Projector augmented wave method

The projector augmented wave method (PAW) is a technique used in ab initio electronic structure calculations. It is a generalization of the pseudopotential and linear augmented-plane-wave methods, and allows for density functional theory calculations to be performed with greater computational efficiency. The projector augmented wave method (PAW) is a technique used in ab initio electronic structure calculations. It is a generalization of the pseudopotential and linear augmented-plane-wave methods, and allows for density functional theory calculations to be performed with greater computational efficiency. Valence wavefunctions tend to have rapid oscillations near ion cores due to the requirement that they be orthogonal to core states; this situation is problematic because it requires many Fourier components (or in the case of grid-based methods, a very fine mesh) to describe the wavefunctions accurately. The PAW approach addresses this issue by transforming these rapidly oscillating wavefunctions into smooth wavefunctions which are more computationally convenient, and provides a way to calculate all-electron properties from these smooth wavefunctions. This approach is somewhat reminiscent of a change from the Schrödinger picture to the Heisenberg picture. The linear transformation T {displaystyle {mathcal {T}}} transforms the fictitious pseudo wavefunction | Ψ ~ ⟩ {displaystyle |{ ilde {Psi }} angle } to the all-electron wavefunction | Ψ ⟩ {displaystyle |Psi angle } : Note that the 'all-electron' wavefunction is a Kohn-Sham single particle wavefunction, and should not be confused with the many-body wavefunction. In order to have | Ψ ~ ⟩ {displaystyle |{ ilde {Psi }} angle } and | Ψ ⟩ {displaystyle |Psi angle } differ only in the regions near the ion cores, we write where T ^ R {displaystyle {hat {mathcal {T}}}_{R}} is non-zero only within some spherical augmentation region Ω R {displaystyle Omega _{R}} enclosing atom R {displaystyle R} .