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  3. Optical cavities hold great promise to manipulate and control the photochemistry of molecules. We demonstrate how molecular photochemical processes can be manipulated by strong light–matter coupling. For a molecule with an inherent conical intersection, optical cavities can induce significant changes in the nonadiabatic dynamics by either splitting the pristine conical intersections into two novel polaritonic conical intersections or by creating light-induced avoided crossings in the polaritonic surfaces. This is demonstrated by exact real-time quantum dynamics simulations of a three-state two-mode model of pyrazine strongly coupled to a single cavity photon mode. We further explore the effects of external environments through dissipative polaritonic dynamics computed using the hierarchical equation of motion method. We find that cavity-controlled photochemistry can be immune to external environments. We also demonstrate that the polariton-induced changes in the dynamics can be monitored by transient absorption spectroscopy. 
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  6. Two-dimensional (2D) spectroscopy, originally developed for nuclear magnetic resonance, has been recently extended to the infrared and visible regimes. In this technique sequences of femtosecond light pulses are used to interrogate molecular systems and show, by a double Fourier transform, the correlation between excitation and detection frequencies. Extension to the ultraviolet (UV) regime is of great interest and promises to deliver rich structural and dynamical information on biomolecules such as DNA and proteins; however, it must overcome significant technical challenges. This review summarizes the current development status of 2DUV spectroscopy. After discussing the scientific case for the technique, we introduce its basic principles and review its experimental implementations, as well as the computational tools that have been developed to model the experiments. We conclude by giving a few application examples, which highlight the potential of 2DUV spectroscopy and motivate its further development. 
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