AI Insight
This paper introduces angular Gausslets, a new mathematical basis for electronic structure calculations that combines localized spherical Gaussian functions with radial Gausslets to create an atom-centered basis where electron-electron interactions can be represented more efficiently. The method uses injection techniques to ensure accuracy for low angular momentum states while maintaining computational advantages through a two-index integral-diagonal form. Tests on various atomic systems, including beryllium atom calculations using density matrix renormalization group (DMRG) methods, demonstrate systematic convergence and achieve energies within 0.1 milliHartree of the exact solution.
Why it matters
This work enables more computationally feasible quantum chemistry calculations for atoms and potentially molecules by reducing the complexity of electron correlation calculations. The demonstrated accuracy for first-row atoms suggests this approach could make high-precision electronic structure calculations practical for larger chemical systems where both static and dynamic electron correlations are important.
Understand the Science
arXiv:2605.04517v2 Announce Type: replace
Abstract: Gausslets are one of the few basis constructions for electronic structure that combine locality, orthonormality, variable resolution, and an accurate diagonal approximation for the electron-electron interaction, but the original construction is tied to one dimension. Radial gausslets extended this idea to atoms while leaving the angular degrees of freedom in spherical harmonics, so the atomic interaction remained only partially diagonal in the combined basis. Here we introduce generalized gausslets on the sphere and combine them shell by shell with radial gausslets to form an atom-centered basis in which the electron-electron interaction takes a two-index integral-diagonal form. The angular basis starts from localized spherical Gaussians and uses injection to make a low-$ell$ spherical-harmonic subspace exact. Tests of the kinetic spectrum, low-$ell$ Coulomb matrix elements, spherium, first-row Hartree–Fock calculations, and He exact diagonalization show systematic convergence with increasing angular resolution. We also develop DMRG methods for this basis, including compact MPOs, correlated small-space starting states, Givens-rotation transfers between nearby angular sizes, and embedded sampled variance extrapolation (ESVE). We show that this combination of ingredients can be used to solve the Be atom, with extrapolations in the number of angular functions but with fixed radial resolution, to within about 0.1 mH of the complete basis set limit exact energy. This shows that DMRG calculations of first row atoms which include both static and accurate dynamic correlation on the same footing are feasible.
Source: Angular Gausslets