Moment of inertia as a simple shape descriptor for diffusion-based shape-constrained molecular generation

Abstract

The article introduces MLConformerGenerator, a machine-learning framework for shape-constrained molecular generation that combines an Equivariant Diffusion Model (EDM), guided by a compact shape descriptor based on the principal components of the moment of inertia tensor, and a Graph Convolutional Network (GCN) model for bond prediction. The compact yet informative descriptor provides concise representation of molecular shape, enabling scalable learning from large datasets and synthetic conformers generated from 2D molecular inputs. The use of a GCN for bond prediction is evaluated in comparison to deterministic methods. The suggested approach provides an ability to fine-tune the model to generate datasets with chemical-feature distributions closely matching those of target datasets of real conformers. The proposed model supports generation conditioned on both explicit conformers and arbitrary shapes, offering flexibility for applications such as dataset augmentation and structure-based molecule design. Trained on over 1.6 million molecules, the model demonstrates the ability to generate chemically valid, structurally diverse molecules that conform to target shape constraints. It achieves an average shape similarity of 0.53 to a reference conformer, with peak similarity exceeding 0.9 - a performance comparable to that of analogous models relying on more complex descriptors. The results show that integrating physically grounded descriptors with modern generative architectures provides a robust and effective strategy for shape-constrained molecular design.