This paper investigates the impact of the increased reaction rate constant due to tunneling effects on planet-forming disks. Our aim is to quantify the astrophysical implications of atom tunneling for simple molecules that are frequently used to infer disk structure information or to define the initial conditions for planet (atmosphere) formation. We explain the tunneling effect on reaction rates by using a scholarly example in comparison to previous UMIST2012 rate constants. In a chemical network with 1299 reactions, we identify all reactions that could show atom tunneling. We devise a simple formulation of reaction rate constants that overestimates tunneling and screen a standard T Tauri disk model for changes in species abundances. For those reactions found to be relevant, we find values of the most recent literature for the rate constants including tunneling and compare the resulting disk chemistry to the standard disk models. The rate constants in the UMIST2012 database in many cases already capture tunneling effects implicitly. A rigorous screening procedure identified three neutral-neutral reactions where atom tunneling could change simple molecule abundances. However, by adopting recent values of the rate constants of these reactions and due to the layered structure of planet-forming disks, the effects are limited to a small region where cold neutral-neutral chemistry dominates. Abundances of water close to the midplane snowline can increase by a factor of two at most compared to previous results with UMIST2012 rates. Observables from the disk surface, such as high excitation (> 500 K) water line fluxes, decrease by 60% at most when tunneling effects are explicitly excluded. On the other hand, disk midplane quantities relevant for planet formation such as the C-to-O ratio and also the ice-to-rock ratio are clearly affected by these gas-phase tunneling effects.
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