ISSN:0021-8979    

DOI:10.1063/1.1728512

出版商:AIP    

年代:1962

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1728514

出版商:AIP    

年代:1962

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1728515

出版商:AIP    

年代:1962

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1728516

出版商:AIP    

年代:1962

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1728517

出版商:AIP    

年代:1962

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1728518

出版商:AIP    

年代:1962

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1728520

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

In the theory of the electronic structure of crystals, the fundamental features of the band theory, the valence bond method, and the tight‐binding approximation are reviewed. The band theory is studied on the basis of the Hartree‐Fock scheme, and the Bloch functions are formed by a projection technique. The main methods for calculating Hartree‐Fock functions in a solid are briefly discussed. The advantages and disadvantages of the band theory and the valence bond method are emphasized, and special attention is paid to the correlation error.In connection with the tight‐binding approximation, the importance of the continuum part and of the approximate linear dependencies is stressed. It is shown that a complete orthonormal set of translationally connected atomic orbitals may be constructed as a convenient basis for this approach. The implication of the virial theorem in interpreting the cohesive properties of the ionic crystals is further emphasized.Some recent refinements of band theory are then discussed. It is shown that a large part of the correlation error can be removed by permitting ``different orbitals for different spins.'' This leads to a scheme intermediate between band theory and valence bond method and, by means of a single parameter, one can obtain an essential lowering of the energy curve and the correct asymptotic behavior for separated atoms or constituents. This approach may be generalized to an extension of the Hartree‐Fock scheme, where the total wave function is defined as a projection of a Slater determinant.The band theory can be further refined and connected to the exact solution of the many‐electron Schro¨dinger equation of the crystal by means of an extension of the self‐consistent‐field scheme, utilizing the so‐called reaction operator here exactly defined by means of a simple partitioning technique. The various types of self‐consistent field theories are finally compared.

ISSN:0021-8979    

DOI:10.1063/1.1777106

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The simplest possible tight‐binding approximation, usingsphybridized bonds and nearest neighbors overlaps, is used to describe the band structure of diamond, silicon, and germanium. This crude approximation has the great advantage of giving explicit and simple formulas for the Bloch functions andE(k) curves in the whole reciprocal space, as a function of two parameters: an overlap integral &lgr; and ansppromotion energy &egr;. The general band structure is discussed as a function of &egr;/&lgr;. The influence ofsphybridization on the band structure, covalent character of the valence electrons, optical and x‐ray spectra are discussed. It is shown how the energy gap should be related to cohesive energy and pressure. The reasonable agreement with experiment of these various predictions shows the usefulness of the method to understand in a rough and somewhat qualitative way general properties of covalent bonds in crystals.

ISSN:0021-8979    

DOI:10.1063/1.1777107

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The cause of the shifts in quadrupole coupling constants between the gas and solid phases and between equivalent positions in a symmetrical polysubstituted molecule is investigated. An assignment of quadrupole resonance frequencies to positions in the unit cell of 1,3,5‐trichlorobenzene is made on the basis of the calculated electric field. There is agreement with the true assignment and with the magnitude of shifts due to external electric fields. It is concluded that shifts in the resonance frequencies of nuclei at equivalent positions are due mainly to crystalline electric fields. Part of the shift between gas and solid phases is ascribed to zero‐point torsional oscillations of the molecule.

ISSN:0021-8979    

DOI:10.1063/1.1777108

出版商:AIP    

年代:1962

数据来源: AIP