example of endothermic luminescence?

Question

Someone posed an interesting question to me the other day: is all production of light accompanied by the generation of heat? I have found that the question as posed invites vague answers, so I thought I would restrict the question to the case of chemiluminescence and sharpen the language to the following:

Is there an example of a spontaneously occuring endothermic chemical reaction which generates light as one of the (possibly many) products?

Assume for the sake of specificity that the reaction occurs at constant temperature and volume. Conceptually, I am envisioning the following energy diagram:

where the reaction begins with a system consisting purely of reactants $R$. These reactants are excited to a metastable product state $P^*$, with the energy for the excitation coming from the temperature bath. The meta stable state relaxes to the final product state $P$, emitting a photon $\gamma$ in the process. We then would have an instance of a process where a system simultaneously produces light and absorbs heat from its surroundings. Note that this is this case whether the energy of the products (neglecting the photon energy) is greater than the reactants (i.e. $P1$) or lower (i.e. $P2$), since in either case the combined energy of $Pn + \gamma n,\,n=1,2$ is greater than $R$.

So I would like to ask if there is a good example which comes to mind of such a reaction, either for final products $(P1, \gamma 1)$ or $(P2, \gamma 2)$?

Answer 1

After some digging around on Google Scholar, I came across the following article:

https://pubs.acs.org/doi/abs/10.1021/ja00499a052

which presents the following class of reactions:

All of these reactions are endothermic in that they have positive molar enthalpies, and also produce near-infrared light at around 1000 nm. Reaction 1 (i.e. $\ce{R_1} = \ce{H}$) in particular has the following energy diagram:

The relevant quantities here are:

• $\Delta H_o$, which is the molar enthalpy for the production of the triplet, i.e. ground state, $\ce{O2}$ product, and
• $\ce{E}_*(\ce{{}^1O2})$, which is the energy of the photon emitted in the singlet to triplet transition.

Interestingly, the authors appear to be assessing the endo/exothermicity of the reaction by $\Delta H_o$, not $\Delta H_o + \ce{E}_*(\ce{{}^1O2})$ as I argued using the diagram in my question. It seems to me that whether one uses the former or the latter to determine endo/exothermicity of the reaction depends on whether one assumes the emitted photon is absorbed by the temperature bath or if it is extracted and used to perform work. In the former case energy conservation would imply that the $\Delta H_o$ determines the heat absorbed by the bath, and $\Delta H_o + \ce{E}_*(\ce{{}^1O2})$ for the latter.