Orthogonalized plane wave method

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... 

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. 

T. O. Woodruff, The orthogonalized plane wave method. Solid State Phys. 4, 367- 11 (1957). 

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... 

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]. 

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... 

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 ... 

Historically speaking, the orthogonalized plane wave (OPW) method should have been discussed before the pseudopotential method (Section 3.6). The work of Phillips and Kleinman, which is... 

The use of orthogonalized plane waves, which has been reviewed by Woodruff, is not very widespread today, partly because equivalent pseudopotentials provide a more physically transparent picture and partly because the method is somewhat more cumbersome than the APW and related methods. 

Prior to 1975 or so, the words ab initio did not exist in the scientific vocabulary for methods describing the electronic structure of the solid state. At that time, a number of very powerful and successful methods had been developed to describe the electronic structure of solids, but these methods did not pretend to be first principles or ab initio methods. The foremost example of electronic structure methods at that time was the empirical pseudopotential method (EPM) [1]. The EPM was based on the Phillips-Kleinman cancelation theorem [2], which justified the replacement of the strong, allelectron potential with a weak pseudopotential [1]. The pseudopotential replicated only the chemically active valence electron states. Physically, the cancelation theorem is based on the orthogonality requirement of the valence states to the core states [1]. This requirement results in a repulsive part of the pseudopotential which cancels the strongly attractive part of the core potential and excludes the valence states from the core region. Because of this property, simple bases such as plane waves can be used efficiently with pseudopotentials. 

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