Application of Cholesky-Like Matrix Decomposition Methods to the Evaluation of Atomic Orbital Integrals and Integral Derivatives

Abstract

When viewed as a square two-indexed matrix, the array of atomic orbital based, two-electron integrals (ij/kl) is a positive semidefinite array. Beebe and Linderberg showed, in 1977, that actual or near linear dependencies often exist within the types of atomic orbital basis sets employed in conventional quantum chemical calculations. In fact, large (i.e., higher quality) bases were shown to be substantially more redundant than smaller or more spatially separated bases. In situations where these exists significant basis near redundancy, the rank (r) of the ij/kl) = V sub I, J matrix of integrals will be significantly smaller than the matrix dimension M.

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Document Details

Document Type
Technical Report
Publication Date
Jun 28, 1989
Accession Number
ADA209682

Entities

People

  • Douglas W. O'neal
  • Jack Simons

Organizations

  • University of Utah

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Angular Momentum
  • Atomic Orbitals
  • Cartesian Coordinates
  • Chemistry
  • Contracts
  • Decomposition
  • Electrons
  • Governments
  • Integrals
  • Military Research
  • Momentum
  • Notation
  • Numbers
  • Procurement
  • Quantum Chemistry
  • Universities

Readers

  • Linear Algebra
  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.

Technology Areas

  • Microelectronics
  • Microelectronics - Microelectromechanical Systems
  • Quantum Computing
  • Space