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Nitrogen fertilizer delivery inefficiencies limit crop productivity and contribute to environmental pollution. Herein, we developed Zn- and Fe-doped hydroxyapatite nanomaterials (ZnHAU, FeHAU) loaded with urea (∼26% N) through hydrogen bonding and metal-ligand interactions. The nanomaterials attach to the leaf epidermal cuticle and localize in the apoplast of leaf epidermal cells, triggering a slow N release at acidic conditions (pH 5.8) that promote wheat (Triticum aestivum) growth and increased N uptake compared to conventional urea fertilizers. ZnHAU and FeHAU exhibited prolonged N release compared to urea in model plant apoplast fluid pH in vitro (up to 2 days) and in leaf membranes in plants (up to 10 days) with a high N retention (32% to 53%) under simulated high rainfall events (50 mm). Foliar N delivery doses of up to 4% as ZnHAU and FeHAU did not induce toxicity in plant cells. The foliar-applied ZnHAU and FeHAU enhanced fresh and dry biomass by ∼214% and ∼161%, and N uptake by ∼108% compared to foliar-applied urea under low soil N conditions in greenhouse experiments. Controlled N release by leaf-attached nanomaterials improves N delivery and use efficiency in crop plants, creating nanofertilizers with reduced environmental impact. 

We present a method for calculating first-order response properties in phaseless auxiliary field quantum Monte Carlo by applying automatic differentiation (AD). Biases and statistical efficiency of the resulting estimators are discussed. Our approach demonstrates that AD enables the calculation of reduced density matrices with the same computational cost scaling per sample as energy calculations, accompanied by a cost prefactor of less than four in our numerical calculations. We investigate the role of self-consistency and trial orbital choice in property calculations. We find that orbitals obtained using density functional theory perform well for the dipole moments of selected molecules compared to those optimized self-consistently.