Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets

Abstract

The superposition of atomic potentials (SAP) approach has recently been shown to be a simple and efficient way to initialize electronic structure calculations [S. Lehtola, J. Chem. Theory Comput. 15, 1593].Here, we study the differences between effective potentials from fully numerical density functional and optimized effective potential calculations for fixed configurations. We find that the differences are small, overall, and choose exchange-only potentials at the local density approximation level of theory computed on top of Hartree-Fock densities as a good compromise. The differences between potentials arising from different atomic configurations are also found to be small at this level of theory.Furthermore, we discuss the efficient Gaussian-basis implementation of SAP via error function fits to fully numerical atomic radial potentials. The guess obtained from the fitted potentials can be easily implemented in any Gaussian-basis quantum chemistry code in terms of two-electron integrals. Fits covering the whole periodic table from H to Og are reported for non-relativistic as well as fully relativistic four-component calculations that have been carried out with fully numerical approaches.

Meta-Local Density Functionals: A New Rung on Jacob’s Ladder

“…Atomic Calculations. The errors of exchange-only density-functional calculations compared to the unrestricted Hartree−Fock (HF) total and exchange energies for atoms from H to Sr were studied with HELFEM; the reference unrestricted HF total energies have been recently reported in ref 17. Due to the similarity of the results, data is shown here only for the noble gases Ne, Ar, and Kr in Figure 1; the rest of the data can be found in the Supporting Information.…”

“…Fully numerical, fully variational calculations on closed and partially closed shell atoms from H to Sr were performed with the finite-element method as implemented in the HelFEM program, which allows for an efficient approach to the complete basis set limit. , The atomic calculations employed five radial elements, yielding 69 numerical radial basis functions, which suffice to converge the energy to better than μ E h precision for these systems.…”

The DIRAC code for relativistic molecular calculations

“…By default, the start guess is provided by a sum of atomic local-density approximation (LDA) potentials, which have been prepared using the GRASP atomic code 40 and are fitted to an analytical expression. 41 Other options include (i) bare nucleus potentials corrected with screening factors based on Slater's rules, 42 (ii) atomic start based on densities from atomic SCF runs for the individual centers, 43 and (iii) an extended Hückel start based on atomic fragments. 44 In each SCF iteration, orbitals are by default ordered according to energy, and orbital classes are assigned by simple counting in the following order: (secondary) negative-energy orbitals, inactive (fully occupied) orbitals, active (if any) orbitals, and virtual orbitals.…”

SPAHM: the spectrum of approximated Hamiltonian matrices representations

“…1 using the PBE0 potential, as all the properties were computed with this functional. Finally, the superposition of atomic potentials (SAP) 60,64 and the Laikov-Briling (LB) 65 guesses use effective one-electron potentials to construct sophisticated, yet computationally lightweight, guess Hamiltonians.…”