Efficient molecular numerical integration schemes
Эффективные схемы численного интегрирования в молекулярной теории
1995-01-01
SCID: 54.1/y4x54cqr
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Gauss–Chebyshev radial mappingLebedev gridsLobatto quadraturedensity functional calculationsmolecular numerical integration
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Abstract (AI)
New grids for three-dimensional numerical integration are introduced. They include a new mapping for radial integration of the Gauss–Chebyshev type which seems to surpass in accuracy the existing integration schemes as proposed by Becke [J. Chem. Phys. 88, 2547 (1988)], Murray et al. [Mol. Phys. 78, 997 (1993)], or Gill et al. [Chem. Phys. Lett. 209, 506 (1993)]. Lebedev grids are employed for spherical integration. Open ended quadrature schemes are presented using the efficient Lobatto formula for the θ integration. These grids are employed for self-consistent density functional calculations using local approximation and nonlocal corrections and are implemented into the program package turbomole. The results of grid tests and demonstrative applications of energy and especially analytical gradient calculations are given.
Key Findings
1
Implements the new grids into the turbomole program and applies them in self-consistent density functional calculations with local approximations and nonlocal corrections.
2
Introduces new 3D numerical integration grids including a novel Gauss–Chebyshev–type radial mapping that outperforms existing schemes (Becke, Murray et al., Gill et al.) in accuracy.
3
Provides grid tests and demonstrative applications showing improved performance for energy calculations and especially for analytical gradient evaluations.
4
Uses Lebedev grids for spherical integration combined with open-ended quadrature schemes employing an efficient Lobatto formula for θ integration.
Research Object
Three-dimensional numerical integration grids for molecular electronic-structure calculations (radial Gauss–Chebyshev mapping, Lebedev spherical grids, Lobatto θ quadrature) implemented in the Turbomole program
Research Subject
Accuracy and efficiency of the proposed molecular numerical-integration schemes for self-consistent density functional calculations, including energy and analytical gradient evaluations
Publication Details
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1995-01-01
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