Practicing enhanced‐sampling techniques on the classic two‐dimensional Müller–Brown potential energy surface, we first illustrate the limitations of conventional Langevin dynamics—plain MD remains trapped in a single minimum even when temperature and friction are tuned. Introducing well-tempered metadynamics over the Cartesian coordinates (cv.x, cv.y) rapidly fills energy basins and enables repeated barrier crossings without distorting the underlying landscape. Building on this, we employ path-meta-dynamics: a linear initial path between reactant and product basins is adaptively bent by iteratively depositing Gaussian biases on the progress coordinate σ, while a harmonic “tube” potential confines sampling near the evolving trajectory. In the narrow-tube limit, the algorithm converges onto the minimum free-energy path; in a wider tube, it captures the average reactive flux. Applied to the Müller–Brown surface, this protocol recovers both the optimal transition corridor and the one-dimensional free-energy profile—with only tens of Gaussians—demonstrating sublinear scaling in collective-variable dimensionality. These exercises pave the way for applying adaptive meta-dynamics to complex chemical processes, such as glycine formation in water.
