Spherical quadrature formulas exact to orders 25?29

Lebedev, V. I.

doi:10.1007/bf00966954

Cited by 180 publications

(94 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The necessary integrations have been performed using our own code, which implements Becke's partition scheme. 19 A Lebedev grid for spherical integration with 230 grid points 20 was borrowed from the DFT repository. 21 The Chebyshev scheme for radial integration with a total of 135 radial grid points has been used throughout.…”

Section: Resultsmentioning

confidence: 99%

Density functional energy decomposition into one- and two-atom contributions

Vyboishchikov

Salvador

Duran

2005

The Journal of Chemical Physics

View full text Add to dashboard Cite

The present work provides a generalization of Mayer's energy decomposition for the density-functional theory ͑DFT͒ case. It is shown that one-and two-atom Hartree-Fock energy components in Mayer's approach can be represented as an action of a one-atom potential V A on a one-atom density A or B . To treat the exchange-correlation term in the DFT energy expression in a similar way, the exchange-correlation energy density per electron is expanded into a linear combination of basis functions. Calculations carried out for a number of density functionals demonstrate that the DFT and Hartree-Fock two-atom energies agree to a reasonable extent with each other. The two-atom energies for strong covalent bonds are within the range of typical bond dissociation energies and are therefore a convenient computational tool for assessment of individual bond strength in polyatomic molecules. For nonspecific nonbonding interactions, the two-atom energies are low. They can be either repulsive or slightly attractive, but the DFT results more frequently yield small attractive values compared to the Hartree-Fock case. The hydrogen bond in the water dimer is calculated to be between the strong covalent and nonbonding interactions on the energy scale.

show abstract

Section: Resultsmentioning

confidence: 99%

Density functional energy decomposition into one- and two-atom contributions

Vyboishchikov

Salvador

Duran

2005

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…[47] The atom-centric radial integrals in the Becke scheme are computed using Gauss-Chebyshev quadrature of the second kind. [63] The angular integrals on each radial shell are performed by default with Lebedev quadrature, [65][66][67][68][69][70] but Lobatto quadrature [71] is available as well. The local nature of the basis functions is used to screen and select only the numerically significant functions in the formation of K DFT [72] by requiring that the absolute value of the basis function is at least = 10 −10 a.u.…”

Section: Formation Of Matricesmentioning

confidence: 99%

ERKALE—A flexible program package for X‐ray properties of atoms and molecules

et al. 2012

View full text Add to dashboard Cite

ERKALE is a novel software program for computing X-ray properties, such as ground-state electron momentum densities, Compton profiles, and core and valence electron excitation spectra of atoms and molecules. The program operates at Hartree-Fock or density-functional level of theory and supports Gaussian basis sets of arbitrary angular momentum and a wide variety of exchange-correlation functionals. ERKALE includes modern convergence accelerators such as Broyden and ADIIS and it is suitable for general use, as calculations with thousands of basis functions can routinely be performed on desktop computers. Furthermore, ERKALE is written in an object oriented manner, making the code easy to understand and to extend to new properties while being ideal also for teaching purposes.

show abstract

“…The relative speed-up compared with the unoptimized code is shown in Table 4 for both the Lebedev and the SG-1 grids. The unoptimized code uses the default EM-GL grid (96,12,24); the default Lebedev grid of comparable accuracy (96, 194) contains a factor of 1.48 fewer points. As indicated in Table 4, the SG-1 grid of lower accuracy gives a total energy difference of 0.0095 Hartree from the EM-GL grid and a total Figure 6.…”

Section: Pruned Grid Resultsmentioning

confidence: 99%

“…[9] Most high-performance DFT codes use Lebedev spheres, which integrate spherical harmonics exactly and are well suited for the angular momentum quadrature of molecular integrals. [10][11][12][13] In the first task area, a Lebedev grid was added as well as the SG-1 grid [14] ; a pruned grid approach built off of a Lebedev grid. Two other pruned grids developed by Janssen (Personal Communication) were also added.…”

Section: Introductionmentioning

confidence: 99%

Recent performance improvements to the DFT and TDDFT in GAMESS

Lasinski¹,

Romero²,

Brown

et al. 2012

J Comput Chem

View full text Add to dashboard Cite

The general atomic and molecular electronic structure system (GAMESS) is a quantum chemistry package used in the first-principles modeling of complex molecular systems using density functional theory (DFT) as well as a number of other post-Hartree-Fock methods. Both DFT and time-dependent DFT (TDDFT) are of particular interest to the materials modeling community. Millions of CPU hours per year are expended by GAMESS calculations on high-performance computing systems; any substantial reduction in the time-to-solution for these calculations represents a significant saving in CPU hours. As part of this work, three areas for improvement were identified: (1) the exchange-correlation (XC) integration grid, (2) profiling and optimization of the DFT code, and (3) TDDFT parallelization. We summarize the work performed in these task areas and present the resulting performance improvement. These software enhancements are available in 12JAN2009R3 or later versions of GAMESS.

show abstract

Spherical quadrature formulas exact to orders 25?29

Cited by 180 publications

References 0 publications

Density functional energy decomposition into one- and two-atom contributions

Density functional energy decomposition into one- and two-atom contributions

ERKALE—A flexible program package for X‐ray properties of atoms and molecules

Recent performance improvements to the DFT and TDDFT in GAMESS

Contact Info

Product

Resources

About