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While exploring potential superconductors in the C-S-H ternary system using first-principles crystal structure prediction methods, we uncovered a class of hydride perovskites based on the intercalation of methane into an ${\mathrm{H}}_{3}\mathrm{S}$ framework. These intriguing ${\mathrm{H}}_{3}\mathrm{S}\text{\ensuremath{-}}{\mathrm{CH}}_{4}$ structures emerge as metastable at $\ensuremath{\sim}100$ GPa. Electron-phonon coupling calculations indicate that phases with ${\mathrm{CSH}}_{7}$ stoichiometry are potential superconductors with ${T}_{c}$ values ranging from 100 K to 190 K at megabar pressures. The results are expected to guide the experimental search for new high-${T}_{c}$ superconductors, including those stable at lower pressures than previously documented superconducting hydrides such as ${\mathrm{H}}_{3}\mathrm{S}$ and ${\mathrm{LaH}}_{10}$.

A framework for computing the anharmonic free energy (FE) of metallic crystals using Born-Oppenheimer ab initio molecular dynamics (AIMD) simulation, with unprecedented efficiency, is introduced and demonstrated for the hcp phase of iron at extreme conditions (up to $\ensuremath{\approx}290$ GPa and 5000 K). The advances underlying this work are: (1) A recently introduced harmonically-mapped averaging temperature integration (HMA-TI) method that reduces the computational cost by order(s) of magnitude compared to the conventional TI approach. The TI path starts from zero Kelvin, where it assumes the behavior is given exactly by a harmonic treatment; this feature restricts application to systems that have no imaginary phonons in this limit. (2) A Langevin thermostat with the HMA-TI method that allows the use of a relatively large MD time step (4 fs, which is about eight times larger than the size needed for the Andersen thermostat) without loss of accuracy. (3) AIMD sampling is accelerated by using density functional theory (DFT) with a low-level parameter set, then the measured quantities of selected configurations are robustly reweighted to a higher level of DFT. This introduces a speedup of about 20--$30\ifmmode\times\else\texttimes\fi{}$ compared to directly simulating the accurate system. (4a) The temperature ($T$) dependence of the hcp equilibrium shape (i.e., $c/a$ axial ratio) is determined (including anharmonicity), with uncertainty less than $\ifmmode\pm\else\textpm\fi{}0.001$. (4b) Electronic excitation is included through Mermin's finite-temperature extension of the $T=0$ K DFT. A simple FE perturbation method is introduced to handle the difficulty associated with applying the TI method with a $T$-dependent geometry and (due to electronic excitation) potential-energy surface. (5) The FE in the thermodynamic limit is attained through extrapolation of only the (computationally inexpensive) quasiharmonic FE, because the anharmonic FE contribution has negligible finite-size effects. All methods introduced here do not affect the AIMD sampling---results are obtained through post-processing---so established AIMD codes can be employed without modification. Analytical formulas fitted to the results for the variation of the equilibrium $c/a$ ratio and FE components with $T$ are provided. Notably, effects of magnetic excitations are not included and may yet prove important to the overall FE; if so, it is plausible that such contributions can be added perturbatively to the FE values reported here. Notwithstanding these considerations, FE values are obtained with an estimated accuracy and precision of 2 meV/atom, suggesting that the capability to compute the phase diagram of iron at Earth's inner core conditions is within reach.

Density functional theory calculations using the quasiharmonic approximation have been used to calculate the solid Hugoniot of two polytypes of boron carbide up to 100 GPa. Under the assumption that segregation into the elemental phases occurs around the pressure that the ${\mathrm{B}}_{11}{\mathrm{C}}_{\text{p}}$(CBC) polytype becomes thermodynamically unstable with respect to boron and carbon, two discontinuities in the Hugoniot, one at 50 GPa and one at 90--100 GPa, are predicted. The former is a result of phase segregation, and the latter a phase transition within boron. First-principles molecular dynamics (FPMD) simulations were employed to calculate the liquid Hugoniot of ${\mathrm{B}}_{4}\mathrm{C}$ up to 1.5 TPa, and the results are compared to recent experiments carried out at the Omega Laser Facility up to 700 GPa [D. E. Fratanduono, Phys. Rev. B 94, 184107 (2016)]. A generally good agreement between theory and experiment was observed. Analysis of the FPMD simulations provides evidence for an amorphous, but covalently bound, fluid below 438 GPa, and an atomistic fluid at higher pressures and temperatures.

A equation of state (EOS) experimental technique that enables the study of thermodynamic derivatives into the TPa regime is described and applied to boron carbide (${\mathrm{B}}_{4}\mathrm{C}$). Data presented here are principal Hugoniot sound speed measurements reported using a laser-driven shock platform, providing a means to explore the high-pressure off-Hugoniot response of opaque materials. The extended ${\mathrm{B}}_{4}\mathrm{C}$ Hugoniot suggests the presence of a high-pressure phase, as recently predicted by molecular dynamics simulations, adding to the complexity of the existing phase diagram.

The structure and cooperative proton ordering of two-dimensional sheets of croconic acid were studied with scanning tunneling microscopy and first-principles calculations. Unlike in the crystalline form, which exhibits a pleated, densely packed polar sheet structure, the confinement of the molecules to the surface results in hydrogen-bonded chiral clusters and networks. First-principles calculations suggest that the surface stabilizes networks of configurational isomers, which arise from direct hydrogen transfer between their constituent croconic acid monomers. Some of these configurations have a net polarization. It is demonstrated through constrained molecular dynamics simulations that simultaneous proton transfer between any two molecules can occur spontaneously. This finding is a prerequisite for the occurrence of in-plane ferroelectricity based on proton transfer in 2D sheets.