Enhanced Static Approximation to the Electron Self-Energy Operator for Efficient Calculation of Quasiparticle Energies

An enhanced static approximation for the electron self energy operator is proposed for efficient calculation of quasiparticle energies. Analysis of the static COHSEX approximation originally proposed by Hedin shows that most of the error derives from the short wavelength contributions of the assumed adiabatic accumulation of the Coulomb-hole. A wavevector dependent correction factor can be incorporated as the basis for a new static approximation. This factor can be approximated by a single scaling function, determined from the homogeneous electron gas model. The local field effect in real materials is captured by a simple ansatz based on symmetry consideration. As inherited from the COHSEX approximation, the new approximation presents a Hermitian self-energy operator and the summation over empty states is eliminated from the evaluation of the self energy operator. Tests were conducted comparing the new approximation to GW calculations for diverse materials ranging from crystals and nanotubes. The accuracy for the minimum gap is about 10% or better. Like in the COHSEX approximation, the occupied bandwidth is overestimated.Comment: Submitted to Physical Review

Optical excitations of Si by time-dependent density-functional theory based on the exact-exchange Kohn-Sham band structure

We calculate the imaginary part of the frequency-dependent dielectric function of bulk silicon by applying time-dependent density-functional theory based on the exact-exchange (EXX) Kohn-Sham (KS) band structure and the adiabatic local-density approximation (ALDA) kernel. The position of the E2 absorption peak calculated with the EXX band structure at the independent-particle level is in excellent agreement with experiments, which demonstrates the good quality of EXX `KS quasiparticles'. The excitonic E1 peak that is missing at the independent-particle level remains absent if two-particle interaction effects are taken into account within the time-dependent LDA, demonstrating the incapability of the ALDA kernel to describe excitonic effects.Comment: 6 pages, 2 figures; contribution to "DFT 2001", Sep. 10-14, San Lorenzo de El Escorial, Spain; to be published in Int. J. Quantum. Che

The GW space-time method for the self-energy of large systems

We present a detailed account of the GW space-time method. The method increases the size of systems whose electronic structure can be studied with a computational implementation of Hedin's GW approximation. At the heart of the method is a representation of the Green function G and the screened Coulomb interaction W in the real-space and imaginary-time domain, which allows a more efficient computation of the self-energy approximation Sigma = iGW. For intermediate steps we freely change between representations in real and reciprocal space on the one hand, and imaginary time and imaginary energy on the other, using fast Fourier transforms. The power of the method is demonstrated using the example of Si with artificially increased unit cell sizes. (C) 1999 Elsevier Science B.V

Quasiparticle and Optical Properties of Rutile and Anatase TiO2_{2}

Quasiparticle excitation energies and optical properties of TiO$_{2}$ in the rutile and anatase structures are calculated using many-body perturbation theory methods. Calculations are performed for a frozen crystal lattice; electron-phonon coupling is not explicitly considered. In the GW method, several approximations are compared and it is found that inclusion of the full frequency dependence as well as explicit treatment of the Ti semicore states are essential for accurate calculation of the quasiparticle energy band gap. The calculated quasiparticle energies are in good agreement with available photoemission and inverse photoemission experiments. The results of the GW calculations, together with the calculated static screened Coulomb interaction, are utilized in the Bethe-Salpeter equation to calculate the dielectric function $\epsilon_{2}(\omega)$ for both the rutile and anatase structures. The results are in good agreement with experimental observations, particularly the onset of the main absorption features around 4 eV. For comparison to low temperature optical absorption measurements that resolve individual excitonic transitions in rutile, the low-lying discrete excitonic energy levels are calculated with electronic screening only. The lowest energy exciton found in the energy gap of rutile has a binding energy of 0.13 eV. In agreement with experiment, it is not dipole allowed, but the calculated exciton energy exceeds that measured in absorption experiments by about 0.22 eV and the scale of the exciton binding energy is also too large. The quasiparticle energy alignment of rutile is calculated for non-polar (110) surfaces. In the GW approximation, the valence band maximum is 7.8 eV below the vacuum level, showing a small shift from density functional theory results.Comment: Submitted to Physical Review

First-Principles Approach for Energy Level Alignment at Aqueous Semiconductor Interfaces

A first-principles approach is demonstrated to calculate the relationship between aqueous semiconductor interface structure and energy level alignment. The physical interface structure is sampled using density functional theory based molecular dynamics, yielding the interface electrostatic dipole. The $GW$ approach is used to place the electronic band edge energies of the semiconductor relative to the occupied $1b_1$ energy level in water. Application to the specific cases of non-polar $(10\bar{1}0)$ facets of GaN and ZnO reveals a significant role for the structural motifs at the interface, including the degree of interface water dissociation and the dynamical fluctuations in the interface Zn-O and O-H bond orientations. These effects contribute up to 0.5 eV.Comment: Accepted in Phys. Rev. Lett. 5 pages, 4 figures, Supplemental Material: 3 pages, 4 figure