Themed collection Real-space numerical grid methods in quantum chemistry

This themed issue reports on recent progress in the fast developing field of real-space numerical grid methods in quantum chemistry.

Multiwavelets are emerging as an attractive alternative to traditional basis sets such as Gaussian-type orbitals and plane waves.

Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method.

The sparsity pattern obtained in the wavelet Galerkin boundary element representation of the PCM boundary integral operators. By employing a wavelet basis on a smooth solvent-excluded molecular surface the method is able to guarantee solutions with high accuracy at a linear cost in memory and computational time.

The calculation of electrostatic integrals is performed using domain decomposition and auxiliary non-uniform grids for density functional theory real-space implementation.

A highly economic prediction method for fine resolution wavelet coefficients of wave functions and energy expectation values is presented.

Real space pseudopotentials have a number of advantages in solving for the electronic structure of materials.

The primary motivation for systematic bases in first principles electronic structure simulations is to derive physical and chemical properties of molecules and solids with predetermined accuracy. This requires, however, a detailed asymptotic analysis of singularities.

The calculation of Fock-exchange interaction is an important task in the computation of molecule and solid properties.

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations.

Regular to chaotic transition takes place in a driven van der Pol oscillator in both classical and quantum domains.

A grid-based fast multipole method has been developed for calculating two-electron interaction energies for non-overlapping charge densities.

A novel stochastic approach aimed at solving for the ground-state one-particle density matrix in density functional theory is developed.

A systematic study of the parameter space of a kinetic functional is used as a route to understand the transferability problems and improve the kinetic density functionals.

Density functional theory calculations are computationally extremely expensive for systems containing many atoms due to their intrinsic cubic scaling.

The spatial extent of the singlet 2¹B_3u excitation of the ethylene molecule. The depicted box is 50 bohr wide.

A snapshot of ab initio molecular dynamics simulations for a polymer electrolyte membrane at low hydration.

We developed a program code of CIS based on a numerical grid method and showed that Kohn–Sham orbitals from the Krieger–Li–Iafrate (KLI) approximation provide better reference configurations for CIS than the standard Hartree–Fock and Kohn–Sham orbitals.

Newly introduced numerical optimization of multi-site support functions in the linear-scaling DFT code CONQUEST improves the accuracy and stability of the support functions with small cutoffs.

A fully numerical method for the time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation is presented in a multiresolution analysis (MRA) approach.

The Lagrange-mesh method has the simplicity of a calculation on a mesh and can have the accuracy of a variational method.

We explore how strategies to simulate various phenomena of electronic systems have been implemented in the Octopus code, using the versatility and performance of real-space grids.

We use DGDFT based AIMD calculations to reveal that a 2 × 1 edge reconstruction appears in ACPNRs at room temperature.