Comparative Analysis of GFN Methods in Geometry Optimization of Small Organic Semiconductor Molecules: A DFT Benchmarking Study

Abstract: This study benchmarks the GFN family of semiempirical methods (GFN1-xTB, GFN2-xTB, GFN0-xTB, and GFN-FF) against density functional theory (DFT) for the evaluation of optimized molecular geometries and electronic properties of small organic semiconductor molecules. This work offers a systematic assessment of these computationally efficient quantum chemical methods and their accuracy-cost profiles when applied to a challenging class of systems, characterized, for instance, by extended $\pi$-conjugation, conformational flexibility, and sensitivity of properties to subtle structural changes. Two datasets are evaluated: a QM9-derived subset of small organic molecules and the Harvard Clean Energy Project (CEP) database of extended $\pi$-systems relevant to organic photovoltaics. Structural agreement is quantified using heavy-atom RMSD, equilibrium rotational constants, bond lengths, and angles, while electronic property prediction is assessed via HOMO-LUMO energy gaps. Computational efficiency is assessed via CPU time and scaling behavior. GFN1-xTB and GFN2-xTB demonstrate the highest structural fidelity, while GFN-FF offers an optimal balance between accuracy and speed, particularly for larger systems. The results indicate that GFN-based methods are suitable for high-throughput molecular screening of small organic semiconductors, with the choice of method depending on accuracy-cost trade-offs. The findings support the deployment of GFN approaches in computational pipelines for the discovery of organic electronics and materials, providing information on their strengths and limitations relative to established DFT methods.