# Revisiting and revising rungs of Jacob's ladder of density functional theory, with application to problems of molecular adsorption on metal surfaces

Kohn-Sham (KS) density-functional theory (DFT), where only the exchange-correlation energy needs to be approximated, is one of the most frequently applied methods in many-body theory. On the Jacob's ladder for the exchange-correlation energy of density functional approximations, higher rungs are usually built on and thus improve accuracy over lower ones. However, climbing from the lowest three semilocal rungs (local spin density approximation (LSDA), generalized gradient approximation (GGA), and meta-GGA (MGGA)) to the higher fully-nonlocal rungs increases the computational cost dramatically. Due to the efficiency of the semilocal approximations, there are still efforts to refine the widely used semilocal approximations To make a firmer base for the higher rungs, a new model called density parameter interpolation is designed for the correlation energy per electron, ec(rs, &zgr;), of the uniform electron gas for LSDA. It shows that known or knowable information about the high- (rs → 0) and low-density ( rs → infinity) asymptotes can be used to predict the correlation energy per electron, ec(r s, &zgr;), of the three-dimensional (3D) uniform electron gas over the whole range of the density parameter (0 ≤ rs < 1) and relative spin polarization (0 ≤∣&zgr;∣≤ 1), without Quantum Monte Carlo or other input At the MGGA level, The Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA and its revised version, the newly proposed revTPSS, are implemented self-consistently within the framework of project augmented wavefunction (PAW) in the Vienna Abinitio Simulation Package (VASP). The application of revTPSS on a set of 61 solids shows that revTPSS performs on average as well as Perdew-Burke-Ernzerhof (PBE)sol and Armiento-Mattsson (AM)05, the two GGA's designed for solids, in terms of lattice constants and bulk moduli. But revTPSS is also known to be accurate for the atomization energies of molecules, as PBEsol and AM05 are not. As for the magnetic properties, revTPSS predicts for Fe the right ground-state solid phase, the ferromagnetic (FM) body-centered-cubic (bcc) structure, with an accurate magnetic moment. However, there still remains the challenge of finding a semilocal functional which can predict the right adsorption site with an accurate adsorption energy for the problem of CO adsorption on Pt (111) surface and, meanwhile, yield an accurate lattice constant for Pt, since revTPSS still fails to predict the right adsorption site Two new nonlocal exchange and correlation functionals, the interaction strength interpolation extended to negative coupling constant (ISIN) functional and its enhanced version ISIN2, of the fifth rung in the Jacob's ladder are presented. They are based on the explicit approximation of Wlambda , the integrand in the adiabatic connection (AC) with lambda representing the coupling constant. The results of ISIN2 show that the correlation energies and the information about the limit lambda → -- infinity of the ideal system of two electrons on the surface of a sphere (2ESS) can be useful for the construction of new functionals