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Related Concept Videos

Van der Waals Interactions01:24

Van der Waals Interactions

Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.
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Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
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Noncovalent Attractions in Biomolecules02:35

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Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
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Attractive electron-electron interactions within robust local fitting approximations.

Patrick Merlot1, Thomas Kjærgaard, Trygve Helgaker

  • 1Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, N-0315 Oslo, Norway.

Journal of Computational Chemistry
|April 5, 2013
PubMed
Summary
This summary is machine-generated.

Dunlap's fitting approach can yield an indefinite integral matrix, causing issues in some quantum chemistry calculations. A new Pair-Atomic Resolution-of-the-Identity (PARI) method offers speed-ups but requires careful implementation to ensure matrix positivity.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Dunlap's robust fitting approach for evaluating two-electron integrals can lead to non-positive semidefinite matrices.
  • The use of local fitting domains or non-Coulomb metrics exacerbates this issue, potentially causing convergence problems in electronic structure calculations.

Purpose of the Study:

  • To present a highly local approximate method for evaluating four-center two-electron integrals.
  • To apply this method to construct Coulomb and exchange contributions to the Fock matrix within the resolution-of-the-identity (RI) approximation.
  • To investigate the properties and performance of this new approach, termed Pair-Atomic Resolution-of-the-Identity (PARI).

Main Methods:

  • Developed the Pair-Atomic Resolution-of-the-Identity (PARI) approach, expanding atomic-orbital (AO) products in auxiliary functions centered on two atoms.
  • Applied PARI to calculate Coulomb and exchange contributions to the Fock matrix.
  • Tested PARI in Hartree-Fock and Kohn-Sham calculations, comparing accuracy and speed with conventional and standard RI methods.
  • Investigated methods to recover a positive semidefinite integral matrix using local auxiliary basis functions and Cholesky decomposition.

Main Results:

  • The PARI method provides significant speed-ups for Coulomb and exchange integral calculations, particularly for exchange contributions (up to eightfold with triple-zeta basis sets).
  • In a small fraction of cases (≤1%), the indefinite integral matrix caused self-consistent-field (SCF) nonconvergence, leading to unphysically negative total energies.
  • In most cases, PARI demonstrated convergence and achieved total energy accuracy comparable to standard RI methods.
  • Recovering matrix positivity via local completion slowed the algorithm considerably.

Conclusions:

  • The PARI method offers a computationally efficient approach for evaluating two-electron integrals in quantum chemistry.
  • While generally robust, the potential for SCF nonconvergence due to matrix indefiniteness in a small percentage of calculations needs consideration.
  • Ensuring matrix positivity is crucial for reliable calculations, though methods to achieve this can negate the speed advantages.