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**JIANWEI SUN and JOHN PERDEW
Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118**

On Jacob’s ladder of density functional approximations^{1}, higher rungs usually improve accuracy over lower ones. However, climbing from the lowest three semilocal rungs (LSDA, GGA, meta-GGA) to the higher fully-nonlocal rungs increases the computational cost dramatically, and some codes are not yet ready to do even selfconsistent meta-GGA. Evaluating the energy of one functional using the densities and geometries of another is often accurate for atoms and molecules, but not necessarily so for solids, which are not as stiff as molecules. We will demonstrate this for CO adsorbed on the top and fcc sites of Pt(111) surface at the generalized gradient approximation(GGA) level. In the CO/Pt(111) system, we identify two relevant sets of geometric effects and one set of electronic density effects: (1) the size of the supercell, as set by the bulk lattice constant, (2) relaxation of the atomic positions within the supercell, and (3) electronic density optimization for the relaxed structure. We determine each of these independently using two different GGA’s, the Perdew-Burke-Ernzerhof (PBE)^{2} and the PBEsol^{3}. We find that the electronic density effect is negligible, while the supercell and relaxation effects are roughly of equal importance. In order to diminish the non-selfconsistent supercell and relaxation errors in meta-GGA calculations, a GGA functional with bulk lattice constant close to that of the meta-GGA should be chosen to relax the structure within the supercell set by the meta-GGA’s lattice constants. We will present results for the TPSS^{4} and revTPSS^{5} meta-GGA’s. [Supported by NSF.]

[1] J.P. Perdew, and K. Schmidt, AIP Conf. Proc. **577**, 1(2001).

[2] J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. **77**, 3865(1996).

[3] J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, and K. Burke, Phys. Rev. Lett. **100**, 136406(2008).

[4] J. Tao, J.P. Perdew, V.N. Staroverov, and G.E. Scuseria, Phys. Rev. Lett. **91**, 146401 (2003).

[5] J.P. Perdew, A. Ruzsinszky, G.I. Csonka, L.A. Constantin, and J. Sun, Phys. Rev. Lett. **103**, 026403(2009).

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