A review on non-relativistic fully numerical electronic structure calculations on atoms and diatomic molecules

Abstract

The need for accurate calculations on atoms and diatomic molecules is motivated by the opportunities and challenges of such studies. The most commonly-used approach for all-electron electronic structure calculations in general - the linear combination of atomic orbitals (LCAO) method - is discussed in combination with Gaussian, Slater a.k.a. exponential, and numerical radial functions. Even though LCAO calculations have major benefits, their shortcomings motivate the need for fully numerical approaches based on, e.g. finite differences, finite elements, or the discrete variable representation, which are also briefly introduced. Applications of fully numerical approaches for general molecules are briefly reviewed, and their challenges are discussed. It is pointed out that the high level of symmetry present in atoms and diatomic molecules can be exploited to fashion more efficient fully numerical approaches for these special cases, after which it is possible to routinely perform all-electron Hartree-Fock and density functional calculations directly at the basis set limit on such systems. Applications of fully numerical approaches to calculations on atoms as well as diatomic molecules are reviewed. Finally, a summary and outlook is given.

77 pages, 5 figures, 697 references. Added discussion on numerical methods

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• Fully numerical Hartree-Fock and density functional calculations. I. Atoms
• Fully numerical electronic structure calculations on diatomic molecules in weak to strong magnetic fields
• Microhartree Precision in Density-Functional-Theory Calculations
• Fully numerical Hartree-Fock and density functional calculations. II. Diatomic molecules
• Hybrid grid/basis set discretizations of the Schrödinger equation
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• Towards quantum-chemical method development for arbitrary basis functions

Cited by in corpus (34)

• An overview of self-consistent field calculations within finite basis sets
• Many recent density functionals are numerically ill-behaved
• Fully numerical calculations on atoms with fractional occupations. Range-separated exchange functionals
• Fully numerical Hartree-Fock and density functional calculations. I. Atoms
• 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
• Communication: Curing basis set overcompleteness with pivoted Cholesky decompositions
• 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
• Repulsive interatomic potentials calculated at three levels of theory
• Meta-local density functionals: a new rung on Jacob's ladder
• How good are recent density functionals for ground and excited states of one-electron systems?
• An evaluation for geometries, formation enthalpies, and dissociation energies of diatomic and triatomic (C, H, N, O), NO3, and HNO3 molecules from the PAW DFT method with PBE and optB88-vdW functionals
• Insight on Gaussian basis set truncation errors in weak to intermediate magnetic fields with an approximate Hamiltonian
• Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices
• Tight-binding bond parameters for dimers across the periodic table from density-functional theory
• On the accuracy of a recent regularized nuclear potential
• OpenOrbitalOptimizer -- a reusable open source library for self-consistent field calculations
• Direct determination of optimal real-space orbitals for correlated electronic structure of molecules
• Systematic study of confinement induced effects on atomic electronic structure
• Ensemble Generalization of the Perdew-Zunger Self-Interaction Correction: a Way Out of Multiple Minima and Symmetry Breaking
• Fully numerical Hartree-Fock calculations for atoms and small molecules with quantics tensor trains
• Review of the finite difference Hartree-Fock method for atoms and diatomic molecules, and its implementation in the x2dhf program
• A Reusable Library for Second-Order Orbital Optimization Using the Trust Region Method
• Extending the definition of atomic basis sets to atoms with fractional nuclear charge
• Importance profiles. Visualization of atomic basis set requirements
• Atomic Confinement Potentials and the Generation of Numerical Atomic Orbitals
• Basis set convergence and extrapolation of connected triple excitation contributions (T) in computational thermochemistry: the W4-17 benchmark with up to k functions