Abstract
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.
Highlights
Because of the difficulties in convergence and implementation, all-electron implementations of orbital-free density functional theory (OFDFT) have only been used to derive the energies of small systems, such as atoms and dimers.5,6 On the other hand, OFDFT codes for studying solids rely on the use of local pseudopotentials (LPPs)
After a general introduction to OFDFT equations and projector-augmented wave (PAW) transformation, we present results computed with an atomic all-electron code first and with a real-space PAW code
The binding energy is calculated as the difference between the molecule and the atoms energy obtained in all cases with the PAW method
Summary
Because of the difficulties in convergence and implementation, all-electron implementations of OFDFT have only been used to derive the energies of small systems, such as atoms and dimers. On the other hand, OFDFT codes for studying solids rely on the use of local pseudopotentials (LPPs). As we will demonstrate in the following, using PAW in OFDFT allows the calculation of all-electron energies while improving the convergence capabilities of the OFDFT implementations reusing KS codes. The grid-based projector augmented-wave method (GPAW) rises above others as a potential platform for OFDFT It provides all-electron accuracy, real-space grids and the PAW formalism, which has proven itself as a viable method to obtain all-electron values. As it turns out, the use of the PAW method helps to stabilize some of the convergence problems observed earlier in similar OFDFT calculations (see Ref. 6). We present a novel OFDFT implementation in GPAW that simultaneously preserves linear OFDFT scaling, provides access to all-electron values, and offers improved convergence capabilities. We present some considerations on the performance of the OFDFT implementation using GPAW
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