Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations c
an be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer (LMon) model and a mixed quantum-classical (MQC) model as representatives of the first family of methods, and centroid molecular dynamics (CMD) and thermostatted ring polymer molecular dynamics (TRPMD) as examples of the latter. We use as benchmarks D$_2$O doped with HOD and pure H$_2$O at three distinct thermodynamic state points (ice Ih at 150K, and the liquid at 300K and 600K), modeled with the simple q-TIP4P/F potential energy and dipole moment surfaces. With few exceptions the different techniques yield IR absorption frequencies that are consistent with one another within a few tens of cm$^{-1}$. Comparison with classical molecular dynamics demonstrates the importance of nuclear quantum effects up to the highest temperature, and a detailed discussion of the discrepancies between the various methods let us draw some (circumstantial) conclusions about the impact of the very different approximations that underlie them. Such cross validation between radically different approaches could indicate a way forward to further improve the state of the art in simulations of condensed-phase quantum dynamics.
The concept of chemical bonding can ultimately be seen as a rationalization of the recurring structural patterns observed in molecules and solids. Chemical intuition is nothing but the ability to recognize and predict such patterns, and how they tran
sform into one another. Here we discuss how to use a computer to identify atomic patterns automatically, so as to provide an algorithmic definition of a bond based solely on structural information. We concentrate in particular on hydrogen bonding -- a central concept to our understanding of the physical chemistry of water, biological systems and many technologically important materials. Since the hydrogen bond is a somewhat fuzzy entity that covers a broad range of energies and distances, many different criteria have been proposed and used over the years, based either on sophisticate electronic structure calculations followed by an energy decomposition analysis, or on somewhat arbitrary choices of a range of structural parameters that is deemed to correspond to a hydrogen-bonded configuration. We introduce here a definition that is univocal, unbiased, and adaptive, based on our machine-learning analysis of an atomistic simulation. The strategy we propose could be easily adapted to similar scenarios, where one has to recognize or classify structural patterns in a material or chemical compound.
Light nuclei at room temperature and below exhibit a kinetic energy which significantly deviates from the predictions of classical statistical mechanics. This quantum kinetic energy is responsible for a wide variety of isotope effects of interest in
fields ranging from chemistry to climatology. It also furnishes the second moment of the nuclear momentum distribution, which contains subtle information about the chemical environment and has recently become accessible to deep inelastic neutron scattering experiments. Here we show how, by combining imaginary time path integral dynamics with a carefully designed generalized Langevin equation, it is possible to dramatically reduce the expense of computing the quantum kinetic energy. We also introduce a transient anisotropic Gaussian approximation to the nuclear momentum distribution which can be calculated with negligible additional effort. As an example, we evaluate the structural properties, the quantum kinetic energy, and the nuclear momentum distribution for a first-principles simulation of liquid water.
Two of the most successful methods that are presently available for simulating the quantum dynamics of condensed phase systems are centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD). Despite their conceptual differences, pra
ctical implementations of these methods differ in just two respects: the choice of the Parrinello-Rahman mass matrix and whether or not a thermostat is applied to the internal modes of the ring polymer during the dynamics. Here we explore a method which is halfway between the two approximations: we keep the path integral bead masses equal to the physical particle masses but attach a Langevin thermostat to the internal modes of the ring polymer during the dynamics. We justify this by showing analytically that the inclusion of an internal mode thermostat does not affect any of the desirable features of RPMD: thermostatted RPMD (TRPMD) is equally valid with respect to everything that has actually been proven about the method as RPMD itself. In particular, because of the choice of bead masses, the resulting method is still optimum in the short-time limit, and the transition state approximation to its reaction rate theory remains closely related to the semiclassical instanton approximation in the deep quantum tunneling regime. In effect, there is a continuous family of methods with these properties, parameterised by the strength of the Langevin friction. Here we explore numerically how the approximation to quantum dynamics depends on this friction, with a particular emphasis on vibrational spectroscopy. We find that a broad range of frictions approaching optimal damping give similar results, and that these results are immune to both the resonance problem of RPMD and the curvature problem of CMD.
Recent developments in path integral methodology have significantly reduced the computational expense of including quantum mechanical effects in the nuclear motion in ab initio molecular dynamics simulations. However, the implementation of these deve
lopments requires a considerable programming effort, which has hindered their adoption. Here we describe i-PI, an interface written in Python that has been designed to minimise the effort required to bring state-of-the-art path integral techniques to an electronic structure program. While it is best suited to first 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 forcefield 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 effects in high pressure water.
Even at room temperature, quantum mechanics plays a major role in determining the quantitative behaviour of light nuclei, changing significantly the values of physical properties such as the heat capacity. However, other observables appear to be only
weakly affected by nuclear quantum effects (NQEs): for instance, the melting temperatures of light and heavy water differ by less than 4 K. Recent theoretical work has attributed this to a competition between intra and inter molecular NQEs, which can be separated by computing the anisotropy of the quantum kinetic energy tensor. The principal values of this tensor change in opposite directions when ice melts, leading to a very small net quantum mechanical effect on the melting point. This paper presents the first direct experimental observation of this phenomenon, achieved by measuring the deuterium momentum distributions n(p) in heavy water and ice using Deep Inelastic Neutron Scattering (DINS), and resolving their anisotropy. Results from the experiments, supplemented by a theoretical analysis, show that the anisotropy of the quantum kinetic energy tensor can also be captured for heavier atoms such as oxygen.
We discuss the use of a Langevin equation with a colored (correlated) noise to perform constant-temperature molecular dynamics simulations. 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 to thermalize the system and generate independent configurations. We show how this frequency-dependent response can be exploited to control the temperature of Car-Parrinello-like dynamics, keeping at low temperature the electronic degrees of freedom, without affecting the adiabatic separation from the vibrations of the ions.
