Improvement of initial guess via grid‐cutting for efficient grid‐based density functional calculations

Abstract

We introduced an efficient initial guess method, namely the grid-cutting, which is specialized for grid-based density functional theory (DFT) calculations. It produces initial density and orbitals through pre-DFT calculations in an inner simulation box made by cutting out the outer region of a full-size one. To assess its performance, we carried out DFT calculations for small molecules included in the G2-1 set and two large molecules with various combinations of mixing and diagonalization conditions, relative size of the inner box, and grid spacing. For all cases, the grid-cutting method was more efficient than conventional ones such as extended H€ uckel, superposition of atomic densities, and linear combination of atomic orbitals. For instance, it was about 20% faster in computational time and about 45% smaller in the number of self-consistent-field cycles than the superposition of atomic densities because it provided high-quality initial density and orbitals closer to the corresponding fully converged values. In addition, it showed good performance for non-Coulombic model systems such as harmonic oscillator. K E Y W O R D Sdensity functional theory, grid method, initial guess

Study of Li Adsorption on Graphdiyne Using Hybrid DFT Calculations

“…The flake size was increased by repeating the unit cell geometry. The actual adsorption energy on the GDY flake was calculated using our in-house grid-based code, ACE-Molecule, ,− for direct comparison with the results of VASP, because ACE-Molecule also employs the projector augmented wave (PAW) method for core electrons like VASP. In addition, it supports an accelerated LC-ωPBE method for the efficient hybrid DFT calculation of large GDY flakes.…”

Multilevel approach to the initial guess for self‐consistent field calculations

“…Based on the previous findings of Green [31], Amat and Card o-Dorca [32], and Nazari and Whitten [33], Lehtola used the superposition of precalculated effective atomic potentials for the initial guess of the Fock operator to design a convenient alternative of SAD for real-space calculations [14,34], and new tunable atomic potentials are proposed by Laikov and Briling [35]. Lee et al investigated the application of the EHT in the grid-based real-space techniques [36], while Lim and coworkers utilized a multi-grid approach [37] which has some similarities with the multiple-step, projection-based techniques of atom-centered Gaussian basis sets. Jansík et al employed a projection-free multilevel approach [30,38], where the initial density of a target basis set is obtained by a three-step procedure which utilized the configurationaveraged SAD method with a specially-derived minimal AO basis set calculation.…”

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

“…Orbital optimization is usually the simpler, the closer the initial guess is to the converged result. However, despite its pronounced importance, the choice of initial orbitals has attracted surprisingly little interest in the literature. − (Note that although the optimization problem can also be reformulated only in terms of density matrices in the case of HF and KS theory, this has no implications for the present study, as the two approaches are equivalent. )…”

“…In addition to the aforementioned approaches, calculations may be initialized recursively by reading in a converged density computed in a smaller basis set. Such a procedure has recently been advocated for real-space calculations; the use of confinement potentials has also been found to help SCF convergence in the case of extended real-space basis sets . In some cases it is also possible to decompose the system into either single molecules or chemically meaningful molecular fragments, ,, and “glue” the orbitals together to form a good guess density for the original calculation.…”