Coordinate Scaling Requirements for Approximating Exchange and Correlation

  • Mel Levy
Part of the NATO ASI Series book series (NSSB, volume 337)


In order to continue to better approximate the exact exchange-correlation density functional, Exc[n], for electronic structure calculations, sets of exact coordinate scaling and convexity requirements are reviewed for the purpose of testing approximations. The scaling requirements dictate how Exc[n] must transform when n(x, y, z) is replaced by αβγn(αx,βy,γz). High-density and low-density limits are explored. Simple formulas are shown which isolate the kinetic component of Exc[n] and which generate Exc[n] from just its electron-electron repulsion component, or exchange-correlation hole, at a coupling constant of unity. The scaling and convexity conditions are derived with help from the constrained-search formulation and through the development of a coupling-constant perturbation expansion. The local density approximation and various gradient approximations are compared against the exact conditions, with emphasis upon where the conditions are respected and where the conditions are violated. Numerical results are presented.


Local Density Approximation Correlation Energy Electronic Structure Calculation Virial Theorem Uniform Scaling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Mel Levy
    • 1
  1. 1.Department of Chemistry and Quantum Theory GroupTulane UniversityNew OrleansUSA

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