Orthogonalized plane waves

OPW (orthogonalized plane wave) a band-structure computation method P89 (Perdew 1986) a gradient corrected DFT method parallel computer a computer with more than one CPU Pariser-Parr-Pople (PPP) a simple semiempirical method PCM (polarized continuum method) method for including solvation effects in ah initio calculations... 

For the conduction electrons, it is reasonable to consider that the inner-shell electrons are all localized on individual nuclei, in wave functions very much like those they occupy in the free atoms. The potential V should then include the potential due to the positively charged ions, each consisting of a nucleus plus filled inner shells of electrons, and the self-consistent potential (coulomb plus exchange) of the conduction electrons. However, the potential of an ion core must include the effect of exchange or antisymmetry with the inner-shell or core electrons, which means that the conduction-band wave functions must be orthogonal to the core-electron wave functions. This is the basis of the orthogonalized-plane-wave method, which has been successfully used to calculate band structures for many metals.41... 

Formally, each orthogonalized-plane-wave basis function may be written as (1 - P), where ijjk is a plane wave and P is the projection operator such that Pif/k gives the core-state component of Il>k ... 

In 1940 Herring circumvented this problem by starting at the outset with a basis of plane waves that had already been orthogonalized to the core states, the so-called orthogonalized plane wave (OPW) basis. Retaining only the two lowest orthogonalized plane waves we can look for the OPW solution that is analogous to eqn (5.35), namely... 

Orthogonalized Plane Waves (OPW). This method makes the plane waves orthogonal to the core electron wavef unctions, to avoid the slow convergence due to oscillations of the conduction electron states in the neighborhood of the atomic core electrons [30]. 

Perhaps the most successful representation of the wave functions for band calculations for semiconductors has been the OPW method (orthogonalized plane-wave method), developed by Herring (1940). The success of the method has been due to the ease of obtaining and using realistic potentials in the calculation, in contrast to methods that utilize the muffin-tin approximation to the potential (discussed in Chapter 20). Only recently have difficulties with the application of muffin-tin potentials to semiconductors been overcome. (P or discussion and references see Johnson, Norman, and Connolly, 1973.) For any given potential, any of the accurate methods should give the same bands if the necessary effort is applied. 

If I is replaced by a plane wave on the right side of Eq. (D-1), this gives exactly what is called an orthogonalizedplane ivave, or OPW, The orthogonalized plane wave method of band calculation consists of expanding the true wave function in OPW s. It was invented by Herring (1940) and provides the conceptual basis of pseudopotential theory. 

In fact, because of its importance in solid-state science, a large variety of band-structure approaches have been used to calculate the electronic structure of sphalerite. These have included self-eonsistent and semiem-pirical orthogonalized-plane-wave (OPW) (Stukel et al., 1969), empirical-pseudopotential (Cohen and Bergstresser, 1966), tight-binding (Pantelides and Harrison, 1975), APW (Rossler and Lietz, 1966), and modified OPW (Farberovich et al., 1980), as well as KKR (Eckelt, 1967) methods. In a recent and extremely detailed study using a density-functional approach (specifically a method termed the self-consistent potential variation... 

Stukel, D. J., R. N. Euwema, T. C. Collins, F. Herman, and R. L. Kortum (1969). Self-consistent orthogonalized-plane-wave and empirically refined ortho-gonalized-plane-wave energy band models for cubic ZnS, ZnSe, CdS, and CdSe. Phys. Rev. 179, 740-51. 

Orthogonalized Plane Waves (OPW) This method, due to Herring [47], is an elaboration on the APW approach. The trial valence wavefunctions are written at the outset as a combination of plane waves and core-derived states ... 

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