Theory of variational calculation with a scaling correct moment functional to solve the electronic schrodinger equation directly for ground state one-electron density and electronic energy

The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N-dimensions to a nonlinear, approximate density functional of a three spatial dimension one-electron density for an N electron system which is tractable in practice, is a long-desired goal in electronic structure calculation. In a seminal work, Parr et al. (Phys. Rev. A 1997, 55, 1792) suggested a well behaving density functional in power series with respect to density scaling within the orbital-free framework for kinetic and repulsion energy of electrons. The updated literature on this subject is listed, reviewed, and summarized. Using this series with some modifications, a good density functional approximation is analyzed and solved via the Lagrange multiplier device. (We call the attention that the introduction of a Lagrangian multiplier to ensure normalization is a new element in this part of the related, general theory.) Its relation to Hartree-Fock (HF) and Kohn-Sham (KS) formalism is also analyzed for the goal to replace all the analytical Gaussian based two and four center integrals (∫g i(r 1)g k(r 2)r12-1dr 1dr 2, etc.) to estimate electron-electron interactions with cheaper numerical integration. The KS method needs the numerical integration anyway for correlation estimation. © 2012 Wiley Periodicals, Inc