Electronic structure based on the local atomic environment for tight-binding bands. II

Some new methods are presented for calculating the density of states n(E) and other aspects of electronic structure in a tight-binding band, without use of Bloch's theorem or the band structure E(k). The methods are therefore applicable to calculating the local density of states at surfaces, impurities etc. and relate the electronic structure to the local atomic environment. They depend on developing the Green function as an infinite continued fraction. There is no difficulty in obtaining n(E) in a few minutes computing time correct to the first 50 moments for an s-band and 10 moments for d-bands. The present paper discusses the methods and ideas, with specific applications to follow.

[1]  J. Shohat,et al.  The problem of moments , 1943 .

[2]  D. V. Widder,et al.  Review: J. A. Shohat and J. D. Tamarkin, The problem of moments , 1945 .

[3]  Electronic structure of primary solid solutions in metals , 1954 .

[4]  P. Anderson Absence of Diffusion in Certain Random Lattices , 1958 .

[5]  Charles Kittel,et al.  Quantum Theory of Solids , 1963 .

[6]  J. H. Wilkinson The algebraic eigenvalue problem , 1966 .

[7]  H. Mori A Continued-Fraction Representation of the Time-Correlation Functions , 1965 .

[8]  E. Cheney Introduction to approximation theory , 1966 .

[9]  F. Cyrot-Lackmann On the electronic structure of liquid transitional metals , 1967 .

[10]  F. Cyrot-Lackmann Sur le calcul de la cohésion et de la tension superficielle des métaux de transition par une méthode de liaisons fortes , 1968 .

[11]  R. Jaffee,et al.  Molecular processes on solid surfaces , 1969 .

[12]  Energie De Formation De Monolacunes Dans Les Metaux De Transition , 1969 .

[13]  D. Pettifor An energy-independent method of band-structure calculation for transition metals , 1969 .

[14]  D. Pettifor Theory of the crystal structures of transition metals at absolute zero. , 1970 .

[15]  V. Heine,et al.  Pseudopotential Theory of Cohesion and Structure , 1970 .

[16]  F. Ducastelle,et al.  Moments developments and their application to the electronic charge distribution of d bands , 1970 .

[17]  G. Slodzian,et al.  Processus de formation d'ions à partir d'atomes éjectés dans des états électroniques surexcités lors du bombardement ionique des métaux de transition , 1970 .

[18]  Moments of the density of states and s−d mixing , 1970 .

[19]  W. Brinkman,et al.  Single-Particle Excitations in Magnetic Insulators , 1970 .

[20]  M. Thorpe,et al.  Electronic properties of an amorphous solid. II. Further aspects of the theory , 1971 .

[21]  E. Economou,et al.  Localization in One-Dimensional Disordered Systems , 1971 .

[22]  F. Ducastelle,et al.  Binding Energies of Transition-Metal Atoms Adsorbed on a Transition Metal , 1971 .

[23]  P. Soven,et al.  A green's function theory of surface states , 1971 .

[24]  C. Paige Computational variants of the Lanczos method for the eigenproblem , 1972 .

[25]  V. Heine,et al.  Electronic Density of States at Transition-Metal Surfaces , 1972 .

[26]  On the surface specific heat of a cyclic crystal lattice , 1972 .

[27]  A. Mookerjee Averaged density of states in disordered systems , 1973 .

[28]  M. Kelly,et al.  The electronic structure of the (111) surface of silicon , 1973 .

[29]  Étude des systèmes covalents parfaits et imparfaits par deux méthodes d'approximation , 1973 .

[30]  E. S. Giuliano,et al.  Electron density of states in disordered systems , 1973 .

[31]  A. Mookerjee A new formalism for the study of configuration-averaged properties of disordered systems , 1973 .

[32]  F. Cyrot-Lackmann,et al.  Density of states from moments. Application to the impurity band , 1973 .

[33]  J. Weeks,et al.  Non‐Hermitian representations in localized orbital theories , 1973 .

[34]  S. Swain A continued fraction solution to the problem of a single atom interacting with a single radiation mode in the electric dipole approximation , 1973 .

[35]  M. Kelly,et al.  Surface densities of states in the tight-binding approximation , 1973 .

[36]  R. L. Jacobs The theory of disordered alloys. I. Continued fractions and off-diagonal disorder , 1973 .

[37]  S. Swain Continued fraction expressions for the eigensolutions of the hamiltonian describing the interaction between a single atom and a single field mode: comparisons with the rotating wave solutions , 1973 .