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Observations from Spitzer and ground-based infrared spectroscopy reveal significant diversity in the molecular emission from the inner few AU of T Tauri disks. We explore theoretically the possible origin of this diversity by expanding on our earlier thermal-chemical model of disk atmospheres. We consider how variations in grain settling, X-ray irradiation, accretion-related mechanical heating, and the oxygen-to-carbon ratio can affect the thermal and chemical properties of the atmosphere at 0.25-40 AU. We find that these model parameters can account for many properties of the detected molecular emission. The column density of the warm (200-2000K) molecular atmosphere is sensitive to grain settling and the efficiency of accretion-related heating, which may account, at least in part, for the large range in molecular emission fluxes that have been observed. The dependence of the atmospheric properties on the model parameters may also help to explain trends that have been reported in the literature between molecular emission strength and mid-infrared color, stellar accretion rate, and disk mass. We discuss whether some of the differences between our model results and the observations (e.g., for water) indicate a role for vertical transport and freeze-out in the disk midplane. We also discuss how planetesimal formation in the outer disk (beyond the snowline) may imprint a chemical signature on the inner few AU of the disk and speculate on possible observational tracers of this process.
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