Local volume effects in the generalized pseudopotential theory

Abstract

The generalized pseudopotential theory (GPT) is a powerful method for deriving real-space transferable interatomic potentials. Using a coarse-grained electronic structure, one can explicitly calculate the pair ion-ion and multi-ion interactions in simple and transition metals. Whilst successful in determining bulk properties, in central force metals the GPT fails to describe crystal defects for which there is a significant local volume change. A previous paper [PhysRevLett.66.3036 (1991)] found that by allowing the GPT total energy to depend upon some spatially-averaged local electron density, the energetics of vacancies and surfaces could be calculated within experimental ranges. In this paper, we develop the formalism further by explicitly calculating the forces and stress tensor associated with this total energy. We call this scheme the adaptive GPT (aGPT) and it is capable of both molecular dynamics and molecular statics. We apply the aGPT to vacancy formation, divacancy binding and stacking faults in hcp Mg. We also calculate the local electron density corrections to the bulk elastic constants and phonon dispersion for which there is refinement over the baseline GPT treatment.

Ising-like models for stacking faults in a free electron metal

“…Our benchmark calculations are the four fault energies calculated using supercells in the LMTO implementation of DFT [26] using modified tetrahedron method in the Brillouin zone integrations [25]—table 3, column 5. There is excellent agreement between these and our results using the GPT (column 3), indicating that the approximations to the DFT made in constructing the GPT pair potential, v 2 , are validated [12,24]. As is evident from table 3, already at the level of first neighbours—the Ising model—fault energies are in reasonable agreement with supercell calculations using the same level of theory.…”

“…We take two approaches to this. First, we use a standard procedure for obtaining solutions of the Kohn–Sham equations of DFT, here in a basis of linear muffin tin orbitals in a full potential implementation [ 22 ]; second, we exploit the fact that Mg is a free electron metal to apply the first principles pair potential formulation of the DFT total energy within the generalized pseudopotential theory (GPT) [ 11 , 12 , 23 , 24 ].…”

“…[ 34 ]. The GPT for Mg in this form has been thoroughly tested against experiment and standard DFT calculations [ 12 , 23 , 24 ]. For example, the GPT predicts that the atomic volume is Ω 0 = 160.9 bohr 3 and the axial ratio is c / a = 1.621.…”

“…One answer is that we implicitly smooth the Fermi surface discontinuity by applying a cut-off to the pair potential. This is indicated in figure 1 as two vertical lines: the pair potential is not taken to an infinite number of neighbours in the computation but is smoothly interpolated to zero using a polynomial which replaces v 2 between two distances which we choose to be 26.7 bohr and 28.3 bohr [24]. While applying an appropriate electron temperature in the LMTO-DFT has the desirable effect of removing the excessive scatter in the J-parameters there is a price to pay, namely 3 which shows that the supercell fault energies using the finite electron temperature are not as well in accord with the most precise LMTO-DFT values which in turn are in very good agreement with the GPT.…”

Metallic islands in the Kondo insulator SmB$_{6}$

“…SmB 6 is not expected to host a hydrogen-like doping mechanism [57]. Furthermore, the non-parabolic band structure of SmB 6 leads to a significant increase of the calculated density of impurities required for percolation [58]. Hence, the origin of the insulator-to-metal evolution in SmB 6 should differ from that in CaB 6 .…”