Slater's nonlocal exchange potential and beyond
Faculty of Sciences. Physics
New York, N.Y.
International journal of quantum chemistry. - New York, N.Y.
, p. 64-71
University of Antwerp
The local density approximation (LDA) to the exchange potential V-x(r), namely the rho(1/3) electron gas form, was already transcended in Slater's 1951 paper. Here, using Dirac's 1930 form for the exchange energy density epsilon(x)(r), the Slater (SI) nonlocal exchange potential V-x(sl)(r) is defined by 2epsilon(x)(r)/rho(r). In spherical atomic ions, say the Be or Ne-like series, this form already has the correct behavior in both r --> 0 and r --> infinity limits when known properties of the exchange energy density E,(r) and the ground-state electron density rho(r) are invoked. As examples, some emphasis will first be given to the use of the so-called 1/Z expansion in such spherical atomic ions, for which analytic results can be obtained for both epsilon(x)(r) and rho(r) as the atomic number Z becomes large. The usefulness of the 1/Z expansion is directly demonstrated for the U atomic ion with 18 electrons by comparison with the optimized effective potential prediction. A rather general integral equation for the exchange potential is then proposed. Finally, without appeal to large Z, two-level systems are considered, with specific reference to the Be atom and to the LiH molecule. In all cases treated, the Slater potential V-x(sl)(r) is a valuable starting point, even though it needs appreciable quantitative corrections reflecting directly atomic shell structure. (C) 2004 Wiley Periodicals, Inc. Int J Quantum Chem 102: 64-71, 2005.