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Calculated with molecular force fields
For the vast majority of molecules, geometries were obtained through a two-stage optimization pipeline implemented in a custom Python script. Starting from SMILES notation, the script generates ~2,000 conformers using the Merck Molecular Force Field (MMFF94) [1] to broadly sample the conformational space. The top 10 lowest-energy conformers from this classical screening are then refined using density functional theory (DFT) at the ωB97X-D/def2-SVP level [2]. The lowest-energy DFT-optimized structure is selected as the final geometry. Atoms are rendered as spheres scaled to van der Waals radii [3], and bond orders correspond to the dominant resonance contributor as encoded in the input SMILES. Each model is visually verified against PubChem [4], exported as STL, and manually colored with the CPK convention in a slicer. Running on an Intel Core i7-14700T using all 20 cores, the pipeline averaged approximately 10 minutes per molecule.
For larger molecules that are not practical to treat with the full two-stage optimization, initial geometries were taken from publicly available experimental structural datasets obtained by X-ray diffraction, nuclear magnetic resonance spectroscopy, or cryogenic electron microscopy. If needed, hydrogen atoms were added according to local VSEPR and the resulting structure was relaxed with MMFF94 to place the added atoms in a low-energy geometry. The final geometry was then mapped onto the input SMILES representation so that connectivity and bond orders reflect the major resonance contributor before STL export.
X-ray diffraction (XRD) determines molecular structure by measuring how a crystal scatters an incident X-ray beam. The resulting diffraction pattern is used to calculate an electron-density map, from which atomic coordinates are refined. This method is especially effective for determining the three-dimensional arrangement of heavier atoms in a crystalline sample, although hydrogen positions are often less precise because hydrogen scatters X-rays weakly.
Nuclear magnetic resonance (NMR) spectroscopy infers molecular structure from the magnetic environments of nuclei placed in a strong magnetic field. Chemical shifts, spin-spin couplings, and nuclear Overhauser effects provide information about connectivity, local bonding, and distances between atoms. Because NMR measurements are commonly performed in solution, they can also describe conformational flexibility and the structures of molecules that do not readily form suitable crystals.
Cryogenic electron microscopy (cryo-EM) determines molecular structures from many images of particles that have been rapidly frozen in a thin layer of vitreous ice. Computational reconstruction combines these different views to generate a three-dimensional map of the molecule or molecular assembly. Cryo-EM is particularly valuable for studying large biomolecules and macromolecular complexes, including membrane proteins, because it does not require the formation of crystals. For example, membrane proteins can be examined while embedded in native membranes.
The initial conformational search relies on MMFF94, a well-established classical force field parameterized against high-level ab initio data for a broad range of organic and drug-like molecules [1]. MMFF94 describes the potential energy surface through analytical terms for bond stretching, angle bending, torsional rotation, van der Waals interactions, and electrostatics. Its parameters were derived by fitting to HF/6-31G* geometries and MP2-level energetics, which gives it reliable accuracy for conformer ranking at a fraction of the cost of quantum mechanical methods [5]. This makes it well suited for rapidly screening thousands of candidate geometries before passing a small subset to DFT refinement.
Final geometry optimizations are performed with the ωB97X-D functional [6] paired with the def2-SVP basis set [7], executed through the Psi4 electronic structure package [2]. ωB97X-D is a range-separated hybrid functional that includes an empirical dispersion correction, making it particularly effective for capturing both covalent bonding and non-covalent intramolecular interactions that influence molecular conformation. The def2-SVP basis set provides a balanced trade-off between computational cost and accuracy for geometry optimizations of this kind. This level of theory has been widely benchmarked and shown to produce reliable equilibrium geometries for organic molecules [8].