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In this study, we analyzed the pressure-volume ($P-V$) relationship of elements using the equation of state at an ambient temperature within the multi-megabar pressure range of 200-300 GPa. We investigated the compressibility of elements under ultra-high pressures based on their positions in the periodic table. For the elemental materials in this region, pressure ($P$) can be approximated as an $N$-order function of volume ($V$): $P$ $\propto$ $1/V^N$. By determining the $N$ value, we can evaluate the contribution of the volume change to the total energy of the system. The $N$ value is also an indicator the bulk modulus in this pressure range and shows periodicity with increasing atomic number, and shows significant values in the range of 4.5-6, for transition metals with close-packed structures (fcc, hcp). This suggests that the total energy of these elements increases rapidly as volume decreases. Furthermore, the current results provide basic data for understanding the compressibility of elemental materials under extreme ultra high-pressure conditions based on the quantum theory of solids.

We introduce new type of ferromagnets, CaN and SrN, which were designed using first-principles calculations. These are half-metallic ferromagnets and they have magnetic moments of 1 $\mu_{\rm B}$ per chemical formula unit. Out of the typical structures of binary compounds, the rock-salt structure is the most stable form for both CaN and SrN. The majority of the magnetic moment of these compound originates from the N sites since the $p$ states of N are spin-polarized. Their formation energies were calculated and the results show that it should be feasible to synthesize these materials. The structural stability of CaN was confirmed by performing first-principles molecular dynamics simulations. We propose a synthesis process for CaN basd on the first-principles., Comment: 5 pages,5 figures

Existence of ferromagnetism in bulk calcium compounds is discovered theoretically. First-principles calculations of calcium phosphide, calcium arsenide and calcium antimonide in the zinc-blende structure have been performed to show the half-metallic ground state in each optimized stable structure. Magnetism comes from spin-polarization of electrons in $p$-orbitals of P, As or Sb and $d$-orbitals of calcium atoms. The half-metallicity is analogous to the half-metallic zinc-blende compounds, {\it e.g.} CrAs or CrSb, but the predicted compounds become ferromagnetic without transition metals. In (In$_{1-x}$Ca$_x$)Sb, the magnetism remains to be stable in a range of the doping rate ($x>0.8$).

Parallelism of tight-binding molecular dynamics simulations is presented by means of the order-N electronic structure theory with the Wannier states, recently developed (J. Phys. Soc. Jpn. 69,3773 (2000)). An application is tested for silicon nanocrystals of more than millions atoms with the transferable tight-binding Hamiltonian. The efficiency of parallelism is perfect, 98.8 %, and the method is the most suitable to parallel computation. The elapse time for a system of $2\times 10^6$ atoms is 3.0 minutes by a computer system of 64 processors of SGI Origin 3800. The calculated results are in good agreement with the results of the exact diagonalization, with an error of 2 % for the lattice constant and errors less than 10 % for elastic constants., Comment: 5 pages, 3 figures