Grid-free DFT implementation of local and gradient-corrected XC functionals

A grid-based real-space implementation of the projector augmented wave ͑PAW͒ method of Blöchl ͓Phys. Rev. B 50, 17953 ͑1994͔͒ for density functional theory ͑DFT͒ calculations is presented. The use of uniform three-dimensional ͑3D͒ real-space grids for representing wave functions, densities, and potentials allows for flexible boundary conditions, efficient multigrid algorithms for solving Poisson and Kohn-Sham equations, and efficient parallelization using simple real-space domain-decomposition. We use the PAW method to perform all-electron calculations in the frozen core approximation, with smooth valence wave functions that can be represented on relatively coarse grids. We demonstrate the accuracy of the method by calculating the atomization energies of 20 small molecules, and the bulk modulus and lattice constants of bulk aluminum. We show that the approach in terms of computational efficiency is comparable to standard plane-wave methods, but the memory requirements are higher.

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“…Alternatively, one can expand the atomic densities in spherical harmonics, as described in Ref. 27 or use grid free approaches 38,39 .…”

Section: B the Paw Total Energymentioning

confidence: 99%

Real-space grid implementation of the projector augmented wave method

2005

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“…There are reports in the literature of stability problems while evaluating the derivative this way. 12 Therefore, the ٌn and n 4/3 terms need to be calculated together as either y or y 2 .…”

Section: A Grid-free Approach To Gradient Corrected Dftmentioning

confidence: 99%

“…[9][10][11] Other functionals require the more general approach proposed by Almlöf and Zheng ͑AZ͒. [12][13][14][15][16] The AZ grid-free approach is based on the resolution of the identity ͑RI͒.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of gradient corrections in grid-free density functional theory

Glaesemann

Gordon

1999

The Journal of Chemical Physics

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The Almlöf-Zheng approach to grid-free density functional theory(DFT) uses the resolution of the identity (RI) instead of a finite grid to evaluate the integrals. Application of the RI can lead to stability problems, particularly when gradients are involved. The focus of the current work is on choosing a stable method of evaluating the gradient correction using the RI. A stable method is compared to several unstable methods. Keywords Density functional theory, Gradient approximations Disciplines Chemistry CommentsThe following article appeared in Journal of Chemical Physics 110 (1999)

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“…The canonical example of this third weakness is the Dirac-Slater exchange energy, which is proportional to the integral over all space of the 4/3 power of the electron density. 4 There have been a number of attempts to avoid the quadrature problem, [5][6][7][8] and the best of these proceed by expanding the problematic integral in an auxiliary basis set. However, this tactic is less progressive than it appears because, in the final analysis, it only replaces the task of choosing optimal grid points with the task of selecting optimal auxiliary basis functions.…”

Section: Introductionmentioning

confidence: 99%

SG‐0: A small standard grid for DFT quadrature on large systems

Chien

Gill

2006

J Comput Chem

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Abstract:We report the development of a new standard quadrature grid for DFT calculations. Standard Grid 0 (SG-0) is designed to be approximately half as large as, and to provide approximately half the accuracy of, the established SG-1 grid. It is based on MultiExp and Lebedev quadrature for radial and angular coordinates, respectively. We find that SG-0 is typically 50% faster than SG-1 for energy, gradient, and hessian calculations for the exchange-correlation energy. This leads to a 35-38% speedup in the total gradient and hessian computations, and we particularly recommend its use for preliminary calculations on moderately large biochemical systems. It has been implemented as the default grid for DFT calculations in the Q-Chem 3.0 package.

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Grid-free DFT implementation of local and gradient-corrected XC functionals

Cited by 13 publications

References 7 publications

Real-space grid implementation of the projector augmented wave method

Real-space grid implementation of the projector augmented wave method

Evaluation of gradient corrections in grid-free density functional theory

SG‐0: A small standard grid for DFT quadrature on large systems

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