Direct minimization technique for metals in density functional theory

Freysoldt, Christoph; Boeck, Sixten; Neugebauer, Jörg

doi:10.1103/physrevb.79.241103

Cited by 61 publications

(53 citation statements)

References 9 publications

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“…Freysoldt et al 42 have attempted to address this issue by developing an equivalent scheme where one works directly with the molecular orbital energies instead of the occupancies. In the spirit of the Marzari approach, they employ a non-diagonal representation of orbital energies, which is the Hamiltonian matrix, and minimize the following functional:…”

Section: B Ensemble Dft (Edft)mentioning

confidence: 99%

Perspective: Methods for large-scale density functional calculations on metallic systems

Aarons

Sarwar

Thompsett

et al. 2016

The Journal of Chemical Physics

122

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Perspective: Explicitly correlated electronic structure theory for complex systems The Journal of Chemical Physics 146, 080901 (2017) Current research challenges in areas such as energy and bioscience have created a strong need for Density Functional Theory (DFT) calculations on metallic nanostructures of hundreds to thousands of atoms to provide understanding at the atomic level in technologically important processes such as catalysis and magnetic materials. Linear-scaling DFT methods for calculations with thousands of atoms on insulators are now reaching a level of maturity. However such methods are not applicable to metals, where the continuum of states through the chemical potential and their partial occupancies provide significant hurdles which have yet to be fully overcome. Within this perspective we outline the theory of DFT calculations on metallic systems with a focus on methods for large-scale calculations, as required for the study of metallic nanoparticles. We present early approaches for electronic energy minimization in metallic systems as well as approaches which can impose partial state occupancies from a thermal distribution without access to the electronic Hamiltonian eigenvalues, such as the classes of Fermi operator expansions and integral expansions. We then focus on the significant progress which has been made in the last decade with developments which promise to better tackle the lengthscale problem in metals. We discuss the challenges presented by each method, the likely future directions that could be followed and whether an accurate linear-scaling DFT method for metals is in sight. Published by AIP Publishing. [http://dx

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Section: B Ensemble Dft (Edft)mentioning

confidence: 99%

Perspective: Methods for large-scale density functional calculations on metallic systems

Aarons

Sarwar

Thompsett

et al. 2016

The Journal of Chemical Physics

122

View full text Add to dashboard Cite

show abstract

“…lot of attention, and several methods for minimization of the ground state energy are available. [7][8][9][10] These methods are typically based on constructing a search direction and subsequently minimizing the energy functional on the search direction. [6][7][8]10 One challenge present in direct minimization is the requirement that the Kohn-Sham orbitals remain orthogonal, and the minimizers are therefore constrained to a nonlinear surface.…”

Section: Introductionmentioning

confidence: 99%

“…[7][8][9][10] These methods are typically based on constructing a search direction and subsequently minimizing the energy functional on the search direction. [6][7][8]10 One challenge present in direct minimization is the requirement that the Kohn-Sham orbitals remain orthogonal, and the minimizers are therefore constrained to a nonlinear surface. [11][12][13] SCF problems are also encountered in several other computational science problems, and several strategies are available for solving these problems.…”

Section: Introductionmentioning

confidence: 99%

Robust acceleration of self consistent field calculations for density functional theory

Baarman

Eirola

Havu

2011

The Journal of Chemical Physics

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We show that the type 2 Broyden secant method is a robust general purpose mixer for self consistent field problems in density functional theory. The Broyden method gives reliable convergence for a large class of problems and parameter choices. We directly mix the approximation of the electronic density to provide a basis independent mixing scheme. In particular, we show that a single set of parameters can be chosen that give good results for a large range of problems. We also introduce a spin transformation to simplify treatment of spin polarized problems. The spin transformation allows us to treat these systems with the same formalism as regular fixed point iterations.

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“…JDFTx supports interactions with custom external potentials and fields, and allows accurate calculations of systems of any dimensionality: molecules (0D), wires (1D), slabs / 2D materials and bulk (3D), using truncated Coulomb interactions [22]. Importantly, JDFTx implements two distinct classes of algorithms for electronic DFT, variational minimization of the (analytically-continued) total energy [39,40] and the self-consistent field (SCF) iteration method [41]. Variational minimization is stable and guaranteed to converge, while SCF (the default method available in all DFT codes) is less stable in general, but faster when it converges well.…”

Section: Software Architecturementioning

confidence: 99%

JDFTx: Software for joint density-functional theory

et al. 2017

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Density-functional theory (DFT) has revolutionized computational prediction of atomic-scale properties from first principles in physics, chemistry and materials science. Continuing development of new methods is necessary for accurate predictions of new classes of materials and properties, and for connecting to nano- and mesoscale properties using coarse-grained theories. JDFTx is a fully-featured open-source electronic DFT software designed specifically to facilitate rapid development of new theories, models and algorithms. Using an algebraic formulation as an abstraction layer, compact C++11 code automatically performs well on diverse hardware including GPUs (Graphics Processing Units). This code hosts the development of joint density-functional theory (JDFT) that combines electronic DFT with classical DFT and continuum models of liquids for first-principles calculations of solvated and electrochemical systems. In addition, the modular nature of the code makes it easy to extend and interface with, facilitating the development of multi-scale toolkits that connect to ab initio calculations, e.g. photo-excited carrier dynamics combining electron and phonon calculations with electromagnetic simulations.

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Direct minimization technique for metals in density functional theory

Cited by 61 publications

References 9 publications

Perspective: Methods for large-scale density functional calculations on metallic systems

Perspective: Methods for large-scale density functional calculations on metallic systems

Robust acceleration of self consistent field calculations for density functional theory

JDFTx: Software for joint density-functional theory

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