Algorithm 654

DiDonato, A. R.; Morris, Alfred H.

doi:10.1145/29380.214348

Cited by 13 publications

(3 citation statements)

References 2 publications

(1 reference statement)

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“…654. [32] The VoskoWilk-Nusair (VWN) [33] local density approximation (LDA) along with the Perdew-Burke-Ernzerhof (PBE) [34] generalized gradient approximation (GGA) terms were used for the "pure" DFT computations. A corresponding PBE0 functional with 25 % Hartree-Fock exchange [35] was used for hybrid DFT computations.…”

Section: Computational Detailsmentioning

confidence: 99%

Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

Autschbach

2009

ChemPhysChem

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A spherical Gaussian nuclear charge distribution model has been implemented for spin-free (scalar) and two-component (spin-orbit) relativistic density functional calculations of indirect NMR nuclear spin-spin coupling (J-coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J-couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg(2) (2+), and Tl--X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite-nucleus effects.

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Section: Computational Detailsmentioning

confidence: 99%

Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

Autschbach

2009

ChemPhysChem

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“…For applications in mathematical statistics and probability theory the ratios in (3.2) are more relevant. Furthermore, [38] in we described algorithms for inverting the incomplete gamma ratios, and the algorithm improves the one given in [8,9]. The results of the algorithms for the incomplete gamma ratios are used in our current project on the the generalized Marcum Q−function, which is defined in (3.5) and (3.6).…”

Section: Incomplete Gamma Functions Marcum Q−functionmentioning

confidence: 99%

Recent software developments for special functions in the Santander–Amsterdam project

Gil

Segura

Temme

2014

Science of Computer Programming

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We give an overview of published algorithms by our group and of current activities and future plans. In particular, we give details on methods for computing special functions and discuss in detail two current lines of research. Firstly, we describe the recent developments for the computation of central and non-central χ-square cumulative distributions (also called Marcum Q−functions), and we present a new quadrature method for computing them. Secondly, we describe the fourth-order methods for computing zeros of special functions recently developed, and we provide an explicit example for the computation of complex zeros of Bessel functions. We end with an overview of published software by our group for computing special functions.

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“…In order to compute the inverse regularized incomplete gamma function Q −1 (a, θ), we used the software from Refs. [38,39].…”

Section: The Relation Between the Auto-correlation Functionmentioning

confidence: 99%

Relationship between dynamical heterogeneities and stretched exponential relaxation

Simdyankin

Mousseau

2003

Phys. Rev. E

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We identify the dynamical heterogeneities as an essential prerequisite for stretched exponential relaxation in dynamically frustrated systems. This heterogeneity takes the form of ordered domains of finite but diverging lifetime for particles in atomic or molecular systems, or spin states in magnetic materials. At the onset of the dynamical heterogeneity, the distribution of time intervals spent in such domains or traps becomes stretched exponential at long time. We rigorously show that once this is the case, the autocorrelation function of the renewal process formed by these time intervals is also stretched exponential at long time.

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Algorithm 654

Cited by 13 publications

References 2 publications

Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

Recent software developments for special functions in the Santander–Amsterdam project

Relationship between dynamical heterogeneities and stretched exponential relaxation

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