Wavefunction orthogonalized plane wave

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 ... 

This is precisely the type of expression we saw in chapter 2, for the states we called pseudo-wavefunctions, Eq. (2.114), which contain a sum that projects out the core part. So the construction of the orthogonalized plane waves has led us to consider valence states from which the core part is projected out, which in turn leads to the idea of pseudopotentials, discussed in detail in chapter 2. 

The expansion of the plane wave into partial waves yields F m(K)I m(f) components. If these are multiplied by loo V 71) t ie orthogonality condition for spherical harmonics then leads to the result that only the (/ = 0)-component remains. Hence, there is no dependence on k in equ. (4.74b). Similarly, in equ. (4.75b) only the ( f = l)-component is proved. Note, in addition, the typical overlap property of these integrals if a Coulomb wave with Z = 2 were used for the continuum electron the result of the integration would be proportional to Z — Zeff and would vanish for Zeff = 2. In other words, the dependence on Z — Zeff reflects the fact that the final and initial wavefunctions belong to different sets of... 

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