Comparison of Molecular Mechanics with GPU-Accelerated, DFT-Accuracy Quantum Mechanical Optimization via Differentiable GFN1-xTB and GFN2-xTB Methods

Geometry optimization is the most critical initial step in computational chemistry. This study presents a GPU-accelerated geometry optimization workflow built upon dxtb, a fully differentiable PyTorch implementation of the semi-empirical GFN1-xTB method. The structural accuracy of the developed workflow was benchmarked against high-resolution X-ray crystal structures obtained from the Cambridge Structural Database (CSD), and compared with the MMFF94 force field and the GFN2-xTB method. For this purpose, a test set of 25 organic molecules representing distinct physical and chemical foundations was utilized: push-pull systems (p-nitroaniline), halogen-rich structures (hexachlorobenzene), rigid cage systems (cubane, adamantane, dodecahedrane, hexamethylenetetramine), flexible macrocyclic rings (18-crown-6), and polar disaccharides (sucrose). In the overall comparison based on heavy-atom RMSD values, GFN1-xTB exhibited the best mean performance (0.2686 Å), followed by MMFF94 (0.3119 Å) and GFN2-xTB (0.3818 Å). The superiority of GFN1-xTB is particularly pronounced in conjugated systems such as biphenyl, yielding a twofold increase in accuracy compared to MMFF94, and in highly flexible structures like cholesterol. Despite its more sophisticated electronic structure definition, GFN2-xTB lagged in mean RMSD, though it showed specific strengths in certain polycyclic and heteroaromatic systems; notably, its computational cost increased disproportionately for large molecules compared to GFN1-xTB. The results demonstrate that GFN1-xTB provides structural accuracy approaching the Density Functional Theory (DFT) level while significantly reducing computational costs compared to standard quantum mechanical methods. Although it may appear to lag behind MMFF94 in terms of absolute speed, GFN1-xTB offers highly practical utility for novel molecules, as it eliminates the need for predefined parameterization.