New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem

Abstract

A set of successively niore accurate self-consistent equations for the one-electron Green's functionhavebeen derived. They correspond to an expansion. in a screened potential rather than the bare Coulomb potential. The first equation is adequate for many purposes. Each equation follows from the demand that a corresponding expression for the total energy be stationary with respect to variations in the Green's function. The main information to be obtained, besides the total energy, is one-particle-like excitation spectra, i.e. , spectra characterized by the quantum numbers of a single particle. This includes the low-excitation spectra in metals as well as configurations in atoms, molecules, and solids with one electron outside or one electron missing from a closed. -shell structure. In the latter cases we obtain an approximate description by a modified Hartree-Pock equation involving a "Coulomb hole" and a static screened potential in the exchange term. As an example, spectra of some atoms are discussed. To investigate the convergence of successive approximations for the Green's function, extensive calculations have been made for the electron gas at a range of metallic densities. The results are expressed in terms of quasiparticle energies E(k} and quasiparticle interaction. :f(k, k ). The very first approximation gives a good value for the magnitude of E(k). To estimate the derivative of E(k) we need both the first-and the second-order terms. The derivative, and thus the specific heat, is found to diRer from the free-particle value by only a few percent. Our correction to the specific heat keeps the same sign down to the lowest alkali-metal densities, and is smaller than those obtained recently by Silverstein and by Rice. Our results for the paramagnetic susceptibility are unreliable in the alkali-metaldensity region owing to poor convergence of the expansion for f. Besides the proof of a modified LuttingerWard-Klein variational principle and a related self-consistency idea, there is not much new in principle in this paper. The emphasis is on the devcloIiment of a numerically manageable approximation scheme.

Hole Transfer Dynamics from a CdSe/CdS Quantum Rod to a Tethered Ferrocene Derivative

“…By definition, the E(N)−E(N−1) energies are the quasi-particle energies for the QD HOMO state (or Fc HOMO state) as described in the many-body GW equation. 51 In practice, it is impossible to calculate the GW quasi-particle energies directly for a thousand-atom system. We thus calculate these energies by additional corrections on top of the LDA Kohn−Sham eigenenergies.…”

Role of defects in ferromagnetism inZn1−xCoxO: A hybrid density-functional study

“…Fock exchange in the B3LYP functional also results in an increased band gap of ZnO compared to that predicted by the LSDA. The success of the B3LYP functional in predicting improved properties of metal oxides, 21 compared to DFT or Hartrtee-Fock approaches, may lie in the fact that manybody theories of matter 53 prescribe screening of Fock exchange in solids. Practical experience with the GW approximation, starting with a Kohn-Sham Hamiltonian, 54 would suggest that Fock exchange is screened to a large extent; the B3LYP functional contains Fock exchange with a weight factor of 0.2, and this can be regarded as a uniform screening of Fock exchange by 80%.…”

Synergy of van der Waals and self-interaction corrections in transition metal monoxides

“…Unlike PBE, RPA includes both non-local SIC and van der Waals correction (vdWC): the total energy from RPA is in analogy to the quasi-particle band structure from G0W0 [27][28][29], one of the state-of-the-art approaches for SIC, and vdW interaction is seamlessly included in RPA [30]. Hence, a semilocal functional, such as PBE, with proper SIC and vdWC, may improve the polymorphism energetics for TM oxides.…”