Computational study of non-conventional molecular topologies

Non-conventional topologies within the field of chemistry are molecules whose structure cannot be fully identified by chemical formula and connectivity. Knots are an example of this class of molecules. Particular emphasis has been given to the subclass of knots that can be represented on the surface of a torus, i.e. torus knots. Their study spans here three main branches: (1) Quantum Mechanical exploration using matrix formulation to study free particles tracing torus knots; (2) Molecular Dynamics (MD) investigations of synthetic and in silico knots with varying structures and chain lengths; (3) knot identification using a 3D Convolutional Neural Network (3D-CNN) classifier with a voxel-based molecular representation. Key contributions include the formulation of a matrix Hamiltonian for a particle on a torus knot, characterization of dynamic behavior via MD and principal component analysis, and examination of hydrogen-bond stability in knotted versus unknotted systems. A novel voxel-based molecular representation and a dataset for pretraining classifiers were developed to enhance machine learning applications in chemistry. Additionally, the KIMH Python package was created to facilitate the automated manipulation of knots in this field.