Exchange contributions in the electronic structure of systems with 1D‐periodicity: Importance and computation

Abstract

ABSTRACT:The purpose of this article is to point out to the scientific community interested in Hartree-Fock ab initio calculations that accurate calculations of the exchange contributions are essential. An extremely simple system such as the infinite chain of Be atoms, (-Be-) ∞ , treated in direct space at the RHF level with the 3-21G basis fails to converge to physically meaningful results. An analysis based on the convergence properties of finite Fourier series points to the exchange contributions as the source of the problem. Owing to its capability of handling with the necessary accuracy all lattice summations, including the exchange sums, the Fourier representation is able to treat the problem effectively and is confirmed as a procedure of choice for RHF electronic structure calculations of systems with 1D periodicity.

Virtues and potentialities of the Fourier transform method for electronic structure calculations of 1‐D periodic systems at the Hartree–Fock level and beyond

“…From the values in Table II, it is observed that all calculations, except at 2.6 Å, have converged for acceptable numbers of SCF iterations. The minimum in E T is attained for a 0 equal to 2.10 Å, and the present results are consistent with an earlier calculation in which we reported an energy E T = −14.487927 hartree at a 0 = 2.32 Å 25. During the scan over the values of a 0 from 3.0 to 2.0 Å, we note that S min attained values as small as 0.3 × 10 −3 without affecting the minimization process.…”

Convergence of exchange lattice summations in direct‐space polymer calculations

“…In a recent article, Delhalle and coworkers 41, using a distributed s ‐type Gaussian function (DSGF) basis set, pointed out that the exchange contribution should converge extremely slowly in infinite linear Be chains of which the geometrical parameter and the basis set have been chosen to enforce a difficult situation. Indeed, despite a large band gap (6.2 eV), the authors were not able to obtain, using the real‐space approach, a physical energy, whereas they found it possible, with a Fourier‐space technique, to get a meaningful energy per UC (−14.487927 a.u.).…”

“…Up to now, a multipole technique adapted to the exchange has been developed only at the Pariser‐Parr‐Pople level 37, 38. To obtain a fully converged (i.e., exactly up to infinity) exchange term, the Fourier transform method developed by Delhalle, Fripiat, and Harris is, at present, the only available ab initio technique, although, so far, it is limited, to s ‐type atomic orbitals 39–41.…”

Density functional theory investigation on the electronic structure of furo[3,4-b]pyridine-type heterocyclics: from monomer to polymer

“…With homologous polymers, the geometry and electronic properties are calculated by means of the DFT methods for one-dimensional periodic systems [9][10][11][12][13][14][15][16][17]. This was achieved by incorporating in the molecular formalisms the periodic boundary conditions (PBCs) which are a set of boundary conditions that are often used to simulate a large system by modeling a small part that is far from its edge in mathematical models and computer simulations, and distance-based truncation of lattice sums of molecular integrals in a controlled manner (see Trickey et al [18] and Jacquemin et al [19,20] for integral evaluations tailored to lattice sums, Delhalle, Harris, and coworkers [21][22][23][24][25][26] for a Fourier method for lattice sums, Kudin, Scuseria, Champagne and Hirata et al [27][28][29][30][31] for fast multipole methods). To test the difference of functionals, we employ the local spin density approximation (LSDA) [32], the electron-correlated Perdew-BurkeErnzerhof (PBEPBE) [33,34] and B3LYP method for the calculation of PBCs.…”