In electronic structure calculations, the electron-electron interaction is the hard part. Two electrons interact through the Coulomb potential, which depends on the distance between them. In a basis set of N functions, this creates N⁴ interaction terms — every pair of basis functions with every other pair. For large systems, this quartic scaling dominates the computational cost.
White (arXiv:2603.22646) extends gausslets — a rare class of basis functions that produce diagonal (two-index) electron-electron interaction terms instead of the usual four-index terms — from Cartesian coordinates to radial coordinates in three dimensions. The N⁴ problem becomes N². The diagonal property means each basis function interacts with itself and its neighbors, not with all other functions.
The construction is technically demanding: radial gausslets must handle the singularity at the origin and the boundary conditions of atomic wavefunctions. The resulting basis is compact — a modest number of functions captures the relevant physics — and the diagonal interaction terms make Hartree-Fock and exact diagonalization on atoms significantly cheaper.
The through-claim: the interaction bottleneck in quantum chemistry isn't fundamental — it's a basis set choice. Standard Gaussian basis sets spread the Coulomb interaction across all pairs of functions because they weren't designed to localize it. Gausslets are designed around the interaction, not the wavefunction, and the scaling drops from quartic to quadratic.