Path Integral Molecular Dynamics of Liquid Water in a Mean‐Field Particle Reservoir

Abstract

We present a simulation scheme for path integral simulation of molecular liquids where a small open region is embedded in a large reservoir of non interacting point‐particles. The scheme is based on the latest development of the adaptive resolution technique AdResS and allows for the space‐dependent change of molecular resolution from a path integral representation with 120 degrees of freedom to a point particle that does not interact with other molecules and vice versa. The method is applied to liquid water and implies a sizable gain regarding the request of computational resources compared to full path integral simulations. Given the role of water as universal solvent with a specific hydrogen bonding network, the path integral treatment of water molecules is important to describe the quantum effects of hydrogen atoms’ delocalization in space on the hydrogen bonding network. The method presented here implies feasible computational efforts compared to full path integral simulations of liquid water which, on large scales, are often prohibitive.

Nuclear quantum effects in fullerene–fullerene aggregation in water

“…Tracer particles entering the Δ region acquire the chemical structure of the water molecule and the corresponding path integral resolution; on the contrary, molecules leaving the Δ region for the TR region lose their high resolution and become non-interacting particles. Recent results have demonstrated the reliability of this technique for the four-site water model used here with 30 beads per atom, which means that molecules entering the TR region lose 120 degrees of freedom, while molecules entering the Δ region acquire 120 degrees of freedom ( Evangelakis et al, 2021 ). The size of the Δ region is equal to the cut-off distance of the interaction potential such that there is no missing interaction between molecules in the PI and TR regions.…”

“…These functions represent relevant structural properties that characterize a liquid and its solvation action at certain thermodynamic conditions. In addition, at the statistical mechanics level, their combination expresses the probability distribution function of the system in configuration space up to the two-body approximation ( Wang et al, 2013 ; Agarwal et al, 2015 ; Evangelakis et al, 2021 ). 3) The probability distribution function of the particle number in PI, P ( N ), must be consistent with P ( N ) of an equivalent subregion in the full reference path integral simulation so that the exchange of particles between the PI region and the reservoir (TR) is physically consistent.…”

“…Overcoming this challenge requires the use of simulation tools that drastically reduce the mandatory degrees of freedom but provide reliable results. One such method is the recently developed open system MD technique ( Delle Site et al, 2019 ) based on the AdResS technique which has been extensively tested regarding its merging to PIMD ( Poma and Delle Site, 2010 ; Poma and Delle Site, 2011 ; Potestio and Delle Site, 2012 ; Agarwal and Delle Site, 2015 ; Agarwal and Delle Site, 2016 ; Evangelakis et al, 2021 ).…”

“…AdResS treats an open subregion of the simulation domain at full quantum resolution and the rest as a thermodynamic reservoir of energy and particles, that is, as a large domain of non-interacting particles (tracers) thermalized by an external thermostat [the latest version is described in Delle Site et al (2019 ) and Evangelakis et al (2021 )]. Figure 2 illustrates the concept, showing a high-resolution region (PI) embedded in a (usually) much larger region of tracers (TR) thermalized by an external reservoir that assures the correct thermodynamic conditions.…”

An effective Hamiltonian for the simulation of open quantum molecular systems

“…This field is, in our view, still in its infancy, since most of the current open-system ab initio algorithms are built on empirical basis and thus are often numerically not reliable [14] due to conceptual inconsistencies that lead to incorrect statistical sampling [1,15]. This means that the construction of a solid theoretical framework would assure physical consistency and computational robustness to the underlying numerical methods, as it occurred for molecular dynamics of classical and semi-classical open systems with a system-reservoir exchange of particles [16][17][18][19][20].…”