Size and Quality of Quantum Mechanical Data Set for Training Neural Network Force Fields for Liquid Water.

Molecular dynamics simulations have been used in different scientific fields to investigate a broad range of physical systems. However, the accuracy of calculation is based on the model considered to describe the atomic interactions. In particular, ab initio molecular dynamics (AIMD) has the accuracy of density functional theory (DFT) and thus is limited to small systems and a relatively short simulation time. In this scenario, Neural Network Force Fields (NNFFs) have an important role, since they provide a way to circumvent these caveats. In this work, we investigate NNFFs designed at the level of DFT to describe liquid water, focusing on the size and quality of the training data set considered. We show that structural properties are less dependent on the size of the training data set compared to dynamical ones (such as the diffusion coefficient), and a good sampling (selecting data reference for the training process) can lead to a small sample with good precision.

Using Neural Network Force Fields to Ascertain the Quality of Ab Initio Simulations of Liquid Water.

Accurately simulating the properties of bulk water, despite the apparent simplicity of the molecule, is still a challenge. In order to fully understand and reproduce its complex phase diagram, it is necessary to perform simulations at the ab initio level, including quantum mechanical effects both for electrons and nuclei. This comes at a high computational cost, given that the structural and dynamical properties tend to require long timescales and large simulation cells. In this work, we evaluate the errors that density functional theory (DFT)-based simulations routinely incur into due time- and size-scale limitations. These errors are evaluated using neural-network-trained force fields that are accurate at the level of DFT methods. We compare different exchange and correlation potentials for properties of bulk water that require large timescales. We show that structural properties are less dependent on the system size and that dynamical properties such as the diffusion coefficient have a strong dependence on the simulation size and timescale. Our results facilitate comparisons of DFT-based simulation results with experiments and offer a path to discriminate between model and convergence errors in these simulations.

Interaction of Water with the Gypsum (010) Surface: Structure and Dynamics from Nonlinear Vibrational Spectroscopy and Ab Initio Molecular Dynamics.

Water-mineral interfaces are important for several environmental, industrial, biological, and geological processes. Gypsum, CaSO4·2H2O, is a widespread mineral of high technological, medical, and environmental relevance, but little is known about its surface structure and its interaction with water. A molecular-level understanding of gypsum/water interface is given here by a combined experimental/theoretical study. We investigate the structure and dynamics of water adsorbed from vapor on the gypsum (010) single-crystal surface at room temperature, combining sum-frequency generation (SFG) vibrational spectroscopy experiments and ab initio molecular dynamics (AIMD) simulations. The SFG spectra of gypsum at low relative humidity (RH) show an anisotropic arrangement of structural water molecules and the presence of dangling OH groups. The AIMD simulations allow a detailed assignment of the SFG spectra and show that the cleaved (010) surface rearranges to have only 25% of the OH groups pointing away from the surface. At higher RHs, the first adsorbed water layer binds to these OH groups and forms an anisotropic arrangement, but with the amount of free OH groups significantly suppressed and without any significant diffusion. Upon adsorption of a second water layer, although the topmost layer of molecules is more disordered and dynamic than the previous one, its structure is still influenced by the gypsum surface underneath because it has a much reduced amount of free OH groups with respect to the free surface of water, and a slower surface diffusion with respect to bulk water. The theoretical results corroborate the experimental ones and provide an accurate atomic characterization of the surface structure.

Bias-dependent local structure of water molecules at a metallic interface.

Understanding the local structure of water at the interfaces of metallic electrodes is a key issue in aqueous-based electrochemistry. Nevertheless a realistic simulation of such a setup is challenging, particularly when the electrodes are maintained at different potentials. To correctly compute the effect of an external bias potential applied to truly semi-infinite surfaces, we combine Density Functional Theory (DFT) and Non-Equilibrium Green's Function (NEGF) methods. This framework allows for the out-of-equilibrium calculation of forces and dynamics, and directly correlates to the chemical potential of the electrodes, which is introduced experimentally. In this work, we apply this methodology to study the electronic properties and atomic forces of a water molecule at the interface of a gold surface. We find that the water molecule tends to align its dipole moment with the electric field, and it is either repelled or attracted to the metal depending on the sign and magnitude of the applied bias, in an asymmetric fashion.

Local order of liquid water at metallic electrode surfaces.

We study the structure and dynamics of liquid water in contact with Pd and Au (111) surfaces using ab initio molecular dynamics simulations with and without van der Waals interactions. Our results show that the structure of water at the interface of these two metals is very different. For Pd, we observe the formation of two different domains of preferred orientations, with opposite net interfacial dipoles. One of these two domains has a large degree of in-plane hexagonal order. For Au, a single domain exists with no in-plane order. For both metals, the structure of liquid water at the interface is strongly dependent on the use of dispersion forces. The origin of the structural domains observed in Pd is associated to the interplay between water/water and water/metal interactions. This effect is strongly dependent on the charge transfer that occurs at the interface and which is not modeled by current state of the art semi-empirical force fields.

Temperature and composition dependence of short-range order and entropy, and statistics of bond length: the semiconductor alloy (GaN)(1-x)(ZnO)(x).

We present total energy and force calculations for the (GaN)1-x(ZnO)x alloy. Site-occupancy configurations are generated from Monte Carlo (MC) simulations, on the basis of a cluster expansion model proposed in a previous study. Local atomic coordinate relaxations of surprisingly large magnitude are found via density-functional calculations using a 432-atom periodic supercell, for three representative configurations at x = 0.5. These are used to generate bond-length distributions. The configurationally averaged composition- and temperature-dependent short-range order (SRO) parameters of the alloys are discussed. The entropy is approximated in terms of pair distribution statistics and thus related to SRO parameters. This approximate entropy is compared with accurate numerical values from MC simulations. An empirical model for the dependence of the bond length on the local chemical environments is proposed.

Adiabatic intramolecular movements for water systems.

An effective treatment of the intramolecular degrees of freedom is presented for water, where these modes are decoupled from the intermolecular ones, "adiabatically" allowing these coordinates to be positioned at their local minimum of the potential energy surface. We perform ab initio Monte Carlo simulations with the configurational energies obtained via density functional theory. We study a water dimer as a prototype system, and even in this simple case the intramolecular relaxations are very important to properly describe properties such as the dipole moment. We show that rigid simulations do not correctly sample the phase space, resulting in an average dipole moment smaller than the one obtained with the adiabatic model, which is closer to the experimental result.

Simple implementation of complex functionals: scaled self-consistency.

We explore and compare three approximate schemes allowing simple implementation of complex density functionals by making use of self-consistent implementation of simpler functionals: (i) post-local-density approximation (LDA) evaluation of complex functionals at the LDA densities (or those of other simple functionals) (ii) application of a global scaling factor to the potential of the simple functional, and (iii) application of a local scaling factor to that potential. Option (i) is a common choice in density-functional calculations. Option (ii) was recently proposed by Cafiero and Gonzalez [Phys. Rev. A 71, 042505 (2005)]. We here put their proposal on a more rigorous basis, by deriving it, and explaining why it works, directly from the theorems of density-functional theory. Option (iii) is proposed here for the first time. We provide detailed comparisons of the three approaches among each other and with fully self-consistent implementations for Hartree, local-density, generalized-gradient, self-interaction corrected, and meta-generalized-gradient approximations, for atoms, ions, quantum wells, and model Hamiltonians. Scaled approaches turn out to be, on average, better than post approaches, and unlike these also provide corrections to eigenvalues and orbitals. Scaled self-consistency thus opens the possibility of efficient and reliable implementation of density functionals of hitherto unprecedented complexity.