A first detailed study of the ground state of the H _ { 3 } ^ { + } molecular ion in linear configuration , parallel to a magnetic field direction , and its low-lying \Sigma, \Pi, \Delta states is carried out for magnetic fields B = 0 - 4.414 \times 10 ^ { 13 } G in the Born-Oppenheimer approximation .
The variational method is employed with a single trial function which includes electronic correlation in the form \exp { ( \gamma r _ { 12 } ) } , 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 } 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 } G. Local stability of the linear parallel configuration with respect to possible small deviations is checked .