Electronic Structure Reading Group: Computing thermal conductivity with the Green-Kubo method and neural networks

In the last reading group, we learned how to derive the Green-Kubo (GK) relations, which relate transport coefficients like diffusivity or thermal conductivity to equilibrium fluctuations. This session will continue on that path and discuss how to get from the abstract relations to practical computations using molecular dynamics (MD) and neural network interatomic potentials, focusing on the case of thermal conductivity. On the way, we will discuss the challenges in relating MD, a method that works with point particles and classical mechanics, with the GK method, which is usually derived in a density-based, “hydrodynamic”, framework. We will find that the main task is defining the “heat flux”, a quantity loosely related to the flow of energy within a simulation box, and discuss how this can be done efficiently with automatic differentiation.

Reading:

The talk will be based on sections 2.5 and 4.2 of my PhD thesis, http://data.marcel.science/da-2.1-pdfa.pdf. 

Related references:

J. H. Irving and J. G. Kirkwood, ‘The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics’, The Journal of Chemical Physics 18, 817 (1950)
W. Noll, ‘Die Herleitung der Grundgleichungen der Thermomechanik der Kontinua aus der statistischen Mechanik’, Journal of Rational Mechanics and Analysis 4, 627 (1955)
R. J. Hardy, ‘Energy-flux operator for a lattice’, Physical Review 132, 168 (1963)
R. J. Hardy, ‘Formulas for determining local properties in molecular-dynamics simulations: Shock waves’, The Journal of Chemical Physics 76, 622 (1982)

This event is jointly organized with the COSMO seminar.
---
The electronic structure reading group brings together researchers and students interested in mathematical aspects of electronic structure problems and adjacent topics, including:

• Density Functional Theory
• Many-body Schrödinger equation for electrons
• Born-Oppenheimer Molecular Dynamics
• Numerical analysis and error control