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Orbital-free density functional theory implementation with the projector augmented-wave method
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12.Within the present approximation, where the wave function ϕo equals n1/2, . In the above equation, the first equality is given by the divergence theorem. The surface integral associated with the divergence theorem, , can be easily shown to vanish: for finite systems, ϕ0 → 0 as r → ∞; for periodic systems, each infinitesimal contribution to the integral has an equivalent contribution of opposite sign because of the periodic boundary conditions. The second equality follows from the chain rule , which gives .
16. E. Fermi, Rend. Accad. Lincei 6, 602 (1927).
25. C. Kittel, Introduction to Solid State Physics (John Wiley and Sons, USA, 2005).
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We present a computational scheme for orbital-free density functional theory (OFDFT) that simultaneously provides access to all-electron values and preserves the OFDFT linear scaling as a function of the system size. Using the projector augmented-wave method (PAW) in combination with real-space methods, we overcome some obstacles faced by other available implementation schemes. Specifically, the advantages of using the PAW method are twofold. First, PAW reproduces all-electron values offering freedom in adjusting the convergence parameters and the atomic setups allow tuning the numerical accuracy per element. Second, PAW can provide a solution to some of the convergence problems exhibited in other OFDFT implementations based on Kohn-Sham (KS) codes. Using PAW and real-space methods, our orbital-free results agree with the reference all-electron values with a mean absolute error of 10 meV and the number of iterations required by the self-consistent cycle is comparable to the KS method. The comparison of all-electron and pseudopotential bulk modulus and lattice constant reveal an enormous difference, demonstrating that in order to assess the performance of OFDFT functionals it is necessary to use implementations that obtain all-electron values. The proposed combination of methods is the most promising route currently available. We finally show that a parametrized kinetic energy functional can give lattice constants and bulk moduli comparable in accuracy to those obtained by the KS PBE method, exemplified with the case of diamond.
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