MolNet_Equi: A Chemically Intuitive, Rotation-Equivariant Graph Neural Network

Although deep-learning (DL) models suggest unprecedented prediction capabilities in tackling various chemical problems, their demonstrated tasks have so far been limited to the scalar properties including the magnitude of vectorial properties, such as molecular dipole moments. A rotation-equivariant MolNet_Equi model, proposed in this paper, understands and recognizes the molecular rotation in the 3D Euclidean space, and exhibits the ability to predict directional dipole moments in the rotation-sensitive mode, as well as showing superior performance for the prediction of scalar properties. Three consecutive operations of molecular rotation RM ${\left(R\left(M\right)\right)}$, dipole-moment prediction phi mu RM ${\left({\phi{} }_{\mu }\left(R\left(M\right)\right)\right)}$, and dipole-moment inverse-rotation R-1 phi mu RM ${\left({R}<^>{-1}\left({\phi{} }_{\mu }\left(R\left(M\right)\right)\right)\right)}$ do not alter the original prediction of the total dipole moment of a molecule phi mu M ${\left({\phi{} }_{\mu }\right(M\left)\right)}$, assuring the rotational equivariance of MolNet_Equi. Furthermore, MolNet_Equi faithfully predicts the absolute direction of dipole moments given molecular poses, albeit the model has been trained only with the information on dipole-moment magnitudes, not directions. This work highlights the potential of incorporating fundamental yet crucial chemical rules and concepts into DL models, leading to the development of chemically intuitive models. The MolNet_Equi deep-learning model accurately captures rotational changes in the dipole-moment direction, closely matching the results of DFT calculation. Notably, MolNet_Equi achieves the high level of accuracy for both magnitude and direction despite being trained solely on dipole-moment magnitudes.image