← 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

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