Theory, codes, and numerical simulation of heat transport in multicomponent systems

Heat transport is a topic that is fundamental in many fields, from materials engineering to planetary models. The calculation of the thermal transport coefficient with the Green-Kubo theory in multicomponent fluids, especially in ab-initio simulations, had a severe data analysis issue that this work solved. In this thesis, we derive the entire theory and data analysis framework for the multicomponent Green-Kubo. Then we show the computer codes we developed, allowing the user to apply the approach previously derived. We believe that in science, replicability and reproducibility are essential requirements. Every new technique must come with an open-source and reliable implementation. In the end, we demonstrate a significant application to superionic ammonia, fundamental to understanding the behavior of icy giant planets like Uranus and Neptune, providing an estimate for the thermal transport coefficient

Theory and Numerical Simulation of Heat Transport in Multicomponent Systems

The thermal conductivity of classical multicomponent fluids is seemingly affected by the intrinsic arbitrariness in the definition of the atomic energies, and it is ill conditioned numerically, when evaluated from the Green-Kubo theory of linear response. To cope with these two problems, we introduce two new concepts: a convective invariance principle for transport coefficients, in the first case, and multivariate cepstral analysis, in the second. A combination of these two concepts allows one to substantially reduce the noise affecting the estimate of the thermal conductivity from equilibrium molecular dynamics, even for one-component systems

Heat Transport in Insulators from Ab Initio Green-Kubo Theory

The Green-Kubo theory of thermal transport has long been considered incompatible with modern simulation methods based on electronic-structure theory, because it is based on such concepts as energy density and current, which are ill-defined at the quantum-mechanical level. Besides, experience with classical simulations indicates that the estimate of heat-transport coefficients requires analyzing molecular trajectories that aremore than one order of magnitude longer than deemed feasible using ab initio molecular dynamics. In this paper we report on recent theoretical advances that are allowing one to overcome these two obstacles. First, a general gauge invariance principle has been established, stating that thermal conductivity is insensitive to many details of the microscopic expression for the energy density and current from which it is derived, thus permitting to establish a rigorous expression for the energy flux from Density-Functional Theory, from which the conductivity can be computed in practice. Second, a novel data analysis method based on the statistical theory of time series has been proposed, which allows one to considerably reduce the simulation time required to achieve a target accuracy on the computed conductivity. These concepts are illustrated in detail, starting from a pedagogical introduction to the Green-Kubo theory of linear response and transport, and demonstrated with a few applications done with both classical and quantum-mechanical simulation methods

Quantum ESPRESSO: One Further Step toward the Exascale

We review the statusof the Quantum ESPRESSO softwaresuite for electronic-structure calculations based on plane waves,pseudopotentials, and density-functional theory. We highlight therecent developments in the porting to GPUs of the main codes, usingan approach based on OpenACC and CUDA Fortran offloading.We describe, in particular, the results achieved on linear-responsecodes, which are one of the distinctive features of the QuantumESPRESSO suite. We also present extensive performance benchmarkson different GPU-accelerated architectures for the main codes of thesuite

SporTran: A code to estimate transport coefficients from the cepstral analysis of (multivariate) current time series

SporTran is a Python utility designed to estimate generic transport coefficients in extended systems, based on the Green-Kubo theory of linear response and the recently introduced cepstral analysis of the current time series generated by molecular dynamics simulations. SporTran can be applied to univariate as well as multivariate time series. Cepstral analysis requires minimum discretion from the user, in that it weakly depends on two parameters, one of which is automatically estimated by a statistical model-selection criterion that univocally determines the resulting accuracy. In order to facilitate the optimal refinement of these parameters, SporTran features an easy-to-use graphical user interface. A command-line interface and a Python API, easy to embed in complex data-analysis workflows, are also provided. (C) 2022 Elsevier B.V. All rights reserved

Heat transport in liquid water from first-principles and deep neural network simulations

We compute the thermal conductivity of water within linear response theory from equilibrium molecular dynamics simulations, by adopting two different approaches. In one, the potential energy surface (PES) is derived on the fly from the electronic ground state of density functional theory (DFT) and the corresponding analytical expression is used for the energy flux. In the other, the PES is represented by a deep neural network (DNN) trained on DFT data, whereby the PES has an explicit local decomposition and the energy flux takes a particularly simple expression. By virtue of a gauge invariance principle, established by Marcolongo, Umari, and Baroni, the two approaches should be equivalent if the PES were reproduced accurately by the DNN model. We test this hypothesis by calculating the thermal conductivity, at the GGA (PBE) level of theory, using the direct formulation and its DNN proxy, finding that both approaches yield the same conductivity, in excess of the experimental value by approximately 60%. Besides being numerically much more efficient than its direct DFT counterpart, the DNN scheme has the advantage of being easily applicable to more sophisticated DFT approximations, such as meta-GGA and hybrid functionals, for which it would be hard to derive analytically the expression of the energy flux. We find in this way that a DNN model, trained on meta-GGA (SCAN) data, reduces the deviation from experiment of the predicted thermal conductivity by about 50%, leaving the question open as to whether the residual error is due to deficiencies of the functional, to a neglect of nuclear quantum effects in the atomic dynamics, or, likely, to a combination of the two

Theory and Numerical Simulation of Heat Transport in Multicomponent Systems

The thermal conductivity of classical multicomponent fluids is seemingly affected by the intrinsic arbitrariness in the definition of the atomic energies, and it is ill conditioned numerically, when evaluated from the Green-Kubo theory of linear response. To cope with these two problems, we introduce two new concepts: a convective invariance principle for transport coefficients, in the first case, and multivariate cepstral analysis, in the second. A combination of these two concepts allows one to substantially reduce the noise affecting the estimate of the thermal conductivity from equilibrium molecular dynamics, even for one-component systems