Wave-function functionals for the density
- Sacred Heart University, Fairfield, Connecticut 06825 (United States)
We extend the idea of the constrained-search variational method for the construction of wave-function functionals {psi}[{chi}] of functions {chi}. The search is constrained to those functions {chi} such that {psi}[{chi}] reproduces the density {rho}(r) while simultaneously leading to an upper bound to the energy. The functionals are thereby normalized and automatically satisfy the electron-nucleus coalescence condition. The functionals {psi}[{chi}] are also constructed to satisfy the electron-electron coalescence condition. The method is applied to the ground state of the helium atom to construct functionals {psi}[{chi}] that reproduce the density as given by the Kinoshita correlated wave function. The expectation of single-particle operators W={Sigma}{sub i}r{sub i}{sup n}, n=-2,-1,1,2, W={Sigma}{sub i}{delta}(r{sub i}) are exact, as must be the case. The expectations of the kinetic energy operator W=-(1/2){Sigma}{sub i}{nabla}{sub i}{sup 2}, the two-particle operators W={Sigma}{sub n}u{sup n}, n=-2,-1,1,2, where u=|r{sub i}-r{sub j}|, and the energy are accurate. We note that the construction of such functionals {psi}[{chi}] is an application of the Levy-Lieb constrained-search definition of density functional theory. It is thereby possible to rigorously determine which functional {psi}[{chi}] is closer to the true wave function.
- OSTI ID:
- 22093505
- Journal Information:
- Physical Review. A, Vol. 84, Issue 5; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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