Density functional theory in the solid state

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 372, Issue 2011, 2014, Pages

  Hasnip, Philip J ^a   Refson, Keith ^b   Probert, Matt I J ^a   Yates, Jonathan R ^c   Clark, Stewart J ^d   Pickard, Chris J ^e  

^a UNIVERSITY OF YORK   (United Kingdom)

^b RUTHERFORD APPLETON LABORATORY   (United Kingdom)

^c UNIVERSITY OF OXFORD   (United Kingdom)

^d DURHAM UNIVERSITY   (United Kingdom)

^e UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Computational chemistry; Computational materials science; Condensed matter theory; Density functional theory; Electronic structure theory

Indexed keywords

EID: 84894268077     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2013.0270     Document Type: Review

References (81)

1. Hohenberg P, Kohn W. 1964 Inhomogeneous electron gas. Phys. Rev. 136, B864-B871. (doi:10.1103/PhysRev.136.B864)
2. Kohn W, Sham LJ. 1965 Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133-A1138. (doi:10.1103/PhysRev.140. A1133)
3. Perdew JP, Zunger A. 1981 Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23, 5048-5079. (doi:10.1103/PhysRevB.23.5048)
4. Ceperley DM, Alder BJ. 1980 Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566-569. (doi:10.1103/PhysRevLett.45. 566)
5. Gunnarsson O, Lundqvist BI. 1976 Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism. Phys. Rev. B 13, 4274-4298. (doi:10.1103/ PhysRevB.13.4274)
6. Perdew JP, Wang Y. 1992 Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B 45 13 244-13 249. (doi:10.1103/PhysRevB.45.13244)
7. Perdew JP, Burke K, Ernzerhof M. 1995 Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865-3868. (doi:10.1103/PhysRevLett.77.3865)
8. Perdew JP, Chevary JA, Vosko SH, Jackson KA, Pederson MR, Singh DJ, Fiolhais C. 1992 Atoms, molecules, solids and surfaces-applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 46, 6671-6687. (doi:10.1103/Phys RevB.46.6671)
9. Winkler B, Milman V, Hennion B, Payne MC, Lee M-H, Lin JS. 1995 Ab initio total energy study of brucite, diaspore and hypothetical hydrous wadsleyite. Phys. Chem. Miner. 22, 461-467. (doi:10.1007/BF00200324)
10. Tao J, Perdew JP, Staroverov VN, Scuseria GE. 2003 Climbing the density functional ladder: non-empirical meta-generalized gradient approximation designed for molecules and solids. Phys. Rev. Lett. 91, 146401. (doi:10.1103/PhysRevLett.91.146401)
11. Martin R. 2004 Electronic structure: basic theory and practical methods. Cambridge, UK: Cambridge University Press.
12. Payne MC, Teter MP, Allan DC, Arias TA, Joannopoulos JD. 1992 Iterative minimization techniques for ab initio total-energy calculations-molecular- dynamics and conjugate gradients. Rev. Mod. Phys. 64, 1045-1097. (doi:10.1103/RevModPhys.64.1045)
13. Gillan MJ. 1989 Calculation of the vacancy formation energy in aluminium. J. Phys.: Condens. Matter 1, 689-711. (doi:10.1088/0953-8984/1/4/005)
14. Clark SJ, Segall MD, Pickard CJ, Hasnip PJ, Probert MJ, Refson K, Payne MC. 2005 First principles methods using CASTEP. Z. Kristallogr. 220, 567-570. (doi:10.1524/zkri.220. 5.567.65075)
15. Gonze X et al. 2005 A brief introduction to the ABINIT software package. Z. Kristallogr. 220, 558-562. (doi:10.1524/zkri.220.5.558.65066)
16. Gonze X et al. 2009 ABINIT: first-principles approach of materials and nanosystem properties. Comp. Phys. Comm. 180, 2582-2615. (doi:10.1016/j.cpc. 2009.07.007)
17. VandeVondele J, Krack M, Mohamed F, Parrinello M, Chassaing T, Hutter J. 2005 Quickstep: fast and accurate density functional calculations using a mixed Gaussian and plane waves approach. Comp. Phys. Comm. 167, 103-128. (doi:10.1016/j.cpc.2004.12.014)
18. Hutter J, Iannuzzi M. 2005 CPMD: Car-Parrinello molecular dynamics. Z. Kristallogr. 220, 549-551. (doi:10.1524/zkri.220.5.549.65080)
19. Dovesi R, Orlando R, Civalleri B, Roetti C, Saunders VR, Zicovich-Wilson CM. 2005 CRYSTAL: a computational tool for the ab initio study of the electronic properties of crystals. Z. Kristallogr. 220, 571-573. (doi:10.1524/zkri.220.5. 571.65065)
20. Delley B. 2000 From molecules to solids with the DMol approach. J. Chem. Phys. B 113, 7756-7764. (doi:10.1063/1.1316015)
21. Blum V, Gehrke R, Hanke F, Havu P, Havu V, Ren XG, Reuter K, Scheffler M. 2009 Ab initio molecular simulations with numeric atom-centered orbitals. Comp. Phys. Comm. 180, 2175-2196. (doi:10.1016/j.cpc.2009.06.022)
22. Enkovaara J et al. 2010 Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wavemethod. J. Phys.: Condens. Matter 22, 253202. (doi:10.1088/0953-8984/22/25/253202)
23. Giannozzi P et al. 2009 QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 21, 395502. (doi:10.1088/0953-8984/21/39/395502)
24. Soler JM, Artacho E, Gale JD, Garcia A, Junquera J, Ordejon P, Sanchez-Portal D. 2002 The SIESTA method for ab initio order-N materials simulation. J. Phys: Condens. Matter 14, 2745-2780. (doi:10.1088/0953-8984/14/ 11/302)
25. Kresse G, Furthmüller J. 1996 Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11 169-11 186. (doi:10.1103/PhysRevB.54.11169)
26. Schwarz K, Blaha P. 2003 Solid state calculations using WIEN2k. Comput. Mater. Sci. 28, 259-273. (doi:10.1016/S0927-0256(03)00112-5)
27. Perdew JP, Parr RG, Levy M, Balduz JL. 1982 Density-functional theory for fractional particle number: derivative discontinuities of the energy. Phys. Rev. Lett. 49, 1691-1694. (doi:10.1103/ PhysRevLett.49.1691)
28. Hedin L. 1965 New method for calculating the one-particle Green's function with application to the electron-gas problem. Phys. Rev. 139, A796-A823. (doi:10.1103/PhysRev.139.A796)
29. Lichtenstein AI, Anisimov VI, Zaanen J. 1995 Density-functional theory and strong interactions: orbital ordering in Mott-Hubbard insulators. Phys. Rev. B 52, 5467. (doi:10.1103/ PhysRevB.52.R5467)
30. Hasnip PJ, Smith JH, Lazarov VK. 2013 Ab initio studies of disorder in the full Heusler alloy Co2FexMn1-xSi. J. Appl. Phys. 113, 17B106. (doi:10.1063/1.4801745)
31. Cococcioni M, de Gironcoli S. 2005 Linear response approach to the calculation of the effective interaction parameters in the LDA + Umethod. Phys. Rev. B 71, 035105. (doi:10.1103/ PhysRevB.71.035105)
32. Heyd J, Scuseria GE, Ernzerhof M. 2003 Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207. (doi:10.1063/1.1564060)
33. Cora F, Alfredsson M, Mallia G, Middlemiss DS, Mackrodt WC, Dovesi R. 2004 The performance of hybrid density functionals in solid state chemistry. Struct. Bonding 113, 171-232. (doi:10.1007/b97944)
34. Clark SJ, Robertson J. 2010 Screened exchange density functional applied to solids. Phys. Rev. B 82, 085208. (doi:10.1103/PhysRevB.82.085208)
35. Xiong K, Robertson J, Gibson MC, Clark SJ. 2005 Defect energy levels in HfO2 high-dielectricconstant gate oxide. Appl. Phys. Lett. 87, 183505. (doi:10.1063/1.2119425)
36. Clark SJ, Robertson J, Lany S, Zunger A. 2010 Intrinsic defects in ZnO calculated by screened exchange and hybrid functionals. Phys. Rev. B 81, 115311. (doi:10.1103/PhysRevB.81.115311)
37. Lazarov VK, Cai ZH, Yoshida K, Zhang KHLL, Weinert M, Ziemer KS, Hasnip PJ. 2011 Dynamically stabilized growth of polar oxides: the case of MgO(111). Phys. Rev. Lett. 107, 056101. (doi:10.1103/PhysRevLett.107.056101)
38. Schon JC, Jansen M. 2001 Determination, prediction, and understanding of structures, using the energy landscapes of chemical systems. I. Z. Kristallgr. 216, 307-325. (doi:10.1524/ zkri.216.6.307.20339)
39. Hart GLW, Blum V, WalorskiMJ, Zunger A. 2005 Evolutionary approach for determining firstprinciples Hamiltonians. Nat. Mater. 4, 391-394. (doi:10.1038/nmat1374)
40. Abraham NL, Probert MIJ. 2006 A periodic genetic algorithm with real-space representation for crystal structure and polymorph prediction. Phys. Rev. B 73, 224104. (doi:10.1103/Phys RevB.73.224104)
41. Abraham NL, Probert MIJ. 2008 An improved real-space genetic algorithm for crystal structure and polymorph prediction. Phys. Rev. B 77, 134117. (doi:10.1103/PhysRevB.77. 134117)
42. Glass CW, Oganov AR, Hansen N. 2006 USPEX-evolutionary crystal structure prediction. Comp. Phys. Comm. 175, 713-720. (doi:10.1016/j.cpc.2006.07.020)
43. Goedecker S. 2004 Minima hopping: an efficient search method for the global minimum of the potential energy surface of complex molecular systems. J. Chem. Phys. 120, 9911-9917. (doi:10.1063/1.1724816)
44. Wang YC, Lv JA, Zhu L, Ma YM. 2010 Crystal structure prediction via particle-swarm optimization. Phys. Rev. B 82, 094116. (doi:10.1103/PhysRevB.82. 094116)
45. Pickard CJ, Needs RJ. 2006 High-pressure phases of silane. Phys. Rev. Lett. 97, 045504. (doi:10.1103/PhysRevLett.97.045504)
46. Pickard CJ, Needs RJ. 2011 Ab initio random structure searching. J. Phys.: Condens. Matter 23, 053201. (doi:10.1088/0953-8984/23/5/053201)
47. Sluiter MHF, Kawazoe Y. 2003 Cluster expansion method for adsorption: application to hydrogen chemisorption on graphene. Phys. Rev. B 68, 085410. (doi:10.1103/PhysRevB.68. 085410)
48. Sofo JO, Chaudhari AS, Barber GD. 2007 Graphane: a two-dimensional hydrocarbon. Phys. Rev. B 75, 153401. (doi:10.1103/PhysRevB.75.153401)
49. Elias DC et al. 2009 Control of Graphene's properties by reversible hydrogenation: evidence for Graphane. Science 323, 610-613. (doi:10.1126/ science.1167130)
50. Pickard CJ, Needs RJ. 2007 Metallization of aluminum hydride at high pressures: a firstprinciples study. Phys. Rev. B 76, 024401. (doi:10.1103/PhysRevB.76.024401)
51. Pickard CJ, Needs RJ. 2007 Structure of phase III of solid hydrogen. Nat. Phys. 3, 473-476. (doi:10.1038/nphys.6258)
52. Howie RT, Guillaume CL, Scheler T, Goncharov AF, Gregoryanz E. 2012 Mixed molecular and atomic phase of dense hydrogen. Phys. Rev. Lett. 108, 125501. (doi:10.1103/PhysRevLett. 108.125501)
53. Pickard CJ, Martinez-Canales M, Needs RJ. 2012 Density functional theory study of phase IV of solid hydrogen. Phys. Rev. B 85, 214114. (doi:10.1103/PhysRevB.85.214114)
54. LiuHY, Zhu L, CuiWW, Ma YM. 2012 Room-temperature structures of solid hydrogen at high pressures. J. Chem. Phys. 137, 074501. (doi:10.1063/1.4745186)
55. Eremets MI, Troyan IA. 2011 Conductive dense hydrogen. Nat. Mater. 10, 927-931. (doi:10.1038/nmat3175)
56. Pickard CJ, Needs RJ. 2008 Highly compressed ammonia forms an ionic crystal. Nat. Mater. 7, 775-779. (doi:10.1038/nmat2261)
57. Pickard CJ, Needs RJ. 2009 Stable phases of iron at terapascal pressures. J. Phys.: Condens. Matter 21, 452205. (doi:10.1088/0953-8984/21/45/452205)
58. Martinez-Canales M, Pickard CJ, Needs RJ. 2012 Thermodynamically stable phases of carbon at multiterapascal pressures. Phys. Rev. Lett. 108, 045704. (doi:10.1103/PhysRevLett. 108.045704)
59. Sun J, Martinez-Canales M, Klug DD, Pickard CJ, Needs RJ. 2012 Persistence and eventual demise of oxygen molecules at terapascal pressures. Phys. Rev. Lett. 108, 045503. (doi:10.1103/PhysRevLett.108.045503)
60. Pickard CJ, Needs RJ. 2010 Aluminium at terapascal pressures. Nat. Mater. 9, 624-627. (doi:10.1038/nmat2796)
61. Pickard CJ, Needs RJ. 2011 Predicted pressure-induced s-band ferromagnetism in alkali metals. Phys. Rev. Lett. 107, 087201. (doi:10.1103/PhysRevLett.107.087201)
62. Kunc K, Martin RM. 1982 Ab initio force constants of GaAs: a new approach to calculation of phonons and dielectric properties. Phys. Rev. Lett. 48, 406-409. (doi:10.1103/ PhysRevLett.48.406)
63. Baroni S, Giannozzi P, Testa A. 1987 Green's-function approach to linear response in solids. Phys. Rev. Lett. 58, 1861-1864. (doi:10.1103/PhysRevLett.58. 1861)
64. Baroni S, de Gironcoli S, Dal Corso A. 2001 Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73, 515-562. (doi:10.1103/Rev ModPhys.73.515)
65. Parker SF, Refson K, Bewley RI, Dent G. 2011 Assignment of the vibrational spectra of lithium hydroxide monohydrate, LiOH · H2O. J. Chem. Phys. 134, 084503. (doi:10.1063/1.3553812)
66. Refson K, Tulip PR, Clark SJ. 2006 Variational density-functional perturbation theory for dielectrics and lattice dynamics. Phys. Rev. B 73, 155114. (doi:10.1103/PhysRevB.73.155114)
67. Parker SF, Bennington SM, Taylor JW, Herman H, Silverwood I, Albers P, Refson K. 2011 Complete assignment of the vibrational modes of C60 by inelastic neutron scattering spectroscopy and periodic-DFT. PCCP 13, 7789-7804. (doi:10.1039/c0cp02956d)
68. Marx D, Hutter J. 2009 Ab initio molecular dynamics: basic theory and advanced methods. Cambridge, UK: Cambridge University Press.
69. Li X-Z, Probert MIJ, Alavi A, Michaelides A. 2010 Quantum nature of the proton in water-hydroxyl overlayers on metal surfaces. Phys. Rev. Lett. 104, 066102. (doi:10.1103/Phys RevLett.104.066102)
70. Li X-Z, Walker B, Probert MIJ, Pickard CJ, Needs RJ, Michaelides A. 2013 Classical and quantum ordering of protons in cold solid hydrogen under megabar pressures. J. Phys.: Condens. Matter 25, 085402. (doi:10.1088/0953-8984/25/8/ 085402)
71. Bonhomme C et al. 2012 First-principle calculation of NMR parameters using the GIPAW (Gauge Including Projector Augmented Wave) Method: a chemist's point of view. Chem. Rev. 112, 5733-5779. (doi:10.1021/cr300108a)
72. Kibalchenko M, Lee D, Shao L, Payne MC, Titman JJ, Yates JR. 2010 Distinguishing hydrogen bonding networks in alpha-D-galactose usingNMRexperiments and first principles calculations. Chem. Phys. Lett. 498, 270-276. (doi:10.1016/j.cplett.2010.08.077)
73. Cadars S, Layrac G, Geìrardin C, Deschamps M, Yates JR, Tichit D, Massiot D. 2011 Identification and quantification of defects in the cation ordering in Mg/Al layered double hydroxides. Chem. Mater. 23, 2821-2831. (doi:10.1021/cm200029q)
74. Hoehne F, Lu J, Stegner AR, Stutzmann M, Brandt MS, Rohrmüller M, Schmidt WG, Gerstmann U. 2011 Electrically detected electron-spin-echo envelope modulation: a highly sensitive technique for resolving complex interface structures. Phys. Rev. Lett. 106, 196101. (doi:10.1103/PhysRevLett.106.196101)
75. Gerstmann U, Rohrmüller M, Mauri F, Schmidt WG. 2010 Ab initio g-tensor calculation for paramagnetic surface states: hydrogen adsorption at Si surfaces. Phys. Status Solidi (c) 7, 157-160. (doi:10.1002/pssc.200982462)
76. Nicholls RJ, Murdock AT, Tsang J, Britton J, Pennycook TJ, Koós A, Nellist PD, Grobert N, Yates JR. 2013 Probing the bonding in nitrogen-doped graphene using electron energy loss spectroscopy. ACS Nano 7, 7145-7150. (doi:10.1021/nn402489v)
77. Peverati R, Truhlar DG. 2014 Quest for a universal density functional: the accuracy of density functionals across a broad spectrum of databases in chemistry and physics. Phil. Trans. R. Soc. A 372, 20120476. (doi:10.1098/rsta.2012.0476)
78. Björkman T, Gulans A, Krasheninnikov AV, Nieminen RM. 2012 Are we van derWaals ready? J. Phys.: Condens. Matter 24, 424218. (doi:10.1088/0953- 8984/24/42/424218)
79. Bowler DR, Miyazaki T, Gillan MJ. 2002 Recent progress in linear-scaling ab initio electronic structure techniques. J. Phys. Condens. Matter 14, 2781-2798. (doi:10.1088/0953-8984/ 14/11/303)
80. Bowler DR, Choudhury R, Gillan MJ, Miyazaki T. 2006 Recent progress with large-scale ab initio calculations: the CONQUEST code. Phys. Stat. Sol. 243, 989-1000. (doi:10.1002/pssb. 200541386)
81. Skylaris C-K, Haynes PD, Mostofi AA, Payne MC. 2005 Introducing ONETEP: linear-scaling density functional simulations on parallel computers. J. Chem. Phys. 122, 084119. (doi:10.1063/1.1839852)