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We present a general scheme of range-separated hybrid functionals in which the mixing parameters of Fock exchange are fully nonempirical and determined solely from the dielectric function.We showthat the full dielectric dependence leads to an unscreened Fock exchange in the short range, while in the long range the Fock exchange is correctly screened by the macroscopic dielectric constant. The range separation is obtained by fitting to the calculated static dielectric function in the long-wavelength limit. The resulting hybrid functional accurately accounts for electronic and structural properties of various semiconductors and insulators spanning a wide range of band gaps. We present a general scheme of range-separated hybrid functionals in which the mixing parameters of Fock exchange are fully nonempirical and determined solely from the dielectric function. We show that the full dielectric dependence leads to an unscreened Fock exchange in the short range, while in the long range the Fock exchange is correctly screened by the macroscopic dielectric constant. The range separation is obtained by fitting to the calculated static dielectric function in the long-wavelength limit. The resulting hybrid functional accurately accounts for electronic and structural properties of various semiconductors and insulators spanning a wide range of band gaps.

Note: This article is part of the JCP Special Topic on Electronic Structure Software.

In the design of materials with low lattice thermal conductivity, compounds with high density, low speed of sound, and complexity at either the atomic, nano-or microstructural level are preferred. The layered compound Mg 3 Sb 2 defies these prevailing paradigms, exhibiting lattice thermal conductivity comparable to PbTe and Bi 2 Te 3 , despite its low density and simple structure. The excellent thermoelectric performance (zT ∼ 1.5) in n-type Mg 3 Sb 2 has thus far been attributed to its multi-valley conduction band, while its anomalous thermal properties have been largely overlooked. To explain the origin of the low lattice thermal conductivity of Mg 3 Sb 2 , we have used both experimental methods and ab initio phonon calculations to investigate trends in the elasticity, thermal expansion and anharmonicity of AMg 2 Pn 2 Zintl compounds with A = Mg, Ca, Yb, and Pn = Sb and Bi. Phonon calculations within the quasiharmonic approximation reveal large mode Grüneisen parameters in Mg 3 Sb 2 compared with isostructural compounds, in particular in transverse acoustic modes involving shearing of adjacent anionic layers. Measurements of the elastic moduli and sound velocity as a function of temperature using resonant ultrasound spectroscopy provide a window into the softening of the acoustic branches at high temperature, confirming their exceptionally high anharmonicity. We attribute the anomalous thermal behavior of Mg 3 Sb 2 to the diminutive size of Mg, which may be too small for the octahedrally-coordinated site, leading to weak, unstable interlayer Mg-Sb bonding. This suggests more broadly that soft shear modes resulting from undersized cations provide a potential route to achieving low lattice thermal conductivity low-density, earth-abundant materials.