Transferable Boltzmann Generator for Direct Air Capture

Screening metal–organic frameworks (MOFs) for direct air capture requires efficient estimation of dilute-limit CO${}_2$ adsorption. Conventional Widom insertion spends many energy evaluations on unfavorable configurations, limiting the scale of screening with machine-learned interatomic potentials (MLIPs). We introduce a transferable MOF-conditioned Boltzmann generator for estimating the Henry coefficient without per-material retraining. The model uses equivariant MOF features from a pretrained MLIP to construct a normalized proposal over CO${}_2$ position, orientation, and internal deformation, enabling importance-weighted estimation with flexible molecules. Periodically wrapped Gaussian position mixtures and conditional orientation and deformation mixtures support direct sampling and density evaluation, while MOF features are computed once and reused across draws. Across unseen MOFs spanning weak to strong adsorption, our model maintains high sampling efficiency and closely matches reference configuration and energy distributions after reweighting. It estimates flexible-gas Henry coefficients at roughly 700-fold lower inference cost than rigid-gas Widom insertion while capturing systematic effects of molecular deformation that additional rigid-gas sampling cannot recover.