▪ Abstract This article reviews the concepts and methods of transition path sampling. These methods allow computational studies of rare events without requiring prior knowledge of mechanisms, reaction coordinates, and transition states. Based upon a statistical mechanics of trajectory space, they provide a perspective with which time dependent phenomena, even for systems driven far from equilibrium, can be examined with the same types of importance sampling tools that in the past have been applied so successfully to static equilibrium properties.

Local bond order parameters based on spherical harmonics, also known as Steinhardt order parameters, are often used to determine crystal structures in molecular simulations. Here we propose a modification of this method in which the complex bond order vectors are averaged over the first neighbor shell of a given particle and the particle itself. As demonstrated using soft particle systems, this averaging procedure considerably improves the accuracy with which different crystal structures can be distinguished.

We have developed a method to study transition pathways for rare events in complex systems. The method can be used to determine rate constants for transitions between stable states by turning the calculation of reactive flux correlation functions into the computation of an isomorphic reversible work. In contrast to previous dynamical approaches, the method relies neither on prior knowledge nor on explicit specification of transition states. Rather, it provides an importance sampling from which transition states can be characterized statistically. A simple model is analyzed to illustrate the methodology.

The dissociation of a water molecule in liquid water is the fundamental event in acid-base chemistry, determining the pH of water. Because of the short time scales and microscopic length scales involved, the dynamics of this autoionization have not been directly probed by experiment. Here, the autoionization mechanism is revealed by sampling and analyzing ab initio molecular dynamics trajectories. We identify the rare fluctuations in solvation energies that destabilize an oxygen-hydrogen bond. Through the transfer of protons along a hydrogen bond “wire,” the nascent ions separate by three or more neighbors. If the hydrogen bond wire connecting the two ions is subsequently broken, a metastable charge-separated state is visited. The ions may then diffuse to large separations. If, however, the hydrogen bond wire remains unbroken, the ions recombine rapidly. Because of their concomitant large electric fields, the transient ionic species produced in this case may provide an experimentally detectable signal of the dynamics we report.

Significance: Despite its simple chemical formula, H ₂ O, water is a complex substance with a variety of unusual properties resulting from its ability to form hydrogen bonds. A famous example for the anomalous behavior of water is the fact that it exhibits a density maximum at 4 °C. Here, we unravel the density anomaly of water on the molecular level using a powerful ab initio-based simulation technique. We show that weak van der Waals forces crucially modulate the flexibility of the hydrogen bond network, giving rise to the density maximum in water and causing ice to be less dense than the liquid.

The momentum transfer between a photon and an object defines a fundamental limit for the precision with which the object can be measured. If the object oscillates at a frequency ${\mathrm{\Omega }}_0$, this measurement backaction adds quanta $\hslash {\mathrm{\Omega }}_0$ to the oscillator’s energy at a rate ${\mathrm{\Gamma }}_{\text{recoil}}$, a process called photon recoil heating, and sets bounds to coherence times in cavity optomechanical systems. Here, we use an optically levitated nanoparticle in ultrahigh vacuum to directly measure ${\mathrm{\Gamma }}_{\text{recoil}}$. By means of a phase-sensitive feedback scheme, we cool the harmonic motion of the nanoparticle from ambient to microkelvin temperatures and measure its reheating rate under the influence of the radiation field. The recoil heating rate is measured for different particle sizes and for different excitation powers, without the need for cavity optics or cryogenic environments. The measurements are in quantitative agreement with theoretical predictions and provide valuable guidance for the realization of quantum ground-state cooling protocols and the measurement of ultrasmall forces.