Local properties of electronic structure

In the second part (applications) we discuss some recent applications of LCAO methods to calculations of various crystalline properties. We consider, as is traditional for such books the results of some recent band-structure calculations and also the ways of local properties of electronic- structure description with the use of LCAO or Wannier-type orbitals. This approach allows chemical bonds in periodic systems to be analyzed, using the well-known concepts developed for molecules (atomic charge, bond order, atomic covalency and total valency). The analysis of models used in LCAO calculations for crystals with point defects and surfaces and illustrations of their applications for actual systems demonstrate the eflSciency of LCAO approach in the solid-state theory. A brief discussion about the existing LCAO computer codes is given in Appendix C. 

To study the influence of the correlation effects on the local properties of electronic-structure DFT or post-HF methods can be used. If the KS equations are solved the definitions (9.8) (9.13) of local properties include the correlated density matrix and therefore take into account the correlation effects. 

As we have seen above chemical bonding in crystals (as well as in molecules) is analyzed in terms of the local properties of the electronic structure, obtained from the one-electron density matrix, written in a localized basis. Since local properties of electronic structure are essential ingredients of a number of theories and models (for example, the numerical values of atomic charges are used in the atom-atom potentials of the shell model), their estimation is of great importance. TVaditionally, the same AO basis is used both in LCAO SCF calculations and in the local properties definition, as was noted above. However, this approach is not always reliable, since the results of the population analyses are often strongly dependent on an inclusion of diffuse orbitals into the basis (useful for the electronic-structure calculations) and on the scheme chosen for the population analysis. 

Table 9.13. Local properties of electronic structure of cubic LaMnOs...

In Table 9.18 we give the local properties of electronic structure (atomic charges Qa, covalencies Ca, bond orders Wab and overlap populations Rab) calculated by projection techniques A and B for the crystals with different nature of chemical bonding Si, SiC, GaAs, MgO, cubic BN, and Ti02 with a rutile structure, Rq is the nearest-neighbor distance, given in A. 

Table 9.20. Local properties of electronic structure of SrMOa crystals (M=Ti, Zr) in Mul-liken population analysis, projection techniques and WTAO population analysis [611]...

These properties of the d-shell chromophore (group) prove the necessity of the localized description of d-electrons of transition metal atom in TMCs with explicit account for effects of electron correlations in it. Incidentally, during the time of QC development (more than three quarters of century) there was a period when two directions based on two different approximate descriptions of electronic structure of molecular systems coexisted. This reproduced division of chemistry itself to organic and inorganic and took into account specificity of the molecules related to these classical fields. The organic QC was then limited by the Hiickel method, the elementary version of the HFR MO LCAO method. The description of inorganic compounds — mainly TMCs,— within the QC of that time was based on the crystal field... 

The areas of inorganic and organic positron chemistry deal mainly with material characterization and industrial applications using PAS. Both chemical and electronic industries have found PAS to be a powerful method. In addition to the traditional solution chemistry of the positron and Ps [11], PAS has been developed to determine the free volume Bom-Oppenheimer approximation, such as molecular solids [14] and polymers [15]. The unique localization property of Ps in free volumes and holes has opened new hope in polymer scientific research that determination of atomic-level free volumes at the nanosecond scale of motion is possible. During the last ten years, most positron annihilation research has involved a certain amount of polymer chemistry, polymers and coatings, which will be discussed in Chapters 12 and 13. For inorganic systems, oxides are mostly studied using the positron and Ps. Silicon oxides and zeolites are the most important systems in positron and Ps chemistry. The developments in this area have on the cavity structure and chemical states of inner surfaces. Chapters 8 and 14 will discuss this subject. 

In this contribution we have reviewed the applicability, accuracy and computational efficiency of the local spin density functional approach to the chemistry of transition metal complexes and clusters using a linear combination of Gaussian-type orbital basis set for the calculation of electronic structures, ground state geometries and vibrational properties. 

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