## Intro to molecular dynamics - Deterministic is an important concept in MD, namely once the initial positions and velocities are given, the subsequent evolution of the system should be fixed in principle. - Trajectory is a way to obtain a set of configurations distributed *according to some statistical distribution functions* (or ensemble). > [!notice] > Such distribution writes like $P(p,q) \mathrm{d}p\mathrm{d}q \propto \delta(\ldots)\mathrm{d}p\mathrm{d}q$ >[!note] >But what we gets is typically $q$ and $v$ (evolve by time) - For classical MD, we use classical mechanics. - To achieve this, we use certain algorithm to integrate the equation of motion of particles and follow the trajectory. - This is typically “time integration algorithm”, use finite difference method, discrete time into small steps $\Delta t$, compute next position, and velocity at $t+\Delta t$ based on result at $t$. >[!notice] >This may lead to *truncate error* (algorithm related, like short expansion) and *round-off error* (machine/computer related). Decreasing $\Delta t$ lower the truncate error, and round-off error becomes significant and determine.