Earth’s magnetic field is sustained by magnetohydrodynamic convection within the metallic liquid core. In a thermally advecting core, the fraction of heat available to drive the geodynamo is reduced by heat conducted along the core geotherm, which depends sensitively on the thermal conductivity of liquid iron and its alloys with candidate light elements. The thermal conductivity for Earth’s core is very poorly constrained, with current estimates based on a set of scaling relations that were not previously tested at high pressures. We perform first-principles electronic structure computations to determine the thermal conductivity and electrical resistivity for Fe, Fe–Si, and Fe–O liquid alloys. Computed resistivity agrees very well with existing shock compression measurements and shows strong dependence on light element concentration and type. Thermal conductivity at pressure and temperature conditions characteristic of Earth’s core is higher than previous extrapolations. Conductive heat flux near the core–mantle boundary is comparable to estimates of the total heat flux from the core but decreases with depth, so that thermally driven flow would be constrained to greater depths in the absence of an inner core.

Quasiparticle (QP) excitations are extremely important for understanding and predicting charge transfer and transport in molecules, nanostructures, and extended systems. Since density functional theory (DFT) within the Kohn-Sham (KS) formulation does not provide reliable QP energies, many-body perturbation techniques such as the GW approximation are essential. The main practical drawback of GW implementations is the high computational scaling with system size, prohibiting its use in extended, open boundary systems with many dozens of electrons or more. Recently, a stochastic formulation of GW (sGW) was presented (Phys. Rev. Lett. 2014, 113, 076402) with a near-linear-scaling complexity, illustrated for a series of silicon nanocrystals reaching systems of more than 3000 electrons. This advance provides a route for many-body calculations on very large systems that were impossible with previous approaches. While earlier we have shown the gentle scaling of sGW, its accuracy was not extensively demonstrated. Therefore, we show that this new sGW approach is very accurate by calculating the ionization energies of a group of sufficiently small molecules where a comparison to other GW codes is still possible. Using a set of 10 such molecules, we demonstrate that sGW provides reliable vertical ionization energies in close agreement with benchmark deterministic GW results (J. Chem. Theory Comput, 2015, 11, 5665), with mean (absolute) deviation of 0.05 and 0.09 eV. For completeness, we also provide a detailed review of the sGW theory and numerical implementation.

We introduce the concept of fractured stochastic orbitals (FSOs), short vectors that sample a small number of space points and enable an efficient stochastic sampling of any general function. As a first demonstration, FSOs are applied in conjunction with simple direct-projection to accelerate our recent stochastic GW technique; the new developments enable accurate prediction of G0W0 quasiparticle energies and gaps for systems with up to Ne > 10, 000 electrons, with small statistical errors of ±0.05 eV and using less than 2000 core CPU hours. Overall, stochastic GW scales now linearly (and often sub-