  The OI 777 nm triplet is a key diagnostic of oxygen abundances in the
atmospheres of FGK-type stars; however it is sensitive to departures from local
thermodynamic equilibrium (LTE). The accuracy of non-LTE line formation
calculations has hitherto been limited by errors in the inelastic O+H
collisional rate coefficients: several recent studies have used the so-called
Drawin recipe, albeit with a correction factor $\mathrm{S_{H}}$ that is
calibrated to the solar centre-to-limb variation of the triplet. We present a
new model oxygen atom that incorporates inelastic O+H collisional rate
coefficients using an asymptotic two-electron model based on linear
combinations of atomic orbitals, combined with a free electron model, based on
the impulse approximation. Using a 3D hydrodynamic stagger model solar
atmosphere and 3D non-LTE line formation calculations, we demonstrate that this
physically-motivated approach is able to reproduce the solar centre-to-limb
variation of the triplet to 0.02 dex, without any calibration of the inelastic
collisional rate coefficients or other free parameters. We infer
$\log\epsilon_{\mathrm{O}}=8.69\pm0.03$ from the triplet alone, strengthening
the case for a low solar oxygen abundance.
