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A New-Generation Density Functional pp 1–24Cite as

An Overview of Modern Density Functional Theory

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Abstract

Density functional theory (DFT) has become the leading method in computing the electronic structures and properties from first principles. Its foundation was laid on Hohenberg-Kohn theorems, which proved that there exists a one-to-one correspondence between the ground state electron density ρ0 of a many-body system and its total energy. In practice, DFT is most frequently applied in the framework of Kohn–Sham (KS) scheme, where an approximate exchange-correlation functional has to be chosen. Hence, the success of a DFT calculation critically depends on the quality of the exchange-correlation functional. In this chapter, we first briefly discuss the Hohenberg-Kohn theorems (Sect. 1.1). After introducing the KS scheme, various approximations for the exchange-correlation functionals are presented in Sect. 1.2. These functionals are grouped according to Perdew’s classification of Jacob’s ladder. Finally, some general trends for the functional performances along the Jacob’s ladder are outlined.

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References

  1. McWeeny R (1992) Methods of molecular quantum mechanics. Academic Press, London

    Google Scholar 

  2. Perdew JP, Kurth S (2003) In: Fiolhais C, Nogueira F, Marques M (eds) A primer in density functional theory. Springer, Berlin

    Google Scholar 

  3. Parr RG, Yang WT (1989) Density functional theory of atoms and molecules. Oxford University Press, New York

    Google Scholar 

  4. Koch W, Holthausen MC (2001) A chemist’s guide to density functional theory, 2nd edn. Wiley-VCH, New York

    Book  Google Scholar 

  5. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev B 136:B864–B871. doi:10.1103/PhysRev.136.B864

    Article  Google Scholar 

  6. Levy M (1979) Universal variational functionals of electron densities, 1st-order density matrices, and natural spin-orbitals and solution of the V-representability problem. Proc Natl Acad Sci USA 76:6062–6065. doi:10.1073/pnas.76.12.6062

    Article  CAS  Google Scholar 

  7. Teller E (1962) On stability of molecules in Thomas-Fermi theory. Rev Mod Phys 34:627–631. doi:10.1103/RevModPhys.34.627

    Article  CAS  Google Scholar 

  8. Lieb E, Simon B (1977) Thomas-Fermi theory of atoms, molecules and solids. Adv Math 23:22–116. doi:10.1016/0001-8708(77)90108-6

    Article  Google Scholar 

  9. Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:1133–1138. doi:10.1103/PhysRev.140.A1133

    Article  Google Scholar 

  10. von Barth U, Hedin L (1972) A local exchange-correlation potential for the spin polarized case i. J Phys C: Solid State Phys 5:1629–1642. doi:10.1088/0022-3719/5/13/012

    Article  Google Scholar 

  11. Bloch F (1929) Note to the electron theory of ferromagnetism and electrical conductivity. Z Phys 57:545–555. doi:10.1007/BF01340281

    Article  CAS  Google Scholar 

  12. Dirac PAM (1930) Note on exchange phenomena in the Thomas atom. Math Proc Camb Phil Soc 26:376–385. doi:10.1017/S0305004100016108

    Article  CAS  Google Scholar 

  13. Slater JC (1960) Quantum theory of atomic structure, vol 2. McGraw-Hill, New York

    Google Scholar 

  14. Vosko SH, Wilk L, Nusair M (1980) Accurate spin-dependent electron liquid correlation energies for local spin-density calculations–a critical analysis. Can J Phys 58:1200–1211. doi:10.1139/p80-159

    Article  CAS  Google Scholar 

  15. 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

    Article  CAS  Google Scholar 

  16. Perdew JP, Wang Y (1992) Accurate and simple analytic representation of the electron-gas correlation energy. Phys Rev B 45:13244–13249. doi:10.1103/PhysRevB.45.13244

    Article  Google Scholar 

  17. Langreth DC, Mehl M (1983) Beyond the local-density approximation in calculations of ground-state electronic-properties. Phys Rev B 28:1809–1834. doi:10.1103/PhysRevB.28

    Google Scholar 

  18. Perdew JP (1986) Density-functional approximation for the correlation-energy of the inhomogeneous electron-gas. Phys Rev B 33:8822–8824. doi:10.1103/PhysRevB.33.8822; ibid. (1986) 34:7406 (E)

  19. Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic behavior. Phys Rev A 38:3098–3100. doi:10.1103/PhysRevA.38.3098

    Article  CAS  Google Scholar 

  20. Lee CT, Yang WT, Parr RG (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron-density. Phys Rev B 37:785–789. doi:10.1103/PhysRevB.37.785

    Google Scholar 

  21. Perdew JP (1991) Electronic structure of solids’91. Akademie Verlag, Berlin

    Google Scholar 

  22. Perdew JP, Chevary JA, Vosko SH et al (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/PhysRevB.46.6671

    Article  CAS  Google Scholar 

  23. Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868. doi:10.1103/PhysRevLett.77.3865

    Article  CAS  Google Scholar 

  24. Adamo C, Barone V (1998) Exchange functionals with improved long-range behavior and adiabatic connection methods without adjustable parameters: The mPW and mPW1PW models. J Chem Phys 108:664–675. doi:10.1063/1.475428

    Article  CAS  Google Scholar 

  25. Hamprecht FA, Cohen AJ, Tozer DJ, Handy NC (1998) Development and assessment of new exchange-correlation functionals. J Chem Phys 109:6264–6271. doi:10.1063/1.477267

    Article  CAS  Google Scholar 

  26. Cohen AJ, Handy NC (2001) Dynamic correlation. Mol Phys 99:607–615. doi:10.1080/00268970010023435

    Article  CAS  Google Scholar 

  27. Hammer B, Hansen LB, Nørskov JK (1999) Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals. Phys Rev B 59:7413–7421. doi:10.1103/PhysRevB.59.7413

    Article  Google Scholar 

  28. Zhang YK, Yang WT (1998) Comment on “Generalized gradient approximation made simple”. Phys Rev Lett 80:890–890. doi:10.1103/PhysRevLett.80.890

    Article  CAS  Google Scholar 

  29. Xu X, Goddard WA (2004) The extended Perdew-Burke-Ernzerhof functional with improved accuracy for thermodynamic and electronic properties of molecular systems. J Chem Phys 121:4068–4082. doi:10.1063/1.1771632

    Article  CAS  Google Scholar 

  30. Van Voorhis T, Scuseria GE (1998) A novel form for the exchange-correlation energy functional. J Chem Phys 109:400–410. doi:10.1063/1.476577

    Article  Google Scholar 

  31. Perdew JP, Kurth S, Zupan A, Blaha P (1999) Accurate density functional with correct formal properties: A step beyond the generalized gradient approximation. Phys Rev Lett 82:2544–2547. doi:10.1103/PhysRevLett.82.2544

    Article  CAS  Google Scholar 

  32. Tao JM, Perdew JP, Staroverov VN, Scuseria GE (2003) Climbing the density functional ladder: Nonempirical meta-generalized gradient approximation designed for molecules and solids. Phys Rev Lett 91:146401–146404. doi:10.1103/PhysRevLett.91.146401

    Article  Google Scholar 

  33. Zhao Y, Truhlar DG (2006) A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions. J Chem Phys 125:194101. doi:10.1063/1.2370993

    Article  Google Scholar 

  34. Becke AD (1993) A new mixing of Hartree–Fock and local density-functional theories. J Chem Phys 98:1372–1377. doi:10.1063/1.464304

    Article  CAS  Google Scholar 

  35. Becke AD (1993) Density-functional thermochemistry 3: The role of exact exchange. J Chem Phys 98:5648–5652. doi:10.1063/1.464913

    Article  CAS  Google Scholar 

  36. Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994) Ab-initio calculation of vibrational absorption and circular-dichroism spectra using density-functional force-fields. J Phys Chem 98:11623–11627. doi:10.1021/j100096a001

    Article  CAS  Google Scholar 

  37. Perdew JP, Emzerhof M, Burke K (1996) Rationale for mixing exact exchange with density functional approximations. J Chem Phys 105:9982–9985. doi:10.1063/1.472933

    Article  CAS  Google Scholar 

  38. Becke AD (1997) Density-functional thermochemistry. 5. Systematic optimization of exchange-correlation functionals. J Chem Phys 107:8554–8560. doi:10.1063/1.475007

    Article  CAS  Google Scholar 

  39. Schmider HL, Becke AD (1998) Optimized density functionals from the extended G2 test set. J Chem Phys 108:9624–9631. doi:10.1063/1.476438

    Article  CAS  Google Scholar 

  40. Ernzerhof M, Scuseria GE (1999) Assessment of the Perdew-Burke-Ernzerhof exchange-correlation functional. J Chem Phys 110:5029–5036. doi:10.1063/1.478401

    Article  CAS  Google Scholar 

  41. Adamo C, Barone V (1999) Toward reliable density functional methods without adjustable parameters: the PBE0 model. J Chem Phys 110:6158–6170. doi:10.1063/1.478522

    Article  CAS  Google Scholar 

  42. Xu X, Goddard WA (2004) Assessment of Handy-Cohen optimized exchange density functional (OPTX). J Phys Chem A 108:8495–8504. doi:10.1021/jp047428v

    Article  CAS  Google Scholar 

  43. Xu X, Goddard WA (2004) The X3LYP extended density functional for accurate descriptions of nonbond interactions, spin states, and thermochemical properties. Proc Natl Acad Sci USA 101:2673–2677. doi:10.1073/pnas.0308730100

    Article  CAS  Google Scholar 

  44. Xu X, Zhang QS, Muller RP, Goddard WA (2005) An extended hybrid density functional (X3LYP) with improved descriptions of nonbond interactions and thermodynamic properties of molecular systems. J Chem Phys 122:014105. doi:10.1063/1.1812257

    Article  Google Scholar 

  45. Boese AD, Martin JML (2004) Development of density functionals for thermochemical kinetics. J Chem Phys 121:3405–3416. doi:10.1063/1.1774975

    Article  CAS  Google Scholar 

  46. Zhao Y, Lynch BJ, Truhlar DG (2004) Doubly hybrid meta DFT: New multi-coefficient correlation and density functional methods for thermochemistry and thermochemical kinetics. J Phys Chem A 108:4786–4791. doi:10.1021/jp049253v

    Article  CAS  Google Scholar 

  47. Zhao Y, Truhlar DG (2005) Design of density functionals that are broadly accurate for thermochemistry, thermochemical kinetics, and nonbonded interactions. J Phys Chem A 109:5656–5667. doi:10.1021/jp050536c

    Article  CAS  Google Scholar 

  48. Zhao Y, Truhlar DG (2008) The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor Chem Acc 120:215–241. doi:10.1007/s00214-007-0310-x

    Article  CAS  Google Scholar 

  49. Zhang Y, Wu AA, Xu X, Yan YJ (2006) OPBE: A promising density functional for the calculation of nuclear shielding constants. Chem Phys Lett 421:383–388. doi:10.1016/j.cplett.2006.01.095

    Article  CAS  Google Scholar 

  50. Mori-Sánchez P, Cohen AJ, Yang WT (2006) Self-interaction-free exchange-correlation functional for thermochemistry and kinetics. J Chem Phys 124:091102. doi:10.1063/1.2179072

    Article  Google Scholar 

  51. Grimme S (2006) Semiempirical hybrid density functional with perturbative second-order correlation. J Chem Phys 124:034108. doi:10.1063/1.2148954

    Article  Google Scholar 

  52. Karton A, Tarnopolsky A, Lamere JF et al (2008) Highly accurate first-principles benchmark data sets for the parametrization and validation of density functional and other approximate methods. Derivation of a robust, generally applicable, double-hybrid functional for thermochemistry and thermochemical kinetics. J Phys Chem A 112:12868–12886. doi:10.1021/jp801805p

    Article  CAS  Google Scholar 

  53. Chai J-D, Head-Gordon M (2009) Long-range corrected double-hybrid density functionals. J Chem Phys 131:174105. doi:10.1063/1.3244209

    Article  Google Scholar 

  54. Zhang Y, Xu X, Goddard WA (2009) Doubly hybrid density functional for accurate descriptions of nonbond interactions, thermochemistry, and thermochemical kinetics. Proc Natl Acad Sci USA 106:4963–4968. doi:10.1073/pnas.0901093106

    Article  CAS  Google Scholar 

  55. Zhang IY, Xu X, Jung Y, Goddard WA (2011) A fast doubly hybrid density functional method close to chemical accuracy using a local opposite spin ansatz. Proc Natl Acad Sci USA 108:19896–19900. doi:10.1073/pnas.1115123108

    Article  CAS  Google Scholar 

  56. Goerigk L, Grimme S (2011) Efficient and accurate double-hybrid-meta-GGA density functionals—Evaluation with the extended GMTKN30 database for general main group thermochemistry, kinetics, and noncovalent interactions. J Chem Theory Comput 7:291–309. doi:10.1021/ct100466k

    Article  CAS  Google Scholar 

  57. Perdew JP, Ruzsinszky A, Tao JM et al (2005) Prescription for the design and selection of density functional approximations: more constraint satisfaction with fewer fits. J Chem Phys 123:062201. doi:10.1063/1.1904565

    Article  Google Scholar 

  58. Furche F, Perdew JP (2006) The performance of semilocal and hybrid density functionals in 3d transition-metal chemistry. J Chem Phys 124:044103. doi:10.1063/1.2162161

    Article  Google Scholar 

  59. Wigner E, Seitz F (1934) On the constitution of metallic sodium II. Phys Rev 46:509–524. doi:10.1103/PhysRev.46.509

    Article  CAS  Google Scholar 

  60. Gell-Mann M, Brueckner KA (1957) Correlation energy of an electron gas at high density. Phys Rev 106:364–368. doi:10.1103/PhysRev.106.364

    Article  CAS  Google Scholar 

  61. Carr WJ, Maradudin AA (1964) Ground-state energy of a high-density electron gas. Phys Rev 133:A371–A374. doi:10.1103/PhysRev.133.A371

    Article  CAS  Google Scholar 

  62. Nozières P, Pines D (1958) Correlation energy of a free electron gas. Phys Rev 111:442–454. doi:10.1103/PhysRev.111.442

    Article  Google Scholar 

  63. Carr WJ (1961) Energy, specific heat, and magnetic properties of the low-density electron gas. Phys Rev 122:1437–1446. doi:10.1103/PhysRev.122.1437

    Article  Google Scholar 

  64. 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

    Article  CAS  Google Scholar 

  65. Frisch MJ et al. (2003) Gaussian 03, revision A. 1. Gaussian, Inc, Pittsburgh

    Google Scholar 

  66. Oliver GL, Perdew JP (1979) Spin-density gradient expansion for the kinetic energy. Phys Rev A 20:397–403. doi:10.1103/PhysRevA.20.397

    Article  CAS  Google Scholar 

  67. Lieb EH, Oxford S (1981) Improved lower bound on the indirect Coulomb energy. Int J Quantum Chem 19:427–439. doi:10.1002/qua.560190306

    Article  CAS  Google Scholar 

  68. Della Sala F, Görling A (2002) Asymptotic behavior of the Kohn-Sham exchange potential. Phys Rev Lett 89:033003. doi:10.1103/PhysRevLett.89.033003

    Article  Google Scholar 

  69. Levy M, Perdew JP (1993) Tight bound and convexity constraint on the exchange-correlation-energy functional in the low-density limit, and other formal tests of generalized-gradient approximations. Phys Rev B 48:11638–11645. doi:10.1103/PhysRevB.48.11638

    Article  CAS  Google Scholar 

  70. Rasolt M, Geldart DJW (1986) Exchange and correlation energy in a nonuniform fermion fluid. Phys Rev B 34:1325–1328. doi:10.1103/PhysRevB.34.1325

    Article  Google Scholar 

  71. Sham LJ (1971) Computational Methods in Band Theory. Plenum, New York

    Google Scholar 

  72. Colle R, Salvetti O (1975) Approximate calculation of the correlation energy for the closed shells. Theoret Chim Acta 37:329–334. doi:10.1007/BF01028401

    Article  CAS  Google Scholar 

  73. Becke AD (1983) Hartree–Fock exchange energy of an inhomogeneous electron gas. Int J Quantum Chem 23:1915–1922. doi:10.1002/qua.560230605

    Article  CAS  Google Scholar 

  74. Becke AD (1998) A new inhomogeneity parameter in density-functional theory. J Chem Phys 109:2092–2098. doi:10.1063/1.476722

    Article  CAS  Google Scholar 

  75. Weizsäcker CF v (1935) Zur theorie der kernmassen. Z Physik 96:431–458. doi:10.1007/BF01337700

    Google Scholar 

  76. Stoll H, Pavlidou CME, Preuß H (1978) On the calculation of correlation energies in the spin-density functional formalism. Theoret Chim Acta 49:143–149. doi:10.1007/BF02399063

    Article  CAS  Google Scholar 

  77. Svendsen PS, von Barth U (1996) Gradient expansion of the exchange energy from second-order density response theory. Phys Rev B 54:17402–17413. doi:10.1103/PhysRevB.54.17402

    Article  CAS  Google Scholar 

  78. Perdew JP, Ruzsinszky A, Csonka GI et al (2009) Workhorse semilocal density functional for condensed matter physics and quantum chemistry. Phys Rev Lett 103:026403. doi:10.1103/PhysRevLett.103.026403

    Article  Google Scholar 

  79. Lagowski JB, Vosko SH (1988) An analysis of local and gradient-corrected correlation energy functionals using electron removal energies. J Phys B: At Mol Opt Phys 21:203. doi:10.1088/0953-4075/21/1/016

  80. Clementi E, Chakravorty SJ (1990) A comparative study of density functional models to estimate molecular atomization energies. J Chem Phys 93:2591–2602. doi:10.1063/1.458899

    Article  CAS  Google Scholar 

  81. Cohen AJ, Mori-Sánchez P, Yang WT (2011) Challenges for density functional theory. Chem Rev 112:289–320. doi:10.1021/cr200107z

    Article  Google Scholar 

  82. Merkle R, Savin A, Preuss H (1992) Singly ionized first–row dimers and hydrides calculated with the fully-numerical density-functional program numol. J Chem Phys 97:9216–9221. doi:10.1063/1.463297

    Article  CAS  Google Scholar 

  83. Zhang YK, Yang WT (1998) A challenge for density functionals: Self-interaction error increases for systems with a noninteger number of electrons. J Chem Phys 109:2604–2608. doi:10.1063/1.476859

    Article  CAS  Google Scholar 

  84. Gräfenstein J, Kraka E, Cremer D (2004) The impact of the self-interaction error on the density functional theory description of dissociating radical cations: Ionic and covalent dissociation limits. J Chem Phys 120:524–539. doi:10.1063/1.1630017

    Article  Google Scholar 

  85. Ciofini I, Adamo C, Chermette H (2005) Self-interaction error in density functional theory: a mean-field correction for molecules and large systems. Chem Phys 309:67–76. doi:10.1016/j.chemphys.2004.05.034

    Article  CAS  Google Scholar 

  86. Gritsenko OV, Schipper PRT, Baerends EJ (1997) Exchange and correlation energy in density functional theory: Comparison of accurate density functional theory quantities with traditional Hartree–Fock based ones and generalized gradient approximations for the molecules Li2, N2, F2. J Chem Phys 107:5007–5015. doi:10.1063/1.474864

    Article  CAS  Google Scholar 

  87. Levy M, March NH, Handy NC (1996) On the adiabatic connection method, and scaling of electron–electron interactions in the Thomas–Fermi limit. J Chem Phys 104:1989–1992. doi:10.1063/1.470954

    Article  CAS  Google Scholar 

  88. 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

    Article  CAS  Google Scholar 

  89. Langreth DC, Perdew JP (1977) Exchange-correlation energy of a metallic surface: Wave-vector analysis. Phys Rev B 15:2884–2901. doi:10.1103/PhysRevB.15.2884

    Article  Google Scholar 

  90. Adamo C, Barone V (1997) Toward reliable adiabatic connection models free from adjustable parameters. Chem Phys Lett 274:242–250. doi:10.1016/S0009-2614(97)00651-9

    Article  CAS  Google Scholar 

  91. Becke AD (1996) Density-functional thermochemistry. 4. A new dynamical correlation functional and implications for exact-exchange mixing. J Chem Phys 104:1040–1046. doi:10.1063/1.470829

    Article  CAS  Google Scholar 

  92. Sousa SF, Fernandes PA, Ramos MJ (2007) General performance of density functionals. J Phys Chem A 111:10439–10452. doi:10.1021/jp0734474

    Article  CAS  Google Scholar 

  93. Johnson BG, Gill PMW, Pople JA (1993) The performance of a family of density functional methods. J Chem Phys 98:5612–5626. doi:10.1063/1.464906

    Article  CAS  Google Scholar 

  94. Johnson BG, Gonzales CA, Gill PMW, Pople JA (1994) A density functional study of the simplest hydrogen abstraction reaction. Effect of self-interaction correction. Chem Phys Lett 221:100–108. doi:10.1016/0009-2614(94)87024-1

    Article  CAS  Google Scholar 

  95. Curtiss LA, Raghavachari K, Trucks GW, Pople JA (1991) Gaussian-2 theory for molecular-energies of 1st-row and 2nd-row compounds. J Chem Phys 94:7221–7230. doi:10.1063/1.460205

    Article  CAS  Google Scholar 

  96. Roy D, Marianski M, Maitra NT, Dannenberg JJ (2012) Comparison of some dispersion-corrected and traditional functionals with CCSD(T) and MP2 ab initio methods: Dispersion, induction, and basis set superposition error. J Chem Phys 137:134109. doi:10.1063/1.4755990

    Article  Google Scholar 

  97. Ogilvie JF, Wang FYH (1992) Potential-energy functions of diatomic molecules of the noble gases I. Like nuclear species. J Mol Struct 273:277–290. doi:10.1016/0022-2860(92)87094-C

    Article  CAS  Google Scholar 

  98. Odutola JA, Dyke TR (1980) Partially deuterated water dimers: microwave spectra and structure. J Chem Phys 72:5062–5070. doi:10.1063/1.439795

    Article  CAS  Google Scholar 

  99. Curtiss LA, Frurip DJ, Blander M (1979) Studies of molecular association in H2O and D2O vapors by measurement of thermal conductivity. J Chem Phys 71:2703–2711. doi:10.1063/1.438628

    Article  CAS  Google Scholar 

  100. Taketsugu T, Wales DJ (2002) Theoretical study of rearrangements in water dimer and trimer. Mol Phys 100:2793–2806. doi:10.1080/00268970210142648

    Article  CAS  Google Scholar 

  101. Klopper W, Rijdt JGCM van D de, Duijneveldt FB van (2000) Computational determination of equilibrium geometry and dissociation energy of the water dimer. Phys Chem Chem Phys 2:2227–2234. doi:10.1039/A910312K

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    Igor Ying Zhang & Xin Xu

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Zhang, I.Y., Xu, X. (2014). An Overview of Modern Density Functional Theory. In: A New-Generation Density Functional. SpringerBriefs in Molecular Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40421-4_1

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