Fully numerical Hartree-Fock and density functional calculations. I. Atoms

Abstract

Although many programs have been published for fully numerical Hartree--Fock (HF) or density functional (DF) calculations on atoms, we are not aware of any that support hybrid DFs, which are popular within the quantum chemistry community due to their better accuracy for many applications, or that can be used to calculate electric properties. Here, we present a variational atomic finite element solver in the HelFEM program suite that overcomes these limitations. A basis set of the type ${\chi }_{nlm}(r,\theta ,\varphi )=r^{-1}{B}_n(r)Y_l^m(\hat{\mathbf{r}})$ is used, where $B_n(r)$ are finite element shape functions and $Y_l^m$ are spherical harmonics, which allows for an arbitrary level of accuracy. HelFEM supports nonrelativistic HF and DF including hybrid functionals, which are not available in other commonly available program packages. Hundreds of functionals at the local spin density approximation (LDA), generalized gradient approximation (GGA), as well as the meta-GGA levels of theory are included through an interface with the Libxc library. Electric response properties are achievable via finite field calculations. We introduce an alternative grid that yields faster convergence to the complete basis set than commonly used alternatives. We also show that high-order Lagrange interpolating polynomials yield the best convergence, and that excellent agreement with literature HF limit values for electric properties, such as static dipole polarizabilities, can be achieved with the present approach. Dipole moments and dipole polarizabilities at finite field are reported with the PBE, PBEh, TPSS, and TPSSh functionals. Finally, we show that a recently published Gaussian basis set is able to reproduce absolute HF and DF energies of neutral atoms, cations, as well as anions within a few dozen microhartrees.

44 pages, 11 figures. Small reorganization of intro

References in corpus (7)

• A User-Friendly Hybrid Sparse Matrix Class in C++
• Accurate Electron Affinities and Orbital Energies of Anions from a Non-Empirically Tuned Range-Separated Density Functional Theory Approach
• Halogen Bonding Interactions: Revised Benchmarks and a New Assessment of Exchange vs. Dispersion
• An assessment of initial guesses for self-consistent field calculations. Superposition of Atomic Potentials: simple yet efficient
• A review on non-relativistic fully numerical electronic structure calculations on atoms and diatomic molecules
• Fully numerical electronic structure calculations on diatomic molecules in weak to strong magnetic fields
• Fully numerical Hartree-Fock and density functional calculations. II. Diatomic molecules

Cited by in corpus (27)

• An assessment of initial guesses for self-consistent field calculations. Superposition of Atomic Potentials: simple yet efficient
• An overview of self-consistent field calculations within finite basis sets
• A review on non-relativistic fully numerical electronic structure calculations on atoms and diatomic molecules
• Stretched or noded orbital densities and self-interaction correction in density functional theory
• Many recent density functionals are numerically ill-behaved
• Fully numerical calculations on atoms with fractional occupations. Range-separated exchange functionals
• Straightforward and accurate automatic auxiliary basis set generation for molecular calculations with atomic orbital basis sets
• Meta-GGA density functional calculations on atoms with spherically symmetric densities in the finite element formalism
• Fully numerical electronic structure calculations on diatomic molecules in weak to strong magnetic fields
• Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets
• A call to arms: making the case for more reusable libraries
• Atomic electronic structure calculations with Hermite interpolating polynomials
• Fully numerical Hartree-Fock and density functional calculations. II. Diatomic molecules
• Polarized Gaussian basis sets from one-electron ions
• On the accurate reproduction of strongly repulsive interatomic potentials
• Reproducibility of density functional approximations: how new functionals should be reported
• Automatic Generation of Accurate and Cost-efficient Auxiliary Basis Sets
• Hartree-Fock Critical Nuclear Charge in Two-Electron Atoms
• How good are recent density functionals for ground and excited states of one-electron systems?
• Meta-local density functionals: a new rung on Jacob's ladder
• Insight on Gaussian basis set truncation errors in weak to intermediate magnetic fields with an approximate Hamiltonian
• On the accuracy of a recent regularized nuclear potential
• OpenOrbitalOptimizer -- a reusable open source library for self-consistent field calculations
• Systematic study of confinement induced effects on atomic electronic structure
• Atomic Confinement Potentials and the Generation of Numerical Atomic Orbitals
• Extending the definition of atomic basis sets to atoms with fractional nuclear charge
• Importance profiles. Visualization of atomic basis set requirements