Quantum to Classical Mechanics: Fundamentals

This lecture covers the transition from quantum to classical mechanics, discussing assumptions, adiabaticity, non-adiabaticity, and nuclear quantum dynamics. It also delves into statistical mechanics, focusing on thermodynamic ensembles, microstates, entropy, energy, and the canonical partition function. Additionally, Monte Carlo simulations are explained, including importance sampling, the Metropolis algorithm, Markov chains, and detailed balance. Molecular dynamics simulations are explored, comparing MD and MC, integrating Newton's equations, time propagators, time step selection, constraint algorithms, and Noether's theorem. The lecture concludes with topics on potential energy surfaces, force fields, water models, and thermostats.