On the direct calculation of the free energy of quantization for molecular systems in the condensed phase

Water-air interface revisited by means of path-integral ab initio molecular dynamics

Although nuclear quantum effects (NQEs) have been considered on bulk liquid water, the impact of these latter on the air-water interface has not yet been reported. Herein, by performing and comparing ab initio molecular dynamics (AIMD) and path integral AIMD (PI-AIMD) simulations, we reveal the impact of NQEs on structural, dynamical and electronic properties as well as IR spectra of the air-water interface at room temperature. NQEs, being able to describe a more accurate proton delocalization in H-bonded system than AIMD, reveal a different structural arrangement and dynamical behaviour of both bulk and interfacial water molecules in comparison to AIMD results. A more de-structured and de-bound water arrangement and coordination are identified when the quantum nature of nuclei are considered for both bulk and interfacial water molecules. Structural properties, such as inter-/intra-molecular bond lengths, coordination numbers and H-bonding angles of bulk and interfacial water molecules here calculated, are affected by NQEs mitigating the overstructured description given by AIMD. Further evidences of an AIMD overstructured description of bulk water are in the computed IR spectra, where an increased absorption peak intensity and an increased strength of the hydrogen-bond network are alleviated by NQEs. In addition, NQEs show a valuable impact on the electronic structure of the air-water interface, reducing the total valence bandwidth and the electronic energy band-gap when passing from bulk to interfacial water. This work proves how NQEs significantly affect properties and features of the air-water interface, that are essential to accurately describe H-bonded interfacial systems.

Nuclear Quantum Effects from the Analysis of Smoothed Trajectories: Pilot Study for Water

Nuclear quantum effects have significant contributions to thermodynamic quantities and structural properties; furthermore, very expensive methods are necessary for their accurate computation. In most calculations, these effects, for instance, zero-point energies, are simply neglected or only taken into account within the quantum harmonic oscillator approximation. Herein, we present a new method, Generalized Smoothed Trajectory Analysis, to determine nuclear quantum effects from molecular dynamics simulations. The broad applicability is demonstrated with the examples of a harmonic oscillator and different states of water. Ab initio molecular dynamics simulations have been performed for ideal gas up to the temperature of 5000 K. Classical molecular dynamics have been carried out for hexagonal ice, liquid water, and vapor at atmospheric pressure. With respect to the experimental heat capacity, our method outperforms previous calculations in the literature in a wide temperature range at lower computational cost than other alternatives. Dynamic and structural nuclear quantum effects of water are also discussed.

Harmonic-phase path-integral approximation of thermal quantum correlation functions

We present an approximation to the thermal symmetric form of the quantum time-correlation function in the standard position path-integral representation. By transforming to a sum-and-difference position representation and then Taylor-expanding the potential energy surface of the system to second order, the resulting expression provides a harmonic weighting function that approximately recovers the contribution of the phase to the time-correlation function. This method is readily implemented in a Monte Carlo sampling scheme and provides exact results for harmonic potentials (for both linear and non-linear operators) and near-quantitative results for anharmonic systems for low temperatures and times that are likely to be relevant to condensed phase experiments. This article focuses on one-dimensional examples to provide insights into convergence and sampling properties, and we also discuss how this approximation method may be extended to many-dimensional systems.

Roles for ordered and bulk solvent in ligand recognition and docking in two related cavities

A key challenge in structure-based discovery is accounting for modulation of protein-ligand interactions by ordered and bulk solvent. To investigate this, we compared ligand binding to a buried cavity in Cytochrome c Peroxidase (CcP), where affinity is dominated by a single ionic interaction, versus a cavity variant partly opened to solvent by loop deletion. This opening had unexpected effects on ligand orientation, affinity, and ordered water structure. Some ligands lost over ten-fold in affinity and reoriented in the cavity, while others retained their geometries, formed new interactions with water networks, and improved affinity. To test our ability to discover new ligands against this opened site prospectively, a 534,000 fragment library was docked against the open cavity using two models of ligand solvation. Using an older solvation model that prioritized many neutral molecules, three such uncharged docking hits were tested, none of which was observed to bind; these molecules were not highly ranked by the new, context-dependent solvation score. Using this new method, another 15 highly-ranked molecules were tested for binding. In contrast to the previous result, 14 of these bound detectably, with affinities ranging from 8 µM to 2 mM. In crystal structures, four of these new ligands superposed well with the docking predictions but two did not, reflecting unanticipated interactions with newly ordered waters molecules. Comparing recognition between this open cavity and its buried analog begins to isolate the roles of ordered solvent in a system that lends itself readily to prospective testing and that may be broadly useful to the community.