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This paper introduces "angular gausslets," a novel basis construction that extends radial gausslets to include generalized gausslets on the sphere, creating an atom-centered basis with a two-index integral-diagonal form for the electron-electron interaction. The angular basis employs localized spherical Gaussians and injection to ensure an exact low-$\ell$ spherical-harmonic subspace. Validated through various tests and DMRG methods, the approach achieves highly accurate solutions for the Be atom, demonstrating the feasibility of DMRG calculations for first-row atoms with both static and dynamic correlation.
Unlock highly accurate and efficient electronic structure calculations with "angular gausslets," a new basis that diagonalizes the electron-electron interaction, enabling precise DMRG computations for complex atoms.
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.
