Emission from the molecular ion H is a powerful diagnostic of the upper atmosphere of Jupiter, Saturn, and Uranus, but it remains undetected at Neptune. In search of this emission, we present near-infrared spectral observations of Neptune between 3.93 and 4.00 m taken with the newly commissioned iSHELL instrument on the NASA Infrared Telescope Facility in Hawaii, obtained 17-20 August 2017. We spent 15.4 h integrating across the disk of the planet, yet were unable to unambiguously identify any H line emissions. Assuming a temperature of 550 K, we derive an upper limit on the column integrated density of m, which is an improvement of 30% on the best previous observational constraint. This result means that models are over-estimating the density by at least a factor of 5, highlighting the need for renewed modelling efforts. A potential solution is strong vertical mixing of polyatomic neutral species from Neptune’s upper stratosphere to the thermosphere, reacting with H, thus greatly reducing the column integrated H densities. This upper limit also provide constraints on future attempts at detecting H using the James Webb Space Telescope.

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