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Abstract

In quantum chemistry, a full quantum dynamical description of large many-body systems is not currently feasible. One can consider both classical and semi-classical treatments of approximating the quantum dynamics of molecular systems to simulate simpler dynamics. Motivated by their cost-effectiveness and the fact that chemical dynamics take place often in an energy and density-of-states regime where a classical description can be meaningful, a classical description of the quantum dynamics of systems is explored in this dissertation. We first illustrate how the reaction rate is affected by the cavity effect. cis-trans iso�merization of HONO is used as an example to demonstrate the cavity-controlled reactivity. Due to the high dimensionality of the potential energy surface, we describe the reaction rate through a classical reactive flux method. The quantum Hamiltonian for simulating cavity-modified molecular dynamics is transformed into a classical mapping Hamiltonian. We consider a single molecule inside the cavity. For simplicity, we assume the cavity is coupled to an aligned molecule. The x− aligned case is studied in both low-friction and strong-friction regimes of the reaction coordinate. The low(strong)-friction regime is also known as the underdamped(overdamped) regime, which is mentioned in Grote-Hynes theory. In the underdamped regime, we illustrate the key difference between a single molecule and a collective of molecules with fixed Rabi splitting. We also show a modification of the reaction rate with different cavity frequencies for different aligned cases. Our results show that the modification of the reaction rate is related to the solvent environment. This will be described in chapter 3. We then consider free-orientated molecules inside the cavity within the underdamped regime. Compared with aligned cases, the free orientation of molecules leads to a disorder of light-matter coupling, which should be observed in experimental results. Since a thermally excited molecule passing through the barrier is a rare event, we consider N molecules inside the cavity with 1 activated molecule and N −1 non-activated molecule. We aim to see how the reaction rate is affected by the number of molecules with fixed coupling strength. We connect the enhancing rate by increasing the number of molecules with the energy transfer efficiency from the activated molecule to the cavity. And the efficiency is sensitive to the resonant frequency. Based on this observation, we also show the modification of the reaction rate by tuning the lifetime of the cavity. Our findings shed important new light on the question of collective effects in chemical reactivity under vibrational strong coupling. This will be described in chapter 4. On the other hand, we turn to describe the fermionic dynamics through Meyer-Miller mapping. In chapter 5, We proceed by describing the relation between the initial phase space density of the classically mapped system and the initial configuration of the electrons, and propose strategies to sample this phase space density. We compare the MM mapping with exact quantum results and with different mappings explicitly designed for fermions, namely the SM with and without the inclusion of antisymmetry (the latter corresponds to the original MW mapping), and to the LMM. We then compare Hubbard and impurity Hamiltonians, with and without interactions, and consider as well a model for excitonic energy transfer between chromophores. In this model with interactions we show that the classical MM mapping is able to capture interference effects caused by the presence of different energy transfer pathways leading to the same final state, both when the interferences are constructive and destructive. Our results show that the construction of the maximal fermionic occupation does not seem to be necessary. Also, the performance of the mappings is sensitive to sampling strategies of the initial phase-space distribution for fermions