Slater potential asymptotic structure

A somewhat different and promising approach has been proposed recently by Gritsenko, van Leeuwen and Baerends [95]. These authors decomposed the potential into the Slater potential vs and the response to density variations vTCtp. They showed that the latter exhibits the peaks which reflect the atomic shell structure which is poorly described by usual GGAs potentials. The potential they proposed possesses correct asymptotic and scaling properties. Although there is still room for improvements, it would be worthwhile to see how molecular properties... 

For the self-consistent orbitals, we have determined1"4 the exact analytical asymptotic structure in the classically forbidden vacuum region of (i) the Slater potential VJ (r), (u) the functional derivative (exchange potential)... 

Finally, the asymptotic structure of the Slater potential is derived1,2 as... 

The most significant point f the results is that the KS exchjnge potential vx(r), the Pauli component Wx (r), and the Slater potential Vx (r) all decay asymptotically as -x"1. This is consistent with the work of Harbola and Sahni21"24 who also determined these structures but did so numerically and for specific metals only. Furthermore, their calculations were performed for model potential orbitals. The present results are valid for fully-self-consistently determined orbitals, and the decay coefficients for arbitrary metal can be obtained... 

It is easy to see that since z Umoopn(z) = 1, where z = kFx, then for any value of the parameter p, the potential V ,app(r) reproduces the correct asymptotic structure of the exact Slater potential V (r) in the metal bulk ... 

For the nonuniform electron gas at a metal surface, the Slater potential has an erroneous asymptotic behavior both in the classically forbidden region as well as in the metal bulk. In the vacuum region, the Slater potential has the analytical [10] asymptotic structure [35,51] V r) = — Xs(p)/x, with the coefficient otsiP) defined by Eq. (103). In the metal bulk this potential approaches [35] a value of ( — 1) in units of (3kp/27r) instead of the correct Kohn-Sham value of ( — 2/3). Further, in contrast to finite systems, the Slater potential V (r) and the work W,(r) are not equivalent [31, 35, 51] asymptotically in the classically forbidden region. This is because, for asymptotic positions of the electron in the vacuum, the Fermi hole continues to spread within the crystal and thus remains a dynamic charge distribution [34]. 

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