The bifunctional formalism: an alternative treatment of density functionals

The bifunctional formalism presents an alternative how to obtain the functional value from its functional derivative by exploiting homogeneous density scaling. In the bifunctional formalism the density dependence of the functional derivative is suppressed. Consequently, those derivatives have to be treated as formal functional derivatives. For a pointwise correspondence between the true and the formal functional derivative, the bifunctional expression yields the same value as the density functional. Within the bifunctional formalism the functional value can directly be obtained from its derivative (while the functional itself remains unknown). Since functional derivatives are up to a constant uniquely defined, this approach allows for a pointwise comparison between approximate potentials and reference potentials. This aspect is especially important in the field of orbital-free density functional theory, where the burden is to approximate the kinetic energy. Since in the bifunctional approach the potential is approximated directly, full control is given over the latter, and consequently over the final electron densities obtained from variational procedure. Besides the bifunctional formalism itself another concept is introduced, dividing the total non-interacting kinetic energy into a known functional part and a remainder, called Pauli kinetic energy. Only the remainder requires further approximations. For practical purposes sufficiently accurate Pauli potentials for application on atoms, molecular and solid-state systems are presented.

Fast Orbital-Free Full-Potential Calculations for Large Nano Objects: C, Al and Ti

In the context of a full-potential orbital-free approach for the modeling of multi-atomic systems we investigated the dependence of the cohesive energies and bulk elastic modules of the large nanosystems Cn (n is up to 4096 atoms), Aln (n is up to 23,328 atoms) and tin (n is up to 2160 atoms). It was shown that the cohesive energies and elastic modules tend towards bulk crystal values at n ≈ 3000 for Cn systems, at n ≈ 1500 for Tin and at n ≈ 20,000 for Aln. The execution time for one energy iteration for Ti23328 was only 23 min.

Mini Review: Quantum Confinement of Atomic and Molecular Clusters in Carbon Nanotubes

We overview our recent developments on a computational approach addressing quantum confinement of light atomic and molecular clusters (made of atomic helium and molecular hydrogen) in carbon nanotubes. We outline a multi-scale first-principles approach, based on density functional theory (DFT)-based symmetry-adapted perturbation theory, allowing an accurate characterization of the dispersion-dominated particle–nanotube interaction. Next, we describe a wave-function-based method, allowing rigorous fully coupled quantum calculations of the pseudo-nuclear bound states. The approach is illustrated by showing the transition from molecular aggregation to quasi-one-dimensional condensed matter systems of molecular deuterium and hydrogen as well as atomic 4He, as case studies. Finally, we present a perspective on future-oriented mixed approaches combining, e.g., orbital-free helium density functional theory (He-DFT), machine-learning parameterizations, with wave-function-based descriptions.

Development of novel kinetic energy functional for orbital-free density functional theory applications

The development of novel Kinetic Energy (KE) functionals is an important topic in density functional theory (DFT). In particular, this happens by means of an analysis with newly developed benchmark sets. Here, I present a study of Laplacian-level kinetic energy functionals applied to metallic nanosystems. The nanoparticles are modeled using jellium sph eres of different sizes, background densities, and number of electrons. The ability of different functionals to reproduce the correct kinetic energy density and potential of various nanoparticles is investigated and analyzed in terms of semilocal descriptors. Most semilocal KE functionals are based on modifications of the second-order gradient expansion GE2 or GE4. I find that the Laplacian contribute is fundamental for the description of the energy and the potential of nanoparticles.

Bonding features in Appel's salt from the orbital-free quantum crystallographic perspective

Bonding properties in the crystal of 4,5-dichloro-l,2,3-dithiazolium chloride (Appel's salt) were studied using a combination of single-crystal high-resolution X-ray diffraction data and the orbital-free quantum crystallography approach. A QTAIM-based topological model shows the proximity of S—C and S—N bonds to the sesquialteral type and establishes the low S—S bond order in the l,2,3-dithiazolium heterocycle. It is found that the electrostatic potential carries the traces of a common positive area on the junction of interatomic zero-flux surfaces of S1 and S2 atomic basins; meanwhile the exchange energy density per particle shows perfectly here two separate minima through which the two bond paths run. Thus, the pair intermolecular interactions Cl−...S1 and Cl−...S2 formed by the common chloride anion placed near the center of the S—S bond are categorized as chalcogen bonds.