The third-order term Fpot(ρ)[ρq] Fpot(ρ)[ρq] above corresponds to the third-order energy in the structural expansion for electron systems. This energy plays an important role in the structural stability of metallic hydrogen 16 (Z= 1). This is because the kernel (10) has a strong wave-vector dependence, which cannot properly be treated in the square-gradient type theory. This brings a special stability of the structure in which as many equilateral triangles with q=3kF appear in the reciprocal lattice. It requires an anisotropic structure or a periodic modulation of the lattice for an atomic phase of hydrogen. Another possibility is to form a crystal with two ions in a unit cell (molecular phase). In any case, the atomic phase of bcc structure would not be realized just under the melting line as log as the third order term in Fc[ρq] does not suppress the effect. We shall investigate this problem numerically in the near future.
