## Document Type

Article

## Publication Date

2011

## Abstract

We extend the idea of the constrained-search variational method for the construction of wave-function functionals ψ[χ] of functions χ. The search is constrained to those functions χ such that ψ[χ] reproduces the density ρ(**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 ψ[χ] 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 ψ[χ] that reproduce the density as given by the Kinoshita correlated wave function. The expectation of single-particle operators W = ∑_{i} r^{ n}_{i} , n = −2,−1,1,2, W = ∑_{i} δ(**r**_{i} ) are exact, as must be the case. The expectations of the kinetic energy operator W = −½ ∑_{i} ∇^{2}_{i}; , the two-particle operators W = ∑_{n} u^{n}, n = −2,−1,1,2, where u = |**r**i − **r**j|, and the energy are accurate. We note that the construction of such functionals ψ[χ] is an application of the Levy-Lieb constrained-search definition of density functional theory. It is thereby possible to rigorously determine which functional ψ[χ] is closer to the true wave function.

## Recommended Citation

Slamet, Marlina, "Wave-Function Functionals for the Density" (2011). *Physics Faculty Publications*. 2.

https://digitalcommons.sacredheart.edu/phys_fac/2

## Comments

Originally published:

Slamet, Marlina, Pan Xiao-Yin, and Viraht Sahnit. "Wave-Function Functionals For The Density."

Physical Review A: Atomic, Molecular & Optical Physics84.5-A (2011): 052504-1-0525O4-6.DOI: 10.1103/PhysRevA.84.052504