Atomic transport properties of liquid iron at conditions of planetary cores.

Atomic transport properties of liquid iron are important for understanding the core dynamics and magnetic field generation of terrestrial planets. Depending on the sizes of planets and their thermal histories, planetary cores may be subject to quite different pressures (P) and temperatures (T). However, previous studies on the topic mainly focus on the P-T range associated with the Earth's outer core; a systematic study covering conditions from small planets to massive exoplanets is lacking. Here, we calculate the self-diffusion coefficient D and viscosity η of liquid iron via ab initio molecular dynamics from 7.0 to 25 g/cm3 and 1800 to 25 000 K. We find that D and η are intimately related and can be fitted together using a generalized free volume model. The resulting expressions are simpler than those from previous studies where D and η were treated separately. Moreover, the new expressions are in accordance with the quasi-universal atomic excess entropy (Sex) scaling law for strongly coupled liquids, with normalized diffusivity D⋆ = 0.621 exp(0.842Sex) and viscosity η⋆ = 0.171 exp(-0.843Sex). We determine D and η along two thermal profiles of great geophysical importance: the iron melting curve and the isentropic line anchored at the ambient melting point. The variations of D and η along these thermal profiles can be explained by the atomic excess entropy scaling law, demonstrating the dynamic invariance of the system under uniform time and space rescaling. Accordingly, scale invariance may serve as an underlying mechanism to unify planetary dynamos of different sizes.

Two-phase thermodynamic model for computing entropies of liquids reanalyzed.

The two-phase thermodynamic (2PT) model [S.-T. Lin et al., J. Chem. Phys. 119, 11792-11805 (2003)] provides a promising paradigm to efficiently determine the ionic entropies of liquids from molecular dynamics. In this model, the vibrational density of states (VDoS) of a liquid is decomposed into a diffusive gas-like component and a vibrational solid-like component. By treating the diffusive component as hard sphere (HS) gas and the vibrational component as harmonic oscillators, the ionic entropy of the liquid is determined. Here we examine three issues crucial for practical implementations of the 2PT model: (i) the mismatch between the VDoS of the liquid system and that of the HS gas; (ii) the excess entropy of the HS gas; (iii) the partition of the gas-like and solid-like components. Some of these issues have not been addressed before, yet they profoundly change the entropy predicted from the model. Based on these findings, a revised 2PT formalism is proposed and successfully tested in systems with Lennard-Jones potentials as well as many-atom potentials of liquid metals. Aside from being capable of performing quick entropy estimations for a wide range of systems, the formalism also supports fine-tuning to accurately determine entropies at specific thermal states.

Lattice Thermal Conductivity of MgSiO3 Perovskite from First Principles.

We investigate lattice thermal conductivity κ of MgSiO3 perovskite (pv) by ab initio lattice dynamics calculations combined with exact solution of linearized phonon Boltzmann equation. At room temperature, κ of pristine MgSiO3 pv is found to be 10.7 W/(m · K) at 0 GPa. It increases linearly with pressure and reaches 59.2 W/(m · K) at 100 GPa. These values are close to multi-anvil press measurements whereas about twice as large as those from diamond anvil cell experiments. The increase of k with pressure is attributed to the squeeze of weighted phase-spaces phonons get emitted or absorbed. Moreover, we find κ exhibits noticeable anisotropy, with κ zz being the largest component and [Formula: see text] being about 25%. Such extent of anisotropy is comparable to those of upper mantle minerals such as olivine and enstatite. By analyzing phonon mean free paths and lifetimes, we further show that the weak temperature dependence of κ observed in experiments should not be caused by phonons reaching 'minimum' mean free paths. These results clarify the microscopic mechanism of thermal transport in MgSiO3 pv, and provide reference data for understanding heat conduction in the Earth's deep interior.

Approximate treatment of semicore states in GW calculations with application to Au clusters.

We address the treatment of transition metal atoms in GW electronic-structure calculations within the plane-wave pseudo-potential formalism. The contributions of s and p semi-core electrons to the self-energy, which are essential to grant an acceptable accuracy, are dealt with using a recently proposed scheme whereby the exchange components are treated exactly at the G0W0 level, whereas a suitable approximation to the correlation components is devised. This scheme is benchmarked for small gold nano-clusters, resulting in ionization potentials, electron affinities, and density of states in very good agreement with those obtained from calculations where s and p semicore states are treated as valence orbitals, and allowing us to apply this same scheme to clusters of intermediate size, Au20 and Au32, that would be otherwise very difficult to deal with.

Harnessing molecular excited states with Lanczos chains.

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculating diagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators by elegantly expressing them in terms of continued fractions. In this paper we extend the recursion method to off-diagonal matrix elements of general (possibly non-Hermitian) operators and apply it to the simulation of molecular optical absorption and photoemission spectra within time-dependent density-functional and many-body perturbation theories, respectively. This method is demonstrated with a couple of applications to the optical absorption and photoemission spectra of the caffeine molecule.