** the scan density functional**

Due to its accuracy and efficiency, density functional theory (DFT) is the choice to calculate electronic structures in chemistry, condensed matter physics, and materials science. In principle, DFT is exact for the ground state electron density and energy. Its exchange correlation energy as a functional of electron density however must be approximated. DFT with the local density approximation (LDA) became popular in condensed matter physics, and then in quantum chemistry after generalized gradient approximations (GGAs) and hybrid GGAs were introduced. Along with its successes however come challenges to DFT, among which is to describe simultaneously accurately various types of bonds forming between atoms and molecules with strengths ranging from several meV to several eV.

The local density approximation (LDA), the earliest approximation in DFT, constructs a local energy density at position from just the local electron density , where the are occupied Kohn-Sham orbitals (spin is suppressed here). Derived from and exact for any uniform electron gas, LDA tends to minimize the inhomogeneity of electron densities of real materials and overestimates the strengths of all bonds near equilibrium. By building in the electron density gradient to reduce this tendency, generalized gradient approximations (GGAs) soften the bonds. Depending on how the electron density gradient is built in, a GGA can be rather accurate for structures or energies, but not both. This dilemma reflects a formal limitation: A GGA cannot satisfy all the known exact constraints appropriate to a semilocal functional (LDA, GGAs, and meta-GGAs) where the exchange-correlation energy is efficiently evaluated as a single integral over three-dimensional space. By mixing GGAs with nonlocal exact exchange, hybrid GGAs can further improve the description of covalent, ionic, and hydrogen bonds. However, hybrid GGAs still fail to describe vdW interactions. The computational cost of a hybrid functional can be 10 to 100 times that of a semilocal functional in standard plane-wave codes, even more so for metallic systems. Another problem with hybrids is that a universal exact-exchange mixing parameter is not determined by any exact condition.

The inclusion of the kinetic energy density on top of and its gradient enables meta-GGAs to have the flexibility to satisfy more exact constraints and thus circumvent the “structure or energy” dilemma experienced by GGAs. By using a dimensionless variable properly constructed from , meta-GGAs can recognize the slowly-varying densities (, characterizing metallic bonds), the single-orbital systems (, characterizing covalent single bonds), and noncovalent bonds with between two closed shells. is directly related to the electron localization function (ELF) with , and therefore identifies different chemical bonds.

By taking the above advantages, the nonempirical strongly constrained and appropriately normed (SCAN) meta-GGA was recently developed. SCAN is the first meta-GGA that is fully constrained, obeying all 17 known exact constraints that a semilocal functional can. It is also exact or nearly exact for a set of “appropriate norms”, including rare-gas atoms and nonbonded interactions. SCAN predicts accurate geometries and energies of diversely-bonded molecules and materials (including covalent, metallic, ionic, hydrogen, and van der Waals bonds), significantly and systematically improving at comparable efficiency over its predecessors, the GGAs. Often SCAN matches or improves upon the accuracy of a computationally expensive hybrid functional, at almost-GGA cost. SCAN is therefore expected to have a broad impact on chemistry, condensed matter physics, and materials science.

Details on SCAN and its applications can be found in the following references and therein:

[1] J. Sun, A. Ruzsinszky, and J.P. Perdew, Strongly constrained and appropriately normed semilocal density functional, PRL 115, 036402 (2015).

[2] J. Sun, R.C. Remsing, Y. Zhang, Z. Sun, A. Ruzsinszky, H. Peng, Z. Yang, A. Paul, U. Waghmare, X. Wu, M.L. Klein, and J.P. Perdew, Accurate First-principles structures and energies of diversely-bonded systems from an efficient density functional, Nat. Chem. 8, 831 (2016).

[3] H. Peng and J.P. Perdew, Synergy of van der Waals and Self-Interaction Corrections in Transition Metal Monoxides,

[4] M. Chen, H.-S. Ko, R.C. Remsing, M.F. Calegari Andrade, B. Santra, Z. Sun, A. Selloni, R. Car, M.L. Klein, J.P. Perdew, and X. Wu, Ab Initio Theory and Modeling of Water,

[5] Y. Zhang, J. Sun. J.P. Perdew, and X. Wu, Comparative First-Principles Studies of Prototypical Ferrolectric Materials by LDA, GGA, and SCAN Meta-GGA,

[6] A. Patra, J.E. Bates, J. Sun, and J.P. Perdew, Properties of Real Metallic Surfaces: Effects of Density Functional Semilocality and van der Waals Nonlocality,

[7] Y. Zhang, D.A. Kitchaev, J. Yang, T. Chen, S.T. Dacek, R.A. Sarmiento-Perez, M. Marques, H. Peng, G. Ceder, J.P. Perdew, and J. Sun, Efficient First-Principles Prediction of Solid Stability: Towards Chemical Accuracy, submitted.

The local density approximation (LDA), the earliest approximation in DFT, constructs a local energy density at position from just the local electron density , where the are occupied Kohn-Sham orbitals (spin is suppressed here). Derived from and exact for any uniform electron gas, LDA tends to minimize the inhomogeneity of electron densities of real materials and overestimates the strengths of all bonds near equilibrium. By building in the electron density gradient to reduce this tendency, generalized gradient approximations (GGAs) soften the bonds. Depending on how the electron density gradient is built in, a GGA can be rather accurate for structures or energies, but not both. This dilemma reflects a formal limitation: A GGA cannot satisfy all the known exact constraints appropriate to a semilocal functional (LDA, GGAs, and meta-GGAs) where the exchange-correlation energy is efficiently evaluated as a single integral over three-dimensional space. By mixing GGAs with nonlocal exact exchange, hybrid GGAs can further improve the description of covalent, ionic, and hydrogen bonds. However, hybrid GGAs still fail to describe vdW interactions. The computational cost of a hybrid functional can be 10 to 100 times that of a semilocal functional in standard plane-wave codes, even more so for metallic systems. Another problem with hybrids is that a universal exact-exchange mixing parameter is not determined by any exact condition.

The inclusion of the kinetic energy density on top of and its gradient enables meta-GGAs to have the flexibility to satisfy more exact constraints and thus circumvent the “structure or energy” dilemma experienced by GGAs. By using a dimensionless variable properly constructed from , meta-GGAs can recognize the slowly-varying densities (, characterizing metallic bonds), the single-orbital systems (, characterizing covalent single bonds), and noncovalent bonds with between two closed shells. is directly related to the electron localization function (ELF) with , and therefore identifies different chemical bonds.

By taking the above advantages, the nonempirical strongly constrained and appropriately normed (SCAN) meta-GGA was recently developed. SCAN is the first meta-GGA that is fully constrained, obeying all 17 known exact constraints that a semilocal functional can. It is also exact or nearly exact for a set of “appropriate norms”, including rare-gas atoms and nonbonded interactions. SCAN predicts accurate geometries and energies of diversely-bonded molecules and materials (including covalent, metallic, ionic, hydrogen, and van der Waals bonds), significantly and systematically improving at comparable efficiency over its predecessors, the GGAs. Often SCAN matches or improves upon the accuracy of a computationally expensive hybrid functional, at almost-GGA cost. SCAN is therefore expected to have a broad impact on chemistry, condensed matter physics, and materials science.

Details on SCAN and its applications can be found in the following references and therein:

[1] J. Sun, A. Ruzsinszky, and J.P. Perdew, Strongly constrained and appropriately normed semilocal density functional, PRL 115, 036402 (2015).

[2] J. Sun, R.C. Remsing, Y. Zhang, Z. Sun, A. Ruzsinszky, H. Peng, Z. Yang, A. Paul, U. Waghmare, X. Wu, M.L. Klein, and J.P. Perdew, Accurate First-principles structures and energies of diversely-bonded systems from an efficient density functional, Nat. Chem. 8, 831 (2016).

[3] H. Peng and J.P. Perdew, Synergy of van der Waals and Self-Interaction Corrections in Transition Metal Monoxides,

__Physical Review B__**96**, 100101 (R) (2017).[4] M. Chen, H.-S. Ko, R.C. Remsing, M.F. Calegari Andrade, B. Santra, Z. Sun, A. Selloni, R. Car, M.L. Klein, J.P. Perdew, and X. Wu, Ab Initio Theory and Modeling of Water,

__Proceedings of the National Academy of Sciences__(__USA)__, to appear (2017).[5] Y. Zhang, J. Sun. J.P. Perdew, and X. Wu, Comparative First-Principles Studies of Prototypical Ferrolectric Materials by LDA, GGA, and SCAN Meta-GGA,

__Physical Review B__**96**, 035143 (2017).[6] A. Patra, J.E. Bates, J. Sun, and J.P. Perdew, Properties of Real Metallic Surfaces: Effects of Density Functional Semilocality and van der Waals Nonlocality,

__Proceedings of the National____Academy of Sciences (USA)__, to appear (2017).[7] Y. Zhang, D.A. Kitchaev, J. Yang, T. Chen, S.T. Dacek, R.A. Sarmiento-Perez, M. Marques, H. Peng, G. Ceder, J.P. Perdew, and J. Sun, Efficient First-Principles Prediction of Solid Stability: Towards Chemical Accuracy, submitted.