Neutral atom reference densities

Solution is by an iterative process.The neutral atom reference densities are used as the initial guess for WA(rA). The WA(rA) estimate is improved by a series of charge cycles. In each charge cycle, the current wA(rA) estimate is used to compute estimates of pA (rA) and a which are subsequently used to update the wA(rA) estimate. This process is repeated until a self-consistent solution is reached. 

Morrison, R. C., Zhao, Q., 1995, Solution to the Kohn-Sham Equations Using Reference Densities from Accurate, Correlated Wave Functions for the Neutral Atoms Hehum Through Argon , Phys. Rev. A, 51, 1980. 

In DFT the total energy is expressed as a functional of the electron density p of the molecular system of interest. The derivation of the SCC-DFTB method starts by choosing a reference density po as a superposition of densities p of the neutral atoms a constituting the molecular system,... 

Morrison, R. C., Q. Zhao, R. C. Morrison, and R. G. Parr. 1995. Solution of the Kohn-Sham equations using reference densities from accurate, correlated wave functions for the neutral atoms helium through argon. Phys. Rev. A51, 1980. 

Clearly, equation (49) reduces to equation (24) if tr is replaced by the approximation (18) formally it now takes full account of the (rapid) variation of electron density in the atom, in contrast to the semiclassical TF Euler equation. Unfortunately, tr is only presently known in two special cases (i) to low order in gradient expansion corrections to equation (18) as in equation (76) below and (ii) in a perturbative development about the uniform electron assembly.13 Form (i) will be referred to again below. However, as Scott14 was first to argue for the neutral atom, the origin of the Z2 term in equation (48) resides in the inhomogeneity correction to the TF theory, which is formally contained in equation (49). Fortunately, an approximation based on the Coulomb field treatment of Section 4 suffices to gain a useful estimate of the order of the Z2 term in the neutral atom. 

However, other approaches have also been formulated, aiming to more accurately exploit the electronic bond by using electronic density directly, so as to include the Pauli Exclusion Principle - the vital ingredient when it comes to electronic pairs. In this respect, the next quoted contribution comes from the Daudel s lodges (Daudel et al., 1983), resulting in the difference density between the actual molecular density and the so called reference density a h q)othetical entity associated with the obtained molecular density when at each nuclear position neutral spherical ground states atoms are placed ... 

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