A detailed study of the ground state of the $\mathrm{H}_3{}^{+}$ molecular ion in linear configuration, parallel to the magnetic field direction, and its low-lying $\Sigma$, $\Pi$, and $\Delta$ states is carried out for magnetic fields $B=0–4.414\times {10}^{13}\mathrm{G}$ in the Born-Oppenheimer approximation. The variational method is employed with a single trial function which includes electronic correlation in the form $\exp \left(\gamma r_{12}\right)$, where $\gamma$ is a variational parameter. It is shown that the quantum numbers of the state of the lowest total energy (ground state) depend on the magnetic field strength. The ground state evolves from the spin-singlet ${}^1\Sigma _g$ state for weak magnetic fields $B\lesssim 5\times {10}^8\mathrm{G}$ to a weakly bound spin-triplet ${}^3\Sigma _u$ state for intermediate fields and, eventually, to a spin-triplet ${}^3\Pi _u$ state for $5\times {10}^{10}\lesssim B\lesssim 4.414\times {10}^{13}\mathrm{G}$. Local stability of the linear parallel configuration with respect to possible small deviations is checked.

• Received 24 February 2007

DOI:https://doi.org/10.1103/PhysRevA.75.053408