Assessment of Initial Guesses for Self-Consistent Field Calculations. Superposition of Atomic Potentials: Simple yet Efficient

Electronic structure
calculations, such as in the Hartree–Fock
or Kohn–Sham density functional approach, require an initial
guess for the molecular orbitals. The quality of the initial guess
has a significant impact on the speed of convergence of the self-consistent
field (SCF) procedure. Popular choices for the initial guess include
the one-electron guess from the core Hamiltonian, the extended Hückel
method, and the superposition of atomic densities (SAD). Here, we
discuss alternative guesses obtained from the superposition of atomic
potentials (SAP), which is easily implementable even in real-space
calculations. We also discuss a variant of SAD which produces guess
orbitals by purification of the density matrix that could also be
used in real-space calculations, as well as a parameter-free variant
of the extended Hückel method, which resembles the SAP method
and is easy to implement on top of existing SAD infrastructure. The
performance of the core Hamiltonian, the SAD, and the SAP guesses
as well as the extended Hückel variant is assessed in nonrelativistic
calculations on a data set of 259 molecules ranging from the first
to the fourth periods by projecting the guess orbitals onto precomputed,
converged SCF solutions in single- to triple-ζ basis sets. It
is shown that the proposed SAP guess is the best guess on average.
The extended Hückel guess offers a good alternative, with less
scatter in accuracy.