Water is an ubiquitous chemical substance and a key ingredient for life, but its structure remains poorly understood. Dr Michele Casula and his colleagues from Sorbonne University, Paris, and from SISSA, Trieste have been shedding light on the complex arrangement of the intermolecular network in water using newly-devised numerical methods.
Despite about half a century of numerical investigations aimed at providing a quantitative and reliable microscopic description of liquid water, it remains difficult to accurately describe proton hopping inside the strong and well-structured hydrogen bond network that gives water its numerous peculiar features.
Simulating and understanding the properties of water is of paramount importance, as water is a key ingredient for life and plays a central role as the solvent in most of the chemical and biological processes occurring on Earth. However, a comprehensive description of its structure at different thermal conditions is still elusive.
The project “ProDyn/Q – Quantum proton dynamics in water charge defects by quantum Monte Carlo”, led by Dr Michele Casula of CNRS, was initiated with the aim of shedding light on the complex arrangement of the intermolecular network in water by studying the behaviour of hydronium (H3O+) ions solvated in water clusters.
The solvation and transport properties of hydronium in aqueous environments have enormous impacts on areas ranging from aqueous acid-base chemistry, enzymatic proton transfer, proton transfer in biological channels, fuel cell membranes and ice surfaces facilitating atmospheric reactions.
The calculations were carried out in the recently developed quantum Monte Carlo (QMC) based molecular dynamics (MD) framework, which also includes quantum nuclear effects. The approach combines three main theoretical ingredients: the accurate solution of the electronic problem from first principles provided by QMC, a Langevin-based molecular dynamics driven by the noisy QMC ionic forces, and the quantum description of nuclei via the path integral Langevin molecular dynamics framework with a new solver which accelerates both the harmonic quantum part and the Langevin damped dynamics.
The image is the protonated water hexamer where ions are quantum. In Casula’s framework, the ions are no longer point-like particles as in standard mechanics, but are described by a “cluster”, also called a ring polymer, thanks to the quantum- to-classical isomorphism. Oxygens are in red, hydrogens in blue.
Due to a variety of interactions present in water such as weak and dispersive dipolar interactions that compete during the formation and breaking of hydrogen bonds inside a strongly polar network, an accurate description of the potential energy surface is required to fully understand the microscopic properties of water.
From a theoretical point of view, liquid water has been studied through molecular dynamics techniques such as the empirical force fields methods and ab initio molecular dynamics (AIMD). Because of its good scalability with the system size which is suited to study liquids, density functional theory (DFT) has been the most employed technique to perform AIMD simulations of bulk water. Nevertheless, DFT-based calculations usually give rise to an over structuration of water. For instance, the melting point temperature and oxygen-oxygen radial distribution function are poorly reproduced.
Quantum Monte Carlo (QMC) techniques constitute a very interesting alternative to study aqueous systems, since the scalability of the method makes the simulations of very large systems computationally affordable with a much greater accuracy than DFT in most cases. Consequently, QMC can now be used as a benchmark method and certainly benefits from its intrinsically parallel formulation in modern supercomputers.
“The methodology developed in the project could potentially open the way to more accurate and systematic studies of water properties”
It is well known that nuclear quantum effects play a crucial role in the description of water or ice by deeply affecting the radial distribution functions and distorting hydrogen bonds because of quantum disorder. The Sorbonne/SISSA research team have addressed this by including a nuclear quantum description within the QMC-driven dynamics. This is achieved within a path integral Langevin dynamics (PILD) approach.
The methodology developed in the project could potentially open the way to more accurate and systematic studies of water properties. The importance of the theoretical development goes well beyond the specific application, as the proposed framework is very general and capable of dealing with electronic correlation, thermal and proton quantum effects playing together on equal footing.
This project has proven the potential of QMC methods combined with the PILD approach to perform fully quantum calculations of water-like and aqueous systems. In the perspective of performing such simulations on larger systems, the scheme overcomes two major scalability problems. On the one hand, it benefits from the QMC reasonable scaling with respect to the number of electrons contrary to other post-Hartree- Fock electronic structure methods. On the other hand, by grouping the beads describing quantum particles, the team was able to carry out fully ab initio dynamics of the ions with almost the same computational cost as for classical nuclei, without deteriorating NQE. Within this approximation, the quantum simulations are paradoxically more efficient than their classical counterparts. Indeed, the nuclear observables statistics is improved, because the phase space is more efficiently explored, thanks to the quantum fluctuations included in the framework, while the QMC statistical fluctuations of the electronic part are not detrimental, as they are averaged over the beads.
Consequently, this work paves the way to study, at the theoretical level, proton transfer mechanisms in more complex water clusters, starting, for instance, with the protonated water hexamer H13O6+, and larger protonated clusters, where the proton dynamics is still under debate.
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Resources awarded by PRACE
Michele Casula was awarded 32 400 000 core hours on FERMI and Marconi hosted by CINECA, Italy