Multi-Photon Heating of PAHs

• Multi-photon heating of PAHs is a process of sequential photon absorption that elevates molecular energy, leading to fragmentation or ionization in laboratory and astrophysical environments.
• Advanced experimental methods like MPD spectroscopy and theoretical models such as TDDFT and Monte Carlo simulations enable quantitative analysis of absorption cross-sections and dissociation thresholds.
• This process plays a critical role in ISM heating, DIB carrier identification, and fullerene formation, illustrating the influence of photon field intensity on astrochemical evolution.

Polycyclic aromatic hydrocarbons (PAHs) undergo “multi-photon heating” when exposed to strong photon fields, such as ultraviolet (UV), visible, or X-ray radiation in astrophysical and laboratory environments. This process is central to the photochemistry, stability, and spectral characteristics of PAHs, with direct implications for interstellar medium (ISM) heating, PAH destruction, and fullerene formation. The following sections provide an in-depth examination of the underlying mechanisms, experimental and theoretical approaches, molecular processes, and astrophysical implications, emphasizing quantitative formalisms and reported empirical results.

1. Fundamental Principles of Multi-Photon Heating in PAHs

Multi-photon heating refers to the sequential absorption of multiple photons by a PAH molecule before it has fully cooled via emission of infrared (IR) photons. Each absorbed photon increases the molecule’s internal energy, $U$, resulting in a transiently “hot” molecule. If the total energy exceeds dissociation thresholds ($E_d$), photofragmentation ensues; otherwise, the molecule may relax by IR emission or photoionization.

For gas-phase PAHs, the key rates governing this process are:

• Photon absorption rate:

$$k_{\mathrm{abs}} = \sigma_{\mathrm{abs}} \cdot S \cdot \phi = \sigma_{\mathrm{abs}} \cdot S \cdot \frac{\lambda}{hc} \cdot \frac{E_{\mathrm{laser}}}{t_{\mathrm{pulse}}}$$

where $\sigma_{\mathrm{abs}}$ is the absorption cross-section, $S$ is laser spot area, $\phi$ is photon flux, $\lambda$ the excitation wavelength, $E_{\mathrm{laser}}$ the pulse energy, and $t_{\mathrm{pulse}}$ the pulse duration.

• Fragmentation (dissociation) rate:

$k_d(U) = A_d \cdot \frac{\rho(U-E_d)}{\rho(U)}$

where $A_d$ is a pre-exponential factor, $E_d$ is the dissociation energy (e.g., $\sim4.8$\,eV for H-loss), and $\rho(U)$ the vibrational state density at energy $U$.

Through a series of such absorption events, energy accumulates in the PAH, and multiphoton-induced “vibrational heating” determines the fragmentation and, under intense regimes, the subsequent photochemistry and spectral signatures.

2. Experimental and Modeling Approaches

2.1. Laboratory Techniques

• Multiphoton Dissociation (MPD) Spectroscopy: The PIRENEA experiment utilizes a cold Fourier Transform Ion Cyclotron Resonance (FT-ICR) ion trap and an optical parametric oscillator (OPO) laser (430–480 nm) to measure electronic spectra and photodissociation yield of PAH cations and derivatives (e.g., pyrene, coronene) under multiphoton excitation (Useli-Bacchitta et al., 2010). Photon absorption and fragmentation rates are inferred via kinetic Monte Carlo simulations by comparing measured yields as functions of laser parameters.
• Action Spectroscopy and IRMPD: Gas-phase IR Multiple Photon Dissociation (IRMPD) probes vibrational spectra of PAHs over 100–1700 cm⁻¹ (mid- to far-IR) by monitoring fragmentation yields as a function of IR laser fluence, requiring many photon absorptions for dissociation in strongly bound species (Wiersma et al., 2021).
• Synchrotron Experiments (VUV/X-ray): Photoionization and fragmentation cross-sections are directly measured for PAH cations exposed to synchrotron VUV or X-ray irradiation in the range 8–40 eV and up to keV energies, using time-of-flight mass spectrometry and partial ion yield analysis (Zhen et al., 2015, Monfredini et al., 2018).

2.2. Theoretical and Computational Methods

• Kinetic Monte Carlo Simulations: Used to stochastically model the sequential nature of photon absorption (rate $k_{\mathrm{abs}}$) and dissociation (rate $k_d$) events in the presence of fluctuating photon densities and molecular energies (Useli-Bacchitta et al., 2010).
• Time-Dependent Density Functional Theory (TDDFT): Used to compute vertical excitation energies, oscillator strengths, and absorption cross-sections, facilitating the assignment of experimental bands and evaluating how structural changes influence transitions (Useli-Bacchitta et al., 2010).
• Detailed Chemical Evolution Models: Internal energy distributions are tracked in discrete bins to model non-linear, size-dependent multiphoton effects, including dehydrogenation and ionization in photodissociation regions (PDRs) (Montillaud et al., 2013).

3. Molecular Processes and Observable Consequences

3.1. Sequential Energy Buildup and Fragmentation

Upon absorption of a photon resonant with a PAH transition, energy is rapidly redistributed from the excited electronic state into vibrational modes of the ground state. Successive absorptions result in accumulation of internal vibrational energy, $U$, yielding a temperature probability distribution $P(T)$ for the PAH. When $U \geq E_d$, unimolecular dissociation occurs. For pyrene cations, $\sim$3 photons ($\sim$8–9 eV total energy) are needed to trigger backbone fragmentation; for fully hydrogenated analogs, fewer photons are required due to weakened aromatic bonds (Wolf et al., 2016).

3.2. Vibronic and Structural Effects

Multi-photon heating influences the observed spectra in several ways:

• Appearance of Hot Bands: For pyrene cations, additional vibronic features in the red of the main band arise from transitions between thermally populated vibrational states after initial photon absorption (Useli-Bacchitta et al., 2010).
• Conformer-dependent Splitting: In methyl-substituted PAHs (e.g., 1-methylpyrene), two sets of features correspond to nearly isoenergetic conformers whose splitting is only resolved at elevated internal energies in the multiphoton regime.
• Jahn–Teller Distortion and Symmetry Breaking: In coronene cation, multiphoton-induced symmetry breaking broadens and shifts electronic bands (Useli-Bacchitta et al., 2010).
• Dehydrogenated Species: The first gas-phase spectra of dehydrogenated coronene cations illustrate sensitivity of electronic transitions to the specific pattern of hydrogen loss and provide new constraints on the photostability of reactive PAHs.

3.3. Competition Between Ionization and Fragmentation

Photo-stability is size-dependent: in large PAHs (e.g., hexa-peri-hexabenzocoronene, $C_{42}H_{18}^+$), multiphoton absorption predominantly drives ionization to higher charge states, while in smaller PAHs (e.g., coronene, $C_{24}H_{12}^+$), fragmentation via H-loss is more competitive. The transition energy thresholds for successive ionizations ($\mathrm{IP}_{n}$) and relative densities of electronic/vibrational states underlie this competition (Zhen et al., 2015).

4. Quantitative Determination of Cross-Sections and Rate Parameters

Absorption cross-sections—key to modeling the astrophysical and laboratory MPD processes—are constrained by comparing simulated and measured fragment yields. Reported values include (Useli-Bacchitta et al., 2010):

• Pyrene cation: $\sigma_{\mathrm{abs}} \approx 1.6 \times 10^{-16}$ cm²
• Coronene cation: $\sigma_{\mathrm{abs}} \approx 0.6 \times 10^{-16}$ cm²

Dissociation (fragmentation) rates follow:

$k_d(U) = A_d \cdot \frac{\rho(U - E_d)}{\rho(U)}$

The density of vibrational states, $\rho(U)$, is determined numerically (e.g., via Steglich–Jortner modeling), and $A_d$ is taken as the pre-exponential frequency for bond cleavage ($\sim10^{16}\,\mathrm{s}^{-1}$).

Time-dependent spectra reflect not only the rates but also the photon flux (experimentally controlled by laser pulse energy and spot size), leading to observable trends such as the fluence dependence of fragmentation yields ($Y \propto E^n$ where $n$ is the average photon number absorbed before dissociation) (Wolf et al., 2016).

5. Astrophysical and Chemical Implications

Multi-photon heating is essential for interpreting observed emission features in the mid-IR and visible regimes—both in the laboratory and in astronomical settings such as PDRs or the diffuse ISM.

• ISM and DIB Carriers: Gas-phase spectra of multiply excited, dehydrogenated PAH cations are candidate carriers for diffuse interstellar bands (DIBs) and provide spectral templates for comparison with astronomical data (Useli-Bacchitta et al., 2010).
• Photochemical Stability: Multiphoton absorption explains the non-linear dependence of dehydrogenation and backbone destruction on radiation field intensity and PAH size, leading to thresholds below which only large, compact PAHs survive significant UV/visible fields (Montillaud et al., 2013). Ionization becomes the dominant relaxation pathway for the largest systems, thereby enhancing their photostability (Zhen et al., 2015).
• Photophysics of Reactive Derivatives: First-time measurements of gas-phase dehydrogenated PAH cations enable quantification of electronic structure changes attributable to sequential H-loss and allow assessment of their role in the carbon cycle of diffuse and UV-irradiated environments, including potential routes to fullerene formation in top-down chemistry (Zhen et al., 2014).

6. Integrative Experimental–Theoretical Framework

The coupled use of advanced TDDFT electronic structure calculations and kinetic Monte Carlo modeling enables a holistic understanding of multi-photon heating:

• Assignment of observed bands to specific electronic transitions, including prediction of band positions and intensities as functions of conformation, charge, and hydrogenation state.
• Simulation of sequential photon absorption, vibrational energy redistribution, and stochastic fragmentation yields as measured in controlled MPD experiments.
• Extraction of fundamental photophysical parameters—absorption cross-sections, dissociation energy thresholds, and rates—that are essential for quantitative modeling in astrospectroscopy and ISM chemistry.

Such an approach bridges “cold” laboratory spectral assignments with the “hot” molecular conditions encountered in astrophysically relevant photon fields, offering a benchmark for models of PAH evolution, emission, and destruction in space.

7. Summary Table: MPD Observables and Inferred Parameters

PAH/Species	Main Spectral Feature (nm)	Key Photophysical Insight	$\sigma_{\mathrm{abs}}$ (cm²)
Pyrene cation (C₁₆H₁₀⁺)	~436 (+hot bands)	Vibronic structure, hot bands	$1.6 \times 10^{-16}$
1-Methylpyrene cation	~442, 454; ~480	Conformer splitting	–
Coronene cation (C₂₄H₁₂⁺)	~457 (+vib. progression)	Broadening, Jahn–Teller effects	$0.6 \times 10^{-16}$
C₂₄H₁₀⁺ (dehydrogenated)	~442, ~458	Multiple transitions, geometry-dep.	–

The cumulative data and analyses across a range of molecular sizes and derivatives underline the vital role of multi-photon heating in defining the vibrational and electronic landscape, dissociation thresholds, stability, and astrophysical signatures of PAH cations and their derivatives.