Quantal Density Functional Theory of the Density Amplitude
In quantal density functional theory (Q-DFT) and Kohn-Sham density functional theory (KS-DFT), the basic idea is the construction of the model S system of N noninteracting Fermions whereby the density ρ(r) and total energy E equivalent to that of the interacting electronic system is obtained. In Q-DFT, both the total energy E and the local electron-interaction potential energy υ ee(r) of the model Fermions, are defined in terms of fields and quantal sources. The potential energy υ ee(r) is the work done to move the Fermion in a conservative field. The components of the total energy E are expressed in integral virial form in terms of fields associated with these components. In time-independent KS-DFT, the energy E is expressed in terms of component energy functionals of the ground state density ρ(r). The potential energy υ ee(r) of the model Fermions is then defined as the functional derivative of the KS electron-interaction energy functional component. Irrespective of the definition of the potential energy employed to generate the Fermion orbitals, the S system differential equation must be solved N times to obtain the density ρ(r).
KeywordsPotential Energy Ground State Energy Interact System Schrodinger Equation Functional Derivative
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