Local ab initio methods for calculating optical band gaps in periodic systems. I. Periodic density fitted local configuration interaction singles method for polymers

Abstract

We present a density fitted local configuration interaction singles (CIS) method for calculating optical band gaps in 1D-periodic systems. The method is based on the Davidson diagonalization procedure, carried out in the reciprocal space. The one-electron part of the matrix-vector products is also evaluated in the reciprocal space, where the diagonality of the Fock matrix can be exploited. The contraction of the CIS vectors with the two electron integrals is performed in the direct space in the basis of localized occupied (Wannier) and virtual (projected atomic) orbitals. The direct space approach allows to utilize the sparsity of the integrals due to the local representation and locality of the exciton. The density fitting approximation employed for the two electron integrals reduces the nominal scaling with unit cell size to O(N 4 ). Test calculations on a series of prototypical systems demonstrate that the method in its present stage can be used to calculate the excitonic band gaps of polymers with up to a few dozens of atoms in the cell. The computational cost depends on the locality of the exciton, but even relatively delocalized excitons occurring in the polybiphenyl in the parallel orientation, can be routinely treated with this method.

Ab Initio Calculation of the Ultraviolet–Visible (UV-vis) Absorption Spectrum, Electron-Loss Function, and Reflectivity of Solids

“…In the following section, we show how it is computed in the full range of UV-visible energies for periodic systems, by slightly modifying the frequency-dependent CPHF(KS) method already implemented in the CRYSTAL code. The performance of the method, similar to the time-dependent Hartree-Fock (TDHF) method 9 or to the configuration interaction singles (CIS) method 10,11 as implemented in a molecular context, or to the time-dependent DFT (TDDFT) and equivalent Bethe-Salpeter equation (BSE), 12,13 as used for periodic compounds, is discussed in the present work by considering bulk Silicon (Si), SiC and LiF. The effect of the computational parameters controlling the calculation will be considered in the Si case for which high quality experimental results [14][15][16] and many previous computations 17 are available.…”

Local ab initio methods for calculating optical bandgaps in periodic systems. II. Periodic density fitted local configuration interaction singles method for solids

“…Such a model features a finite number of k-points in the reciprocal space representation of the wavefunction (1), equal to the number of unit cells A in the supercell of the cyclic system. 20,36,37 The transformations between the direct and reciprocal spaces correspond in this case to the discrete Fourier and inverse-Fourier transforms [e.g., in Eq. (3)].…”

“…There are two fundamental complications compared to the 1D case. First, the infinite lattice sums occurring in the Coulomb part of the matrix-vector product 20 no longer converge. Second, the direct space density fitting approach based on a single common fit-domain, as employed in the 1D case to calculate the exchange part of the matrix-vector product becomes prohibitively expensive for bulky systems.…”

“…In a previous paper 20 (denoted in the following as Paper I), we have presented formalism, implementation, and test applications of a periodic local density fitted CIS method for 1D periodic systems like polymers. In the present work, the second paper in this series, the method is generalized to full 3D periodic systems (crystals).…”

Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension

“…During the centennial year of Gregory Hugh Wannier, nearly a hundred publications have demonstrated that functions named after him are key computational tools in several research areas, such as insulators, 1 magnetism, 2,3 metals, 4 photonics, 5 polymers, 6 semiconductors, 7,8 superconductivity, 9 and electronic transport. 10 Of course, applications have fueled basic research where Wannier functions (WFs) are the subject matter, 11 and textbooks devote some attention to these functions.…”