Hydrogen molecules and chains in a superstrong magnetic field

We study the electronic structures of hydrogen polymolecules ${\mathrm{H}}_{\mathit{n}}$ (n=2,3,4,. . .) in a superstrong magnetic field (B\ensuremath{\gtrsim}${10}^{12}$ G) typically found on the surface of a neutron star. Simple analytical scaling relations for several limiting cases (e.g., large n, high B field) are derived. We numerically calculate the binding energies of ${\mathrm{H}}_{\mathit{n}}$ molecules for various magnetic-field strengths. For n=2,3,4 we employ a Hartree-Fock method to determine the ground-state structure of the molecule in the Born-Oppenheimer approximation. For n=\ensuremath{\infty} (a bound infinite chain) we use a variational method. For a given magnetic-field strength, the binding energy per atom in the ${\mathrm{H}}_{\mathit{n}}$ molecule is found to approach a constant value as n increases. For typical field strengths of interest, energy saturation is essentially achieved once n exceeds 3 to 4. We also consider the structure of negative H ions in a high magnetic field. For B\ensuremath{\sim}${10}^{12}$ G the dissociation energy of an atom in a hydrogen chain and the ionization potential of ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ are smaller than the ionization potential of neutral atomic hydrogen.