Computation of the heat capacity of water from first principles

Water is a unique solvent with many remarkable properties. An example is its exceptionally high heat capacity, which plays an important role in storing and transporting thermal energy, with implications for many processes from regulating the body temperature of living organisms to moderating our climate at the global scale. To elucidate the microscopic origin of the heat capacity of water from first principles, highly accurate computer simulations are required. Apart from a reliable description of the atomic interactions, the presence of light hydrogen atoms necessitates the explicit consideration of nuclear quantum effects through path integral molecular dynamics (PIMD) simulations. The high computational costs of PIMD simulations, which are even further increased by the need for an extensive statistical sampling of energy fluctuations to determine the heat capacity, can be strongly reduced by replacing first principles calculations with machine learning potentials to represent the atomic interactions. In this study, we use high-dimensional neural network potentials (HDNNPs) constructed from density functional theory calculations employing the RPBE-D3 and revPBE0-D3 functionals. To further enhance the computational performance, we introduce a highly efficient PIMD algorithm computing in parallel not only the energies and forces but also the coordinate and thermostat time evolutions. Using this approach, we are able to determine converged data for the heat capacity from a 4 ns simulation employing 128 beads. In particular, for the revPBE0-D3 functional we find excellent agreement with experiment, providing evidence that our approach represents a promising framework for the quantitative understanding of the thermodynamic properties of water and aqueous solutions.