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Register a new userCombining density functional theories to correctly describe the energy, lattice structure and electronic density of functional oxide perovskites
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Functional oxide perovskites are the pillar of cutting-edge technological applications. Density functional theory (DFT) simulations are the theoretical methods of choice to understand and design perovskite materials. However, tests on the reliability of DFT to describe fundamental properties of oxide perovskites are scarce and mostly ill-defined due to a lack of rigorous theoretical benchmarks for solids. Here, we present a quantum Monte Carlo benchmark study of DFT on the archetypal perovskite BaTiO$_{3}$ (BTO). It shows that no DFT approximation can simultaneously reproduce the energy, structure, and electronic density of BTO. Traditional protocols to select DFT approximations are empirical and fail to detect this shortcoming. An approach combining two different non-empirical DFT schemes, SCAN and HSE06, is able to holistically describe BTO with accuracy. Combined DFT approaches should thus be considered as a promising alternative to standard methods for simulating oxide perovskites.
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We propose a method to decompose the total energy of a supercell containing defects into contributions of individual atoms, using the energy density formalism within density functional theory. The spatial energy density is unique up to a gauge transformation, and we show that unique atomic energies can be calculated by integrating over Bader and charge-neutral volumes for each atom. Numerically, we implement the energy density method in the framework of the Vienna ab initio simulation package (VASP) for both norm-conserving and ultrasoft pseudopotentials and the projector augmented wave method, and use a weighted integration algorithm to integrate the volumes. The surface energies and point defect energies can be calculated by integrating the energy density over the surface region and the defect region, respectively. We compute energies for several surfaces and defects: the (110) surface energy of GaAs, the mono-vacancy formation energies of Si, the (100) surface energy of Au, and the interstitial formation energy of O in the hexagonal close-packed Ti crystal. The surface and defect energies calculated using our method agree with size-converged calculations of the difference between the total energies of the system with and without the defect. Moreover, the convergence of the defect energies with size can be found from a single calculation.
The strain effect on electronic structure and thermoelectric properties of Higher Manganese Silicides (HMSs) Mn4Si7 was studied using Density Functional Theory (DFT) and through solving Boltzman Transport Equation (BTE). We found that the tensile strain attempts to reduce the band gap while the compressive strain not much affect to band gap. The Seebeck coeficient was found to be increased with increasing temperature, which is very consistent to experiments. The electrical conductivity and power factor show highly degree of anisotropy, where in-plane direction is more dominant. The different behavior of electrical conductivity along in-plane and outof plane direction was explained due to the change of band dispersion in the valence band maximum (VBM).
These lecture notes contain a brief practical introduction to doing density functional theory calculations for crystals using the open source Quantum Espresso software. The level is aimed at graduate students who are studying condensed matter or solid state physics, either theoretical or experimental.
The direct calculation of the elastic and piezoelectric tensors of solids can be accomplished by treating homogeneous strain within the framework of density-functional perturbation theory. By formulating the energy functional in reduced coordinates, we show that the strain perturbation enters only through metric tensors, and can be treated in a manner exactly paralleling the treatment of other perturbations. We present an analysis of the strain perturbation of the plane-wave pseudopotential functional, including the internal strain terms necessary to treat the atomic-relaxation contributions. Procedures for computationally verifying these expressions by comparison with numerical derivatives of ground-state calculations are described and illustrated.
The class of the Generalized Coherent Potential Approximations (GCPA) to the Density Functional Theory (DFT) is introduced within the Multiple Scattering Theory formalism for dealing with, ordered or disordered, metallic alloys. All GCPA theories are based on a common ansatz for the kinetic part of the Hohenberg-Kohn functional and each theory of the class is specified by an external model concerning the potential reconstruction. The GCPA density functional consists of marginally coupled local contributions, does not depend on the details of the charge density and can be exactly rewritten as a function of the appropriate charge multipole moments associated with each lattice site. A general procedure based on the integration of the qV laws is described that allows for the explicit construction the same function. The coarse grained nature of the GCPA density functional implies great computational advantages and is connected with the O(N) scalability of GCPA algorithms. Moreover, it is shown that a convenient truncated series expansion of the GCPA functional leads to the Charge Excess Functional (CEF) theory [E. Bruno, L. Zingales and Y. Wang, Phys. Rev. Lett. {bf 91}, 166401 (2003)] which here is offered in a generalized version that includes multipolar interactions. CEF and the GCPA numerical results are compared with status of art LAPW full-potential density functional calculations for 62, bcc- and fcc-based, ordered CuZn alloys, in all the range of concentrations. These extensive tests show that the discrepancies between GCPA and CEF are always within the numerical accuracy of the calculations, both for the site charges and the total energies. Furthermore, GCPA and CEF very carefully reproduce the LAPW site charges and the total energy trends.
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