Density functional theory for <i>d</i>‐ and <i>f</i>‐electron materials and compounds

Kullback-Leibler and relative Fisher information functionals are applied in studying deviation from local density approximation. The reduced density gradient s and the local kinetic energy parameter a are key ingredients of these new locality descriptors. The relative Kullback-Leibler information density contains extra knowledge as it is negative where the given probability density is smaller than the reference density. The relative Fisher information incorporates the highest order deviations from the uniform electron gas approximation. K E Y W O R D S density functional theory, descriptors of locality, Kullback-Leibler information, relative Fisher information Int J Quantum Chem. 2018;118:e25557.

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“…ELF has proved to be a very useful quantity for several applications . The uniform electron gas is the reference system here.…”

Section: Comparison Of Descriptors and Discussionmentioning

confidence: 99%

Kullback–Leibler and relative Fisher information as descriptors of locality

Levämäki

Nagy

Vilja

et al. 2017

Int J of Quantum Chemistry

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“…To perform GKS-DFT calculations, we have to deal with the problem that unfortunately there is a lack of any explicit relativistic functional within the 2c approach for TRSB systems, as recalled in the introduction. [12][13][14][15][16][17] We stress that also within the most general 4c approach, where the appropriate density variable is the so-called four-current J , no explicit functionals have been devised for TRSB systems. 12,13,47 Therefore, in practice, DFT relativistic calculations on TRSB systems must be performed by modifying existing non-relativistic 1c functionals using appropriate collinear formulations (in which the functional depends only on n and m z ) or non-collinear formulations (in which the functional depends only on n and m).…”

Section: Time Reversal Symmetry Breaking In Position Spacementioning

confidence: 99%

“…However, explicit relativistic exchange-correlation functionals for TRSB systems (with a dependence on the particlenumber density n, the magnetization vector m = [m x , m y , m z ], as well as the SOC-induced orbital-current density vector j = [j x , j y , j z ], and the three spin-current density vectors J x = [J xx , J xy , J xz ], J y = [J yx , J yy , J yz ], J z = [J zx , J zy , J zz ]) are still to be devised. [12][13][14][15][16][17]46 In practice, relativistic calculations are usually performed with the so-called collinear or non-collinear formulations of the DFT, where use is made of standard nonrelativistic functionals modified to only include the explicit dependence on n and m z (collinear) or n and m (non-collinear). 9,16,[18][19][20][21][22][23][24][25][26][27][28][29][30] In this paper we analyze some of the limitations due to the lack of such explicit relativistic functionals for calculations on TRSB materials and we present a strategy to overcome most of them.…”

Section: Introductionmentioning

confidence: 99%

Spin-orbit coupling in periodic systems with broken time-reversal symmetry: Formal and computational aspects

2020

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We discuss the treatment of spin-orbit coupling (SOC) in time reversal symmetry broken periodic systems for relativistic electronic structure calculations of materials within the generalized noncollinear Kohn-Sham density functional theory (GKS-DFT). We treat SOC self-consistently and express the GKS orbitals in a two-component spinor basis. Crucially, we present a methodology (and its corresponding implementation) for the simultaneous self-consistent treatment of SOC and exact non-local Fock exchange operators. The many advantages of the inclusion of non-local Fock exchange in the self-consistent treatment of SOC, as practically done in hybrid exchange-correlation functionals, are both formally derived and illustrated through numerical examples: i) it imparts a local magnetic torque (i.e. the ability of the two-electron potential to locally rotate the magnetization with respect to a starting guess configuration) that is key to converge to the right solution in non-collinear DFT regardless of the initial guess for the magnetization; ii) because of the local magnetic torque, it improves the rotational invariance of non-collinear formulations of the DFT; iii) it introduces the dependence on specific pieces of the spinors (i.e. those mapped onto otherwise missing spin-blocks of the complex density matrix) into the two-electron potential, which are key to the correct description of the orbital-and spin-current densities and their coupling with the magnetization; iv) when space-inversion symmetry is broken, it allows for the full breaking of timereversal symmetry in momentum space, which would otherwise be constrained by a sum-rule linking the electronic band structure at opposite points in the Brillouin zone (k and -k). The presented methodology is implemented in a developmental version of the public Crystal code. Numerical tests are performed on the model system of an infinite radical chain of Ge2H with both spaceinversion and time-reversal symmetries broken, which allows to highlight all the above-mentioned effects.

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“…The V-DM/17 test set is designed to capture the wide variety of unique physics that arise in TM alloys, a consequence of the interaction of chemically active d -electrons [43]. These interactions are often ill-captured by present functionals [22], as most functionals are designed to focus on and accurately solve one "model" electron system or situation.…”

Section: Density Functional Theory Applied To Transition Metal Elements and Binariesmentioning

confidence: 99%

Summer Proceedings 2018: The Center for Computing Research at Sandia National Laboratories

Cangi¹,

Parks²

2018

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Computational mathematics is concerned with the design, analysis, and implementation of algorithms to solve mathematical problems. Articles in this section describe the discretization of partial differential equations and methods to solve equations, couple multiphysics systems of equations, and quantify uncertainty.Chen, Rajamanickam, Boman, and Darve introduce a parallel, hierarchical solver for linear systems generated from the discretization of elliptic PDEs that is based on the LoRaSp hierarchical solver, which uses block Cholesky factorization and low-rank elimination. The parallel version makes use of the distance-2 connection property to partition the graph nodes based on their distances from processor boundaries and coloring to coordinate computation and communication for processor boundary nodes. They demonstrate that their algorithm achieves nearly linear scaling in solve time and memory usage for 3-D problems and constant iteration count when used as a preconditioner for Poisson problems, and good strong and weak scaling on multiple processors.Eller and Hoemmen derive scalable versions of the preconditioned conjugate gradient method that use a three-term recurrence. By overlapping two iterations of matrix-vector multiplies and preconditioner applications with a single non-blocking allreduce, they address scalability problems associated with blocking allreduce. They give full derivations of their scalable methods and compare them with two existing preconditioned conjugate gradient algorithms. Their approach provides the potential to develop further pipelined, non-blocking methods.Fisher and Cyr construct a discretization for PDE constrained optimization problems based on piecewise Hermite cubic orthogonal spline collocation in one and two dimensions. They also prove the optimality of a preconditioner for the MINRES iteration and confirm it computationally. They apply the method to the problems of distributed control of Poisson's equation and Burgers' equation.Lupo Pasini, Tuminaro, and Hu investigate an additive multigrid method adapted to a domain decomposition setting with the aim of achieving convergence properties comparable with multiplicative approaches while maintaining a computational cost comparable with additive approaches. The approach has the potential to enhance concurrency and improve performance on new and future architectures. They carefully construct the smoothed interpolation operator and use subdomain coloring to compress the prolongator to significantly decrease communication cost and memory storage requirements. They demonstrate that the approach can improve performance if the problem size and number of subdomains are carefully chosen to achieve good load balancing.Ohm and Tuminaro present a multigrid method for linear systems derived from PDEs discretized using meshes that have both structured and unstructured regions that ensures that the prolongation operator is consistent at the interfaces between structured and unstructured regions. They demonstrate significant reductions in th...

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Density functional theory for d‐ and f‐electron materials and compounds

Cited by 9 publications

References 47 publications

Kullback–Leibler and relative Fisher information as descriptors of locality

Kullback–Leibler and relative Fisher information as descriptors of locality

Spin-orbit coupling in periodic systems with broken time-reversal symmetry: Formal and computational aspects

Summer Proceedings 2018: The Center for Computing Research at Sandia National Laboratories

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