The other off-diagonal terms in eq h, j, k, l, m, n, and o (inside blue boxes) correspond to the pJT coupling constants (eq ) between each state. These constants may be calculated from the energy gradients (∂E/∂Q) at the initial minimum geometry with respect to each pJT active normal coordinate Q _i (14 × e′ modes). These gradients were computed from first-principles, and are also included in the Supporting Information. Pseudo-Jahn–Teller coupling between the ground D₀ (A₁ ) state and the excited states was not included, due to the large energy separations (ΔE ∼ 20,000–30,000 cm^–1), which strongly suppress such second-order vibronic interactions.

The vibronic Hamiltonian in eq is fully parametrized by the scaled energies in Table , the 42 JT and 98 pJT coupling constants, and the diabatic frequencies, all of which are provided in the Supporting Information. Therefore, the Hamiltonian may now be solved with respect to each normal coordinate Q _i , allowing for the spectrum of the phenalenyl radical to be calculated in its entirety.

Vibronic Assignments

The vibronic spectrum of the phenalenyl radical, including transitions to five excited electronic states, was simulated using the fully parametrized Hamiltonian in eq and the xsim package of CFOUR. Briefly, the xsim module projects the Hamiltonian onto a vibrational basis, which is then diagonalized using Lanczos algorithm. This produces transition energies and intensities that map to the measured REMPI spectrum. The resulting simulation superimposed with the entire recorded vibronic spectrum of the phenalenyl radical is displayed in Figure .

4.

(Black) REMPI spectrum of the phenalenyl radical. (Colored) Simulated band positions (EOMEE-CCSD/pVDZ) scaled by a factor of 0.94. Intensity of bands in the 27,000–30,000 and 30,000–34,000 cm^–1 regions have been scaled by a factor of 10^–2, and 10^–4, respectively.

A constant scaling factor of 0.94 has been applied to the position of all simulated vibrational peaks presented here, to align the dominant ν₂₅ D₁ ← D₀ transition to the peak at 19,560 cm^–1, that has been previously assigned. The simulated spectrum shows activity across several regions of the spectrum. Sharp features observed between 18,800 and 22,000 cm^–1 correspond to the previously observed D₁ ← D₀ transition. The most intense calculated band in this region resides 760 cm^–1 above the D₁ origin, corresponding to the vibronic transition 25₀ (with a harmonic diabatic frequency of 812 cm^–1). In total, the calculated diabatic frequencies and transition intensities allow for the assignment of 22 peaks in this region of the spectrum. A magnified view of the D₁ ← D ₀ transition along with these vibronic assignments is shown in Figure (a). This includes transitions to both a₁ and e′ vibrational modes, as well as a series of combination bands involving the dominant 25₀ transition. The full spectral assignments are provided in the Supporting Information.

5.

(a) Magnified view and vibronic assignments of the D₁ ← D₀ transition of the phenalenyl radical. Calculated e′transitions are shown in blue and a₁′ transitions are shown in cyan. (b) Magnified view and assignments of the D₃ ← D₀ transition of the phenalenyl radical. Calculated transitions are shown in orange.

The largest feature in Figure is a cluster of bands occurring at ∼ 31,500 cm^–1, which relate to the D₄ ← D₀ transition. Comparison of the simulated bands to the experimentally observed spectrum shows good agreement, both in transition positions and intensities, with the D₄ origin shifted by only ∼ 300 cm^–1. Additionally, the simulated spectrum accurately predicts the doublet feature that is observed at ∼ 31,000 cm^–1. A group of relatively weaker bands calculated at ∼ 32,000 cm^–1 may be assigned to the shoulder peak observed in the experimental spectrum at an equivalent position. The diffuse nature of the experimental spectrum make it impossible to assign particular modes within this transition, however the overall band shape is in good agreement. Several peaks are simulated between 32,000 and 34,000 cm^–1 which show good agreement to the very diffuse band at ∼ 33,000 cm^–1. These features are attributed to the D₅ ← D₀ transition.

Simulated structure in Figure between 27,000 and 30,000 cm^–1 is induced by incorporating the D₃ (A₂ ) state (and respective pJT coupling) into the Hamiltonian in eq . Therefore, this collection of bands may be assigned to the Franck–Condon forbidden D₃ ← D₀ transition. A magnified view of the D₃ ← D₀ transition, comparing the experimental and simulated spectra, is shown in Figure (b). Both the calculated line positions and intensities are in good agreement with the observed experimental spectrum. As this transition is electronically forbidden, the origin band is not observable, with only e′ vibronically coupled transitions active. The first significant observable peak at 27,380 cm^–1, initially referred to as the origin, is now assigned to the transition 25₀ . A series of bands in the experimental spectrum is observed around 29,000 cm^–1 that can not be matched to a counterpart in the simulated spectrum. However, it can be noted that these bands appear distinctly similar − in terms of relative spacing − to a series of e′ modes around 28,000 cm^–1, all equally shifted by ∼ 765 cm^–1 to higher energy. As this shift is similar to the diabatic harmonic frequency of ν₂₅ (812 cm^–1), the peaks around 29,000 cm^–1 may be assigned to combination bands involving ν₂₅. Subsequently, this allows for an extrapolation to the (forbidden) origin by subtracting 765 cm^–1 from the position of the 25₀ transition. This establishes the electronic origin for the D₃ ← D₀ transition at 26,624 cm^–1. In total, 13 peaks are assigned to e′ vibronic transitions in D₃ ← D₀. The full spectral assignments are provided in the Supporting Information. None of the observed spectral features in Figure are assigned to the D₂ ← D₀ transition. This may be explained by the larger separation between the D₂(A₂ ) and D₄(E″) surfaces, as transitions to D₂ are only allowed if they are vibronically coupled to another E″ state.

These results underscore how the apparent simplicity of the highly symmetric phenalenyl radical belies the underlying complexity of its electronic structure. Alternant PAH radicals such as phenalenyl have long been considered promising candidates for the carriers of the diffuse interstellar bands (DIBs), owing to their anticipated abundance in space and accessible low-energy electronic transitions. However, while the D₁ ← D₀ transition lies in the visible region and exhibits sharp vibronic structure, it is only weakly allowed via vibronic coupling. As demonstrated in Figure , transitions to higher excited states are significantly broader and less structured, rendering them poor candidates for DIB assignment.

Nevertheless, the field-free ionization energy of 6.496(3) eV determined here indicates that phenalenyl forms a stable cation, and thus likely exists in its cationic form in the interstellar medium. This supports the growing consensus that symmetric PAH cations, including species such as C₆₀ , are more viable DIB carriers than their neutral counterparts. However, rigorous spectroscopic studies of such cations require a detailed understanding of the corresponding neutral radical. As demonstrated previously in our gas-phase triple resonance study of protonated naphthalene, accurate knowledge of the ionization threshold, electronic term energies, and transition intensities is essential for accessing and interpreting cold ion spectra. The present study provides these critical parameters for phenalenyl, enabling and informing future investigations of its cation and related PAH species under astrophysical conditions.

Conclusions

Gas-phase REMPI spectra of the free phenalenyl radical have been recorded, up to 17,000 cm^–1 above the D₁ origin. This revealed transitions to new higher lying excited states that had not been observed previously, including transitions to states with A₂ symmetry that should be forbidden. Three laser hole-burning techniques were employed to conclusively assign all of the observed spectral structure to the D_3h phenalenyl isomer.

By employing a quasidiabatic approach, a vibronic Hamiltonian was constructed that included both Jahn–Teller and pseudo̵Jahn–Teller interactions between seven excited electronic surfaces. This enabled the phenalenyl spectrum to be simulated in its entirety. These calculations were able to recreate the structure observed in the experimental spectrum, including transitions to the D₁, D₃, D₄, and D₅ electronic states. The simulation allowed for detailed vibronic assignments to be made for the first time, helping to unravel the complex phenalenyl electronic structure. This work helps elucidate the electronic characteristics of the key phenalenyl radical, while also providing a roadmap that can be applied to the study of larger high-symmetry PAHs.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphyschemau.5c00052.

• Ionization energy and lifetime scans; calculated diabatic frequencies, Jahn–Teller and pseudo-Jahn–Teller coupling constants; and assignments of the D₁ ← D₀ and D₃ ← D₀ transitions (PDF)

The authors declare no competing financial interest.

§.

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