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Title: Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality

Abstract

We have computed the surface energies, work functions, and interlayer surface relaxations of clean (111), (100), and (110) surfaces of Al, Cu, Ru, Rh, Pd, Ag, Pt, and Au. We interpret the surface energy from liquid metal measurements as the mean of the solid-state surface energies over these three lowest-index crystal faces. We compare experimental (and random phase approximation) reference values to those of a family of nonempirical semilocal density functionals, from the basic local density approximation (LDA) to our most advanced general purpose meta-generalized gradient approximation, strongly constrained and appropriately normed (SCAN). The closest agreement is achieved by the simplest density functional LDA, and by the most sophisticated one, SCAN+rVV10 (Vydrov–Van Voorhis 2010). The long-range van der Waals interaction, incorporated through rVV10, increases the surface energies by about 10%, and increases the work functions by about 3%. LDA works for metal surfaces through two known error cancellations. The Perdew–Burke–Ernzerhof generalized gradient approximation tends to underestimate both surface energies (by about 24%) and work functions (by about 4%), yielding the least-accurate results. The amount by which a functional underestimates these surface properties correlates with the extent to which it neglects van der Waals attraction at intermediate and long range. Qualitativemore » arguments are given for the signs of the van der Waals contributions to the surface energy and work function. A standard expression for the work function in Kohn–Sham (KS) theory is shown to be valid in generalized KS theory. Interlayer relaxations from different functionals are in reasonable agreement with one another, and usually with experiment.« less

Authors:
; ; ;
Publication Date:
Research Org.:
Energy Frontier Research Centers (EFRC) (United States). Center for the Computational Design of Functional Layered Materials (CCDM)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1399814
Alternate Identifier(s):
OSTI ID: 1470019
Grant/Contract Number:  
DESC0010499; SC0012575
Resource Type:
Published Article
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Volume: 114 Journal Issue: 44; Journal ID: ISSN 0027-8424
Publisher:
Proceedings of the National Academy of Sciences
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; catalysis (heterogeneous), solar (photovoltaic), energy storage (including batteries and capacitors), hydrogen and fuel cells, defects, mechanical behavior, materials and chemistry by design, synthesis (novel materials)

Citation Formats

Patra, Abhirup, Bates, Jefferson E., Sun, Jianwei, and Perdew, John P. Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality. United States: N. p., 2017. Web. doi:10.1073/pnas.1713320114.
Patra, Abhirup, Bates, Jefferson E., Sun, Jianwei, & Perdew, John P. Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality. United States. doi:10.1073/pnas.1713320114.
Patra, Abhirup, Bates, Jefferson E., Sun, Jianwei, and Perdew, John P. Tue . "Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality". United States. doi:10.1073/pnas.1713320114.
@article{osti_1399814,
title = {Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality},
author = {Patra, Abhirup and Bates, Jefferson E. and Sun, Jianwei and Perdew, John P.},
abstractNote = {We have computed the surface energies, work functions, and interlayer surface relaxations of clean (111), (100), and (110) surfaces of Al, Cu, Ru, Rh, Pd, Ag, Pt, and Au. We interpret the surface energy from liquid metal measurements as the mean of the solid-state surface energies over these three lowest-index crystal faces. We compare experimental (and random phase approximation) reference values to those of a family of nonempirical semilocal density functionals, from the basic local density approximation (LDA) to our most advanced general purpose meta-generalized gradient approximation, strongly constrained and appropriately normed (SCAN). The closest agreement is achieved by the simplest density functional LDA, and by the most sophisticated one, SCAN+rVV10 (Vydrov–Van Voorhis 2010). The long-range van der Waals interaction, incorporated through rVV10, increases the surface energies by about 10%, and increases the work functions by about 3%. LDA works for metal surfaces through two known error cancellations. The Perdew–Burke–Ernzerhof generalized gradient approximation tends to underestimate both surface energies (by about 24%) and work functions (by about 4%), yielding the least-accurate results. The amount by which a functional underestimates these surface properties correlates with the extent to which it neglects van der Waals attraction at intermediate and long range. Qualitative arguments are given for the signs of the van der Waals contributions to the surface energy and work function. A standard expression for the work function in Kohn–Sham (KS) theory is shown to be valid in generalized KS theory. Interlayer relaxations from different functionals are in reasonable agreement with one another, and usually with experiment.},
doi = {10.1073/pnas.1713320114},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 44,
volume = 114,
place = {United States},
year = {2017},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1073/pnas.1713320114

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Cited by: 20 works
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Works referenced in this record:

Photoelectric Work Functions of (100) and (111) Faces of Silver Single Crystals and Their Contact Potential Difference
journal, November 1940


Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/PhysRevLett.77.3865

Nonlocal van der Waals density functional made simple and efficient
journal, January 2013


Wave-vector analysis of the jellium exchange-correlation surface energy in the random-phase approximation: Support for nonempirical density functionals
journal, July 2006


Asymptotics of the Dispersion Interaction: Analytic Benchmarks for van der Waals Energy Functionals
journal, February 2006


Surfaces of real metals by the variational self-consistent method
journal, March 1978


Metal surface energy: Persistent cancellation of short-range correlation effects beyond the random phase approximation
journal, January 2003


Projector augmented-wave method
journal, December 1994


Pitfalls in measuring work function using photoelectron spectroscopy
journal, February 2010


Theoretical Heterogeneous Catalysis: Scaling Relationships and Computational Catalyst Design
journal, June 2016


Ab-initio simulations of materials using VASP: Density-functional theory and beyond
journal, October 2008

  • Hafner, Jürgen
  • Journal of Computational Chemistry, Vol. 29, Issue 13
  • DOI: 10.1002/jcc.21057

Surface free energies of solid metals: Estimation from liquid surface tension measurements
journal, January 1977


Communication: Effect of the orbital-overlap dependence in the meta generalized gradient approximation
journal, August 2012

  • Sun, Jianwei; Xiao, Bing; Ruzsinszky, Adrienn
  • The Journal of Chemical Physics, Vol. 137, Issue 5
  • DOI: 10.1063/1.4742312

Converged properties of clean metal surfaces by all-electron first-principles calculations
journal, February 2006

  • Da Silva, Juarez L. F.; Stampfl, Catherine; Scheffler, Matthias
  • Surface Science, Vol. 600, Issue 3
  • DOI: 10.1016/j.susc.2005.12.008

Surface Science Investigations of Thin Metal Films on Metal and Metal Oxide Supports
journal, January 1986


Interaction of metastable noble-gas atoms with transition-metal surfaces: Resonance ionization and Auger neutralization
journal, February 1987


From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999


Image states and local work function for Ag/Pd(111)
journal, February 1993


Theory of nonuniform electronic systems. I. Analysis of the gradient approximation and a generalization that works
journal, June 1980


Surface properties of simple metals via inhomogeneous linear electronic response. I. Theory
journal, December 1982


Understanding band gaps of solids in generalized Kohn–Sham theory
journal, March 2017

  • Perdew, John P.; Yang, Weitao; Burke, Kieron
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 11
  • DOI: 10.1073/pnas.1621352114

Reconstruction of the (111) and (001) surfaces of Au and Pt: thermal behavior
journal, March 1993


The work function of the elements and its periodicity
journal, November 1977

  • Michaelson, Herbert B.
  • Journal of Applied Physics, Vol. 48, Issue 11
  • DOI: 10.1063/1.323539

Semilocal and hybrid meta-generalized gradient approximations based on the understanding of the kinetic-energy-density dependence
journal, January 2013

  • Sun, Jianwei; Haunschild, Robin; Xiao, Bing
  • The Journal of Chemical Physics, Vol. 138, Issue 4
  • DOI: 10.1063/1.4789414

The shortcomings of semi-local and hybrid functionals: what we can learn from surface science studies
journal, June 2008


Density functional theory in surface chemistry and catalysis
journal, January 2011

  • Norskov, J. K.; Abild-Pedersen, F.; Studt, F.
  • Proceedings of the National Academy of Sciences, Vol. 108, Issue 3
  • DOI: 10.1073/pnas.1006652108

Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional
journal, June 2016

  • Sun, Jianwei; Remsing, Richard C.; Zhang, Yubo
  • Nature Chemistry, Vol. 8, Issue 9
  • DOI: 10.1038/nchem.2535

High-Level Correlated Approach to the Jellium Surface Energy, without Uniform-Gas Input
journal, January 2008


Surface energies, work functions, and surface relaxations of low-index metallic surfaces from first principles
journal, December 2009


Pseudojellium, ideal metals, and stabilized jellium
journal, April 1999


Anisotropic work function of clean and smooth low-index faces of aluminium
journal, July 1976


van der Waals Bonding in Layered Compounds from Advanced Density-Functional First-Principles Calculations
journal, June 2012


Physical origin of exchange diffusion on fcc(100) metal surfaces
journal, December 1997


Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965


Ab initio theory and modeling of water
journal, September 2017

  • Chen, Mohan; Ko, Hsin-Yu; Remsing, Richard C.
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 41
  • DOI: 10.1073/pnas.1712499114

Theoretical maps of work-function anisotropies
journal, December 2001


Theory of Metal Surfaces: Charge Density and Surface Energy
journal, June 1970


Surface electronic structure
journal, March 1982


Comparative first-principles studies of prototypical ferroelectric materials by LDA, GGA, and SCAN meta-GGA
journal, July 2017


Photoelectron-spectroscopy study of the electronic structure of Au and Ag overlayers on Pt(100), Pt(111), and Pt(997) surfaces
journal, December 1983


Work function and secondary emission studies of various Cu crystal faces
journal, January 1977

  • Haas, G. A.; Thomas, R. E.
  • Journal of Applied Physics, Vol. 48, Issue 1
  • DOI: 10.1063/1.323329

Extracting convergent surface formation energies from slab calculations
journal, February 1998

  • Boettger, J. C.; Smith, John R.; Birkenheuer, Uwe
  • Journal of Physics: Condensed Matter, Vol. 10, Issue 4
  • DOI: 10.1088/0953-8984/10/4/017

Trends of the surface relaxations, surface energies, and work functions of the 4 d transition metals
journal, August 1992


Reconstruction of charged surfaces: General trends and a case study of Pt(110) and Au(110)
journal, December 2003


Climbing the Density Functional Ladder: Nonempirical Meta–Generalized Gradient Approximation Designed for Molecules and Solids
journal, September 2003


Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces
journal, April 2008


Energies of curved metallic surfaces from the stabilized-jellium model
journal, March 1992


Electronic structure of palladium (100)
journal, February 1981


Electron work function: A parameter sensitive to the adhesion behavior of crystallographic surfaces
journal, December 2001

  • Li, D. Y.; Li, W.
  • Applied Physics Letters, Vol. 79, Issue 26
  • DOI: 10.1063/1.1428766

Surface energy and work function of fcc and bcc crystals: Density functional study
journal, December 2014


Work function measurements on (100), (110) and (111) surfaces of aluminium
journal, September 1973


Surface energies of elemental crystals
journal, September 2016

  • Tran, Richard; Xu, Zihan; Radhakrishnan, Balachandran
  • Scientific Data, Vol. 3, Issue 1
  • DOI: 10.1038/sdata.2016.80

Towards the computational design of solid catalysts
journal, April 2009

  • Nørskov, J.; Bligaard, T.; Rossmeisl, J.
  • Nature Chemistry, Vol. 1, Issue 1, p. 37-46
  • DOI: 10.1038/nchem.121

Quantitative analysis of low-energy-electron diffraction: Application to Pt(111)
journal, December 1979


Surface energies of solid metals
journal, October 1975


Change-in-self-consistent-field theory of the work function
journal, July 1978


Cohesive Properties and Asymptotics of the Dispersion Interaction in Graphite by the Random Phase Approximation
journal, November 2010


Workhorse Semilocal Density Functional for Condensed Matter Physics and Quantum Chemistry
journal, July 2009


Face dependent surface energies of simple metals
journal, January 1981


Surface and curvature energies from jellium spheres: Density functional hierarchy and quantum Monte Carlo
journal, August 2002


Surface energy and work function of elemental metals
journal, September 1992


Liquid-drop model for crystalline metals: Vacancy-formation, cohesive, and face-dependent surface energies
journal, January 1991


The Low Temperature Adsorption of Oxygen on Rh(111)
journal, January 1997


Anisotropy of the Electronic Work Function of Metals
journal, November 1941


Confirmation of an exception to the ‘‘general rule’’ of surface relaxations
journal, May 1990

  • Noonan, J. R.; Davis, H. L.
  • Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, Vol. 8, Issue 3
  • DOI: 10.1116/1.576692

Recommended values of clean metal surface work functions
journal, November 2015

  • Derry, Gregory N.; Kern, Megan E.; Worth, Eli H.
  • Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, Vol. 33, Issue 6
  • DOI: 10.1116/1.4934685

The exchange-correlation energy of a metallic surface
journal, December 1975


Surface structure of gold and silver (110)-surfaces
journal, January 1995


Improved lattice constants, surface energies, and CO desorption energies from a semilocal density functional
journal, March 2011


The surface energy of metals
journal, August 1998


Functional designed to include surface effects in self-consistent density functional theory
journal, August 2005


Tests of a ladder of density functionals for bulk solids and surfaces
journal, February 2004


Exchange-correlation hole of a generalized gradient approximation for solids and surfaces
journal, February 2009


Quantum Monte Carlo calculations of the surface energy of an electron gas
journal, July 2007


Photoelectric Work Function of a Copper Single Crystal for the (100), (110), (111), and (112) Faces
journal, March 1972


Binding energy of image-potential states: Dependence on crystal structure and material
journal, January 1987


Theory of Metal Surfaces: Induced Surface Charge and Image Potential
journal, April 1973


Quantum and classical dynamics of reactive scattering of H 2 from metal surfaces
journal, January 2016

  • Kroes, Geert-Jan; Díaz, Cristina
  • Chemical Society Reviews, Vol. 45, Issue 13
  • DOI: 10.1039/C5CS00336A

Extracting convergent surface energies from slab calculations
journal, September 1996


Exchange-correlation energy of a metallic surface: Wave-vector analysis
journal, March 1977


Leed intensity analysis of the surface structures of Pd(111) and of CO adsorbed on Pd(111) in a (√3 × √3)R30° arrangement
journal, September 1987


Au(111): A theoretical study of the surface reconstruction and the surface electronic structure
journal, June 1991


Image charge at a metal surface
journal, June 1985


Nonconvergence of surface energies obtained from thin-film calculations
journal, June 1994


Structure of Al(111)-(√3 × √3 ) R 30°-Na: A LEED study
journal, August 1994


Structure and phases of the Au(001) surface: Absolute x-ray reflectivity
journal, September 1991


PEEM is a suitable tool for absolute work function measurements
journal, January 2005

  • Li, W. Y.; Goto, K.; Shimizu, R.
  • Surface and Interface Analysis, Vol. 37, Issue 2
  • DOI: 10.1002/sia.1974

Importance of dispersion in density functional calculations of cesium chloride and its related halides
journal, August 2013


Testing the local density approximation with energy-versus-separation curves of jellium slab pairs
journal, June 2004


Empty electronic states at the (1×1) and (5×20) surfaces of Pt(100): An inverse photoemission study
journal, January 1988


Electron spectroscopic study of the interaction of coadsorbed CO and D2 on Rh(100) at low temperature
journal, January 1984


LEED structural analysis of Al(111)-K-(√3 × √3 ) R 30°: Identification of stable and metastable adsorption sites
journal, February 1994


Density Functionals that Recognize Covalent, Metallic, and Weak Bonds
journal, September 2013


Electronic Properties of Molecules and Surfaces with a Self-Consistent Interatomic van der Waals Density Functional
journal, April 2015


Accurate and simple analytic representation of the electron-gas correlation energy
journal, June 1992


Wavelike charge density fluctuations and van der Waals interactions at the nanoscale
journal, March 2016

  • Ambrosetti, Alberto; Ferri, Nicola; DiStasio, Robert A.
  • Science, Vol. 351, Issue 6278
  • DOI: 10.1126/science.aae0509

Versatile van der Waals Density Functional Based on a Meta-Generalized Gradient Approximation
journal, October 2016


Climbing the ladder of density functional approximations
journal, September 2013


Spin polarized photoemission from gold using circularly polarized light
journal, May 1982


Density-functional correction of random-phase-approximation correlation with results for jellium surface energies
journal, April 1999


Theory of inhomogeneous quantum systems. IV. Variational calculations of metal surfaces
journal, November 1985


Diffusion Monte Carlo study of jellium surfaces: Electronic densities and pair correlation functions
journal, December 1996


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    Crystallographic orientation dependence of work function: carbon adsorption on Au surfaces
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