Structural optimization is a fundamental step in density functional theory (DFT) calculations, typically driven by the Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimizer. However, the standard BFGS algorithm relies on a local quadratic approximation of the potential energy surface (PES), which frequently breaks down in highly non-quadratic regimes typical of complex surface adsorption systems and defective bulk materials. This breakdown leads to “Hessian pollution”, a phenomenon where higher-order anharmonicities introduce spurious off-diagonal inter-atomic couplings that distort curvature estimates and significantly stall convergence. Herein, we propose a physics-inspired algorithmic intervention to the BFGS method that systematically suppresses this pollution. Once the maximum residual force drops below a specific activation threshold (e.g., 0.5 or 0.1 eV/Å), our approach conditionally resets all off-diagonal Hessian blocks, and introduces an isotropic background stiffness strategy where these blocks can be repopulated with a small positive constant rather than zeroed completely. This balances the robust stability of diagonal dominance with accelerated convergence speed. Implemented as an add-on to the Atomic Simulation Environment (ASE) Library, the method is lightweight, transferable, and compatible with standard DFT codes. Tests across diverse chemical systems, including atomic and molecular adsorbates (O*, H*, CO*) on Pt(111) surfaces and defective bulk oxides (WO_3–x), demonstrate substantial reductions in the number of required force calls without biasing the final optimized geometry. It offers a practical tool for high-throughput DFT workflows that eliminates the need for domain-specific training. This method is available via our open-source package, Hessian-Engineered Relaxation Optimizer (HERO).

NO oxidation with H₂O₂ as the oxidant is a promising green denitration technology. However, the current metal oxide catalysts still have many disadvantages for this reaction, such as insufficient catalytic activity for H₂O₂ activation, poor selectivity, and low stability. In this study, we employ atomically dispersed Co anchored on SBA-15 with Co-O₄ structure for NO oxidation, which achieves a 90% removal efficiency of NO under low molar ratio of H₂O₂ to NO (1.56), ultra-low temperature (80 °C), and ultra-high space velocity (720,000 h^–1), representing the top-level performance among previously reported catalysts. More interestingly, our work reveals that by taking advantage of the uniform Co-O₄ structure, H₂O₂ is mainly directionally converted into ·O₂^– at the Co-O₄ site, and ·O₂^– plays a key role for achieving the deep-oxidation of NO to produce NO₃^–, which is contrast to the previously reports that ¹O₂ is the main free radical for NO oxidation. This study highlights the great potentials of single-atom catalysts for improving the H₂O₂ utilization performance for NO oxidation.