Despite years of effort, behaviors of materials under extreme conditions, such as those in the deep Earth and planets, are still not well understood. One of the goals of our Post-K Exploratory Challenge Project “Frontiers of Basic Science: Challenging the Limits” is to establish the knowledge of materials science to understand the history of the Earth and planets from birth to death in terms of their materials properties predicted with the first principles molecular dynamics simulations on the Post-K computer, a Japanese future flagship supercomputer candidate, in cooperation with researchers of high pressure science, earth sciences and computer science.

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In this article, recent progresses of the existence of hydrous materials in the Earth's interiors were reviewed. Based on those knowledge, the possible ways to quantify the amount of water in the Earth using the first-principles calculations combined with the high performance computation are discussed.

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In this article, we introduce our linear-scaling first-principles calculation code CONQUEST, which enables us to carry out density functional theory (DFT) calculations on very large systems, of up to millions of atoms. The code uses localized basis sets and linear-scaling (or O(N)) methods, and has high parallel efficiency on large supercomputers like the K computer in Kobe. The code should be a powerful tool for the study of structural and physical properties of materials in the earth's deep interior, and the prospects for this application are discussed.

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The physical properties of silicate liquids show peculiar behaviors under pressure. Shear viscosities of acidic silicate liquids decrease with increasing pressure although that of basic silicate liquids increase. Moreover, the anomalies in compression curves also have been reported. These experimental results indicate that the silicate liquids have several types of characteristic structure in composition/pressure plane. The molecular dynamics simulation is an appropriate method for investigating response of static/dynamic properties of the silicate liquids vs. pressure and composition because it provides the trajectories of the all atoms in simulation cell. Moreover, the first-principles molecular dynamics simulation is more suitable method because the forces are calculated from electronic structure. It enables us to simulate the extreme situation, such as bond exchanging event in liquid, without empirical factor. However, the strong finite size effect does not allow the application of first-principles molecular dynamics simulations because of its heavy calculation cost, because the system composed of at least 10⁴ atoms is required in order to obtain the reliable physical properties. Consequently, the development of linear-scaling first-principles molecular dynamics simulation codes is necessary for the advance of theoretical study of silicate liquids.

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In this article, we review a series of first-principles studies of phase transitions in earth/planet-forming materials under ultrahigh pressure which corresponds to deep interiors of super-Earths and is difficult to be achieved by diamond-anvil-cell experiments. As examples, we discuss dissociations of MgSiO₃ post-perovskite and novel crystalline phases of SiO₂ and Al₂O₃ under ultrahigh pressures. The methods shown in this article are general and can be applied to any structural phase transitions.

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Recently, superconductivity at 203 K was discovered in hydrogen sulfide at 155 GPa, and similar superconductivity has been expected in other hydrogen compounds. Computational predictions are useful for the study on crystal structure and superconductivity of hydrogen compounds under high-pressure. In this paper, we explain the background of the 203 K superconductivity discovery referring previous theoretical and experimental studies, and introduce our recent results on the superconductivity of sulfur-hydrogen and argon-hydrogen systems predicted by first-principles electronic structure calculations and evolutionary techniques for crystal structure search.

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