Simulate ab initio photo-chemical reactions
Trajectory-based quantum dynamics: Ehrenfest, Surface Hopping, symmetric quasi-classical spin-mapping, etc.
Develop/improve, benchmark, apply
Time-Dependent Schrodinger Equation (TDSE):
$$i\hbar~\partial_t |\Psi(t) \rangle = \hat{H} |\Psi(t) \rangle $$
Strong light-matter interactions are able to control chemical reactions in both ground and excited states. Using ab initio simulations, we can probe the cavity-induced modifications to the electronic sub-system by exploring changes to the ground and excited state densities.
Light-Matter (Polaritonic) Hamiltonian:
$$\hat{H} = \hat{H}_\mathrm{el} + \hbar\omega_\mathrm{c}\hat{a}^\dagger\hat{a} + \sqrt{\frac{\omega_\mathrm{c}}{2}} \lambda_\mathrm{c} \hat{\mu}(\hat{a}^\dagger + \hat{a}) + \frac{\lambda_\mathrm{c}^2}{2} \hat{\mu}^2$$