Electronic structure pseudopotential

There are a variety of other approaches to understanding the electronic structure of crystals. Most of them rely on a density functional approach, with or without the pseudopotential, and use different bases. For example, instead of a plane wave basis, one might write a basis composed of atomic-like orbitals ... 

The empirical approach [7] was by far the most fruitful first attempt. The idea was to fit a few Fourier coefficients or form factors of the potential. This approach assumed that the pseudopotential could be represented accurately with around three Fourier form factors for each element and that the potential contained both the electron-core and electron-electron interactions. The form factors were generally fit to optical properties. This approach, called the Empirical Pseudopotential Method (EPM), gave [7] extremely accurate energy band structures and wave functions, and applications were made to a large number of solids, especially semiconductors. [8] In fact, it is probably fair to say that the electronic band structure problem and optical properties in the visible and UV for the standard semiconductors was solved in the 1960s and 1970s by the EPM. Before the EPM, even the electronic structure of Si, which was and is the prototype semiconductor, was only partially known. 

V. Milman, B. Winkler, J. A. White, C. J. Pickard, M. C. Payne, E. V. Akhmatskaya, and R. H. Nobes, Electronic Structure, Properties, and Phase Stability of Inorganic Crystals A Pseudopotential Plane-Wave Study, hit. 

One interesting scheme based on density functional theory (DFT) is particularly appealing, because with the current power of the available computational facilities it enables the study of reasonably extended systems. DFT has been applied with a variety of basis sets (atomic orbitals or plane-waves) and potential formulations (all-electron or pseudopotentials) to complex nu-cleobase assemblies, including model systems [90-92] and realistic structures [58, 93-95]. DFT [96-98] is in principle an ab initio approach, as well as MP2//HF. However, its implementation in manageable software requires some approximations. The most drastic of all the approximations concerns the exchange-correlation (xc) contribution to the total DFT functional. 

Finally, the use of ECP basis sets for heavy elements improves efficiency by reducing the scale of the electronic structure problem. In addition, relativistic effects can be accounted for by construction of the pseudopotential. 

The method employed was similar to that of Ref. 35, but with several improvements. ab initio, norm-conserving, nonlocal pseudopotential were used to represent the metal ions. This capability enables reliably realistic representation of the metal s electronic structure. Thus the cadmium pseudopotential was able, for example, to reproduce the experimental cadmium-vacuum work function using no adjustable parameters (unlike the procedure followed in Ref. 35). Pseudopotentials of the Troullier and Martins form [53] were used with the Kleinman-Bylander [54] separable form, and a real space... 

Also pure density-functional methods combined with plane-wave basis sets and ultrasoft pseudopotentials [58] were used in our studies of extended systems [59]. The computational efficiency of these methods enables larger systems and to some extent dynamical processes to be studied. Generalized-gradient approximation (GGA) or spin-polarized GGA DFT functionals [60, 61] were employed in the electronic structure calculations. 

Durand, P. and Barthelat, J. C. (1975) A theoretical Method to Determine Atomic Pseudopotentials for Electronic Structure Calculations of Molecules and Solids Theor. Chim. Acta, 38,283-302. 

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). 

Electronic structure methods for studies of nanostructures can be divided broadly into supercell methods and real-space methods. Supercell methods use standard k-space electronic structure techniques separating periodically repeated nanostructures by distances large enough to neglect their interactions. Direct space methods do not need to use periodic boundary conditions. Various electronic structure methods are developed and applied using both approaches. In this section we will shortly discuss few popular but powerful electronic structure methods the pseudopotential method, linear muffin-tin orbital and related methods, and tight-binding methods. 

The traditional approach to obtain the electronic structure of a periodic solid with ab initio pseudopotentials has been to solve the Kohn-Sham (KS)... 

In the present calculation, we used two ab initio methods to investigate structural stability and the potential for carrier generation of X B6 and X Bi2 clusters in c-Si. Here X is from H to Br in the periodic table. The following two methodsused were (i) plane wave ultrasoft pseudopotential method for the optimization of atomic structures and (ii) discrete variational-Xa (DV-Xa) molecular orbital method for the analysis of the fine electronic structures and activation energies of the clusters. 

This concludes the formulation of Vsoiv.. Two terms remain, though, in the intermolecular interaction potential between quantum chemical region and solvent. These terms are only added to the total energy and therefore only indirectly influence the electronic structure. The first term is a consequence of the finding that the pseudopotential in Eq. (9-8) does not lead to sufficient repulsion at short separations. With SAPT it is shown that higher-order repulsive terms will appear, terms which have a fourth, sixth and so forth order dependence on the overlap. In QMSTAT, these terms are not included in Vsoiv., instead terms like... 

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