Dietrich Foerster

An O(N3) implementation of Hedin's GW approximation for molecules

We describe an implementation of Hedins GW approximation for molecules and clusters, the complexity of which scales as O(N(3)) with the number of atoms. Our method is guided by two strategies: (i) to respect the locality of the underlying electronic interactions and (ii) to avoid the singularities of Greens functions by manipulating, instead, their spectral functions using fast Fourier transform methods. To take into account the locality of the electronic interactions, we use a local basis of atomic orbitals and, also, a local basis in the space of their products. We further compress the screened Coulomb interaction into a space of lower dimensions for speed and to reduce memory requirements. The improved scaling of our method with respect to most of the published methodologies should facilitate GW calculations for large systems. Our implementation is intended as a step forward towards the goal of predicting, prior to their synthesis, the ionization energies and electron affinities of the large molecules that serve as constituents of organic semiconductors.

Fully self-consistentGWand quasiparticle self-consistentGWfor molecules

P.K. acknowledges support from the CSIC JAE-doc program, co-financed by the European Science Foundation, and the Diputacion Foral de Gipuzkoa. D.S.P. and P.K. acknowledge financial support from the Consejo Superior de Investigaciones Cientificas (CSIC), the Basque Departamento de Educacion, UPV/EHU (Grant No. IT-366-07), the Spanish Ministerio de Ciencia e Innovacion (Grant No. FIS2010-19609-C02-02), the ETORTEK program funded by the Basque Departamento de Industria and the Diputacion Foral de Gipuzkoa, and the German DFG through the SFB 1083. D.F. acknowledges support from the ORGAVOLTANR project and the Euroregion Aquitaine-Euskadi program.

Elimination, in electronic structure calculations, of redundant orbital products

We propose a direct method for reducing the dimension of the space of orbital products that occur, for example, in the calculation of time dependent density functional theory linear response and in Hedins GW approximation to the electron propagator. We do this by defining, within the linear space of orbital products, a subspace of dominant directions that are associated with a certain eigenvalue problem. These directions span the entire linear space of products with an error that decreases approximately exponentially with their number. Our procedure works best for atomic orbitals of finite range and it avoids the use of extra sets of auxiliary fit functions.

Cubic-scaling iterative solution of the Bethe-Salpeter equation for finite systems

The Bethe-Salpeter equation (BSE) is currently the state of the art in the description of neutral electron excitations in both solids and large finite systems. It is capable of accurately treating charge-transfer excitations that present difficulties for simpler approaches. We present a local basis set formulation of the BSE for molecules where the optical spectrum is computed with the iterative Haydock recursion scheme, leading to a low computational complexity and memory footprint. Using a variant of the algorithm we can go beyond the Tamm-Dancoff approximation (TDA). We rederive the recursion relations for general matrix elements of a resolvent, show how they translate into continued fractions, and study the convergence of the method with the number of recursion coefficients and the role of different terminators. Due to the locality of the basis functions the computational cost of each iteration scales asymptotically as

On the Kohn-Sham density response in a localized basis set

O(N^3)

Assessment of Density-Functional Tight-Binding Ionization Potentials and Electron Affinities of Molecules of Interest for Organic Solar Cells Against First-Principles GW Calculations

with the number of atoms, while the number of iterations is typically much lower than the size of the underlying electron-hole basis. In practice we see that , even for systems with thousands of orbitals, the runtime will be dominated by the

Optical response of silver clusters and their hollow shells from linear-response TDDFT

O(N^2)

Fast construction of the Kohn--Sham response function for molecules}

operation of applying the Coulomb kernel in the atomic orbital representation

Metal-insulator transition in TlSr 2 CoO 5 from orbital degeneracy and spin disproportionation

We construct the Kohn-Sham density response function chi(0) in a previously described basis of the space of orbital products. The calculational complexity of our construction is O(N(2)N(omega)) for a molecule of N atoms and in a spectroscopic window of N(omega) frequency points. As a first application, we use chi(0) to calculate the molecular spectra from the Petersilka-Gossmann-Gross equation. With chi(0) as input, we obtain the correct spectra with an extra computational effort that grows also as O(N(2)N(omega)) and, therefore, less steeply in N than the O(N(3)) complexity of solving Casidas equations. Our construction should be useful for the study of excitons in molecular physics and in related areas where chi(0) is a crucial ingredient.

Two-dimensional S = 1/2 antiferromagnet on a plaquette lattice

Ionization potentials (IPs) and electron affinities (EAs) are important quantities input into most models for calculating the open-circuit voltage (Voc) of organic solar cells. We assess the semi-empirical density-functional tight-binding (DFTB) method with the third-order self-consistent charge (SCC) correction and the 3ob parameter set (the third-order DFTB (DFTB3) organic and biochemistry parameter set) against experiments (for smaller molecules) and against first-principles GW (Green’s function, G, times the screened potential, W) calculations (for larger molecules of interest in organic electronics) for the calculation of IPs and EAs. Since GW calculations are relatively new for molecules of this size, we have also taken care to validate these calculations against experiments. As expected, DFTB is found to behave very much like density-functional theory (DFT), but with some loss of accuracy in predicting IPs and EAs. For small molecules, the best results were found with ΔSCF (Δ self-consistent field) SCC-DFTB calculations for first IPs (good to ± 0.649 eV). When considering several IPs of the same molecule, it is convenient to use the negative of the orbital energies (which we refer to as Koopmans’ theorem (KT) IPs) as an indication of trends. Linear regression analysis shows that KT SCC-DFTB IPs are nearly as accurate as ΔSCF SCC-DFTB eigenvalues (± 0.852 eV for first IPs, but ± 0.706 eV for all of the IPs considered here) for small molecules. For larger molecules, SCC-DFTB was also the ideal choice with IP/EA errors of ± 0.489/0.740 eV from ΔSCF calculations and of ± 0.326/0.458 eV from (KT) orbital energies. Interestingly, the linear least squares fit for the KT IPs of the larger molecules also proves to have good predictive value for the lower energy KT IPs of smaller molecules, with significant deviations appearing only for IPs of 15–20 eV or larger. We believe that this quantitative analysis of errors in SCC-DFTB IPs and EAs may be of interest to other researchers interested in DFTB investigation of large and complex problems, such as those encountered in organic electronics.