New integral transforms for molecular properties and application to a massively parallel GIAO-SCF implementation

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Abstract

We present several new Gaussian integral transforms to be used with the Rys quadrature numerical integration method. These transforms lead to an elegant unified methodology for the calculation of the atomic Gaussian integrals that enter the calculation of many molecular wavefunctions and properties. The unified methodology is highlighted for several types of integrals that are at the heart of other modern electronic structure theoretical developments, including electric and magnetic properties. We make use of these transforms in a massively parallel implementation of the Gauge-Invariant-Atomic-Orbital (GIAO) method for the calculation of chemical shifts at the ab initio HF SCF level of theory. The implementation follows the original GIAO theory that bypasses computational tasks that are not massively scalable. Indeed the response of the wavefunction to the magnetic field is calculated by means of the Derivative Hartree-Fock method (DHF). The DHF method is amenable to high parallel efficiency as it involves only the calculation of Fock-like matrices from density-like matrices. The computationally intensive steps are shown to be highly scalable.

Original languageEnglish
Pages (from-to)150-166
Number of pages17
JournalComputer Physics Communications
Volume134
Issue number2
DOIs
Publication statusPublished - Feb 2001

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integral transformations
molecular properties
Gages
self consistent fields
orbitals
Wave functions
methodology
Derivatives
bypasses
Chemical shift
matrices
numerical integration
quadratures
Electronic structure
chemical equilibrium
Magnetic properties
Electric properties
Magnetic fields
electronic structure
magnetic properties

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

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title = "New integral transforms for molecular properties and application to a massively parallel GIAO-SCF implementation",
abstract = "We present several new Gaussian integral transforms to be used with the Rys quadrature numerical integration method. These transforms lead to an elegant unified methodology for the calculation of the atomic Gaussian integrals that enter the calculation of many molecular wavefunctions and properties. The unified methodology is highlighted for several types of integrals that are at the heart of other modern electronic structure theoretical developments, including electric and magnetic properties. We make use of these transforms in a massively parallel implementation of the Gauge-Invariant-Atomic-Orbital (GIAO) method for the calculation of chemical shifts at the ab initio HF SCF level of theory. The implementation follows the original GIAO theory that bypasses computational tasks that are not massively scalable. Indeed the response of the wavefunction to the magnetic field is calculated by means of the Derivative Hartree-Fock method (DHF). The DHF method is amenable to high parallel efficiency as it involves only the calculation of Fock-like matrices from density-like matrices. The computationally intensive steps are shown to be highly scalable.",
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