Weizsacker-Based Functionals

The Weizsacker functional is a lower bound to the true kinetic energy, but it is a very weak lower bound. It is even less accurate than the Thomas-Fermi functional. 

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Corrected Weizsacker-Based Functionals 1.3.4.1 Weizsacker Plus Thomas-Fermi Functionals... 

If one can model the noninteracting one-matrix yj(r,r ) as a functional of the electron density, then, using Equation 1.47 or Equation 1.48, one can compute the kinetic energy. This is the most straightforward approach to deriving kinetic energy functionals, and the Thomas-Eermi functional and the Weizsacker functional can both be derived in this way. (Indeed, all of the most popular functionals can be derived in several different ways.) The one-matrix can also be modeled based on weighted density approximation (WDA), which we will discuss subsequently. 

One might hope that, jnst as the wave function-based hierarchy rapidly converges to the exact kinetic energy, the hierarchy based on electron distribution functions would also do the same. This is not true of the WeizsScker functional only a very small portion of the error in the Weizsacker kinetic energy fnnctional is corrected when one considers the two-electron distribution function. Similarly, results for the three-electron distribntion function are only slightly better than those for the... 

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