Abstract
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.
Highlights
Quantum chemical calculations are used in several applications to determine single-point energies or molecular properties of systems of interest
Like the SADNO guess we have proposed above, the superposition of atomic potentials (SAP) guess should be especially powerful for real-space implementations, as in addition to producing a suitably close guess density, it can be used to produce a starting guess for the orbital eigenvectors, for instance by solving its eigenstates in a small basis of numerical atomic orbitals, or by iterative refinement of the SAP orbitals to finer meshes
We have discussed an alternative method for obtaining an initial guess for self-consistent field calculations that is based on the superposition of atomic potentials (SAP), which is equivalent to the commonly used superposition of atomic densities (SAD) approach in the case of systems of noninteracting closed-shell atoms, for which both guesses are exact
Summary
Quantum chemical calculations are used in several applications to determine single-point energies or molecular properties of systems of interest. The level of theory can range from meanfield Hartree−Fock (HF) or Kohn−Sham (KS) density functional theory[1,2] (DFT) to high-level ab initio methods, such as multiconfigurational (MC) self-consistent field (SCF) theory,[3] coupled-cluster (CC) theory,[4] or the density matrix renormalization group (DMRG) method.[5] In each of these approaches, the energy can be written in terms of a reference set of orbitals. High-level ab initio methods are invariably initialized with HF or KS orbitals. As HF produces by definition the best possible single-configurational wave function, it often offers a reasonable starting point for the treatment of correlation effects. KS typically produces good orbitals in cases where HF is not a good starting point, such as for transition metal complexes. For the present purpose it is sufficient to restrict the discussion to the HF and KS levels of theory
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