The 1A1′,3E′,1E′,3A1′,1A2′,3A2′ representing the ground and the five excited states, which have the common character of being symmetrical with respect to reflection on the plane of the equilateral triangular H3+ molecule, are determined by an original three center wave function constructed by the use of the irreducible representations of the D3h point group. In contrast to past large one center or linear combinations of atomic orbitals functions, our model has the advantage of being well adapted to all internuclear distances, with limited number of basis functions including the electron-electron term. Our functions satisfy, by their nature, the triangular geometry of the molecule and thus permit the study the asymptotic behavior of the potential energy curves of the fundamental and excited levels for which, new experimental and theoretical results are needed to confirm astronomical observations. The results of this work and the implementation of the computational techniques employed opens the way to further studies on complex three center systems. © 2020 Elsevier B.V.