Efficient calculation of the exchange in the Fourier representation of HF‐LCAO‐CO equations for 1D periodic systems

Abstract

Recent advances in the preparation of quasi-1D nano-objects motivate further the development of suitable theoretical models for the calculation of their properties (structural, electronic, etc.). Hartree-Fock crystal orbital-based methodologies and beyond, in spite of their cost, provide a consistent basis for calculations on systems exhibiting periodicity in one direction. One of the often reported drawbacks is the difficulty to deal with the long-range contributions (Coulomb and exchange). In this contribution, it shown that the Fourier representation of the HF-LCAO-CO equations is an appropriate framework to effectively compute the exchange contributions in GTO basis sets. A numerical example illustrates the efficiency of the proposed procedure.

Long ranged interactions in computer simulations and for quasi-2D systems

“…For numerical implementations, convenient algorithms for the computations of the incomplete Bessel functions are needed (see for instance Refs. [496,497]). The energy of a system of pseudo-charges in a quasi-2D geometry is computed as in Eq.…”

Ewald methods for inverse power-law interactions in tridimensional and quasi-two-dimensional systems

“…In table 3, we give some analytical formulas for the computation of the reciprocal space contributions in quasi-two-dimensional Ewald summations for inverse power-law interactions. For numerical implementations, convenient algorithms for the computations of the incomplete Bessel functions are needed (see for instance [36,37]). To close this section, we would like to outline that the equivalence between both derivations allows us to obtain a new analytical relation for the Fourier transform of the incomplete gamma function.…”

Ewald methods for inverse power-law interactions in tridimensional and quasi-two dimensional systems

“…For numerical implementations, convenient algorithms for the computations of the incomplete Bessel functions are needed (see for instance refs. [36,37]).…”