Quasi-Robust Local Density Fitting
David P. Tew
Max Planck Institute for Solid State Research,
Heisenbergstr. 1, Stuttgart 70569, Germany
Local correlation methods exploit the short-ranged (1/r 6 ) nature of electron correlation in insulators by using a spatially local representation of the electronic wavefunction that exposes sparsity in the wavefunction parameters and Hamiltonian matrix elements, leading to methods with sub-quadratic scaling with system size. A key component of local correlation methods is local density fitting, which greatly reduces the costs of integral evaluation and transformation. However, standard robust density fitting introduces unphysical long range contributions to the approximate density when the fitting basis is incomplete. I will present a quasi-robust density fitting formulation where spatial locality is recovered at the expense of permitting a linear error that is made small by the fitting procedure, which involves optimising the Coulomb potential of the approximate charge density. The method is shown to be stable and almost as accurate as standard robust density fitting without local approximations in practical calculations using standard density fitting basis sets.
[1] D. P. Tew, J. Chem. Phys. 148, 011102 (2018).