We give a detailed presentation of the theory and numerical implementation of an expression for the adiabatic energy flux in extended systems, derived from density-functional theory. This expression can be used to estimate the heat conductivity from
equilibrium ab initio molecular dynamics, using the Green-Kubo linear response theory of transport coefficients. Our expression is implemented in an open-source component of the QE suite of computer codes for quantum mechanical materials modelling, which is being made publicly available.
The recently published DeePMD model (https://github.com/deepmodeling/deepmd-kit), based on a deep neural network architecture, brings the hope of solving the time-scale issue which often prevents the application of first principle molecular dynamics
to physical systems. With this contribution we assess the performance of the DeePMD potential on a real-life application and model diffusion of ions in solid-state electrolytes. We consider as test cases the well known Li10GeP2S12, Li7La3Zr2O12 and Na3Zr2Si2PO12. We develop and test a training protocol suitable for the computation of diffusion coefficients, which is one of the key properties to be optimized for battery applications, and we find good agreement with previous computations. Our results show that the DeePMD model may be a successful component of a framework to identify novel solid-state electrolytes.
Thermal and other transport coefficients were recently shown to be largely independent of the microscopic representation of the energy (current) densities or, more generally, of the relevant conserved densities/currents. In this paper we show how thi
s gauge invariance, which is intimately related to the intrinsic indeterminacy of the energy of isolated atoms, can be exploited to optimize the statistical properties of the current time series from which the transport coefficients can be evaluated. To this end, we make use of a variational principle that relies on the metric properties of the conserved currents, treated as elements of an abstract linear space. Different metrics would result in different variational principles. We finally show how a recently proposed data-analysis methodology based on the theory of transport in multi-component systems can be recovered by a suitable choice of this metric.
Thermal transport coefficients are independent of the specific microscopic expression for the energy density and current from which they can be derived through the Green-Kubo formula. We discuss this independence in terms of a kind of gauge invarianc
e resulting from energy conservation and extensivity, and demonstrate it numerically for a Lennard-Jones fluid, where different forms of the microscopic energy density lead to different time correlation functions for the heat flux, all of them, however, resulting in the same value for the thermal conductivity.
Quantum simulation methods based on density-functional theory are currently deemed unfit to cope with atomic heat transport within the Green-Kubo formalism, because quantum-mechanical energy densities and currents are inherently ill-defined at the at
omic scale. We show that, while this difficulty would also affect classical simulations, thermal conductivity is indeed insensitive to such ill-definedness by virtue of a sort of gauge invariance resulting from energy extensivity and conservation. Based on these findings, we derive an expression for the adiabatic energy flux from density-functional theory, which allows heat transport to be simulated using ab-initio equilibrium molecular dynamics. Our methodology is demonstrated by comparing its predictions with those of classical equilibrium and ab-initio non-equilibrium (Muller-Plathe) simulations for a liquid-Argon model, and finally applied to heavy water at ambient conditions.
