Green s function method

Williams A R, Feibelman P J and Lang N D 1982 Green s-function methods for electronic-structure calculations Phys. Rev. B 26 5433... 

Green s function method of Korringa, Kohn, and Rostoker (sometimes denoted KKR)... 

Any orbital-based scheme can be used for crystal-structure calculations. The trend is toward more accurate methods. Some APW and Green s function methods use empirical parameters, thus edging them toward a semiempirical classification. In order of preference, the commonly used methods are ... 

TOTAL ENERGY CALCULATIONS OF ALLOYS LOCALLY SELF-CONSISTENT GREEN S FUNCTION METHOD... 

To improve the latter a number of 0 N) methods have been recently proposed but practically all of them exploit Hamiltonian formalism. However, in Refs. 4,5 the locally self-consistent multiple scattering (LSMS) method based on the real space multiple scattering theory has been outlined, and in Ref. 6 its central idea in the form of the local interaction zone (LIZ) was incorporated into the Green s function technique, leading to the locally self-consistent Green s function method (LSGF). 

The aim of the present paper is to apply the impurity KKR Green s function method to the study of nearest-neighbor effective-pair interaction energies (NN-EPIE s) in low-concentrated fee di.sordered alloys (H = host, X = impurity c < 0.1). It is... 

R. Zeller and P.H. Dederichs, Phys. Rev. Letters, Electronic structure of impurities in Cu, calculated self-consistently by Korringa-Kohn-Rostoker Green s function method , 42 1713 (1979) ... 

For H at T in Si, Katayama-Yoshida and Shindo (1983, 1985) used a Green s function method to carry out spin-density-functional calculations. They found a reduction of the spin density by a factor 0.41. However, their results are subject to some uncertainty because they obtained an erroneous result for the position of the defect state in the band gap, probably due to an insufficiently converged LCAO basis set. 

This position is nothing new it was succinctly and convincingly laid out in a pair of papers by Hedin [7] and Hedin and Lundquist [8], now well over 30 years ago. Particularly, the second paper is an impressive, and valuable review of the full powers of the Green s function method. Frankly, we believe that most, if not all important theoretical aspects have been identified in these papers. 

W. von Niessen, J. Schirmer and L.S. Cederbaum On a Green s Function Method for the calculation of Ionization Spectra in the Outer and Inner Valence Region., in G.H.F. Diercksen and S. Wilson (ed.) Methods in Computational Molecular Physics., D. Reidel Publishing Company, Dordrecht, pp 227—248 (1983). 

To investigate the STM imaging mechanism further, Ohnishi and Tsukada (1989) made a first-principles calculation of the electronic states for a number of W clusters. From the calculations, they found that on the apex atom of many W clusters, there is a <7--like stale protruding from the apex atom, energetically very close to the Fermi level. Using Green s function methods. 

We choose the bisection plane in the barrier as the separation surface. The correction for tunneling current can be obtained from the correction for the wavefunction on the bisection plane. Using the Green s function method, following Eq. (2.42), the correction factor for the wavefunction at z = W/2 is... 

Stepanyuk et al. [471] have applied local approximation of the density-functional theory and the Korringa-Kohn-Rostoker (KKR) Green s function method to determine the energy of Co adatoms located at the ideal Au(lOO) surface. Total-energy calculations have shown that Co atoms and small Co clusters are preferably embedded inside the substrate. 

To solve the diffusion equation and obtain the appropriate rate coefficient with these initial distributions is less easy than with the random distribution. As already remarked, the random distribution is a solution of the diffusion equation, while the other distributions are not. The substitution of Z for r(p(r,s) — p(r, 0)/s) is not possible because an inhomogeneous equation results. This requires either the variation of parameters or Green s function methods to be used (they are equivalent). Appendix A discusses these points. The Green s function g(r, t r0) is called the fundamental solution of the diffusion equation and is the solution to the... 

To solve a second-order inhomogeneous ordinary differential equation, either the Green s function method or the variation of parameters method can be used. Consider the self-adjoint equation... 

The difference between eqn. (330) and eqn. (338) is that y andy2 in eqn. (338) are forced to satisfy the boundary conditions prior to using these independent solutions, while in eqn. (330), the independent solutions do not satisfy the boundary conditions. The form of eqns. s33) and (337) are very similar and shows that the Green s function method and the variation of parameters method of solution are equivalent. 

It should be pointed out that, as used here, the Green s function method implicitly assumes the existence of a continuum or quasicontinuum of states to be coupled with some discrete (or set of discrete) state(s). Thus, the generalized perturbation treatment is valid only in the statistical limit for the isolated molecule. 

V. Averbukh, L.S. Cederbaum, Ab initio calculation of interatomic decay rates by a combination of the Fano ansatz, Green s-function methods, and the Stieltjes imaging technique, J. Chem. Phys. 123 (2005) 204107. 

V is the strength of the coupling to the bridge and i) are the orbitals of the bridge. Using Green s function methods they could obtain the amplitudes 7] by solving a system of linear equations,... 

M.F. Herman et al., Theoretical studies of the equations of motion - Green s function methods and configuration interaction methods Analysis of methods and applications. Adv. Chem. Phys. 48, 1-69 (1981)... 

Keywords Green s function methods, semi-empirical models and model calculations,... 

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