SCAN: AN ACCURATE AND EFFICIENT DENSITY FUNCTIONAL FOR THE MATERIALS GENOME INITIATIVE JOHN P. PERDEW, TEMPLE UNIVERSITY JIANWEI SUN, ADRIENN RUZSINSZKY, AND JOHN P. PERDEW, PHYS. REV. LETT. 115, (2015) SUN, REMSING, ZHANG, SUN, RUZSINSZKY, PENG, YANG, PAUL, WAGHMARE, WU, KLEIN, AND PERDEW, NATURE CHEM., TO APPEAR (AND ARXIV). 1

KOHN-SHAM DENSITY FUNCTIONAL THEORY IS THE STANDARD WAY TO COMPUTE THE PROPERTIES OF MATERIALS, INCLUDING GROUND-STATE ENERGY, ELECTRON DENSITY, AND EQUILIBRIUM NUCLEAR POSITIONS. IT IS CURRENTLY THE ONLY WAY THAT IS FAST ENOUGH TO USE IN HIGH-THROUGHPUT SEARCHES FOR NEW MATERIALS WITH USEFUL PROPERTIES. IN PRINCIPLE, THIS THEORY FINDS THE EXACT GROUND-STATE ENERGY AND SPIN DENSITIES BY SOLVING SELF-CONSISTENT ONE- ELECTRON SCHROEDINGER EQUATIONS. IN PRACTICE, THE DENSITY FUNCTIONAL FOR THE EXCHANGE-CORRELATION ENERGY MUST BE APPROXIMATED. THE EXCHANGE-CORRELATION ENERGY IS THE MANY-BODY GLUE THAT BINDS ONE ATOM TO ANOTHER. 2

SCAN (STRONGLY CONSTRAINED AND APPROPRIATELY NORMED) IS A NEW DENSITY FUNCTIONAL THAT PROVIDES A LARGE INCREASE IN ACCURACY FOR A MODEST INCREASE IN COMPUTATIONAL COST. SCAN SHOULD WORK WELL FOR “NORMALLY-CORRELATED” MATERIALS, INCLUDING LAYERED MATERIALS, AND FOR MOLECULES, WITH DIVERSE BONDS (WEAK, IONIC, METALLIC, COVALENT). SCAN WORKS AS WELL AS IT DOES BECAUSE IT IS CONSTRUCTED TO SATISFY 17 KNOWN “EXACT CONSTRAINTS” ON THE DENSITY FUNCTIONAL FOR THE EXCHANGE-CORRELATION ENERGY. 3

SPECIAL FEATURES OF SCAN: SCAN HAS BEEN IMPLEMENTED IN THE CODES VASP AND BAND (FOR SOLIDS) AND GAUSSIAN (FOR MOLECULES). THE SCAN SUBROUTINES WILL BE RELEASED FREELY TO ALL THIS SUMMER. UNLIKE SOME DENSITY FUNCTIONALS, SCAN IS CONSTRUCTED WITHOUT FITTING TO MOLECULAR DATA. SCAN IS OFTEN AS ACCURATE AS, OR MORE ACCURATE THAN, THE COMPUTATIONALLY MORE EXPENSIVE HYBRID FUNCTIONALS. SCAN CAPTURES THE INTERMEDIATE-RANGE VAN DER WAALS ATTRACTION. THE LONG-RANGE VDW ATTRACTION IS CAPTURED BY SCAN+rVV10 (HAOWEI PENG) OR SCAN+D3 (GERIT BRANDENBURG). 4

WEAK BONDS (HYDROGEN BONDS AND VDW BONDS): ENERGETIC ORDERING OF 7 ICE POLYMORPHS SCAN CAPTURES THE INTERMEDIATE-RANGE VDW PREVIOUSLY BELIEVED IMPOSSIBLE FOR CONVENTIONAL DENSITY FUNCTIONALS (PBE AND PBE0) RIGHT ORDERING FOR 7 POLYMORPHS OF ICE THE RIGHT ORDER OF POLYMORPHS IX AND II ONLY FROM SCAN REF: J. SUN, ET AL, NAT. CHEM., TO APPEAR. 5

IONIC BONDS: ENERGETIC ORDERING OF 6 POLYMORPHS OF MnO2 REF: D.A. KITCHAEV, H. PENG, Y. LIU, J. SUN, J.P. PERDEW, G. CEDER, PHYS. REV. B 115, (2015).

COVALENT AND METALLIC BONDS: SILICON IN DIFFERENT PHASES Si GROUND-STATE: SEMICONDUCTING DIAMOND PHASE HIGH-PRESSURE: METALLIC BETA-Sn PHASE ACCURATE VOLUMES ACCURATE ENERGY DIFFERENCE FROM SCAN, BUT NOT FROM LDA OR PBE REF: J. SUN, ET AL, NAT. CHEM., TO APPEAR. 7

PERFORMANCE OF SCAN FOR SOLID Si Phase transitionInterstitial defect formation (eV) XHT PBE SCAN Ref IT WAS PREVIOUSLY BELIEVED THAT ONLY A HYBRID FUNCTIONAL COULD PREDICT THE CORRECT RESULTS.

CONCLUSION SCAN IS ACCURATE, EFFICIENT, AND VERSATILE FOR DIVERSELY BONDED MATERIALS SYSTEMATIC IMPROVEMENT OVER THE STANDARD PBE GGA OFTEN COMPARABLE TO OR MORE ACCURATE THAN A HYBRID FUNCTIONAL WITH MUCH CHEAPER COMPUTATIONAL COST (FACTOR OF 10 TO 100 IN PLANE-WAVE CODES) SCAN+rVV10 IS A VERSATILE VDW DENSITY FUNCTIONAL FOR LAYERED MATERIALS AND SOFT MATTER SCAN (SCAN+rVV10) IS EXPECTED TO HAVE A BROAD IMPACT ON MATERIALS SCIENCE, CONDENSED MATTER PHYSICS, & CHEMISTRY 9

Accuracy Efficiency META-GGA IS POTENTIALLY MOST ACCURATE SEMILOCAL FUNCTIONAL (REF: J. SUN, et al, PRL, 111, (2013)) ACRONYM GGA: PBE, PBESOL HYBRID GGA: B3LYP, PBE0, HSE 10  SEMILOCAL APPROXIMATION

WHAT PROBLEM IS ADDRESSED? PROBLEM: NO PREVIOUS CONVENTIONAL DENSITY FUNCTIONAL SIMULTANEOUSLY ACHIEVES REASONABLE ACCURACY FOR DIFFERENT CHEMICAL BONDS (COVALENT, METALLIC, IONIC, HYDROGEN, AND VDW) SIGNIFICANCE OF SCAN: AT A COMPUTATIONAL COST COMPARABLE TO PREVIOUS EFFICIENT FUNCTIONALS, SCAN PREDICTS ACCURATE GEOMETRIES AND ENERGIES FOR DIVERSELY-BONDED MOLECULES AND SOLIDS, INCLUDING THOSE WITH THE VDW BONDS, AND THUS SIGNIFICANTLY ENHANCES THE PREDICTIVE POWER OF DFT. 11 BONDCOVALENTMETALLICIONICHYDROGENVDW (INTERMEDIATE-RANGE) EXAMPLE STRENGTH~1.0 eV ~0.1 eV~0.01 eV Ar

12 PROTOTYPICAL FERROELECTRICS: PbTiO 3 AND BaTiO 3

NONLOCAL CORRECTIONS SEMILOCAL APPROXIMATIONS FAIL FOR THE FOLLOWING TWO SITUATIONS WHERE NONLOCAL CORRECTIONS ARE NEEDED. 1.LONG-RANGE VAN DER WAALS (VDW) INSTANTANEOUS INDUCED DIPOLE INTERACTION BETWEEN TWO DISTANT ELECTRON DENSITIES NO DENSITY OVERLAP, NO CONTRIBUTION FROM SEMILOCAL APPROXIMATIONS 2. STRETCHED-BOND SITUATIONS SEMILOCAL APPROXIMATIONS FAIL AS BONDS ARE STRETCHED REF: A.J. COHEN, P. MORI-SANCHEZ, W. YANG, SCIENCE, 321, 792 (2008) 13