Benchmarking GW against exact diagonalization for semi-empirical models

We calculate groundstate total energies and single-particle excitation energies of seven pi conjugated molecules described with the semi-empirical Pariser-Parr-Pople (PPP) model using self-consistent many-body perturbation theory at the GW level and exact diagonalization. For the total energies GW captures around 65% of the groundstate correlation energy. The lowest lying excitations are overscreened by GW leading to an underestimation of electron affinities and ionization potentials by approximately 0.15 eV corresponding to 2.5%. One-shot G_0W_0 calculations starting from Hartree-Fock reduce the screening and improve the low-lying excitation energies. The effect of the GW self-energy on the molecular excitation energies is shown to be similar to the inclusion of final state relaxations in Hartree-Fock theory. We discuss the break down of the GW approximation in systems with short range interactions (Hubbard models) where correlation effects dominate over screening/relaxation effects. Finally we illustrate the important role of the derivative discontinuity of the true exchange-correlation functional by computing the exact Kohn-Sham levels of benzene.Comment: 9 pages, 5 figures, accepted for publication in Phys. Rev.

First-principles GW-BSE excitations in organic molecules

We present a first-principles method for the calculation of optical excitations in nanosystems. The method is based on solving the Bethe-Salpeter equation (BSE) for neutral excitations. The electron self-energy is evaluated within the GW approximation, with dynamical screening effects described within time-dependent density-functional theory in the adiabatic, local approximation. This method is applied to two systems: the benzene molecule, C$_6$H$_6$, and azobenzene, C$_{12}$H$_{10}$N$_2$. We give a description of the photoisomerization process of azobenzene after an $n-\pi^\star$ excitation, which is consistent with multi-configuration calculations

Optical excitations in organic molecules, clusters and defects studied by first-principles Green's function methods

Spectroscopic and optical properties of nanosystems and point defects are discussed within the framework of Green's function methods. We use an approach based on evaluating the self-energy in the so-called GW approximation and solving the Bethe-Salpeter equation in the space of single-particle transitions. Plasmon-pole models or numerical energy integration, which have been used in most of the previous GW calculations, are not used. Fourier transforms of the dielectric function are also avoided. This approach is applied to benzene, naphthalene, passivated silicon clusters (containing more than one hundred atoms), and the F center in LiCl. In the latter, excitonic effects and the $1s \to 2p$ defect line are identified in the energy-resolved dielectric function. We also compare optical spectra obtained by solving the Bethe-Salpeter equation and by using time-dependent density functional theory in the local, adiabatic approximation. From this comparison, we conclude that both methods give similar predictions for optical excitations in benzene and naphthalene, but they differ in the spectra of small silicon clusters. As cluster size increases, both methods predict very low cross section for photoabsorption in the optical and near ultra-violet ranges. For the larger clusters, the computed cross section shows a slow increase as function of photon frequency. Ionization potentials and electron affinities of molecules and clusters are also calculated.Comment: 9 figures, 5 tables, to appear in Phys. Rev. B, 200

Kohn-Sham decomposition in real-time time-dependent density-functional theory: An efficient tool for analyzing plasmonic excitations

The real-time-propagation formulation of time-dependent density-functional theory (RT-TDDFT) is an efficient method for modeling the optical response of molecules and nanoparticles. Compared to the widely adopted linear-response TDDFT approaches based on, e.g., the Casida equations, RT-TDDFT appears, however, lacking efficient analysis methods. This applies in particular to a decomposition of the response in the basis of the underlying single-electron states. In this work, we overcome this limitation by developing an analysis method for obtaining the Kohn-Sham electron-hole decomposition in RT-TDDFT. We demonstrate the equivalence between the developed method and the Casida approach by a benchmark on small benzene derivatives. Then, we use the method for analyzing the plasmonic response of icosahedral silver nanoparticles up to Ag$_{561}$. Based on the analysis, we conclude that in small nanoparticles individual single-electron transitions can split the plasmon into multiple resonances due to strong single-electron-plasmon coupling whereas in larger nanoparticles a distinct plasmon resonance is formed.Comment: 11 pages, 3 figure

Performance of a non-empirical meta-GGA density functional for excitation energies

It is known that the adiabatic approximation in time-dependent density functional theory usually provides a good description of low-lying excitations of molecules. In the present work, the capability of the adiabatic nonempirical meta-generalized gradient approximation (meta-GGA) of Tao, Perdew, Staroverov, and Scuseria (TPSS) to describe atomic and molecular excitations is tested. The adiabatic (one-parameter) hybrid version of the TPSS meta-GGA and the adiabatic GGA of Perdew, Burke, and Ernzerhof (PBE) are also included in the test. The results are compared to experiments and to two well-established hybrid functionals PBE0 and B3LYP. Calculations show that both adiabatic TPSS and TPSSh functionals produce excitation energies in fairly good agreement with experiments, and improve upon the adiabatic local spin density approximation and, in particular, the adiabatic PBE GGA. This further confirms that TPSS is indeed a reliable nonhybrid universal functional which can serve as the starting point from which higher-level approximations can be constructed. The systematic underestimate of the low-lying vertical excitation energies of molecules with time-dependent density functionals within the adiabatic approximation suggests that further improvement can be made with nonadiabatic corrections.Comment: 7 page