Online citations, reference lists, and bibliographies.
← Back to Search

Electronic Structure Calculations With GPAW: A Real-space Implementation Of The Projector Augmented-wave Method.

J. Enkovaara, C. Rostgaard, J. J. Mortensen, J. Chen, M. Dulak, L. Ferrighi, J. Gavnholt, C. Glinsvad, V. Haikola, H. A. Hansen, H. Kristoffersen, M. Kuisma, A. H. Larsen, L. Lehtovaara, M. Ljungberg, O. Lopez-Acevedo, P. G. Moses, J. Ojanen, T. Olsen, V. Petzold, N. A. Romero, J. Stausholm-Møller, M. Strange, G. Tritsaris, M. Vanin, M. Walter, B. Hammer, H. Häkkinen, G. Madsen, R. Nieminen, J. Nørskov, M. Puška, T. Rantala, J. Schiøtz, K. Thygesen, K. W. Jacobsen
Published 2010 · Materials Science, Medicine

Cite This
Download PDF
Analyze on Scholarcy
Share
Electronic structure calculations have become an indispensable tool in many areas of materials science and quantum chemistry. Even though the Kohn-Sham formulation of the density-functional theory (DFT) simplifies the many-body problem significantly, one is still confronted with several numerical challenges. In this article we present the projector augmented-wave (PAW) method as implemented in the GPAW program package (https://wiki.fysik.dtu.dk/gpaw) using a uniform real-space grid representation of the electronic wavefunctions. Compared to more traditional plane wave or localized basis set approaches, real-space grids offer several advantages, most notably good computational scalability and systematic convergence properties. However, as a unique feature GPAW also facilitates a localized atomic-orbital basis set in addition to the grid. The efficient atomic basis set is complementary to the more accurate grid, and the possibility to seamlessly switch between the two representations provides great flexibility. While DFT allows one to study ground state properties, time-dependent density-functional theory (TDDFT) provides access to the excited states. We have implemented the two common formulations of TDDFT, namely the linear-response and the time propagation schemes. Electron transport calculations under finite-bias conditions can be performed with GPAW using non-equilibrium Green functions and the localized basis set. In addition to the basic features of the real-space PAW method, we also describe the implementation of selected exchange-correlation functionals, parallelization schemes, ΔSCF-method, x-ray absorption spectra, and maximally localized Wannier orbitals.
This paper references
J. Chem. Phys
P John (2005)
Phys. Rev. B
X Wang (2008)
Phys. Rev. A
A D Becke (1988)
Phys. Rev. Lett
Leonard Kleinman (1982)
10.1063/1.2193514
A general and efficient pseudopotential Fourier filtering scheme for real space methods using mask functions.
M. Tafipolsky (2006)
10.1103/PhysRevB.73.035309
Electron transport through an interacting region: The case of a nonorthogonal basis set
K. Thygesen (2006)
10.1103/PHYSREVLETT.69.2598
Soft-x-ray resonant inelastic scattering at the C K edge of diamond.
Ma (1992)
Phys. Rev. B
G Kresse (1996)
10.1073/pnas.0801001105
A unified view of ligand-protected gold clusters as superatom complexes
M. Walter (2008)
10.1016/S0927-0256(02)00325-7
First-principles computation of material properties: the ABINIT software project
X. Gonze (2002)
Daniel Sánchez-Portal, and Emilio Artacho
Javier Junquera (2001)
10.1063/1.473182
Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation
L. A. Curtiss (1997)
10.1103/PHYSREVB.73.195107
Oxidation energies of transition metal oxides within the GGA+U framework
L. Wang (2006)
Phys. Rev. B
F Guinea (1983)
Phys. Rev. Lett
P John (2008)
Phys. Rev. Lett
M Dion (2004)
Phys. Rev. Lett
T Olsen (2009)
Phys. Rev. B
J L Martins (1988)
Phys
J. Gavnholt (2008)
Phys. Rev. B
D Djukic (2005)
Phys. Rev. B
M Heiskanen (2001)
10.1103/PHYSREVB.28.4397
Effective two-dimensional Hamiltonian at surfaces
F. Guinea (1983)
10.1016/j.cpc.2005.07.011
Electronic energy minimisation with ultrasoft pseudopotentials
P. Hasnip (2006)
10.1103/PhysRevLett.92.246401
van der Waals density functional for general geometries.
M. Dion (2004)
10.1016/0021-9991(75)90065-0
The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
E. R. Davidson (1975)
Phys
N.A.W. Holzwarth (1997)
Phys. Rev. B
C Rostgaard (2010)
Rev
T. L. Beck (2000)
10.1016/0927-0256(96)00008-0
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
G. Kresse (1996)
Phys. Rev. B
E L Briggs (1996)
Phys. Rev. B
T Olsen (2009)
Phys
K. Yabana (1996)
Phys
P. Hohenberg (1964)
Bull
P. E. Blöchl (2003)
Int
Y. T. Feng (1996)
10.1021/JA073580+
Origin of magic stability of thiolated gold clusters: a case study on Au25(SC6H13)18.
Y. Negishi (2007)
10.1103/PHYSREV.116.287
New Method for Calculating Wave Functions in Crystals and Molecules
J. Phillips (1959)
10.1103/PhysRevB.59.1758
From ultrasoft pseudopotentials to the projector augmented-wave method
G. Kresse (1999)
Phys
M. Brandbyge (2002)
Phys. Rev. B
A H Larsen (2009)
10.1016/S0010-4655(02)00686-0
octopus: a first-principles tool for excited electron-ion dynamics.
M. Marques (2003)
Phys. Rev. B
D J Niklewski (1989)
10.1002/(SICI)1097-461X(1999)75:1<55::AID-QUA6>3.0.CO;2-K
Time-dependent local-density approximation in real time.
Yabana (1996)
10.1103/PHYSREVB.54.4484
Time-dependent local-density approximation in real time
K. Yabana (1996)
Phys
S. Massidda (1993)
10.1103/PhysRevB.79.035403
Hot-electron-mediated desorption rates calculated from excited-state potential energy surfaces
T. Olsen (2009)
10.1007/S11244-010-9443-6
RPBE-vdW Description of Benzene Adsorption on Au(111)
J. Wellendorff (2010)
10.1021/nl072058i
Amine-gold linked single-molecule circuits: experiment and theory.
S. Y. Quek (2007)
10.1103/PhysRevB.80.245427
Polarization-induced renormalization of molecular levels at metallic and semiconducting surfaces
J. M. García-Lastra (2009)
Phys
E. Anglada (2002)
Phys
E. Wimmer (1981)
J. Chem. Phys
Daniel Neuhasuer (1989)
10.1063/1.1904565
Prescription for the design and selection of density functional approximations: more constraint satisfaction with fewer fits.
J. Perdew (2005)
10.1103/PHYSREVB.78.075109
Real-space pseudopotential method for first principles calculations of general periodic and partially periodic systems
A. Natan (2008)
Phys. Rev. B
M Brandbyge (2002)
Comput. Phys. Commun
M A. L Marques (2003)
New J. Phys
Michael Walter (2008)
Phys. Rev. Lett
P John (2009)
Phys
G. Kresse (1996)
10.1103/PhysRevLett.97.216405
Renormalization of molecular electronic levels at metal-molecule interfaces.
J. Neaton (2006)
10.1088/0953-8984/21/8/084204
A grid-based Bader analysis algorithm without lattice bias.
W. Tang (2009)
10.1103/PHYSREVLETT.51.1884
Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities
J. Perdew (1983)
J. Chem. Phys
Lauri Lehtovaara (2009)
Phys. Rev. B
T Olsen (2009)
Modelling Simul
J. E. Pask (2005)
10.1103/PhysRevB.71.161402
Stretching dependence of the vibration modes of a single-molecule Pt-H2-Pt bridge
D. Djukic (2005)
10.1063/1.2943138
Time-dependent density-functional theory in the projector augmented-wave method.
M. Walter (2008)
Comp
G. Kresse (1996)
10.1103/REVMODPHYS.64.1045
Iterative minimization techniques for ab initio total energy calculations: molecular dynamics and co
M. Payne (1992)
10.1063/1.478522
Toward reliable density functional methods without adjustable parameters: The PBE0 model
C. Adamo (1999)
J. Chem. Phys
J P Perdew (2004)
Phys
F. Guinea (1983)
10.1090/S0025-5718-68-99866-9
The optimum addition of points to quadrature formulae.
T. Patterson (1968)
10.1103/PhysRevB.65.165401
Density-functional method for nonequilibrium electron transport
M. Brandbyge (2002)
10.1103/RevModPhys.72.1041
Real-space mesh techniques in density-functional theory
T. Beck (2000)
10.1103/PhysRevB.73.035404
Comparison of the full-potential and frozen-core approximation approaches to density-functional calculations of surfaces
A. Kiejna (2006)
10.1088/0953-8984/21/39/395502
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials.
P. Giannozzi (2009)
Phys
C. Rostgaard (2010)
10.1103/PHYSREVLETT.52.997
Density-Functional Theory for Time-Dependent Systems
Erich Runge (1984)
10.1088/0953-8984/14/11/302
The SIESTA method for ab initio order-N materials simulation
J. M. Soler (2001)
10.1063/1.1672392
Self‐Consistent Molecular‐Orbital Methods. I. Use of Gaussian Expansions of Slater‐Type Atomic Orbitals
W. J. Hehre (1969)
Phys. Rev. B
A Rohrbach (2004)
Phys. Rev. B
David Vanderbilt (1990)
Phys. Rev. Lett
L J Sham (1983)
Phys. Rev. Lett
J J Mortensen (2005)
Comp. Mat. Sci
G Kresse (1996)
Modelling Simul. Mater. Sci. Eng
J E Pask (2005)
10.1103/PHYSREVB.54.11169
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set.
Kresse (1996)
J. Am. Chem. Soc
Y Negishi (2007)
Nano Letters
Su Ying Quek (2007)
The Projector Augmented-wave Method
C. Rostgaard (2009)
10.1103/PHYSREVB.37.6134
Diagonalization of large matrices in pseudopotential band-structure calculations: Dual-space formalism.
Martins (1988)
10.1088/1367-2630/10/4/043018
Photoelectron spectra from first principles: from the many-body to the single-particle picture
M. Walter (2008)
10.1103/PhysRevB.72.125119
Partly occupied Wannier functions: Construction and applications
K. Thygesen (2005)
10.1063/1.1430255
Interpretation of the Kohn-Sham orbital energies as approximate vertical ionization potentials
D. P. Chong (2002)
Phys
T. Olsen (2009)
Phys. Rev. B
Amir Natan (2008)
J. Phys. C: Solid State Phys
R Haydock (1972)
10.1103/PHYSREVB.58.8097
Calculations of near-edge x-ray-absorption spectra of gas-phase and chemisorbed molecules by means of density-functional and transition-potential theory
L. Triguero (1998)
Phys
C. Hartwigsen (1998)
10.1017/CBO9781139207249.009
I and J
William M. Marsden (2012)
10.1103/PHYSREVB.74.155108
Hybrid exchange-correlation energy functionals for strongly correlated electrons: Applications to transition-metal monoxides
F. Tran (2006)
10.1103/PhysRevB.64.235111
Numerical atomic orbitals for linear-scaling calculations
J. Junquera (2001)
10.1088/0965-0393/13/3/R01
Finite element methods in ab initio electronic structure calculations
J. Pask (2005)
J. Chem. Phys
Larry A Curtiss (1997)
J. Chem. Phys
D P Chong (2002)
J. Chem. Phys
C Adamo (1999)
10.1103/PHYSREVB.50.17953
Projector augmented-wave method.
Blöchl (1994)
10.1515/9783111576855-015
J
Seguin Hen (1824)
Phys
A. D. Becke (1988)
10.1103/PHYSREVLETT.72.1240
Finite-difference-pseudopotential method: Electronic structure calculations without a basis.
Chelikowsky (1994)
10.1103/PhysRevB.77.115333
Conserving GW scheme for nonequilibrium quantum transport in molecular contacts
K. Thygesen (2008)
Chem. Phys. Lett
Reinhart Ahlrichs (1989)
Phys
M. Heiskanen (2001)
and Kotliar G
D. Jacob (2009)
10.1063/1.1397797
Detailed study of pyridine at the C 1s and N 1s ionization thresholds: The influence of the vibrational fine structure
Ch. Kolczewski (2001)
10.1016/j.cpc.2009.06.022
Ab initio molecular simulations with numeric atom-centered orbitals
V. Blum (2009)
Phys. Rev
W Kohn (1965)
Topics in Catalysis
J Wellendorff (2010)
Phys. Rev. Lett
Jianmin Tao (2003)
J. Chem. Phys
Osamu Takahashi (2004)
10.1016/0009-2614(80)80396-4
Convergence acceleration of iterative sequences. the case of scf iteration
P. Pulay (1980)
Phys. Rev. B
K Yabana (1996)
Phys. Rev. B
Mathieu Taillefumier (2002)
Chem. Phys. Lett
Peter Pulay (1980)
Math. Comput
T N L Patterson (1968)
Phys
K. S. Thygesen (2005)
10.1063/1.1316015
From molecules to solids with the DMol3 approach
B. Delley (2000)
10.1063/1.1645787
Potential--energy surfaces for excited states in extended systems.
A. Hellman (2004)
10.1103/PhysRevB.63.245106
Multigrid method for electronic structure calculations
M. Heiskanen (2001)
10.1103/PHYSREVA.38.3098
Density-functional exchange-energy approximation with correct asymptotic behavior.
Becke (1988)
10.1103/PhysRevB.79.235414
Inelastic scattering in a local polaron model with quadratic coupling to bosons
T. Olsen (2009)
J. Phys.: Condens. Matter
A Ferretti (2007)
Phys. Rev. Lett
P John (1983)
10.1103/PhysRevB.71.035109
Real-space grid implementation of the projector augmented wave method
J. J. Mortensen (2005)
10.1103/PHYSREVB.55.2005
Comparison of the Projector Augmented-Wave, Pseudopotential, and Linearized Augmented- Plane-Wave Formalisms for Density-Functional Calculations of Solids
N. Holzwarth (1997)
Int. J. Quantum Chem
K Yabana (1999)
Phys. Rev. Lett
P John (1996)
Int. J. Num. Meth. in Engineer
Y T Feng (1996)
Phys. Rev. Lett
Guillermo Román-Pérez (2009)
Comput
X. Gonze (2002)
10.1103/PhysRevB.58.3641
RELATIVISTIC SEPARABLE DUAL-SPACE GAUSSIAN PSEUDOPOTENTIALS FROM H TO RN
C. Hartwigsen (1998)
10.1038/28112
The signature of chemical valence in the electrical conduction through a single-atom contact
E. Scheer (1998)
J. Chem. Phys
Michael Walter (2008)
J. Phys. A: Math. Gen
D M Wood (1985)
10.1016/S0166-1280(99)00445-5
Molecular excitation energies from time-dependent density functional theory
T. Grabo (2000)
10.1103/PhysRevB.77.155402
Effects of self-interaction corrections on the transport properties of phenyl-based molecular junctions
C. Toher (2008)
10.1063/1.2370993
A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions.
Y. Zhao (2006)
10.1103/PHYSREVB.48.5058
Hartree-Fock LAPW approach to the electronic properties of periodic systems.
Massidda (1993)
10.1103/PhysRevLett.95.216401
Bayesian error estimation in density-functional theory.
J. Mortensen (2005)
Phys. Rev
P Hohenberg (1964)
Phys. Rev. B
S Massidda (1993)
Phys. Rev. B
K S Thygesen (2008)
10.1088/0022-3719/8/16/011
Electronic structure based on the local atomic environment for tight-binding bands. II
R. Haydock (1972)
Bull. Mat. Sci
P E Blöchl (2003)
10.1103/PhysRevB.66.205101
Systematic generation of finite-range atomic basis sets for linear-scaling calculations
E. Anglada (2002)
Phys
W. Kohn (1965)
Phys. Rev. B
E Wimmer (1981)
10.1109/5992.998641
An object-oriented scripting interface to a legacy electronic structure code
S. R. Bahn (2002)
10.1103/PhysRevLett.100.136406
Restoring the density-gradient expansion for exchange in solids and surfaces.
J. Perdew (2008)
10.1103/PHYSREVLETT.48.1425
Efficacious Form for Model Pseudopotentials
L. Kleinman (1982)
10.1103/PHYSREVA.51.1944
Self-consistent approximation to the Kohn-Sham exchange potential.
Gritsenko (1995)
10.1103/PHYSREVB.40.3979
Ab initio multicenter tight-binding model for molecular-dynamics simulations and other applications in covalent systems.
Sankey (1989)
10.1063/1.1665298
Meta-generalized gradient approximation: explanation of a realistic nonempirical density functional.
J. Perdew (2004)
Phys
X. Wang (2008)
Phys
Y. Ma (1992)
Phys. Rev. B
J M Garcia-Lastra (2009)
Int
K. Yabana (1999)
Phys
J. J. Mortensen (2005)
10.1103/PhysRevB.66.195107
X-ray absorption near-edge structure calculations with the pseudopotentials: Application to the K edge in diamond and α-quartz
M. Taillefumier (2002)
10.1103/PHYSREV.140.A1133
Self-Consistent Equations Including Exchange and Correlation Effects
W. Kohn (1965)
10.1103/PHYSREVLETT.51.1888
Density-Functional Theory of the Energy Gap
L. J. Sham (1983)
10.1103/PHYSREV.136.B864
THE INHOMOGENEOUS ELECTRON GAS.
P. Hohenberg (1964)
10.1103/PHYSREVB.54.14362
Real-space multigrid-based approach to large-scale electronic structure calculations.
Briggs (1996)
10.1515/9783111548050-024
M
M. Sankar (1824)
10.1103/REVMODPHYS.61.689
The density functional formalism, its applications and prospects
R. O. Jones (1989)
Phys. Rev. B
Fabien Tran (2006)
Phys. Rev. Lett
N Ma (1992)
10.1103/PHYSREVB.24.864
Full-potential self-consistent linearized-augmented-plane-wave method for calculating the electronic structure of molecules and surfaces: O2 molecule
E. Wimmer (1981)
The projector augmented-wave method. arXiv:0910.1921 [condmat .mtrl-sci
Carsten Rostgaard (2009)
Phys. Rev. B
J Gavnholt (2008)
10.1142/9789812830586_0005
Time-Dependent Density Functional Response Theory for Molecules
M. E. Casida (1995)
10.1103/PhysRevB.52.R5471
Large-scale electronic-structure calculations with multigrid acceleration.
Briggs (1995)
Phys. Rev. Lett
M Dion (2004)
10.1103/PHYSREVB.57.1505
Electron-energy-loss spectra and the structural stability of nickel oxide : An LSDA+U study
S. Dudarev (1998)
Phys. Rev. B
G Kresse (1758)
10.1103/PhysRevLett.91.146401
Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids.
J. Tao (2003)
Phys. Rev. B
K S Thygesen (2006)
Phys. Rev. B
Thomas Maxisch (2006)
Phys. Rev
C James (1959)
Comput. Phys. Commun
Volker Blum (2009)
Phys
M. Dion (2004)
10.1103/PHYSREVLETT.106.179902
Erratum: Workhorse Semilocal Density Functional for Condensed Matter Physics and Quantum Chemistry [Phys. Rev. Lett. 103 , 026403 (2009)]
J. Perdew (2011)
10.1103/PhysRevLett.103.016803
Kondo effect and conductance of nanocontacts with magnetic impurities.
D. Jacob (2009)
10.1063/1.1926272
The Perdew-Burke-Ernzerhof exchange-correlation functional applied to the G2-1 test set using a plane-wave basis set.
J. Paier (2005)
10.1103/PhysRevB.80.195112
Localized atomic basis set in the projector augmented wave method
A. H. Larsen (2009)
10.1016/S1380-7323(96)80093-8
Time-Dependent Density Functional Response Theory of Molecular Systems: Theory, Computational Methods, and Functionals
M. E. Casida (1996)
10.1103/PhysRevLett.100.166804
Impact of exchange-correlation effects on the IV characteristics of a molecular junction.
K. Thygesen (2008)
10.1063/1.456646
The time‐dependent Schrödinger equation: Application of absorbing boundary conditions
Daniel Neuhasuer (1989)
10.1103/PHYSREVB.13.4274
Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
O. Gunnarsson (1976)
10.1103/PhysRevB.78.075441
Δ self-consistent field method to obtain potential energy surfaces of excited molecules on surfaces
J. Gavnholt (2008)
Phys. Rev. Lett
R James (1994)
10.1103/PhysRevLett.103.238301
Origin of power laws for reactions at metal surfaces mediated by hot electrons.
T. Olsen (2009)
J. Chem. Phys
A Hellman (2004)
Time-dependent density-functional response theory for molecules Recent Advances in Density Functional Methods, Part I, page 155
M E Casida (1995)
Pablo Ordejón, and Daniel Sánchez-Portal
M José (2002)
10.1177/105345129202700410
MATH
B. M. Fulk (1992)
Phys
L. Triguero (1998)
10.1063/1.435780
Photoelectron spectroscopy with Zr Mζ (151 eV) radiation. A study of the variation of relative photoionization cross sections of molecules containing first row atoms (C, N, O) with exciting radiation from HeI to Mg Kα limits
D. Allison (1978)
Journal of Molecular Structure: THEOCHEM
T Grabo (2000)
Phys. Rev. B
C Hartwigsen (1998)
J. Chem. Phys
C Kolczewski (2001)
Phys. Rev. B
N A W Holzwarth (1997)
Joannopoulos. Rev. Mod. Phys
M C Payne (1992)
10.1103/PHYSREVLETT.103.026403
Workhorse semilocal density functional for condensed matter physics and quantum chemistry.
J. Perdew (2009)
10.1103/PHYSREVB.52.5573
Electronic-structure calculations based on the finite-element method.
Tsuchida (1995)
10.1103/PHYSREVB.41.7892
Soft self-consistent pseudopotentials in a generalized eigenvalue formalism.
Vanderbilt (1990)
J. Chem. Phys
J Paier (2005)
10.1088/0953-8984/19/3/036215
Maximally localized Wannier functions constructed from projector-augmented waves or ultrasoft pseudopotentials
A. Ferretti (2007)
Phys
A. Rohrbach (2004)
10.1016/0009-2614(89)85118-8
ELECTRONIC STRUCTURE CALCULATIONS ON WORKSTATION COMPUTERS: THE PROGRAM SYSTEM TURBOMOLE
R. Ahlrichs (1989)
10.1103/PhysRevB.77.045119
Electronic correlation in nanoscale junctions: Comparison of the GW approximation to a numerically exact solution of the single-impurity Anderson model
Xin Wang (2008)
J. Chem. Phys
D A Allison (1978)
Phys. Rev. A
Oleg Gritsenko (1995)
Phys. Rev. Lett
J B Neaton (2006)
Phys. Rev. B
Eiji Tsuchida (1995)
Gunnarsson. Rev. Mod. Phys
R O Jones (1989)
Phys
O. Gunnarsson (1976)
Rev
R. O. Jones (1989)
Phys
P. E. Blöchl (1994)
10.1088/0305-4470/18/9/018
A new method for diagonalising large matrices
D. Wood (1985)
Phys. Rev. B
C Toher (2008)
Rev. Mod. Phys
T L Beck (1041)
10.1103/PhysRevB.81.115443
Vibrationally mediated control of single-electron transmission in weakly coupled molecule-metal junctions
T. Olsen (2010)
Rev
M. C. Payne (1992)
Hansen L
J. J. Mortensen (2005)
Phys. Rev. B
S L Dudarev (1998)
J. Phys.: Condens. Matter
Paolo Giannozzi (2009)
Phys. Rev. B
E Anglada (2002)
Phys. Rev. B
Y Meir (1992)
Phys. Rev. B
J J Mortensen (2005)
Phys
Y. Meir (1992)
Phys
J. L. Martins (1988)
Phys
S. L. Dudarev (1998)
10.1063/1.1809610
Functional dependence of core-excitation energies.
O. Takahashi (2004)
10.1063/1.2338035
Relaxed core projector-augmented-wave method.
M. Marsman (2006)
10.1103/PHYSREVLETT.68.2512
Landauer formula for the current through an interacting electron region.
Meir (1992)
10.1016/j.otohns.2009.05.016
Nature
R. Rosenfeld (2009)
Phys
E. L. Briggs (1996)
Alberto Castro
M.A.L. Marques (2003)
Phys
L. J. Sham (1983)
and Kresse G
J Paier (2005)
10.1103/PhysRevB.81.085103
Fully self-consistent GW calculations for molecules
C. Rostgaard (2010)
10.1002/(SICI)1097-0207(19960715)39:13<2209::AID-NME951>3.0.CO;2-R
CONJUGATE GRADIENT METHODS FOR SOLVING THE SMALLEST EIGENPAIR OF LARGE SYMMETRIC EIGENVALUE PROBLEMS
Y. Feng (1996)
10.1007/BF02712785
Projector augmented wave method:ab initio molecular dynamics with full wave functions
P. E. Bloechl (2002)
10.1103/PHYSREVLETT.77.3865
Generalized Gradient Approximation Made Simple.
Perdew (1996)
Phys. Rev. B
K S Thygesen (2005)
Phys. Rev. B
T Olsen (2010)
Phys. Rev. Lett
K S Thygesen (2008)
Phys. Rev. Lett
D Jacob (2009)
Phys. Rev. Lett
Erich Runge (1984)
Phys
A. H. Larsen (2009)
Phys. Rev. B
Adam Kiejna (2006)
10.1142/9789812832078
Handbook Series on Semiconductor Parameters
M. Levinshtein (1996)
Phys. Rev. B
L Triguero (1998)
Phys. Rev. B
O Gunnarsson (1976)
Phys. Rev. B
P E Blöchl (1994)
J. Chem. Phys
Yan Zhao (2006)
J. Chem. Phys
W J Hehre (1969)
Time-dependent density functional response theory of molecular systems: Theory
M. E. Casida (1996)
10.1063/1.3176508
All-electron density functional theory and time-dependent density functional theory with high-order finite elements.
L. Lehtovaara (2009)
10.1103/PhysRevLett.103.096102
Efficient implementation of a van der Waals density functional: application to double-wall carbon nanotubes.
G. Román-Pérez (2009)
Comp
P. J. Hasnip (2006)
10.1016/s0927-0256(97)00154-7
Comput. Mater. Sci.
M. Dong (1998)
10.1515/9783111697888-007
E
Adam S. Opalski (1824)
10.1103/PHYSREVB.69.075413
Molecular adsorption on the surface of strongly correlated transition-metal oxides: A case study for CO/NiO(100)
A. Rohrbach (2004)



This paper is referenced by
10.1002/jcc.25208
Real‐space grid representation of momentum and kinetic energy operators for electronic structure calculations
D. Ninno (2018)
10.1021/acs.nanolett.9b04789
Microscopic Theory of Plasmons in Substrate-supported Borophene.
Anubhab Haldar (2020)
10.1039/C2EE22341D
New cubic perovskites for one- and two-photon water splitting using the computational materials repository
Ivano E. Castelli (2012)
10.1016/J.ELECTACTA.2016.01.070
Targeted design of α-MnO2 based catalysts for oxygen reduction
M. Lehtimaeki (2016)
10.1039/C6CY01820C
Nitrate–nitrite equilibrium in the reaction of NO with a Cu-CHA catalyst for NH3-SCR
C. Tyrsted (2016)
10.1016/J.JCAT.2016.09.004
Atomic scale analysis of sterical effects in the adsorption of 4,6-dimethyldibenzothiophene on a CoMoS hydrotreating catalyst
Signe S. Grønborg (2016)
10.1039/c6cp04194a
Decoupling strain and ligand effects in ternary nanoparticles for improved ORR electrocatalysis.
P. C. Jennings (2016)
10.1007/s10853-013-7448-9
Performance of genetic algorithms in search for water splitting perovskites
A. Jain (2013)
10.1103/PhysRevMaterials.3.034003
Definition of a scoring parameter to identify low-dimensional materials components
P. M. Larsen (2018)
10.1038/ncomms3422
All-thiol-stabilized Ag44 and Au12Ag32 nanoparticles with single-crystal structures.
Huayan Yang (2013)
High-harmonic generation in metallic titanium nitride
A. Korobenko (2020)
Quasiparticle GW calculations within the GPAW electronic structure code
Falco Hüser (2013)
10.2172/1118122
Simulating Interface Growth and Defect Generation in CZT – Simulation State of the Art and Known Gaps
Charles H Henager (2012)
10.1038/s41565-020-0717-2
High oscillator strength interlayer excitons in two-dimensional heterostructures for mid-infrared photodetection
S. Lukman (2020)
10.1021/JP503494G
Mechanism of Trichloroethene Hydrodehalogenation: A First-Principles Kinetic Monte Carlo Study
A. Kausamo (2014)
Layer shift factor in layered hybrid perovskites -- new univocal quantitative descriptor of composition-structure-property relationships.
E. Marchenko (2020)
10.1021/acs.jpclett.6b01543
Chemical Bond Activation Observed with an X-ray Laser.
M. Beye (2016)
10.1039/c5cp00352k
Configuration interaction singles based on the real-space numerical grid method: Kohn-Sham versus Hartree-Fock orbitals.
Jaeug Kim (2015)
10.1016/j.cpc.2012.05.007
Libxc: A library of exchange and correlation functionals for density functional theory
M. Marques (2012)
10.1038/srep21990
Unravelling Site-Specific Photo-Reactions of Ethanol on Rutile TiO2(110)
J. Ø. Hansen (2016)
Confinement Heteroepitaxy: Realizing Atomically Thin, Half-van der Waals Materials
N. Briggs (2019)
10.1038/s41467-020-16529-6
A library of ab initio Raman spectra for automated identification of 2D materials
A. Taghizadeh (2020)
10.1021/acs.jctc.0c00214
Validation of Pseudopotential Calculations for the Electronic Band Gap of Solids
Pedro Borlido (2020)
10.1088/1361-648X/ab7f6a
Generation of low-symmetry perovskite structures for ab initio computation.
Na Xie (2020)
10.1063/1.5044765
Toward quantum-chemical method development for arbitrary basis functions.
M. Herbst (2018)
10.1039/c4sc03835e
Design of two-photon molecular tandem architectures for solar cells by ab initio theory† †Electronic supplementary information (ESI) available: Visualizations of molecular orbitals, one-particle mechanisms and a table with Kohn–Sham eigenvalues. See DOI: 10.1039/c4sc03835e
K. B. Ørnsø (2015)
10.1016/J.JCAT.2017.12.001
Modeling the adsorption of sulfur containing molecules and their hydrodesulfurization intermediates on the Co-promoted MoS2 catalyst by DFT
M. Šarić (2018)
10.1038/s41524-020-00428-x
High-throughput computational screening for two-dimensional magnetic materials based on experimental databases of three-dimensional compounds
D. Torelli (2020)
10.1002/pssb.201451174
Theoretical electron energy loss spectroscopy of isolated graphene
D. J. Mowbray (2014)
10.1021/ja405997s
Theoretical investigation of the activity of cobalt oxides for the electrochemical oxidation of water.
M. Bajdich (2013)
10.1038/nmat3454
Singular characteristics and unique chemical bond activation mechanisms of photocatalytic reactions on plasmonic nanostructures.
P. Christopher (2012)
10.1103/PHYSREVLETT.106.146803
Nonlocal screening of plasmons in graphene by semiconducting and metallic substrates: first-principles calculations.
Jun Yan (2011)
See more
Semantic Scholar Logo Some data provided by SemanticScholar