Efficient and reliable numerical integration of exchange-correlation energies and potentials

Köster, Andreas M.; Flores-Moreno, Roberto; Reveles, J. Ulises

doi:doi:10.1063/1.1759323

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Classical spin and quantum-mechanical descriptions of geometric spin frustration

Geometric spin frustration (GSF) in isolated plaquettes with local spin s, i.e., an equilateral-triangle spin trimer and a regular-tetrahedron spin tetramer, was examined on the basis of classical spin and quantum-mechanical descriptions to clarify their differences and similarities. An analytical proof was given for how the state degeneracy and the total spin S of their ground states depend on the local spin s. The quantum-mechanical conditions for the occurrence of GSF in isolated plaquettes w...

Potential energy surface discontinuities in local correlation methods

We have examined the occurence of discontinuities in bond-breaking potential energy surfaces given by local correlation methods based on the Pulay–Saebø orbital domain approach. Our analysis focuses on three prototypical dissociating systems: the C-F bond in fluoromethane, the C-C bond in singlet, ketene, and the central C-C bond in propadienone. We find that such discontinuities do not occur in cases of homolytic bond cleavage due to the inability of the Pipek–Mezey orbital localization method ...

An adaptive numerical integrator for the exchange-correlation energy and potential is presented. It uses the diagonal elements of the exchange-correlation potential matrix as a grid generating function. The only input parameter is the requested grid tolerance. In combination with a defined cell function the adaptive grid generation scales almost linear with the number of basis functions in a system. With the adaptive numerical integrator the self-consistent field energy error, which is due to the numerical integration of the exchange-correlation energy, converges with increasing adaptive grid size to a reference value. The performance of the adaptive numerical integration is analyzed using molecules with first, second, and third row elements. Especially for transition metal systems the adaptive numerical integrator shows considerably improved performance and reliability. © 2004 American Institute of Physics.