  We present a synergic study of protoplanetary disks to investigate links
between inner disk gas molecules and the large-scale migration of solid
pebbles. The sample includes 63 disks where two types of measurements are
available: i) spatially-resolved disk images revealing the radial distribution
of disk pebbles (mm-cm dust grains), from millimeter observations with ALMA or
the SMA, and ii) infrared molecular emission spectra as observed with Spitzer.
The line flux ratios of H2O with HCN, C2H2, and CO2 all anti-correlate with the
dust disk radius R$_{dust}$, expanding previous results found by Najita et al.
(2013) for HCN/H2O and the dust disk mass. By normalization with the dependence
on accretion luminosity common to all molecules, only the H2O luminosity
maintains a detectable anti-correlation with disk radius, suggesting that the
strongest underlying relation is between H2O and R$_{dust}$. If R$_{dust}$ is
set by large-scale pebble drift, and if molecular luminosities trace the
elemental budgets of inner disk warm gas, these results can be naturally
explained with scenarios where the inner disk chemistry is fed by sublimation
of oxygen-rich icy pebbles migrating inward from the outer disk.
Anti-correlations are also detected between all molecular luminosities and the
infrared index n$_{13-30}$, which is sensitive to the presence and size of an
inner disk dust cavity. Overall, these relations suggest a physical
interconnection between dust and gas evolution both locally and across disk
scales. We discuss fundamental predictions to test this interpretation and
study the interplay between pebble drift, inner disk depletion, and the
chemistry of planet-forming material.
