Publications and Research

Document Type


Publication Date



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(i) r(i)(n), n = -2,-1,1,2, W = Sigma(i) delta(r(i)) are exact, as must be the case. The expectations of the kinetic energy operator W = -1/2 Sigma(i) del(2)(i), the two-particle operators W = Sigma(n) u(n), n = -2,-1,1,2, where u = vertical bar r(i) - r(j)vertical bar, 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.


This work was originallu published in Physical Review A, available at



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.