HERO (Hessian-Engineered Relaxation Optimizer): Suppressing “Hessian Pollution” for Accelerated First-Principles Structural Relaxation

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).