Most water in the universe may be superionic, and its thermodynamic and transport properties are crucial for planetary science but difficult to probe experimentally or theoretically. We use machine learning and free energy methods to overcome the lim
itations of quantum mechanical simulations, and characterize hydrogen diffusion, superionic transitions, and phase behaviors of water at extreme conditions. We predict that a close-packed superionic phase with mixed stacking is stable over a wide temperature and pressure range, while a body-centered cubic phase is only thermodynamically stable in a small window but is kinetically favored. Our phase boundaries, which are consistent with the existing-albeit scarce-experimental observations, help resolve the fractions of insulating ice, different superionic phases, and liquid water inside of ice giants.
We present an accurate and efficient real-space formulation of the Hellmann-Feynman stress tensor for $mathcal{O}(N)$ Kohn-Sham density functional theory (DFT). While applicable at any temperature, the formulation is most efficient at high temperatur
e where the Fermi-Dirac distribution becomes smoother and density matrix becomes correspondingly more localized. We first rewrite the orbital-dependent stress tensor for real-space DFT in terms of the density matrix, thereby making it amenable to $mathcal{O}(N)$ methods. We then describe its evaluation within the $mathcal{O}(N)$ infinite-cell Clenshaw-Curtis Spectral Quadrature (SQ) method, a technique that is applicable to metallic as well as insulating systems, is highly parallelizable, becomes increasingly efficient with increasing temperature, and provides results corresponding to the infinite crystal without the need of Brillouin zone integration. We demonstrate systematic convergence of the resulting formulation with respect to SQ parameters to exact diagonalization results, and show convergence with respect to mesh size to established planewave results. We employ the new formulation to compute the viscosity of hydrogen at a million kelvin from Kohn-Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.
A realistic description of partially-ionized matter in extreme thermodynamic states is critical to model the interior and evolution of the multiplicity of high-density astrophysical objects. Current predictions of its essential property, the ionizati
on degree, rely widely on analytical approximations that have been challenged recently by a series of experiments. Here, we propose a novel ab initio approach to calculate the ionization degree directly from the dynamic electrical conductivity using the Thomas-Reiche-Kuhn sum rule. This Density Functional Theory framework captures genuinely the condensed matter nature and quantum effects typical for strongly-correlated plasmas. We demonstrate this new capability for carbon and hydrocarbon, which most notably serve as ablator materials in inertial confinement fusion experiments aiming at recreating stellar conditions. We find a significantly higher carbon ionization degree than predicted by commonly used models, yet validating the qualitative behavior of the average atom model Purgatorio. Additionally, we find the carbon ionization state to remain unchanged in the environment of fully-ionized hydrogen. Our results will not only serve as benchmark for traditional models, but more importantly provide an experimentally accessible quantity in the form of the electrical conductivity.
Atom-in-jellium calculations of the Einstein frequency were used to calculate the mean displacement of an ion over a wide range of compression and temperature. Expressed as a fraction of the Wigner-Seitz radius, the displacement is a measure of the a
symptotic freedom of the ion at high temperature, and thus of the change in heat capacity from 6 to 3 quadratic degrees of freedom per atom. A functional form for free energy was proposed based on the Maxwell-Boltzmann distribution as a correction to the Debye free energy, with a single free parameter representing the effective density of potential modes to be saturated. This parameter was investigated using molecular dynamics simulations, and found to be ~0.2 per atom. In this way, the ion-thermal contribution can be calculated for a wide-range equation of state (EOS) without requiring a large number of molecular dynamics simulations. Example calculations were performed for carbon, including the sensitivity of key EOS loci to ionic freedom.
We present thermodynamic material and transport properties for the extreme conditions prevalent in the interiors of massive giant planets and brown dwarfs. They are obtained from extensive textit{ab initio} simulations of hydrogen-helium mixtures alo
ng the isentropes of three representative objects. In particular, we determine the heat capacities, the thermal expansion coefficient, the isothermal compressibility, and the sound velocity. Important transport properties such as the electrical and thermal conductivity, opacity, and shear viscosity are also calculated. Further results for associated quantities including magnetic and thermal diffusivity, kinematic shear viscosity, as well as the static Love number $k_2$ and the equidistance are presented. In comparison to Jupiter-mass planets, the behavior inside massive giant planets and brown dwarfs is stronger dominated by degenerate matter. We discuss the implications on possible dynamics and magnetic fields of those massive objects. The consistent data set compiled here may serve as starting point to obtain material and transport properties for other substellar H-He objects with masses above one Jovian mass and finally may be used as input for dynamo simulations.
The validity of the widely used linear mixing approximation for the equations of state (EOS) of planetary ices is investigated at pressure-temperature conditions typical for the interior of Uranus and Neptune. The basis of this study are ab initio da
ta ranging up to 1000 GPa and 20 000 K calculated via density functional theory molecular dynamics simulations. In particular, we calculate a new EOS for methane and EOS data for the 1:1 binary mixtures of methane, ammonia, and water, as well as their 2:1:4 ternary mixture. Additionally, the self-diffusion coefficients in the ternary mixture are calculated along three different Uranus interior profiles and compared to the values of the pure compounds. We find that deviations of the linear mixing approximation from the results of the real mixture are generally small; for the thermal EOS they amount to 4% or less. The diffusion coefficients in the mixture agree with those of the pure compounds within 20% or better. Finally, a new adiabatic model of Uranus with an inner layer of almost pure ices is developed. The model is consistent with the gravity field data and results in a rather cold interior ($mathrm{T_{core}} mathtt{sim}$ 4000 K).
