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The crystal structures are successfully established for tetragonal and orthorhombic CH3NH3PbX3 (X = I and Br). The equilibrium lattice parameters are computed by the DFT+D2 method, and the results are compared to experimental values. The band dispersions and electronic densities of states are calculated by HSE06, showing that their band gaps are in the range from 1.63 to 2.3 eV. Although the calculated dielectric functions of MAPbX3 compounds are similar to other semiconductors, the absorption spectra of their bulk crystals are drifted away from visible light spectrum. The effective mass tensors of holes and electrons are also evaluated in three principal directions at the Γ point. The anisotropies in the effective masses of the hole and electron are illustrated for two orthorhombic phases.

Computationally-efficient semilocal approximations of density functional theory at the level of the local spin density approximation (LSDA) or generalized gradient approximation (GGA) poorly describe weak interactions. We show improved descriptions for weak bonds (without loss of accuracy for strong ones) from a newly-developed semilocal meta-GGA (MGGA), by applying it to molecules, surfaces, and solids. We argue that this improvement comes from using the right MGGA dimensionless ingredient to recognize all types of orbital overlap.PACS numbers: 34.20.Gj, 31.15.E-, 87.15.ADue to its computational efficiency and reasonable accuracy, the Kohn-Sham density functional theory [1][2][3] with semilocal approximations to the exchangecorrelation energy, e.g., the local spin density approximation (LSDA) [4,5] and the standard Perdew-BurkeErnzerhof (PBE) generalized gradient approximation (GGA) [6], is one of the most widely-used electronic structure methods in materials science, surface science, condensed matter physics, and chemistry. Semilocal approximations display a well-understood error cancellation between exchange and correlation in bonding regions. Thus some intermediate-range correlation effects, important for strong and weak bonds, are carried by the exchange part of the approximation. However, it is well-known that these approximations cannot yield correct long-range asymptotic dispersion forces [7]. This raises doubts about the suitability of semilocal approximations for the description of weak interactions (including hydrogen bonds and van der Waals interactions), even near equilibrium where most interesting properties occur. These doubts are supported by the performance of LSDA and GGAs, which are not very useful for many important systems and properties (such as DNA, physisorption on surfaces, most biochemistry, etc.).However, these doubts are challenged by recent developments in semilocal meta-GGAs (MGGA) [8][9][10][11][12][13][14] (which are useful by themselves and as ingredients of hybrid functionals [14]). Compared to GGAs, which use the density n(r) and its gradient ∇n as inputs, MGGAs additionally include the positive kinetic energy density τ = k |∇ψ k | 2 /2 of the occupied orbitals ψ k . For simplicity, we suppress the spin here. By including training sets of noncovalent interactions, the moleculeoriented and heavily-parameterized M06L MGGA was trained to capture medium-range exchange and correlation energies that dominate equilibrium structures of noncovalent complexes [9]. Madsen et al. showed that the inclusion of the kinetic energy densities enables MGGAs to discriminate between dispersive and covalent interactions, which makes the M06L MGGA [9] suitable for layered materials bonded by van der Waals interactions [15,16]. Besides improvement for noncovalent bonds, simultaneous improvement for metallic and covalent bonds is also an outstanding problem for semilocal functionals [17,18]. Ref. 18 has shown that the revised Tao-Perdew-Staroverov-Scuseria (revTPSS) [10] MGGA, due to the inclusion of ...

We study for the first time the effect of the dependence of meta generalized gradient approximation (MGGA) for the exchange-correlation energy on its input, the kinetic energy density, through the dimensionless inhomogeneity parameter, α, that characterizes the extent of orbital overlap. This leads to a simple MGGA exchange functional, which interpolates between the single-orbital regime, where α = 0, and the slowly varying density regime, where α ≈ 1, and then extrapolates to α → ∞. When combined with a variant of the Perdew-Burke-Ernzerhof GGA correlation, the resulting MGGA performs equally well for atoms, molecules, surfaces, and solids. In Kohn-Sham (KS) density functional theory (DFT),