Context. In diffuse interstellar clouds, the excitation temperature derived from the lowest levels of H₃⁺ is systematically lower than that derived from H₂. The differences may be attributed to the lack of state-specific formation and destruction rates of H₃⁺, which are needed to thermalize the two species. Aims. In this work, we aim to investigate the possible influence of rotational excitation collisions of H₃⁺ with atomic hydrogen on its excitation temperature. Methods. We used a time-independent close-coupling method to calculate the state-to-state rate coefficients, incorporating a very accurate and full-dimensional potential energy surface recently developed for H₄⁺. We take a symmetric top approach to describe a frozen H₃⁺ as an equilateral triangle. Results. We derive rotational excitation collision rate coefficients of H₃⁺ with atomic hydrogen in a temperature range corresponding to diffuse interstellar conditions up to (J, K, ±) = (7, 6, +) and (J, K, ±) = (6, 4, +) for its ortho and para forms. This allows us to obtain a consistent set of collisional excitation rate coefficients and to improve on a previous study that included speculations regarding these contributions. Conclusions. The new state-specific inelastic H₃⁺ + H rate coefficients yield differences of up to 20% in the excitation temperature, and their impact increases with decreasing molecular fraction. We also confirm the impact of chemical state-to-state destruction reactions on the excitation balance of H₃⁺, and that reactive H + H₃⁺ collisions are also needed to account for possible further ortho to para transitions.

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