Session A31: Advances in Density Functional Theory I

\textbf{SCAN: An Efficient Density Functional Yielding Accurate Structures and Energies of Diversely-Bonded Materials}

The accuracy and computational efficiency of the widely used Kohn-Sham density functional theory (DFT) are limited by the approximation to its exchange-correlation energy E$_{\mathrm{xc}}$. The earliest local density approximation (LDA) overestimates the strengths of all bonds near equilibrium (even the vdW bonds). By adding the electron density gradient to model E$_{\mathrm{xc}}$, generalized gradient approximations (GGAs) generally soften the bonds to give robust and overall more accurate descriptions, except for the vdW interaction which is largely lost. Further improvement for covalent, ionic, and hydrogen bonds can be obtained by the computationally more expensive hybrid GGAs, which mix GGAs with the nonlocal exact exchange. Meta-GGAs are still semilocal in computation and thus efficient. Compared to GGAs, they add the kinetic energy density that enables them to recognize and accordingly treat different bonds, which no LDA or GGA can [1]. We show here that the recently developed non-empirical strongly constrained and appropriately normed (SCAN) meta-GGA [2] improves significantly over LDA and the standard Perdew-Burke-Ernzerhof GGA for geometries and energies of diversely-bonded materials (including covalent, metallic, ionic, hydrogen, and vdW bonds) at comparable efficiency. Often SCAN matches or improves upon the accuracy of a hybrid functional, at almost-GGA cost. [1] J. Sun et al., Phys. Rev. Lett. 111, 106401 (2013). [2] J. Sun, A. Ruzsinszky, and J.P. Perdew, Phys. Rev. Lett. 115, 036402 (2015).   

SCAN+rVV10: A promising van der Waals density functional

The newly developed ``strongly constrained and appropriately normed'' (SCAN) meta-generalized-gradient approximation (meta-GGA) can generally improve over the non-empirical Perdew-Burke-Ernzerhof (PBE) GGA not only for strong chemical bonding, but also for the intermediate-range van der Waals (vdW) interaction. However, the long-range vdW interaction is still missing. To remedy this, we propose here pairing SCAN with the non-local correlation part from the rVV10 vdW density functional, with only two empirical parameters. The resulting \textit{SCAN+rVV10} yields excellent geometric and energetic results not only for molecular systems, but also for solids and layered-structure materials, as well as the adsorption of benzene on coinage metal surfaces. Especially, SCAN+rVV10 outperforms all current methods with comparable computational efficiencies, accurately reproducing the three most fundamental parameters---the inter-layer binding energies, inter-, and intra-layer lattice constants---for 28 layered-structure materials. Hence, we have achieved with SCAN+rVV10 a promising vdW density functional for general geometries, with minimal empiricism.   

The optimized effective potential of meta-generalized gradient approximations in solids

Unlike the local density approximation(LDA) and the generalized gradient approximation(GGA), calculations with meta-GGAs are usually done according to the generalized Kohn-Sham(gKS) formalism. The exchange-correlation potential of the gKS equation is non-multiplicative, which prevents systematic comparison of meta-GGA bandstructures to those of the LDA and the GGA. We implement the optimized effective potential(OEP) of the meta-GGA for periodic systems, which allows us to carry out meta-GGA calculations in the same KS manner as for the LDA and the GGA. We apply the OEP to several popular meta-GGAs, including the new SCAN functional[Phys. Rev. Lett. 115, 036402(2015)]. We find that the KS gaps of meta-GGAs are close to those of GGAs, and they are smaller than the gKS gaps of meta-GGAs. The well-known grid sensitivity of meta-GGAs is much more severe in OEP calculations.   

Characterization of Thin Film Materials using SCAN MetaGGA, an Accurate Nonempirical Density Functional

The exact ground-state properties of a material can be derived from the single-particle Kohn-Sham equations within the framework of the Density Functional Theory (DFT), provided the exact exchange-correlation potential is known. The simplest approximation is the local density approximation (LDA), but it usually leads to overbinding in molecules and solids. On the other hand, the generalized gradient approximation (GGA) introduces corrections that expand and soften bonds. The newly developed nonempirical SCAN (strongly-constrained and appropriately-normed) MetaGGA [Phys. Rev. Lett. 115, 036402] has been shown to be comparable in efficiency to LDA and GGA, and to significantly improve LDA and the Perdew-Burke-Ernzerhof version of the GGA for ground-state properties such as equilibrium geometry and lattice constants for a number of standard datasets for molecules and solids. Here we discuss the performance of SCAN MetaGGA for thin films and monolayers and demonstrate improvements of predicted ground-state properties. Examples include graphene, phosphorene and MoS$_2$.   

Comparative first-principles study of clean-surface properties of metals

Metal surfaces are widely used in different applications from nano-devices to heterogeneous catalysis. Clean-surface properties such as the surface energy, work function and interlayer spacing importantly determine the behavior of metal surfaces. Prior work has been done to understand these properties using high-level methods including the local density approximation (LDA) and the generalized gradient approximation (PBE). In this work, we study (111) (100) and (110) surfaces of Pt, Pd, Cu, Al, Au, Ag, Rh and Ru by extrapolation from a finite number of layers. These surfaces are studied using SCAN, a new member of the computationally-efficient meta-GGA family of density functionals. We have compared the performance of SCAN and three other standard density functionals - LDA, PBE and PBEsol - to available experimental results. We find that the performance of the general-purpose SCAN is at the level of the more-specialized PBEsol, giving accurate metallic properties. Ref: Jianwei Sun, Adrienn Ruzsinszky, John P Perdew, Strongly Constrained and Appropriately Normed Semilocal Density Functional, \textit{Physical Review Letters}115 (3), 036402 (2015). Supported by NSF under DMR-1305135, CNS-09-5884, and by DOE under DE-SC0012575, DE-AC02-05CH11231.   

A Non-Local, Energy-Optimized Kernel: Recovering Second-Order Exchange and Beyond in Extended Systems

The Random Phase Approximation (RPA) is quickly becoming a standard method beyond semi-local Density Functional Theory that naturally incorporates weak interactions and eliminates self-interaction error. RPA is not perfect, however, and suffers from self-correlation error as well as an incorrect description of short-ranged correlation typically leading to underbinding. To improve upon RPA we introduce a short-ranged, exchange-like kernel that is one-electron self-correlation free for one and two electron systems in the high-density limit. By tuning the one free parameter in our model to recover an exact limit of the homogeneous electron gas correlation energy we obtain a non-local, energy-optimized kernel that reduces the errors of RPA for both homogeneous and inhomogeneous solids. To reduce the computational cost of the standard kernel-corrected RPA, we also implement RPA renormalized perturbation theory for extended systems, and demonstrate its capability to describe the dominant correlation effects with a low-order expansion in both metallic and non-metallic systems. Furthermore we stress that for norm-conserving implementations the accuracy of RPA and beyond RPA structural properties compared to experiment is inherently limited by the choice of pseudopotential.   

Semiclassical origins of density functionals

By careful numerical analysis of non-relativistic atomic correlation energies, we show that (a) the local density approximation becomes relatively exact for the correlation energy as the atomic number approaches infinity, (b) we find the leading correction, which is about 38.5 milliHartrees per atom, (c) show how this correction dominates for larger atoms and (d) how to construct a generalized gradient approximation that respects this limit (See KB, A. Cancio, T. Gould, S. Pittalis, arXiv:1409.4834).\\ The relevance to density functional calculations will also be explained.\\   

Semiclassical potential functionals for semiconductor quantum wells

Parabolic semiconductor quantum wells are considered promising candidates for constructing devices emitting radiation in the largely unexplored THz regime. However, progress is impeded by the difficulty of fine-tuning intersubband transitions in these quantum wells which is achieved by modifying the quantum-well geometry and mixing different materials. We predict the electronic structure of parabolic semiconductor quantum wells highly efficiently by iterating the Kohn-Sham self-consistent cycle without solving the Kohn-Sham equations[1]. We achieve this by combining potential functionals[2,3] with a recently derived semiclassical approximation[4]. This (1) demonstrates our method's efficiency and accuracy for realistic systems and (2) illustrates its utility as a high-throughput method for predicting the electronic structure of technologically intriguing microstructures. [1] A. Cangi, C.R. Proetto, S. Pittalis, K. Burke, and E.K.U. Gross, submitted (2016). [2] A. Cangi, D. Lee, P. Elliott, K. Burke, and E.K.U. Gross, PRL 106, 236404 (2011). [3] A. Cangi, E. K. U. Gross, and K. Burke, PRA 88, 062505 (2013). [4] R.F. Ribeiro, D. Lee, A. Cangi, P. Elliott, and K. Burke, PRL 114, 050401 (2015).   

Thermal Corrections to Density Functional Simulations of Warm Dense Matter

Present density functional calculations of warm dense matter often use the Mermin-Kohn-Sham (MKS) scheme at finite temperature, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable non-trivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies, the exact Mermin-Kohn-Sham functionals for this system, and extract the exact XC free energy. For moderate temperatures and weak correlation, we show this approximation is excellent, but fails for stronger correlations. Additionally, we use this system to test various conditions that must be satisfied.   

Study of the large reduced density gradient limit for the exchange energy

The generalized gradient approximation (GGA) for the Kohn-Sham exchange-correlation functional has become widely used in electronic structure calculations of small, medium and large systems, because it provides rather reasonable results with moderate computational effort. Usually the GGA for exchange (X) is expressed in terms of an analytical expression of the X enhancement function, Fx(s), where s is the reduced density gradient. When a non-empirical approach based on constraint satisfaction is followed, the analytical expression of Fx(s) is the result of interpolating between the small- and large-s limits. However, neither of those limits is uniquely defined. In both cases there are several possibilities. The present work is a study of the influence of the several large-s limit possibilities upon the calculation of properties that depend on energy differences, versus those that depend on response functions, and excitation energies.   

Study of adiabatic connection in ground-state density functional theory

By employing modified [1] variational form of Le-Sech wavefunctions [2] for two-electron systems, accurate wavefunctions for He-like atoms corresponding to their ground-state density are obtained for varying strength, given by a parameter $\alpha $ (0 $\le \alpha \le $1), of electron-electron interaction. Using these, it is shown explicitly that (i) the total energy varies almost linearly as a function of $\alpha $, and (ii) the ionization potential remains unchanged [3] as $\alpha $ is varied. Furthermore, kinetic energy contribution to the density-functional exchange-correlation energy is calculated using the adiabatic connection formula [4] and shown to match that calculated on the basis of Kohn-Sham calculation. Finally, the exchange-correlation energy obtained for different values of $\alpha $ is employed to analyze several hybrid exchange-correlation energy functionals in use. [1] R.S. Chauhan and M.K. Harbola, Chem. Phys. Lett. \textbf{639C}, 248(2015) [2] C. Le Sech, J. Phys. B: Atom. Mol. Opt. Phys. \textbf{30}, L47(1997) [3] M. Levy, J. P. Perdew and V. Sahni, Phys. Rev. A \textbf{30}, 2745(1984) [4] R. Harris and R.O. Jones, J. Phys. F: Met. Phys. 4 1170 (1974); D.C. Langreth and J.P. Perdew, Phys. Rev. B \textbf{15}, 2884 (1977)