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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 Article, we show how this gauge invariance, which is intimately related to the intrinsic indeterminacy of the energy of individual atoms in interacting systems, can be exploited to optimize the statistical properties of the current time series from which the transport coefficients are evaluated. To this end, we introduce and exploit 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. In particular, we show that a recently proposed data-analysis technique based on the theory of transport in multicomponent systems can be recovered by a suitable choice of this metric.

Quantum simulation methods based on electronic-structure theory are 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 atomic scale. We show that, although this difficulty would also affect classical simulations, thermal conductivity is indeed insensitive to such ill-definedness by virtue of a kind of gauge invariance resulting from energy extensivity and conservation. On the basis of 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 to those of classical equilibrium and ab initio non-equilibrium (Müller–Plathe) simulations for a liquid-argon model, and by applying it to heavy water at ambient conditions.

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 Quantum ESPRESSO suite of computer codes for quantum mechanical materials modeling, which is being made publicly available. Program title: QEHeat CPC Library link to program files: https://doi.org/10.17632/c6wxkvy4z3.1 Licensing provisions: GPLv3 Programming language: Fortran Nature of problem: The computation of thermal transport coefficients via equilibrium molecular dynamics and the Green-Kubo theory of linear response requires the definition of a heat-flux describing the instantaneous flow of energy. When considering predictive first-principles methods, a definition of the heat-flux compatible with density-functional theory is required [1]. The evaluation of such a heat flux requires an extension of state-of-the-art atomic simulation codes. Solution method: This work describes in detail the numerical implementation of the adiabatic energy current derived in Refs. [1, 2] and makes it available to the users of the Quantum ESPRESSO suite of computer codes [3]. Used in conjunction with the cp.x code, to perform Car-Parrinello ab initio molecular dynamics , and the SPORTRAN post-processing tool for data analysis [4–6], the program allows to estimate heat transport coefficients in extended systems entirely from first principles. The new code provides as well to developers a modular and easily extendable framework to evaluate time derivatives of electronic properties (e.g. electronic densities or potentials) via a finite difference approach. [1] A. Marcolongo, P. Umari, S. Baroni, Nat. Phys. 12 (2016) 80. [2] W. Andreoni, S. Yip (Eds.), in: Handbook of Materials Modeling. Applications: Current and Emerging Materials, 2nd ed., Springer, 2018, Chap. 12-1, https://arxiv.org/abs/1802.08006. [3] P. Giannozzi et al., J. Phys. Condens. Matter 21 (2009) 395502; P. Giannozzi et al., J. Phys. Condens. Matter 29 (2017) 465901; P. Giannozzi et al., J. Chem. Phys. 152 (2020) 154105. [4] L. Ercole, A. Marcolongo, S. Baroni, Sci. Rep. 7 (2017) 15835. [5] R. Bertossa, F. Grasselli, L. Ercole, S. Baroni Phys. Rev. Lett. 122 (2019) 255901. [6] L. Ercole, R. Bertossa, S. Bisacchi, S. Baroni, SporTran: a code to estimate transport coefficients from the cepstral analysis of a multi-variate current stationary time series, https://github.com/lorisercole/sportran , 2017–2021. [ABSTRACT FROM AUTHOR]