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Session Q12 - DCMP: DENSITY FUNCTIONAL THEORY
Mixed session, Friday morning, March 24, 8:00
Room C1, San Jose Convention Center
\def\vxcV_xc \def\vxV_x \def\vcV_c \def\ExcE_xc \def\ExE_x \def\EcE_c
Although the local density approximation (LDA) often yields accurate ground state properties, it has well-known failings and unfortunately there is no systematic method to improve upon it. In recent years, a variety of generalized gradient approximations (GGA) have been proposed in the attempt to go beyond LDA, but there is very little understanding of why the agreement with experiment is better in some cases but not in others.
In order to gain more insight, we have constructed exact density functional quantities for model systems J. Chem. Phys. 100, 1290, (1994) where it is possible to tune from a weak-correlation case to a strong-correlation case. Accurate density functional quantities are also obtained for light atoms High Performance Computing and its Application to the Physical Sciences, proceedings of the Mardi Gras '93 Conference, edited by D. A. Browne et al., (World Scientific, 1993); Phys. Rev. A 50, 3827, (1994) using quantum Monte Carlo. These results are compared with those from commonly used approximate density functionals.
For atoms, the GGAs provide much improved exchange energies E_x and correlation energies E_c while for the model systems the improvements are small.
More interesting than \Ex and \Ec (which are integrated quantities), is the exchange correlation potential \vxc . The GGAs yield densities that are slightly more accurate than the LDA densities and they reproduce approximately the inter-shell peak in \vxc whereas LDA does not. However, all of the commonly used GGA's yield \vxc 's that differ significantly from the true \vxc and exhibit a spurious divergence at the origin and a too rapid long-distance fall off. Close to the nucleus, the true \vxc is nearly quadratic while LDA comes in linearly and all the GGAs have a spurious divergence.
In the case of the correlation potential \vc (which is a small part of \vxc ), none of the approximate functionals bear even a remote resemblance to the true \vc . The correlation potential is a subtle quantity that holds many surprises, such as qualitatively opposite behavior in the 2-electron model system and in the 2-electron atoms or the larger variation of \vc in the light ions than in the heavy ions of the helium iso-electronic series. Although any approximate density functional would have great difficulty in reproducing either of these behaviors of \vc , we show that it is possible to have the correct short- and long-range asymptotics of \vxc by including terms in the Laplacian of the density in an appropriate way. The functional can also be constructed to satisfy most of the known scaling relations for \Exc . This work is supported by the Office of Naval Research.