PHANGS-JWST: the largest extragalactic molecular cloud catalog traced by polycyclic aromatic hydrocarbon emission

High-resolution JWST images of nearby spiral galaxies reveal polycyclic aromatic hydrocarbon (PAH) emission structures that trace molecular gas, including CO-dark regions. We identify ISM cloud structures in PHANGS-JWST 7.7 $μ$m PAH maps for 66 galaxies, smoothed to 30 pc and at native resolution, extracting 108,466 and 146,040 clouds, respectively. Molecular properties were inferred using a linear conversion from PAH to CO. Given the tendency for clouds in galaxy centers to overlap in velocity space, we opted to flag these and omit them from the analysis in this work. The remaining clouds correspond to giant molecular clouds, such as those detected in CO(2-1) emission by ALMA, or lower surface density clouds that either fall below the ALMA detection limits of existing maps or genuinely have no molecular counterpart. Cross-matching with ALMA CO maps at 90 pc in 27 galaxies shows that 41 % of PAH clouds have CO associations. The converted molecular properties vary little across environments, but the most massive clouds are preferentially found in spiral arms. Fitting lognormal mass distributions down to $2\times10^{3} M_{\odot}$ shows that spiral arms host the highest-mass clouds, consistent with enhanced formation in arm gravitational potentials. Cloud molecular surface densities decline by a factor of $\sim 1.5-2$ toward $2 - 3 R_{e}$. However, the trend largely varies in individual galaxies, with flat, decreasing, and even no trend as a function of galactocentric radius. Factors like large-scale processes and morphologies might influence the observed trends. We publish two catalogs online, one at the common resolution of 30 pc and another at the native resolution. We expect them to have broad utility for future PAH clouds, molecular clouds, and star formation studies.