arXiv subjects

J. Arjan Berger

Publications and source records attributed to J. Arjan Berger.

21 records · Page 2Linked to original sources

arXiv2021

Clifford Boundary Conditions for Periodic Systems: the Madelung Constant of Cubic Crystals in 1, 2 and 3 Dimensions

In this work we demonstrate the robustness of a real-space approach for the treatment of infinite systems described with periodic boundary conditions that we have recently proposed [J. Phys. Chem. Lett. 17, 7090]. In our approach we extract a fragment, i.e., a supercell, out of the infinite system, and then modifying its topology into the that of a Clifford torus which is a flat, finite and border-less manifold. We then renormalize the distance between two points by defining it as the Euclidean distance in the embedding space of the Clifford torus. With our method we have been able to calculate the reference results available in the literature with a remarkable accuracy, and at a very low computational effort. In this work we show that our approach is robust with respect to the shape of the supercell. In particular, we show that the Madelung constants converge to the same values but that the convergence properties are different. Our approach scales linearly with the number of atoms. The calculation of Madelung constants only takes a few seconds on a laptop computer for a relative precision of about 10$^{-6}$.

cond-mat.mtrl-sci↗

arXiv2021

Accurate ground-state energies of Wigner crystals from a simple real-space approach

We propose a simple and efficient real-space approach for the calculation of the ground-state energies of Wigner crystals in 1, 2, and 3 dimensions. To be precise, we calculate the first two terms in the asymptotic expansion of the total energy per electron which correspond to the classical energy and the harmonic correction due to the zero-point motion of the Wigner crystals, respectively. Our approach employs Clifford periodic boundary conditions to simulate the infinite electron gas and a renormalized distance to evaluate the Coulomb potential. This allows us to calculate the energies unambiguously and with a higher precision than those reported in the literature. Our results are in agreement with the literature values with the exception of harmonic correction of the 2-dimensional Wigner crystal for which we find a significant difference. Although we focus on the ground state, i.e., the triangular lattice and the body-centered cubic lattice, in two and three dimensions, respectively, we also report the classical energies of several other common lattice structures.

cond-mat.str-el↗

arXiv2020

Potential energy surfaces without unphysical discontinuities: the Coulomb-hole plus screened exchange approach

In this work we show the advantages of using the Coulomb-hole plus screened-exchange (COHSEX) approach in the calculation of potential energy surfaces. In particular, we demonstrate that, unlike perturbative $GW$ and partial self-consistent $GW$ approaches, such as eigenvalue-self-consistent $GW$ and quasi-particle self-consistent $GW$, the COHSEX approach yields smooth potential energy surfaces without irregularities and discontinuities. Moreover, we show that the ground-state potential energy surfaces (PES) obtained from the Bethe-Salpeter equation, within the adiabatic connection fluctuation dissipation theorem, built with quasi-particle energies obtained from perturbative COHSEX on top of Hartree-Fock (BSE@COHSEX@HF) yield very accurate results for diatomic molecules close to their equilibrium distance. When self-consistent COHSEX quasi-particle energies and orbitals are used to build the BSE equation the results become independent of the starting point. We show that self-consistency worsens the total energies but improves the equilibrium distances with respect to BSE@COHSEX@HF. This is mainly due to changes in the screening inside the BSE.

physics.chem-ph↗