More accurate generalized gradient approximation for solids

Abstract

We present a new nonempirical density functional generalized gradient approximation (GGA) that gives significant improvements for lattice constants, crystal structures, and metal surface energies over the most popular Perdew-Burke-Ernzerhof (PBE) GGA. The new functional is based on a diffuse radial cutoff for the exchange-hole in real space, and the analytic gradient expansion of the exchange energy for small gradients. There are no adjustable parameters, the constraining conditions of PBE are maintained, and the functional is easily implemented in existing codes. PACS numbers: 71.15.Mb, 71.45.Gm, Kohn-Sham density functional theory (DFT) [1,2] makes it possible to solve many-electron ground-state problems efficiently and accurately. The DFT is exact if the exchange-correlation (XC) energy E XC were known exactly, but there is no tractable exact expressions of E XC in terms of electron density. Numerous attempts have been made to approximate E XC , starting with the local (spin) density (LSD) approximation (LDA), which is still widely used. The generalized gradient approximations (GGAs) [3,4,5] are semilocal, seeking to improve upon LSD. Other more complicated approximations are often orbital-dependent or/and nonlocal. They suffer from computational inefficiency; it is much harder to treat them self-consistently and to calculate energy derivative quantities.The XC energy of LSD and GGAs areandrespectively. Here the electron density n = n ↑ + n ↓ , and ǫ unif XC is the XC energy density for the uniform electron gas. LSD is the simplest approximation, constructed from uniform electron gas, and very successful for solids, where the valence electron densities vary relatively more slowly than in molecules and atoms, for which GGAs [5, 6] achieved a great improvement over LSD. It is well known that LSD underestimates the equilibrium lattice constant a 0 by 1-3%, and some properties such as ferroelectricity are extremely sensitive to volume. When calculated at the LSD volume, the ferroelectric instability is severely underestimated [7,8,9]. On the other hand, GGAs tend to expand lattice constants. They well predict correct a 0 for simple metals, such as Na and K [6], however for other materials they often overcorrect LSD by predicting a 0 1-2% bigger [10] than experiment. Predicting lattice constants more accurately than LSD remains a tough issue, even for state-of-the-art meta-GGAs; nonempirical TPSS [11] only achieves moderate TABLE I: Calculated equilibrium volume V0 (Å 3 ) and strain (%) of tetragonal PbTiO3 for various GGAs comparing with experimental data at low temperature [24]. PW91 PBE revPBE RPBE Expt. V0 70.78 70.54 74.01 75.47 63.09 strain 24.2 23.9 28.6 30.1 7.1 improvement over PBE, while empirical PKZB [12] is worse than PBE. GGAs are especially poor for ferroelectrics, e.g., PBE [5] predicts the volume and strain of relaxed tetragonal PbTiO 3 more than 10% and 200% too large, respectively [13], and other GGAs [ 4,14,15] are even worse, as seen in Table I. Another more complicated functional, the nonlocal...

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