SE(3)-equivariant prediction of molecular wavefunctions and electronic densities

which describes the physical laws underlying the interactions between nuclei and electrons. Here, Ĥel is the electronic Hamiltonian operator which describes effects due to the kinetic energy of the electrons, the interactions between electrons and nuclei, as well as the inter-electronic interactions. The wavefunction Ψel, an eigenfunction of Ĥel, captures the spatial distribution of electrons and the corresponding eigenvalue Eel represents the electronic energy of the system. Before the eigenvalue problem can be solved, a suitable functional expression for Ψel has to be found. A standard approach is to express the wavefunction as a Slater determinant Ψel = |ψ1 . . . ψn〉, an anti-symmetric product of molecular orbitals ψi, which are constructed as linear combinations of atom-centered basis functions ψi = ∑ j Cijφj . These atomic orbitals φj are typically taken to be products of radial functions Rl and spherical harmonics Y m l

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