Abstract
The emergence of a family of computational methods, known under the label ‘density functional theory∈dex theory! density functional ’ or ‘DFT’, revolutionalized the field of computer modelling of complex molecular systems. Many computational schemes belonging to the DFT family are currently in use. Some of them are designed to be universal (nonempirical) whereas other to treat specific systems and/or properties (empirical). This review starts with the introduction of the formal elements underlying all these methods: Hohenberg-Kohn theorems∈dex theorem! Hohenberg-Kohn , reference system∈dex reference system of noninteracting electrons∈dex reference system! noninteracting electrons , exchange-correlation energy∈dex energy functional! exchange-correlation functional∈dex functional , and the Kohn-Sham equations∈dex equation! Kohn-Sham . The main roads to approximate the exchange-correlation-energy functional based on: local density approximation∈dex approximation! local density (LDA), generalized gradient approximation∈dex approximation! generalized gradient (GGA), meta-GGA∈dex energy functional! exchange-correlation! meta-GGA , and adiabatic connection∈dex adiabatic connection formula (hybrid functionals∈dex energy functional! exchange-correlation! hybrid ), are outlined. The performance of these approximations in describing molecular properties of relevance to intermolecular interaction∈dex interactions! intermolecular s and their interactions with environment in condensed phase (ionization potential∈dex potential! ionization s, electron∈dex electron affinities∈dex electron! affinity , electric moments∈dex electric moment , polarizabilities∈dex polarizability ) is reviewed. Developments concerning new methods situated within the general Hohenberg-Kohn-Sham framework or closely related to it are overviewed in the last section
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hohenberg P, Kohn W (1964) Inhomogeneous electron∈dex electron gas∈dex electron! gas , Phys Rev B 136: 864–871
Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation Effects, Phys Rev, 140A: 1133–1138
Gelfand IM, Fomin SV (2000) Calculus of Variations, Dover Publications Inc., Mineola, New York, p 1
Perdew JP, Zunger A (1981) Self-interaction correction to density-functional∈dex functional approximations for many-electron∈dex electron systems, Phys Rev B, 23: 5048–5079
Shore HB, Rose JH, Zaremba E (1977) Failure of the local exchange approximation in the evaluation of the H- ground state, Phys Rev B, 15: 2858–2861
Ziegler T, Rauk A, Baerends EJ (1977) Calculation of multiplet energies by Hartree-Fock∈dex wavefunction methods! Hartree-Fock -Slater method, Theor Chim Acta, 43: 261–271
Bally T, Sastry GN (1997) Incorrect dissociation∈dex dissociation behavior of radical ions in density functional calculations, J. Phys. Chem. A, 101: 7923–7925
Chermette H (1999) Chemical reactivity index∈dex reactivity indiceses in density functional theory, J. Comput. Chem, 20: 129–154
Levy M (1979) Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem, Proc Natl Acad Sci USA, 76: 6062–6065
Gunnarsson O, Lundqvist BI (1976) Exchange and correlation in atoms, molecules, and solids by spin-density functional formalism, Phys Rev B, 13: 4274–4298
Langreth DC, Perdew JP (1977) Exchange-correlation energy of a metallic surface – wave-vector analysis, Phys Rev B, 15: 2884–2901
Gunnarsson O, Lundqvist BI (1976) Exchange and correlation in atoms, molecules, and solids by spin-density functional formalism, Phys Rev B, 13: 4274–4298
Langreth DC, Perdew JP (1977) Exchange-correlation energy of a metallic surface – wave-vector analysis, Phys Rev B, 15: 2884–2901
Dirac PAM (1930) Note on exchange phenomena in the Thomas atom, Proc Cambridge Philos Soc, 26: 376–385
Slater JC (1951) A simplification of the Hartree-Fock method for the exchange energy (Ex[UPrho]) in the uniform electron gas, Phys Rev, 81: 385–390
Ceperley DM, Alder BJ (1980) Ground State of the Electron Gas by a Stochastic Method, Phys. Rev. Lett, 45: 566–569
Vosko SH, Wilk, Nusair M (1980) Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis, Can J Phys, 58: 1200–1211
Perdew JP, Wang Y (1992) Accurate and simple analytic representation of the electron-gas correlation energy, Phys Rev B, 45: 13244–13249
Perdew JP (1991a) Generalized gradient approximations for exchange and correlation – A look backward and forward, Physica B, 172: 1–6
Herman F, Van Dyke JP, Ortenburger IB (1969) Improved statistical exchange approximation for inhomogeneous many-electron systems, Phys Rev Lett, 22: 807–811
Ma SK, Bruekner KA (1968) Correlation energy of an electron gas with a slowly varying high density, Phys Rev, 165:18–31
Perdew JP, Langreth DC, V Sahni (1977) Corrections to the local density approximation: Gradient expansion versus wave-vector analysis for the metallic surface problem, Phys Rev Lett, 38: 1030–1033
Sahni V, Gruenebaum J, Perdew JP (1982) Study of the density-gradient expansion for the exchange energy, Phys Rev B, 26: 4371–4377
Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic behavior, Phys. Rev. A, 38: 3098–3100
Perdew JP, Yue W (1986) Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation, Phys Rev B, 33: 8800–8802
Perdew JP (1986) Density-functional approximation for the correlation energy of the inhomogeneous electron gas, Phys Rev B, 33: 8822–8824
Perdew JP (1991b) Unified theory of exchange and correlation beyond local density approximation, in: P.Ziesche and H.Eschrig (eds)., Electronic Structure of Solids’91, Akademie Verlag, Berlin,11
Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple, Phys Rev Lett, 77: 3865–3868
Colle R, Salvetti O (1975) Approximate calculation of correlation energy for closed shells, Theoretica Chimica Acta, 37: 329–334
Lee C, Yang W, Parr RG (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys Rev B, 37: 785–789
Hamprecht FA, Cohen AJ, Tozer DJ, Handy NC (1998) Development and assessment of new exchange-correlation functionals, J Chem Phys, 109: 6264–6271
Becke AD (1986) Density functional calculations of molecular-bond energies, J. Chem. Phys, 84: 4524–4529
Gill PWM (1996) A new gradient-corrected exchange functional, Mol Phys, 89: 433–445
Filatov M, Thiel W (1997) A new gradient-corrected exchange-correlation density functional, Mol Phys, 91: 847–859
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
Zhang Y, Yang W (1998) Comment on ‘‘Generalized Gradient Approximation Made Simple’’, Phys Rev Lett, 80: 890
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
Handy NC, Cohen A (2001) Left-right correlation energy, Mol Phys, 99: 403–412
Adamo C, Barone V (2002) Physically motivated density functionals with improved performances: The modified Perdew-Burke-Ernzerhof model, J. Chem. Phys, 116: 5933–5940
Becke AD (1983) Hartree-Fock exchange energy of an inhomogeneous electron-gas, Int. J. Quant. Chem, 23: 1915–1922
Becke A, Roussel ME (1989) Exchange holes in inhomogeneous systems: A coordinate-space model, Phys. Rev. A, 39: 3761–3767
Tao J, 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
Proynov EI, Vela A, Salahub DR (1994) Nonlocal correlation functional involving the Laplacian of the density, Chem Phys Lett, 230: 419–428
Filatov M, Thiel W (1998) Exchange-correlation density functional beyond the gradient approximation, Phys Rev A, 57: 189–199
Gill PW (2001) Obituary: density functional theory (1927–1993), Austr J Chem, 54: 661–662
Görling A, Levy M (1994) Exact Kohn-Sham scheme based on perturbation theory, Phys Rev A, 50: 196–204
Görling A (2005) Orbital- and state-dependent functionals in density-functional theory, J Chem Phys, 123: 062203
Becke AD (1993a) A new mixing of Hartree-Fock and local density-functional theories., J. Chem. Phys., 107: 8554–8560
Becke AD (1993b) Density-functional thermochemistry 3. The role of exact exchange., J. Chem. Phys, 98: 5648–5652
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
Becke AD (1997) Density-functional thermochemistry 5. Systematic optimization of exchange-correlation functionals, J. Chem. Phys, 98: 1372–1377
Adamo C, Barone V (1999) Toward reliable density functional methods without adjustable para-meters: The PBE0 model, J. Chem. Phys, 110: 6158–6170
Ernzerhof M, Scuseria GE (1999) Assessment of the Perdew-Burke-Ernzerhof exchange-correlation functional, J Chem Phys, 110, 5029–5036
Kafafi SA (1998) Novel density functional methodology for the computation of accurate electronic and thermodynamic properties of molecular systems and improved long-range behavior, J Phys Chem A, 102: 10404–10413
Tao J (2002) An accurate MGGA-based hybrid exchange-correlation functional, J Chem Phys, 116: 2335–2337
Toulouse J, Adamo C (2002) A new hybrid functional including a meta-GGA approach, Chem Phys Lett, 362: 72–78
Zhao Y, Truhlar DG (2004) Hybrid meta density functional theory methods for thermochemistry, thermochemical kinetics, and noncovalent interactions: The MPW1B95 and MPWB1K models and comparative assessments for hydrogen bonding and van der Waals interactions, J Phys Chem A, 108: 6908–6918
Perdew JP, Ruzsinsky A, Tao J, Starovyerov V, Scuseria GE, Csonka GI (2005) Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits, J Chem Phys, 123: 062201
Dickson RM, Becke AD (1996) Local density-functional polarizabilities and hyperpolarizabilities at the basis-set limit, J Phys Chem, 100: 16105–16108
Becke AD, Dickson RM (1990) Numerical-solution of Schrödinger equation in polyatomic molecules, J. Chem. Phys, 92: 3610–3612
Cohen AJ, Tantirungrotechai Y (1999) Molecular electric properties: an assessment of recently developed functionals, Chem. Phys. Lett, 299: 465–472
Jasien PG, Fitzgerald G (1990) Molecular dipole moments and polarizabilities from local density functional calculations: Applications to DNA base pairs, J Chem Phys, 93: 2554–2560
St.-Amant A, Cornell WD, Kollman PA, Halgren TA (1995) Calculation of molecular geometries, relative conformational energies, dipole-moments, and molecular electrostatic potential fitted charges of small organic-molecules of biochemical interest by density-functional theory, J Comput Chem, 16: 1483–1506
Rashin AA, Young L, Topol IA, Burt SK (1994) Molecular dipole moments calculated with density functional theory, Chem Phys Lett, 230: 182–188
Bakalarski G, Grochowski P, Kwiatkowski JS, Lesyng B, Leszczynski J (1996) Molecular and electrostatic properties of the N-methylated nucleic acid bases by density functional theory, Chem. Phys, 204: 301–311
de Luca G, Russo N, Sicilia E, Toscano M (1996) Molecular quadrupole moments, second moments, and diamagnetic susceptibilities evaluated using the generalized gradient approximation in the framework of Gaussian density functional method, J Chem Phys, 105: 3206–3210
Scheiner AC, Baker J, Andzelm J (1997) Molecular energies and properties from density functional theory: Exploring basis set dependence of Kohn-Sham equation using several density functionals, J Comput Chem, 18, 775–795
Heidin L, Lundqvist BI (1971) Explicit local exchange-correlation potentials, J Phys C, 4: 2064–2083
McDowell SAC, Amos RD, Handy NC (1995) Molecular polarisabilities - a comparison of density functional theory with standard ab initio methods, Chem Phys Lett, 235: 1–4
Guan J, Duffy P, Carter JT, Chong DP, Casida KC, Casida ME, Wrinn M (1993) Comparison of local-density and Hartree–Fock calculations of molecular polarizabilities and hyperpolarizabilities, J Chem Phys, 98: 4753–4765
van Caillie C, Amos RD (1998) Static and dynamic polarisabilities, Cauchy coefficients and their anisotropies: a comparison of standard methods, Chem. Phys. Lett, 291: 71–77
Calaminici P, Jug K, Koster AM (1998) Density functional calculations of molecular polarizabilities and hyperpolarizabilities, J. Chem. Phys, 109: 7756–7763
Guan J, Casida ME, Salahub DR (1995) ll-Electron Local and Gradient-Corrected Density-Functional Calculations of Na_n Dipole Polarizabilities for n = 1–6, Phys Rev B, 52: 2185–2200
Russell AJ, Spackman MA (1995) Vibrational averaging of electrical-properties development of a routine theoretical method for polyatomic molecules, Mol Phys, 84: 1239–1255
Russell AJ, Spackman MA (1997) An ab initio study of vibrational corrections to the electrical properties of the second-row hydrides, Mol Phys, 90: 251–264
Wilson PJ, Bradley TJ, Tozer DJ (2001) Hybrid exchange-correlation functional determined from thermochemical data and ab initio potentials, J Chem Phys, 115: 9233–9242
Sophy KB, Pal S (2003) Density functional response approach for the linear and nonlinear electric properties of molecules, J Chem Phys, 118: 10861–10866
van Gisbergen SJA, Osinga VP, Gritsenko OV, van Leeuven R, Snijders JG, Baerends EJ (1996) Improved density functional theory for frequency-dependent polarizabilities, by the use of an exchange-correlation potential with correct asymptotic behavior, J Chem Phys, 105: 3142–3151
Zhao Q, Morrison RC, Parr RG (1994) From electron densities to Kohn-Sham kinetic energies, orbital energies, exchange-correlation potentials, and exchange-correlation energies, Phys Rev A, 50: 2138–2142
van Leeuwen, Baerends EJ (1994) Exchange-correlation potential with correct asymptotic behavior, Phys Rev A, 49: 2421–2431
Mori-Sanchez P, Wu Q, Yang WT (2003) Accurate polymer polarizabilities with exact exchange density-functional theory, J Chem Phys, 119: 11001–11004
Hirata S, Ivanov S, Bartlett RJ, Grabowski I (2005) Exact-exchange time-dependent density-functional theory for static and dynamic polarizabilities, Phys. Rev. A, 71: 032507
van Gisbergen SJA, Kootstra F, Schipper PRT, Gritsenko OV, Snijders JG, Baerends (1998) Density-functional-theory response-property calculations with accurate exchange-correlation potentials, Phys Rev A, 57: 2556–2570
Jacob CR, Wesolowski TA, Visscher L (2005) Orbital-free embedding applied to the calculation of induced dipole moments in CO2 .. X (X = He, Ne, Ar, Kr, Xe, Hg) van der Waals complexes, J Chem Phys, 123: 174104
Gritsenko O, Schipper PRT, Baerends EJ (1999) Approximation of the exchange-correlation Kohn-Sham potential with a statistical average of different orbital model potentials, Chem Phys Lett, 302: 199–207
Janak JF (1978) Proof that ∂ E∂ ni=UPvarepsiloni in density functional theory, Phys Rev B, 18: 7165–7168
Perdew JP, Parr RG, Levy M, Balduz Jr JL (1982) Density-functional theory for fractional particle number: Derivative discontinuities of the energy, Phys Rev Lett, 49: 1691–1694
Perdew JP, Levy M (1995) Comment on ‘‘Significance of the highest occupied Kohn-Sham eigenvalue’’, Phys Rev B, 56: 16021–16028
Lindgren I, Salomonson S, Möller F (2005) Construction of accurate Kohn-Sham potentials for the lowest states of the helium atom: Accurate test of the ionization-potential theorem, Int J Quant Chem, 102: 1010–1017
Grabo T, Gross EKU (1995) Density-functional-theory using an optimized exchange-correlation potential, Chem Phys Lett, 240: 141–150
Wu Q, Ayers PW, Yang WT (2003) Density-functional theory calculations with correct long-range potentials, J Chem Phys, 119: 2978–2990
Weimer M, Delle Sala F, Görling A (2004) The Kohn-Sham treatment of anions via the localized Hartree-Fock method, Chem Phys Lett, 372, 538–547
Schwarz K (1978) Instability of stable negative ions in XUPalpha method or other local density functional schemes, Chem Phys Lett, 57: 605–607
Hamel S, Casida ME, Salahub DR (2002b) Exchange-only optimized effective potential for molecules from resolution-of-the-identity techniques: Comparison with the local density approximation, with and without asymptotic correction, J Chem Phys, 116: 8276–8291
Gritsenko O, Baerends EJ (2002) The analog of Koopmans’ theorem in spin-density functional theory, J Chem Phys, 117: 9154–9159
Chong DP, Gritsenko OV, Baerends EJ (2002) Interpretation of the Kohn-Sham orbital energies as approximate vertical ionization potentials, J. Chem. Phys, 116: 1760–1772
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
Vydrov OA, Scuseria GE (2005) Ionization potentials and electron affinities in the Perdew-Zunger self-interaction corrected density-functional theory, J Chem Phys, 122: 184107
Curtiss LA, Raghavachari K, Redfern PC, Pople JA (1997) Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation, J Chem Phys, 106: 1063–1079
Staroverov VN, Scuseria GE, Tao JM, Perdew JP (2003) Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes, J Chem Phys, 119: 12129–12137
Joantéguy S, Pfister-Guillouzo, Chermette H (1999) Asessment of density functional methods for the calculation of ionization potentials of unsaturated molecules, J Phys Chem A, 103, 3505–3511
Hoe WM, Cohen A, Handy NC (2001) Assessment of a new local exchange functional OPTX, Chem Phys Lett, 341: 319–328
Xu X, Goddard III WA (2004a) Assessment of Handy-Cohen optimized exchange density functional (OPTX), J Phys Chem A, 108: 8495–8506
Cole LA, Perdew JP (1982) Calculated electron affinities of the elements, Phys. Rev. A, 25, 1265–1271
Rösch N, Trickey SB (1997) Comment on ‘‘Concerning the applicability of density functional methods to atomic and molecular negative ions’’, [J Chem Phys, 105, 862 (1996)], J Chem Phys, 106, 8940–8941
Galbraith JM, Schaefer HF (1996) Concerning the applicability of density functional methods to atomic and molecular negative ions, J Chem Phys, 105, 862–864
Tschumper GS, Schaefer HF (1997) Predicting electron affinities with density functional theory: Some positive results for negative ion, J Chem Phys, 107: 2529–2541
Sim F, St-Amant A, Papai I, Salahub DR (1992) Gaussian density functional calculations on hydrogen-bonded systems, J Am Chem Soc, 114: 4391–4400
Novoa JJ, Sosa C (1995) Evaluation of the density functional approximation on the computation of hydrogen bond interactions, J Phys Chem, 99: 15837–15845
Zhu T, Yang W (1994) Structure of the ammonia dimer studied by density functional theory, Int J Quant Chem, 49: 613–623
Floriàn J, Johnson B (1995) Structure, energetics, and force fields of the cyclic formamide dimer: MP2, Hartree-Fock, and density functional study, J Phys Chem, 99: 5899–5908
Han WG, Suhai S (1996) Density Functional Studies on N-Methylacatemide-Water Complex, J Phys Chem, 100: 3942–3949
Zhao Y, Truhlar DG (2005a) Benchmark databases for nonbonded interactions and their use to test density functional theory, J Chem Theory Comput, 1: 415–432
Pudzianowski AT, (1995) A systematic appraisal of density functional methodologies for hydrogen bonding in binary ionic complexes, J Phys Chem, 100: 4781–4789
Hobza P, Sponer J, Reschel T (1995) Density-functional theory and molecular clusters, J Comp Chem, 16: 1315–1325
Mele F, Mineva T, Russo N, Toscano M (1995) Hydrogen-bonded and van-der-Waals complexes studied by a gaussian density-functional method – the case of (HF)2, ArHCl, Ar2HCl systems, Theor Chim Acta, 91: 169–177
Süle P, Nagy A (1996) Density Functional study of strong hydrogen-bonded systems: The hydrogen diformate complex, J Chem Phys, 104: 8524–8534
Kim K, Jordan KD (1994) Comparison of density functional and MP2 calculations on the water monomer and dimer, J Phys Chem, 98: 10089–10094
Del Bene JE, Person WB, Szczepaniak K (1995) Properties of hydrogen-bonded Complexes Obtained from B3LYP Functional with 6–31G(d,p) and 6–31 + G(d,p) Basis Sets: Comparison with MP2/631 + G(d,p) Results and Experimental Data, J Phys Chem, 99: 10705–10707
Zhao Y, Tishchenko O, Truhlar DG (2005) How well can density functional methods describe hydrogen bonds to UPpi acceptors?, J Phys Chem B, 109: 19046–19051
Bergés J, Caillet J, Langlet J, Kozelka J (2001) Hydration and ‘inverse hydration’ of platinum(II) complexes: an analysis using the density functionals PW91 and BLYP, Chem. Phys. Lett, 344: 573–577
Milet A, Korona T, Moszynski R, Kochaniski E (1999) Anisotropic intermolecular interactions in van der Waals and hydrogen-bonded complexes: What can we get from density functional calculations? J Chem Phys, 111: 7727–7735
Xu X, Goddard III WA (2004b) The X3LYP extended functional for accurate description of nonbond interactions, spin states, and thermochemical properties, Proc Natl Acad Sci USA, 101: 2673–2677
Klopper W, van Duijneveldt-van de Rijdt JGCM, van Duijneveldt FB (2000) Computational determination of equilibrium geometry and dissociation energy of the water dimer, Phys Chem Chem Phys, 2: 2227–2234
Misquitta AJ, Jeziorski B, Szalewicz K (2003) Dispersion energy from density-functional theory description of monomers, Phys Rev Lett, 91: 033201
Lacks DJ, Gordon RG (1993) Pair interactions of rare-gas atoms as a test of exchange-energy-density functionals in regions of large density gradients, Phys Rev A, 47: 4681–4690
Pérez-Jordà JM, Becke AD (1995) A density-functional study of van-der-Waals forces – rare-gas diatomics, Chem Phys Lett, 233: 134–137
Meijer EJ, Sprik M (1996) A density-functional study of the intermolecular interactions of benzene, J Chem Phys, 105: 8684–8689
Wesolowski TA (2000) Comment on ‘‘Anisotropic intermolecular interactions in van der Waals and hydrogen-bonded complexes: What can we get from density-functional calculations?’’ [J Chem Phys 111: 7727 (1999)], J Chem Phys, 116: 515–524
Tao J, Perdew JP (2005) Test of a nonempirical density functional: Short-range part of the van der Waals interaction in rare-gas dimers, J Chem Phys, 122: 11402
Ruzsinszky A, Perdew JP, Csonka GI (2005) Binding energy curves from nonempirical density functionals II. van der Waals bonds in rare-gas and alkaline-earth diatomics, J Phys Chem A, 109: 11015–11021
Zhang Y, Pan W, Yang W (1997) Describing van der Waals Interaction in diatomic molecules with generalized gradient approximations: The role of the exchange functional, J Chem Phys, 107: 7921–7925
Patton DC, Porezag DV, Pederson MR (1997) Simplified generalized-gradient approximation and anharmonicity: Benchmark calculations on molecules, Phys Rev B, 55: 7454–7459
Kristyan S, Pulay P (1994) Can (semi)local density-functional theory account for London dispersion forces, Chem Phys Lett, 229: 175–180
Ŝponer J, Leszczynski J, Hobza P (1998) Base staking in cytosine dimer. A comparison of correlated ab initio calculations with three empirical models and density functional theory calculations, J Comp Chem, 17: 841–850
Ye XY, Li ZH, Wang WN, Fan KN, Xu W, Hua ZY (2004) The parallel pi-pi stacking: a model study with MP2 and DFT methods, Chem Phys Lett, 397:56–61
Small D, Zaitsev V, Jung Y, Rosokha SV, Head-Gordon M, Kochi JK (2004) Intermolecular UPpi -to- UPpi bonding between stacked aromatic dyads. Experimental and theoretical binding energies and near-IR optical transitions for phenalenyl radical/radical versus radical/cation dimerizations, J Am Chem Soc, 126: 138–13858. (B3LYP results are included as Supporting Materials to this article)
Zhao Y, Truhlar DG (2005b) How well can new-generation density functional methods describe stacking interactions in biological systems, Phys Chem Chem Phys, 7: 2701–2705
Lieb EH, Oxford S (1981) Improved lower bound on the indirect Coulomb energy, Int J Quant Chem, 19: 427–439
Patey MD, Dessent CEH (2002) A PW91 density functional study of conformational choice in 2-pentylethanol, n-butylbenzene, and their cations: Problems for density functional theory?, J Phys Chem A, 106: 4623–4631
Ruiz E, Salahub DR, Vela A (1995) Defining the domain of density functionals– charge-transfer complexes, J Am Chem Soc, 117: 1141–1142
Ruiz E, Salahub DR, Vela A (1996) Charge-transfer complexes: Stringent tests for widely used density functionals, J Phys Chem, 100: 12265–12276
Kamiya M, Tsuneda T, Hirao K (2002) A density functional study of van der Waals interactions, J Chem Phys, 117: 36010–6015
poner J, Jurecka P, Hobza P (2004) Accurate interaction energies of hydrogen-bonded nucleic acid base pairs, J Am Chem Soc, 126: 10142–10151
Wu X, Vargas MC, Nayak S, Lotrich V, Scoles G (2001) Towards extending the applicability of density functional theory to weakly bound systems, J Chem Phys, 115: 8748–8757
Elsner M, Hobza P, Frauenheim T, Suhai S, Kaxiras E (2001) Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment, J Chem Phys, 114: 5149–5155
Grimme S (2004) Accurate description of van der Waals complexes by density functional theory including empirical corrections, J Comp Chem, 25: 1463–1473
Zimmerli U, Parrinello M, Koumoutsakos P (2004) Dispersion corrections to density functionals for water aromatic interactions, J Chem Phys, 120: 2693–2699
Wu Q, Yang W (2002) Empirical correction to density functional theory for van der Waals interactions, J Chem Phys, 116: 515–524
von Lilienfeld OA, Tavernelli I, Rothlisberger U, Sebastiani D (2004) Optimization of effective atom centered potentials for London dispersion forces in density functional theory, Phys Rev Lett, 93: 153004
Pérez-Jordà JM, San-Fabiàn E, Pérez-Jiménez AJ (1999) Density-functional study of van der Waals forces on rare-gas diatomics: Hartree–Fock exchange, J Chem Phys, 110: 1916–1920
Wilson LC, Levy M (1990) Nonlocal Wigner-like correlation-energy density functional through coordinate scaling, Phys Rev B, 41: 12930–12932
Baerends EJ (2001) Exact exchange-correlation treatment of dissociated H2 in density functional theory, Phys. Rev. Lett, 87: 133004
Sharp RT, Horton GG (1953) A variational approach to the unipotential many-electron problem, Phys Rev, 30: 317–317
Hirata S, Ivanov S, Grabowski I, Bartlet RJ, Burke K, Talman JD (2001) Can optimized effective potentials be determined uniquely?, J Chem Phys, 115: 1635–1649
Talman JD, Shadwick WF (1972) Optimized effective atomic central potential, Phys Rev A, 14:36–40
Krieger JB, Li Y, Iafrate GJ (1992a) Systematic approximations to the optimized effective potential: Application to orbital-density-functional theory, Phys Rev A, 46: 5453–5458
Garza J, Nichols JA, Dixon DA (2000) The optimized effective potential and the self-interaction correction in density functional theory: Application to molecules, J Chem Phys, 112: 7880–7890
Hamel S, Duffy P, Casida ME, Salahub DR (2002a) Kohn-Sham orbitals and orbital energies: fictitious constructs but good approximations all the same, J Electr Spectr and Related Phenomena, 123: 345–363
Gunnarsson O, Jonson M, Lundqvist BI (1977) Exchange and correlation in inhomogeneous electron-systems, Solid State Commun, 24: 765–768
Alonso JA, Girifalco LA (1978) Nonlocal approximation to exchange potential and kinetic energy∈dexenergy! kinetic in an inhomogenous electron gas, Phys. Rev. B, 17: 3735–3743
Gunnarsson O, Jonson M, Lundqvist BI (1979) Descriptions of exchange and correlation effects in inhomogeneous electron systems, Phys Rev B, 20: 3136–3164
Singh DJ (1997) Density functional studies of PbZrO3,KTaO3 and KNbO3 , Ferroelectrics, 194: 299–322
Wu Z, Cohen RE, Singh DJ (2004) Comparing the weighted density approximation with the LDA and GGA for ground-state properties of ferroelectric perovskites, Phys Rev B, 70: 104112
Rushton PP, Tozer DJ, Clark SJ (2002) Nonlocal density-functional description of exchange and correlation in silicon, Phys Rev B, 65: 235203
Marzari N, Singh (2004) Dielectric response of oxides in the weighted density approximation, Phys Rev B, 62: 12724–12729
Sadd M, Teter MP (1996) Weighted density approximation applied to diatomic molecules, Phys Rev B, 54: 13643–13648
Kohn W, Meir Y, Makarov DE (1998) van der Waals energies in density functional theory, Phys Rev Lett, 80: 4153–4156
Hult E, Rydberg H, Lundqvist BI, Langreth DC (1999) Unified treatment of asymptotic van der Waals forces, Phys Rev B, 59: 4708–4713
Lein M, Dobson JF, Gross EKU (1999) Dobson JF, Toward the description of van der Waals interactions within density functional theory, J Comput Chem, 20:12–22
Dobson JF, Wang J (1999) Successful test of a seamless van der Waals density functional, Phys Rev Lett, 82: 2123–2123
Yan ZD, Perdew JP, Kurth S (2000) Density functional for short-range correlation: Accuracy of the random-phase approximation for isoelectronic energy changes, Phys Rev B, 61: 16430–16439
Fuchs M, Gonze X (2002) Accurate density functionals: Approaches using adiabatic-connection fluctuation-dissipation theorem, Phys. Rev. B, 65: 235109
Rydberg H, Dion M, Jacobson N, Schroder E, Hyldgaard P, Simak SI, Langreth DC, Lundqvist BI (2003) Van der Waals density functional for layered structures, Phys Rev Lett, 91: 126402
Dion M, Rydberg H, Schroder E, Hyldgaard P, Langreth DC, Lundqvist BI (2003) Van der Waals density functional for general geometries, Phys Rev Lett, 92: 246401
Langreth DC, Dion M, Rydberg H, Schroder E, Hyldgaard P, Lundqvist BI (2005) Van der Waals density functional theory with applications, Int J Quant Chem, 101: 599–610
Fuchs M, Niquet YM, Gonze X, Burke K (2005) Describing static correlation in bond dissociation by Kohn-Sham density functional theory, J Chem Phys, 122: 094116
Chakarova SD, Schröder E (2005) van der Waals interactions of polycyclic aromatic hydrocarbon dimers, J. Chem. Phys, 122: 054102
Kleis J, Schröder E (2005) van der Waals interaction of simple, parallel polymers, J Chem Phys, 122: 164902
Likura H, Tsuneda T, Yanai T, Hirao K (2001) A long-range correction scheme for generalized-gradient-approximation exchange functionals, J Chem Phys, 115: 3540–3544
Champagne B, Perpete EA, van Gisbergen SJA, Baerends EJ, Snijders JG, Soubra-Ghaoui C, Robins KA, Kirtman B (1998) Assessment of conventional density functional schemes for computing the polarizabilities and hyperpolarizabilities of conjugated oligomers: An ab initio investigation of polyacetylene chains, J. Chem. Phys, 109: 10489–10498
van Gisbergen SJA, Schipper PRT, Gritsenko OV, Baerends EJ, Snijders JG, Champagne B, Kirtman B (1999) Electric field dependence of the exchange-correlation potential in molecular chains, Phys Rev Lett, 83: 694–697
van Faassen M, de Boeij PL, van Leeuwen R, Berger JA, Snijders JG (2002) Ultranonlocality in time-dependent current-density-functional theory: Application to conjugated polymers, Phys Rev Lett, 83: 694–697
van Faassen M, de Boeij PL, van Leeuwen R, Berger JA, Snijders JG (2003) Application of time-dependent current-density-functional theory to nonlocal exchange-correlation effects in polymers, J Chem Phys, 118: 1044–1053
Casida ME (1996) Time-Dependent Density Functional Response Theory of Molecular Systems: Computational methods, and Functionals. In: Recent Developments and Applications of Modern Density Functional Theory: Theoretical and Computational Chemistry, Vol. 4., J.M. Seminario ed., Elsevier Science, pp. 391–439
Jacquemin D, André J-M, and Perpéte EA (2004) Geometry, dipole moment, polarizability and first hyperpolarizability of polymethineimine: An assessment of electron correlation contributions, J Chem Phys, 121: 4389–4396
Berger JA, Snijders JG (2002) Ultranonlocality in time-dependent current-density-functional theory: Application to conjugated polymers, Phys. Rev. Lett, 83: 694–697
Vignale G, Kohn W (1996) Current-dependent exchange-correlation potential for dynamical linear response theory, Phys Rev Lett, 77: 2037–2040
Baerends EJ, Branchadell V, Sodupe M (1997) Atomic reference energies for density functional calculations, Chem. Phys. Lett, 265: 481–489
Becke AD (2002) Current density in exchange-correlation functionals: Application to atomic states, J. Chem. Phys, 117: 6935–6938
Savin A (1995) Beyond the Kohn-Sham Determinant. In: Recent Advances in Density Functional Methods, Part I., D. P. Chong (Ed.) Word Scientific, Singapore, pp 123–153
Malcolm NOJ, McDouall JJW (1996) Combining multiconfigurational wave functions with density functional estimates of dynamic electron correlation, J Phys Chem, 100: 10131–10134
Leininger T, Stoll H, Werner HJ, Savin A (1997) Combining long-range configuration interaction with short-range density functionals, Chem Phys Lett, 275: 151–160
Grimme S, Waletzke M (1999) A combination of Kohn-Sham density-functional theory and multi-reference configuration interaction methods, J Chem Phys, 111: 5645–5655
Filatov M, Shaik S (1999) A spin-restricted ensamble-referenced Kohn-Sham method and its application to diradical situations, Chem Phys Lett, 304: 429–437
Gräfenstein J, Cremer D (2000) The combination of density functional theory with multi-configurational methods – CAS-DFT, Chem Phys Lett, 316: 569–577
Pollet J, Savin A, Leininger T, Stoll H (2002a) Combining multideterminantal wave functions with density functionals to handle near-degeneracy in atoms and molecules, J Chem Phys, 116: 1250–1258
Pollet R, Colonna F, Leininger T, Stoll H, Werner HJ, Savin A (2003) Exchange-correlation energies and correlation holes for some two- and four-electron atoms along a nonlinear adiabatic connection in density functional theory, Int J Quant Chem, 91: 84–93
Gusarov S, Malmquist P-A, Lindh R, Roos BO (2004) Correlation potrentials for a multiconfigurational-based density functional theory with exact exchange, Theor Chem Acc, 112:84–94
Becke AD, Johnson ER (2005a) A density-functional model of the dispersion interaction, J. Chem. Phys, 123: 154101
Becke AD, Johnson ER (2005b) Exchange-hole dipole moment and the dispersion interaction, J. Chem. Phys, 122: 154104
Becke AD (1994) Thermochemical tests of a kinetic-energy dependent exchange-correlation approximation, Int. J. Quant. Chem. Symp, 98: 625–632
Cortona P (1991) Self-consistently determined properties of solids without band-structure calculations, Phys. Rev. B, 44: 8454–8458
Wesolowski TA, Weber J (1996) Kohn-Sham equations with constrained electron density: An iterative evaluation of the ground-state electron density of interacting molecules, Chem Phys Lett, 248:71–76
Wesolowski TA, Tran F (2003) Gradient-free and gradient-dependent approximations in the total energy bifunctional for weakly overlapping electron densities, J Chem Phys, 118: 2072–2080
Kevorkiants R, Dulak M, Wesolowski TA (2006) Interaction energies in hydrogen-bonded systems – a testing ground for subsystem formulation of density functional theory, J Chem Phys, 124: 024104
Wesolowski TA, Warshel A (1993) Frozen density-functional approach for ab-initio calculations of solvated molecules, J Phys Chem, 97: 8050–8053
Dulak M, Kevorkiants R, Tran F, Wesolowski TA (2005) Applications of the orbital-free embedding formalism to study electronic structure of atoms and molecules in condensed phase, CHIMIA, 59: 488–492
Wesolowski TA (2006) One-electron equations for embedded electron density: Challenge for theory and practical payoffs in multi-level modeling of complex polyatomic systems, in: Computational Chemistry: Reviews of Current Trends, vol. X, J. Leszczynski, (ed.) World Scientific, pp 1–82
Zumbach G, Maschke K (1985) Density-matrix functional theory for the N -particle ground state, J Chem Phys, 82: 5604–5607
Goedecker S, Umrigar CJ (1998) Natural orbital functional for the many-electron problem, Phys Rev Lett, 81: 866–869
Cioslowski J, Pernal K (1999) Constraints upon natural spin orbital functionals imposed by properties of a homogeneous electron gas, J. Chem. Phys, 111: 3396–3400
Mazziotti DA (2001) Energy functional of the one-particle reduced density matrix: a geminal approach, Chem Phys Lett, 338: 323–328
Buijse MA, Baerends EJ (2002) An approximate exchange-correlation hole density as a functional of the natural orbitals, Mol. Phys, 100: 401–421
Yasuda K (2002) Local approximation of the correlation energy functional in the density matrix functional theory, Phys Rev Lett, 88: 053001
Lathiotakis NN, Helbig N, Gross EKU (2005) Open shells in reduced-density-matrix-functional theory, Phys Rev A, 72: 030501
Gritsenko O, Pernal K, Baerends EJ (2005) An improved density matrix functional by physically motivated repulsive corrections, J Chem Phys, 122: 204102
Staroverov VN, Scuseria GE (2002) Assessment of simple exchange-correlation energy functionals of the one-particle density matrix, J Chem Phys, 117: 2489–2495
Cohen AJ, Baerends EJ (2002) Variational density matrix functional calculations for the corrected Hartree and corrected Hartree-Fock functionals, Chem. Phys. Lett, 364: 409–419
Pernal K, Cioslowski J (2002) Density matrix functional theory of weak intermolecular interactions, J Chem Phys, 116: 4802–4807
Tsuzuki S, Luthi HP (2001) Interaction energies of van der Waals and hydrogen bonded systems calculated using density functional theory: Assessing the PW91 model, J Chem Phys, 114(9): 3949–3957
Furche F (2001) Molecular tests of the random phase approximation to the exchange-correlation energy functional, Phys Rev B, 64(19): Art. No. 195120
Furche F, van Voorhis (2005) Flucluation-dissipateon theorem density – functional theory, J chem phys, 122(6): Art. No. 164106
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this chapter
Cite this chapter
Wesołowski, T.A. (2007). Hohenberg-Kohn-Sham Density Functional Theory. In: Sokalski, W.A. (eds) Molecular Materials with Specific Interactions – Modeling and Design. Challenges and Advances in Computational Chemistry and Physics, vol 4. Springer, Dordrecht. https://doi.org/10.1007/1-4020-5372-X_2
Download citation
DOI: https://doi.org/10.1007/1-4020-5372-X_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-5371-9
Online ISBN: 978-1-4020-5372-6
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)