Description du sujet de thèse

This multidisciplinary project, combining theoretical chemistry and computer science, focuses on non-covalent interactions known as "sigma holes." These occur when an atom, such as a halogen or chalcogen, exhibits an electron-deficient region, which is the "sigma hole." This region can interact with electron-rich species, thereby influencing the stabilization of molecular and crystalline structures. Such interactions are crucial in biochemistry, materials engineering, and catalysis.
Predicting the stability of the complex formed between an electron-deficient species (an "electrophile") and an electron-rich one (a "nucleophile") is a major challenge in optimizing supramolecular structures. The commonly employed approach relies on studying the intrinsic properties of each reactant. Indeed, it has been experimentally shown (Mayr-Patz scale) that reaction rates can be expressed as a function of parameters characteristic of each independent entity. Generally, these are calculated from the lowest energy structures. However, this approach does not account for the dynamic behavior of each partner induced by temperature, which cannot be neglected.
Molecular dynamics can be simulated using quantum chemistry calculations, but these are unfortunately very resource-intensive, limiting their application to small sets of small molecules. A relatively recent development involves using machine learning, specifically deep learning, to efficiently approximate energy calculations, thereby rapidly inferring molecular dynamics. This thesis aims to address this problem and is thus situated at the intersection of theoretical chemistry and machine learning.
A classic approach to applying deep learning in chemistry is to use a molecular graph, where vertices correspond to atoms and edges represent bonds (single, double, triple, aromatic) between atoms. Atoms are typically described by their type without using coordinates. This type of deep learning application cannot intrinsically account for the evolving positions of atoms and, therefore, the dynamics of the molecule. Constraints and Advancements in Deep Learning for Molecular Dynamics
The use of deep learning for dynamic calculation of molecular properties must also address several constraints. It must be equivariant to rotations and invariant to translations that define molecular coordinates. Applying symmetry to the molecule must also produce an equivariant result. Finally, since the order of vertices is arbitrary, the network must be equivariant to this order. It's also important to note that molecular dynamics calculations are performed using the derivatives of molecular energy. A network calculating this energy must therefore provide a twice-differentiable result, which prohibits the use of non-C1 functions like the ReLU function.
These constraints have led to the development of convolutional networks very different from those typically used in chemoinformatics. The convolution operation involves considering, at each iteration, a dynamic graph connecting each atom to all its neighbors located within a certain distance threshold (between 10 and 30 Å). Since these interatomic interactions must be invariant to rotations, many authors initially used only the actual distance between atoms. This results in a general scheme where, after embedding the atoms (encoding the type and coordinates of each atom), a set of interaction modules is applied with residual connections. Weight matrices allow for weighting updates based on these distances. The energy of each atom is then estimated before summing the contributions of all atoms to get an estimate of the molecule's overall energy.
This scheme is reductionist for several reasons: 1) the sole use of distance (a real value) does not allow for accounting for the relative position of atoms. This point has been partially corrected by DimNet and then by GemNet, 2) restricting interactions to a certain threshold is a simplification. This point was noted quite early, as, for example, PhysNET proposes a correction to the energy estimation based on non-local interactions between atoms. However, this correction is applied a posteriori. A more interesting approach is proposed by SpookyNet, which introduces non-local interactions directly into the interaction module, 3) the initialization of atom embedding with their types and positions does not account for the electronic properties of the atoms. This limitation is significant in our case for predicting molecular electronic properties such as sigma holes.

Contexte de travail

The work we are going to undertake will begin with a benchmarking of existing models, prioritizing approaches that use angular functions at least to the first order (see DimNet), as they appear fundamental for effectively predicting reactivity descriptors. Furthermore, the models will necessarily incorporate the electronic properties of atoms into their input data. This follows the work of the theoretical chemistry team, who have precisely identified the relevant quantum descriptors for studying these types of interactions and have implemented them in the reference software, AMS. These modifications will be accompanied by an evaluation of the obtained model's complexity to ensure one of the primary qualities of the machine learning approach: a computation time compatible with processing large datasets. Finally, to achieve practical applications, a collaboration is planned with Dr. Robin Weiss's team (Junior Professor Chair, integrating the new UMR CARMeN in January 2025 in Caen), who specializes in the synthesis and physicochemical characterization of sigma holes. This collaboration should enable the development of new systems of societal interest. This synergy will also be strengthened by the fact that both the Rouen and Caen teams are members of the GDR sigma-hole.

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