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Register a new userAn efficient method for hybrid density functional calculation with spin-orbit coupling
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In first-principles calculations, hybrid functional is often used to improve accuracy from local exchange correlation functionals. A drawback is that evaluating the hybrid functional needs significantly more computing effort. When spin-orbit coupling (SOC) is taken into account, the non-collinear spin structure increases computing effort by at least eight times. As a result, hybrid functional calculations with SOC are intractable in most cases. In this paper, we present an approximate solution to this problem by developing an efficient method based on a mixed linear combination of atomic orbital (LCAO) scheme. We demonstrate the power of this method using several examples and we show that the results compare very well with those of direct hybrid functional calculations with SOC, yet the method only requires a computing effort similar to that without SOC. The presented technique provides a good balance between computing efficiency and accuracy, and it can be extended to magnetic materials.
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We quantify the accuracy of different non-self-consistent and self-consistent spin-orbit coupling (SOC) treatments in Kohn-Sham and hybrid density-functional theory by providing a band structure benchmark set for the valence and low-lying conduction energy bands of 103 inorganic compounds, covering chemical elements up to Po. Reference energy band structures for the PBE density functional are obtained using the full-potential (linearized) augmented plane wave code Wien2k, employing its self-consistent treatment of SOC including Dirac-like p$^{1/2}$ orbitals in the basis set. We use this benchmark set to benchmark a computationally simpler, non-self-consistent all-electron treatment of SOC based on scalar-relativistic orbitals and numeric atom-centered orbital basis functions. For elements up to Z$approx$50, both treatments agree virtually exactly. For the heaviest elements considered (Tl, Pb, Bi, Po), the band structure changes due to SOC are captured with a relative deviation of 11% or less. For different density functionals (PBE vs. the hybrid HSE06), we show that the effect of spin-orbit coupling is usually similar but can be dissimilar if the qualitative features of the predicted underlying scalar-relativistic band structures do not agree. All band structures considered in this work are available online via the NOMAD Repository to aid in future benchmark studies and methods development.
In this paper we revisit the Levy-Perdew-Sahni equation. We establish that the relation implicitly contains the conservation of energy density at every point of the system. The separate contributions to the total energy density are described in detail, and it is shown that the key difference to standard density functional methods is the existence of a general exchange-correlation potential, which does not explicitly depend on electron charge. We derive solutions for the hydrogen-like atoms and analyse local properties. It is found that these systems are stable due to the existence of a vector potential ${bf A}$, related to electron motion, which leads to two general effects: (i) The root of the charge density acquires an additional complex phase; and (ii) for single electrons, the vector potential cancels the effect of electrostatic repulsions. We determine the density of states of a free electron gas based on this model and find that the vectorpotential also accounts for the Pauli exclusion principle. Implications of these results for direct methods in density functional theory are discussed. It seems that the omission of vector potentials in formulating the kinetic energy density functionals may be the main reason that direct methods so far are not generally applicable. Finally, we provide an orbital free self-consistent formulation for determining the groundstate charge density in a local density approximation.
Because inorganic solid electrolytes are one of the key components for application to all-solid-state batteries, high-ionic-conductivity materials must be developed. Therefore, we propose a method of efficiently evaluating the activation energy of ionic diffusion by calculating a potential-energy surface (PES), searching for the optimal diffusion path by an algorithm developed using dynamic programming (DP), and calculating the corresponding activation energy by the nudged elastic band (NEB) method. Taking beta-Li3PS4 as an example, the activation energy of Li-ion diffusion was calculated as 0.43, 0.25, and 0.40 eV in the a-, b-, and c-axis directions, respectively, which is in good agreement with previously reported values. By comprehensively searching for the lowest energy path by PES-DP, the arbitrariness of the path selection can be eliminated, and the activation energy must only be calculated using the NEB method a few times, which greatly reduces the computational cost required for evaluating activation energy and enables the high-throughput screening of solid state electrolytes.
We present a new method to compute the electronic structure of correlated materials combining the hybrid functional method with the dynamical mean-field theory. As a test example of the method we study cerium sesquioxide, a strongly correlated Mott-band insulator. The hybrid functional part improves the magnitude of the pd-band gap which is underestimated in the standard approximations to density functional theory while the dynamical mean-field theory part splits the 4f-electron spectra into a lower and an upper Hubbard band.
An electric current in the presence of spin-orbit coupling can generate a spin accumulation that exerts torques on a nearby magnetization. We demonstrate that, even in the absence of materials with strong bulk spin-orbit coupling, a torque can arise solely due to interfacial spin-orbit coupling, namely Rashba-Eldestein effects at metal/insulator interfaces. In magnetically soft NiFe sandwiched between a weak spin-orbit metal (Ti) and insulator (Al$_2$O$_3$), this torque appears as an effective field, which is significantly larger than the Oersted field and sensitive to insertion of an additional layer between NiFe and Al$_2$O$_3$. Our findings point to new routes for tuning spin-orbit torques by engineering interfacial electric dipoles.
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