User:Ozan Lacinbala/Recurrent fluorescence

Recurrent fluorescence (also called Poincaré fluorescence) is a photophysical mechanism occurring in isolated molecules. Since the isolated condition is required, recurrent fluorescence is not observed on earth as a natural process. However, this process is supposed to be highly involved in various interstellar environments (planetary nebulae, reflection nebulae, molecular cloud, H II region, protoplanetary disk, circumstellar envelopes, etc) which are known to contain complex molecular species.

Historique
Detected emission and absorption signals stemming from interstellar environments and in various wavelength ranges give valuable informations about the carriers and the photophysical mechanism at the origin of these observations. In this context, A. Léger et al. proposed in 1988 the recurrent fluorescence as a plausible explanation for large emission bands in the near-infrared and visible wavelenth ranges.

Mechanism
Molecular systems involve a large number of electrons and atomic nuclei interacting with each other. These interactions give rise to radiationless transitions in molecules and are particularly efficient in polyatomic systems. In polyatomic molecules, the electronically excited system undergoes several internal conversions and/or intersystem crossings toward lower electronically excited state up to reach the ground electronic state in highly excited rovibrational state. Throughout this radiationless processes (which last between several picoseconds and nanoseconds ), electronic energy is indeed entirely converted into rovibrational energy.

Following this process, interactions between electrons and atomic nuclei allow the molecule to occupy again excited electronic states by converting rovibrational energy into electronic energy via inverse internal conversions and/or inverse intersystem crossings. These inverse processes are slower than those described in the previous paragraph. Nevertheless, in isolated conditions, the molecular system has enough time so that these inverse radiationless processes occur and occupy higher electronic states. Additional internal conversions and/or intersystem crossings can be involved and allow the molecular system to occupy even higher electronic states, at the expense of rovibrational energy. Thus, the molecule spends more time to occupy excited electronic states and a vibronic de-excitation can occur.

The occupation of excited electronic states from the excited rovibrational states of the ground electronic state can be described in the framework of dynamical systems. Given that the molecular system is conservative (isolated conditions) and evolves in a finite region of the phase space, the Poincaré recurrence theorem can be applied. In this framework, the recurrent fluorescence is explained as follows. Initially, the molecular system occupies an excited vibronic state and de-excite spontaneously toward the ground electronic state by converting the energy into rovibrational degrees of freedom. Since vibrational emission is very slow (several milliseconds), the molecular system keep exploring the phase space up to occupy various excited electronic states successively, en route to occupy its initial state (according to the Poincaré recurrent theorem). Then, an electronic de-excitation can occur. This emission mechanism is called recurrent fluorescence or Poincaré fluorescence, in tribute to Henri Poincaré for his pioneering research work related to dynamical systems.

The recurrent fluorescence and the well-known electronic fluorescence are different processes. In polyatomic molecules, radiationless transitions are very fast compared to electronic fluorescence (the electronic fluorescence yield is very low). In isolated conditions, excited electronic states can be occupied again following the above-mentioned mechanism and the molecule is likely to undergo electronic de-excitation.

Recurrent fluorescence rate
The recurrent fluorescence rate $$A_{\rm rec}^{n \rightarrow m}(E)$$ from the $$n \longrightarrow m$$ electronic transition at internal energy E (containing the electronic, vibrational and rotational energies) of the molecular system is written as the product of the electronic fluorescence rate $$A_{\rm f}^{n \rightarrow m}$$and the occupation probability $$p_{n}(E)$$ of the excited electronic state $$n$$,$$A_{\rm rec}^{n \rightarrow m}(E)= A_{\rm f}^{n \rightarrow m} \times p_{n}(E).$$Given that the number of rovibronic state is huge, statistical mechanics is appropriate for calculating the occupation probability  $$p_{n}(E)$$. In addition, rates of internal conversions, intersystem crossings, their inverse counterparts (see above) and intramolecular vibrational redistribution are very high compared to electronic fluorescence rates, allowing to consider that the internal energy is statistically distributed among of accessible vibronic states. The occupation probability $$p_{n}(E)$$ is calculated in the microcanonical framework because the system is isolated.

To write $$p_{n}(E)$$, we have to calculate the number of microstates of the molecular system at internal energy $$E$$. Let's $$\Omega_{n}(E)$$ be the number of rovibrational states at internal energy $$E$$ in the electronic state $$n$$. Then, the total number of vibronic states $$\Omega_{\rm tot}(E)$$, is expressed as$$\Omega_{\rm tot}(E)=\sum_{n}\Omega_{n}(E-E_{n}).$$The sum extends over all accessible electronic states ($$E_{n} \leq E$$). We deduce that$$A_{\rm rec}^{n \rightarrow m}(E)= A_{\rm f}^{n \rightarrow m} \times \frac{\Omega_{n}(E-E_{n})}{\Omega_{\rm tot}(E)},$$

with $$\Omega_{n}(E-E_{n})$$the number of rovibrational state of the molecule for which the internal energy $$E$$ is decomposed into the rovibrational energy $$E-E_{n}$$ and electronic energy $$E_{n}$$, meaning that the excited electronic state $$n$$ is occupied. Unlike the electronic fluorescence, the recurrent fluorescence rate depends on the internal energy. The recurrent fluorescence rate decreases with the electronic energy $$E_{n}$$ and increases with the internal energy $$E$$.

Experimental detections
To detect recurrent fluorescence, the isolated conditions of the system require experiments to be performed in the gas phase and at very low pressure (about $$10^{-10}$$ mbar). Detecting emitted photons in the gas phase and in the ultra-high vacuum is highly challenging because of low signal-to-noise ratio of photon emission signals and account for the very recent experimental detection of the recurrent fluorescence in the laboratory. These experiments are performed in ion storage rings.

Several indirect detections have been claimed in experiments measuring the radiative relaxation of anthracene cation, and. More recent experimental investigations reported detection of photons emitted via recurrent fluorescence from and naphthalene ion.

Astrophysical interest
Nowadays, the following photophysical (electronic excitation from stellar photon $$\rightarrow$$ radiationless transitions $$\rightarrow$$ radiative relaxation) is accepted to widely occur in various interstellar environments for molecules able to survive to photon stellar absorption, such as polycyclic aromatic hydrocarbons. Besides vibrational emission, recurrent fluorescence is now considered to have a part in the photophysics of some species such as cationic polycyclic aromatic  hydrocarbons.

During the radiative relaxation induced by stellar photon absorption, recurrent fluorescence is then in competition with vibrational emission and (thermo-)photodissociation. As a consequence, recurrent fluorescence can partly quench (thermo-)photodissociation which allows to reconsider the presence of species thought so far to be destroy by UV photon absorption.