Michele Ceriotti

Efficient stochastic thermostatting of path integral molecular dynamics

The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.

Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges

Nuclear quantum effects influence the structure and dynamics of hydrogen-bonded systems, such as water, which impacts their observed properties with widely varying magnitudes. This review highlights the recent significant developments in the experiment, theory, and simulation of nuclear quantum effects in water. Novel experimental techniques, such as deep inelastic neutron scattering, now provide a detailed view of the role of nuclear quantum effects in waters properties. These have been combined with theoretical developments such as the introduction of the principle of competing quantum effects that allows the subtle interplay of waters quantum effects and their manifestation in experimental observables to be explained. We discuss how this principle has recently been used to explain the apparent dichotomy in waters isotope effects, which can range from very large to almost nonexistent depending on the property and conditions. We then review the latest major developments in simulation algorithms and theory that have enabled the efficient inclusion of nuclear quantum effects in molecular simulations, permitting their combination with on-the-fly evaluation of the potential energy surface using electronic structure theory. Finally, we identify current challenges and future opportunities in this area of research.

Nuclear quantum effects and hydrogen bond fluctuations in water

Significance There is no doubt about the importance of liquid water for climate and life on Earth. Correctly modeling the properties of this substance is still a formidable challenge, however. Here, we show, using state-of-the-art techniques that allow for quantum mechanical effects in the motion of the electrons and nuclei, that room-temperature water is not simply a molecular liquid; its protons experience wild excursions along the hydrogen bond (HB) network driven by quantum fluctuations, which result in an unexpectedly large probability of transient autoionization events. Moreover, these events are strongly correlated across neighboring bonds so that perturbations disrupting the HB network (pressure, confinement, solvated ions, and interfaces) could enhance in a concerted way their impact on water’s behavior. The hydrogen bond (HB) is central to our understanding of the properties of water. However, despite intense theoretical and experimental study, it continues to hold some surprises. Here, we show from an analysis of ab initio simulations that take proper account of nuclear quantum effects that the hydrogen-bonded protons in liquid water experience significant excursions in the direction of the acceptor oxygen atoms. This generates a small but nonnegligible fraction of transient autoprotolysis events that are not seen in simulations with classical nuclei. These events are associated with major rearrangements of the electronic density, as revealed by an analysis of the computed Wannier centers and 1H chemical shifts. We also show that the quantum fluctuations exhibit significant correlations across neighboring HBs, consistent with an ephemeral shuttling of protons along water wires. We end by suggesting possible implications for our understanding of how perturbations (solvated ions, interfaces, and confinement) might affect the HB network in water.

Simplifying the representation of complex free-energy landscapes using sketch-map

A new scheme, sketch-map, for obtaining a low-dimensional representation of the region of phase space explored during an enhanced dynamics simulation is proposed. We show evidence, from an examination of the distribution of pairwise distances between frames, that some features of the free-energy surface are inherently high-dimensional. This makes dimensionality reduction problematic because the data does not satisfy the assumptions made in conventional manifold learning algorithms We therefore propose that when dimensionality reduction is performed on trajectory data one should think of the resultant embedding as a quickly sketched set of directions rather than a road map. In other words, the embedding tells one about the connectivity between states but does not provide the vectors that correspond to the slow degrees of freedom. This realization informs the development of sketch-map, which endeavors to reproduce the proximity information from the high-dimensionality description in a space of lower dimensionality even when a faithful embedding is not possible.

Nuclear Quantum Effects in Solids Using a Colored-Noise Thermostat

We present a method, based on a non-Markovian Langevin equation, to include quantum corrections to the classical dynamics of ions in a quasiharmonic system. By properly fitting the correlation function of the noise, one can vary the fluctuations in positions and momenta as a function of the vibrational frequency, and fit them so as to reproduce the quantum-mechanical behavior, with minimal a priori knowledge of the details of the system. We discuss the application of the thermostat to diamond and to ice Ih. We find that results in agreement with path-integral methods can be obtained using only a fraction of the computational effort.

A self-learning algorithm for biased molecular dynamics

A new self-learning algorithm for accelerated dynamics, reconnaissance metadynamics, is proposed that is able to work with a very large number of collective coordinates. Acceleration of the dynamics is achieved by constructing a bias potential in terms of a patchwork of one-dimensional, locally valid collective coordinates. These collective coordinates are obtained from trajectory analyses so that they adapt to any new features encountered during the simulation. We show how this methodology can be used to enhance sampling in real chemical systems citing examples both from the physics of clusters and from the biological sciences.

Colored-Noise Thermostats à la Carte

Recently, we have shown how a colored-noise Langevin equation can be used in the context of molecular dynamics as a tool to obtain dynamical trajectories whose properties are tailored to display desired sampling features. In the present paper, after having reviewed some analytical results for the stochastic differential equations forming the basis of our approach, we describe in detail the implementation of the generalized Langevin equation thermostat and the fitting procedure used to obtain optimal parameters. We also discuss the simulation of nuclear quantum effects and demonstrate that by carefully choosing parameters one can successfully model strongly anharmonic solids such as neon. For the readers convenience, a library of thermostat parameters and some demonstrative code can be downloaded from an online repository.

i-PI: A Python interface for ab initio path integral molecular dynamics simulations

Recent developments in path integral methodology have signicantly reduced the computational expense of including quantum mechanical eects in the nuclear motion in ab initio molecular dynamics simulations. However, the implementation of these developments requires a considerable programming eort, which has hindered their adoption. Here we describe i-PI, an interface written in Python that has been designed to minimise the eort required to bring state-of-the-art path integral techniques to an electronic structure program. While it is best suited to rst principles calculations and path integral molecular dynamics, i-PI can also be used to perform classical molecular dynamics simulations, and can just as easily be interfaced with an empirical forceeld code. To give just one example of the many potential applications of the interface, we use it in conjunction with the CP2K electronic structure package to showcase the importance of nuclear quantum eects in high pressure water.

Langevin Equation with Colored Noise for Constant-Temperature Molecular Dynamics Simulations

We discuss the use of a Langevin equation with a colored (correlated) noise to perform constant-temperature molecular dynamics. Since the equations of motion are linear in nature, it is easy to predict the response of a Hamiltonian system to such a thermostat and to tune at will the relaxation time of modes of different frequency. This allows one to optimize the time needed for equilibration and to generate independent configurations. We show how this frequency-dependent response can be exploited to control the temperature of Car-Parrinello-like dynamics without affecting the adiabatic separation of the electronic degrees of freedom from the vibrations of the ions.

Accelerating the convergence of path integral dynamics with a generalized Langevin equation

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.