  We study the electronic resonant states of H3 with energies above the
potential energy surface of the H3+ ground state. These resonant states are
important for the dissociative recombination of H3+ at higher collision
energies, and previous studies have indicated that these resonant states
exhibit a triple intersection. We introduce a complex generalization of the
pseudo-Jahn-Teller model to describe these resonant states. The potential
energies and the autoionization widths of the resonant states are computed with
electron scattering calculations using the complex Kohn variational method, and
the complex model parameters are extracted by a least-square fit to the
results. This treatment results in a non-Hermitian pseudo-Jahn-Teller
Hamiltonian describing the system. The non-adiabatic coupling and geometric
phase are further calculated and used to characterize the enriched topology of
the complex adiabatic potential energy surfaces.
