Weizsacker kinetic energy

Hartree-Fock or Kohn-Sham approach and (1 = 1,..., N) are the corresponding molecular orbitals. Here, tyf[p r)] = (Vp) /8p is the Weizsacker kinetic energy density determined by the one-electron density p(r) = V (r)p, and finally tTplpix)) =... 

The logical extension of GGA methods is to allow the exchange and correlation functionals to depend on higher order derivatives of the electron density, with the Laplacian (V ) being the second-order term. Alternatively, the functional can be taken to depend on the orbital kinetic energy density t, which for a single orbital is identical to the von Weizsacker kinetic energy Tw (eq. (6.3)). 

The term [VrP F( )] /p vi ) is known as the von Weizsacker kinetic energy fw[P i (r)] [4]. Hence, in the other words, Corollary 1.1 tells that square-integrable. Usually, the von Weizsacker term is only a part of the total many-electron kinetic energy [4]. The exception is the Hartree-Fock 2-electron model systems for which fw[p>i (r)] is the exact kinetic energy. We further have... 

Because the Weizsacker kinetic energy functional is a lower bound, the Pauli kinetic energy is always If one differentiates the resulting energy... 

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... 

Chakraborty, D. Ayers, P. W. Derivation of generalized Von-Weizsacker kinetic energies from quasi-probabihty distribution functions. In Statistical Complexity. Springer Science, 2011. 

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