# NIR Photoswitching of Azobenzene (with Stefanie and Jan)

###### tags: `PhD projects` `Photoswitching` `Theory` `Experiment` `Collaboration`

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### Owners (the only one with the permission to edit the main text, others can comment)

Alptug, Laura, (Stefanie, Jan)

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## To do

- [ ] Literature review
- [ ] EM model of Ab species
- [ ] Many-body simulations

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## Important questions to address
1. Power dependence: Why is there an optimal power density?
2. Chirality: Why does left circularly polarized light cause faster switching? (Circular dichroism?)
3. Concentration effects
4. Light Coherence
5.
## Literature Review
### Manipulating azobenzene photoisomerization through strong light–molecule coupling (DOI: 10.1038/s41467-018-06971-y)
They focus on modelling azobenzene in a cavity where there is strong coupling with light. Their total Hamiltonian is
$$
\hat H = \hat H_\mathrm{mol} + \hat H_\mathrm{ph} + \hat H_\mathrm{int},
$$
where $\hat H_\mathrm{mol}$ is the single molecule Hamiltonian, $\hat H_\mathrm{int}$ is the light matter interaction, and photonic Hamiltonian is given by:
$$
\hat H_\mathrm{ph} = \omega_\mathrm{ph}\left(\hat b^\dagger \hat b + \frac{1}{2}\right),
$$
where $\omega_\mathrm{ph}$ is the resonant photon frequency and $\hat b^\dagger, \hat b$ are the creation and annihilation operators for the bosonic mode, respectively. This term represents the light mode confined in resonant cavities or nanocavities.

They proceed to introduce the "dipolar Hamiltonian" as the interaction:
$$
\hat H_\mathrm{dip} = i (\hat\mu\cdot\lambda)\sqrt{\omega_\mathrm{ph}}A_0 \left(\hat b - \hat b^\dagger\right) + 2(\hat\mu\cdot\lambda)^2 A_0^2
$$
where $A_0$ is the vector potential intensity, $\lambda$ is the polarization vector of the field, and $\hat \mu$ is the dipolar operator. Furthermore, they argue that extended Jaynes-Cummings model can be used when $A_0 / \sqrt{\omega_\mathrm{ph}}$ is less than $0.4$ au. The interaction is given by:
$$
\hat H_\mathrm{xJC} = (\hat\mu_\mathrm{tr}\cdot\lambda)\sqrt{\omega_\mathrm{ph}}A_0 \left(\hat b + \hat b^\dagger\right),
$$
where $\hat\mu_\mathrm{tr}$ is the transition dipole moment operator acting on the electronic states.

### Dynamics of Azobenzene Dimer Photoisomerization: Electronic and Steric Effects (DOI: 10.1021/acs.jpclett.6b01401)
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## Thinking out Loud

We would like to coarse-grain the molecule into "point"s. E-Ab structures can form a nematic order (literature exists), therefore they are either "rod"s or "ellipsoid"s. Z-Abs don't exibit liquid-crystalline order, then I assume they can be "point"s.

My next question is "What are the relevant interactions?"
* All structures have vanishing total charge, monopole interactions do not exist.
* Z-Ab has a dipole moment and E-Ab does not.
* I could not find the quadrupole moments of the structures in the literature. I believe they should not vanish. Should we calculate them? (Note: quadrupole interactions are important in classical $H_2O$ simulations) Follow up: Yes, we should! We will try to explain the photoswitching behaviour and quadrupole interaction is the strongest coupling of E-Ab with EM field.
* $N-H$ can form a hydrogen bond.
* Does WdW interaction play a role? Can we omit it? Or can we coarse-grain WdW and H-bonds into a LJ type potential?

Before introducing any many-body effects, I think we should focus on the single molecule/pure states to see if we can match the absorption spectra of individual state.

## Simulation Technique

In the experimental system, Ab is dissolved in a solvent. Thus, we assume, the motion of Ab molecules is Brownian. Since the number of molecules is quite high, simulating $N$ Brownian particles becomes unfeasible. Therefore, I propose to use the continuum limit of Brownian particles, which is governed by Dean-Kawasaki equation, that is given by (in conservative form):

$$
\frac{\partial \rho (x,t)}{\partial t} = \nabla\cdot\left(\rho (x,t) \nabla \frac{\delta F[\rho]}{\delta\rho}\right) + \nabla\cdot\left(\sigma \sqrt{\rho (x,t)} \xi\right)
$$
where $\rho(x,t)$ is the density, $F[\rho]$ is the free energy functional, $\sigma$ is a temperature dependent parameter and $\xi$ is the space-time white noise. In the literature, this model is sometimes called "fluctuating hydrodynamics."

In our case, we would have a density field and an orientation vector field per Ab specie since the molecules are directional due to their geometric and EM properties.

In addition, even though the total number of molecules is conserved, the number of molecules per specie is not. We have to modify the model to suit our needs.