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The maximum overlap method (MOM) provides a simple but powerful approach for performing calculations on excited states by targeting solutions with non-Aufbau occupations from a reference set of molecular orbitals. In this work, the MOM is used to access excited states of H 3 + and H 3 in strong magnetic fields. The lowest 1 A 1 ′ , 1 E ′ and 3 E ′ states of H 3 + in the absence of a field are compared with the corresponding states in strong magnetic fields. The changes in molecular structure in the presence of the field are examined by performing excited state geometry optimisations using the MOM. The 3 E ′ state is significantly stabilised by the field, becoming the ground state in strong fields with a preferred orientation perpendicular to the applied field. Its potential energy surface evolves from being repulsive to bound, with an equilateral equilibrium geometry. In contrast, the 1 A 1 ′ state is destabilised and its structure distorts to an isosceles form with the longest H−H bond parallel to the applied field. Comparisons are made with the 4 A 2 ′ state of H3, which also becomes bound with an equilateral geometry at high fields. The structures of the high-spin ground states are rationalised by orbital correlation diagrams constructed using constrained geometry optimisations. [ABSTRACT FROM AUTHOR]