ETKDG

The computational process of generating a diverse set of low-energy three-dimensional structures for a molecule by rotating its torsional bonds to sample the potential energy surface. The goal is to produce an ensemble that contains the bioactive conformation—the shape a molecule adopts when binding to a protein target.

• Systematic search: Enumerates all torsion combinations at fixed increments (combinatorial explosion limits this to small molecules)
• Stochastic search: Randomly perturbs torsions and minimizes, as used in OMEGA and ConfGen
• Distance geometry: Randomly samples distance bounds matrices then embeds 3D coordinates, the foundation of ETKDG
• Molecular dynamics: Simulates physical motion at temperature to overcome rotational barriers

A curated database of torsional angle preferences extracted from experimentally determined small-molecule crystal structures, typically from the Cambridge Structural Database (CSD) or Protein Data Bank (PDB). ETKDG uses these libraries to bias conformer generation toward physically realistic geometries rather than purely random rotations.

• Each rotatable bond type is assigned a probability distribution over its dihedral angle range
• Common patterns include sp³-sp³ bonds (staggered conformations preferred) and sp²-sp² bonds (planar with cis/trans preferences)
• The CSD torsion library contains millions of fragments, binned by SMARTS patterns
• ETKDG applies these as knowledge-based potentials during the distance bounds smoothing phase

A standard metric for quantifying the structural similarity between two superimposed atomic coordinates, calculated as the square root of the average squared distance between corresponding atoms. In conformer generation, RMSD is used to prune duplicate conformers and to evaluate how well generated structures reproduce experimental geometries.

• Heavy-atom RMSD: Only non-hydrogen atoms are considered, the most common variant
• A threshold of 0.5–1.0 Å is typically used to define conformational uniqueness
• Minimum RMSD across an ensemble measures coverage of the bioactive conformation
• Symmetry-corrected RMSD accounts for topologically equivalent atoms (e.g., phenyl ring flips)

A mathematical framework for generating 3D coordinates from an incomplete set of interatomic distance constraints. The algorithm creates a random distance matrix that satisfies upper and lower bounds derived from covalent connectivity and van der Waals radii, then embeds it into Cartesian space using metric matrix decomposition.

• Bound smoothing: The triangle inequality is applied iteratively to tighten distance bounds before sampling
• Embedding: The distance matrix is converted to a metric matrix, and the three largest eigenvalues yield the 3D coordinates
• ETKDG extends classical distance geometry by replacing random torsional sampling with knowledge-based torsion angle preferences
• Implemented in RDKit as the EmbedMolecule function with ETKDG or ETKDGv2 parameters

A critical refinement in ETKDGv2 that adjusts torsion angle preferences for bonds contained within small rings (3- to 5-membered rings). Standard torsion libraries derived from acyclic fragments fail for ring systems because the cyclic geometry imposes additional angular constraints not present in open-chain analogues.

• Cyclopropane, cyclobutane, and cyclopentane rings each have distinct puckering preferences
• ETKDGv2 applies ring-specific torsion potentials parameterized from crystallographic data
• Without these corrections, small rings often adopt physically impossible planar geometries
• The correction also handles fused ring systems and spiro compounds where multiple rings share atoms