Pseudopotential semi-empirical

This chapter reviews models based on quantum mechanics starting from the Schrodinger equation. Hartree-Fock models are addressed first, followed by models which account for electron correlation, with focus on density functional models, configuration interaction models and Moller-Plesset models. All-electron basis sets and pseudopotentials for use with Hartree-Fock and correlated models are described. Semi-empirical models are introduced next, followed by a discussion of models for solvation. 

However, this is definitely the technique for future calculations involving a large number of metal atoms. Furthermore, the idea behind the pseudopotential method is also applied in other types of Hamiltonians described below, e.g., valence effective Hamiltonian and semi-empirical methods. 

In contrast to the pseudopotential methods where the Hartree-Fock method is used to construct the subset of orbitals spanning the core and valence carrier subspaces, whereas the calculation in the valence subspace can be performed at any level of correlation accounting, for the overwhelming majority of the semi-empirical methods, the electronic structure of the valence shell is described by a single determinant (HFR) wave function eq. (1.142). 

The theoretical calculations of the band structure of InN can be grouped into semi-empirical (pseudopotential [10-12] or tight binding [13,14]) ones and first principles ones [15-22], In the former, form factors or matrix elements are adjusted to reproduce the energy of some critical points of the band structure. In the work of Jenkins et al [14], the matrix elements for InN are not adjusted, but deduced from those of InP, InAs and InSb. The bandgap obtained for InN is 2.2 eV, not far from the experimentally measured value. Interestingly, these authors have calculated the band structure of zincblende InN, and have found the same bandgap value [14]. 

Recently, Zunger and coworkers [18, 58-63] employed the semi-empirical pseudopotential method to calculate the electronic structure of Si, CdSe [60] and InP [59] quantum dots. Unlike EMA approaches, this method, based on screened pseudopotentials, allows the treatment of the atomistic character of the nanostructure as well as the surface effects, while permitting multiband and intervalley coupling. The atomic pseudopotentials are extracted from first principles LDA calculations on bulk solids. The single particle LDA equation,... 

The number of reported molecular DHF calculations is sufficiently small that a fairly complete account is possible. The cases which have been studied in the DHF model all involve small molecules, or molecules which exhibit high spatial symmetry. Larger molecules have been studied using more approximate schemes, ranging from semi-empirical and pseudopotential methods to Dirac-Fock-Slater and density functional methods. These are discussed elsewhere in this book. 

The function modelling the core electrons is usually called an Effective Core Potential (ECP) in the chemical community, while the physics community uses the term Pseudopotential (PP). The neglect of an explicit treatment of the core electrons, analogous to the semi-empirical methods in Section 3.10, often gives quite good results at a fraction of the cost of a calculation involving all electrons, and part of the relativis-... 

The basic idea of the pseudopotential approximation was introduced in 1935 by Hellmann, who proposed that the chemically inert core electrons can be replaced by a suitably chosen function, the so-called pseudopotential. We do not discuss the theoretical basis and the historical development of the valence-orbital-only approximation (which is also the basis of most semi-empirical methods ). This has been done elsewhere. For the purpose of this... 

These inconveniences may be partly overcome by using another representation of atom Y, for instance by introducing a pseudohalogen in a semi-empirical computation. In this case the properties of the pseudohalogen may be adjusted to mimic the actual Y atom. This approach is close to the use of a pseudopotential on atom Y, which has been proposed as an efficient solution to this problem. Nevertheless, the extraction of the pseudopotential may not be very familiar to a nonspecialist and it may be difficult to reparametrize this pseudopotential if one wants to adjust the representation of the classical atom to a nonstandard local situation. It is the reason why we looked for another solution which does not require special knowledge other than the standard concepts of quantum chemistry. 

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