One-Electron Density Matrix Models

5 Approaches to Kinetic Energy Functional 1.2.5.1 One-Electron Density Matrix Models 

In molecular quantum mechanics, the kinetic energy is usually computed from the one-matrix 

For finite systems, integration by parts lets one rewrite the kinetic energy in a form where its nonnegativity is manifest 

These two formulas give the same result for any well-behaved one-matrix. 

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. 

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