Skip to main content
SpringerLink
Log in

Systematic treatment of spin-reactivity indicators in conceptual density functional theory

  • Regular Article
  • Published:
Theoretical Chemistry Accounts Aims and scope Submit manuscript

Abstract

The spin-resolved conceptual density functional theory is presented, emphasizing the finite-difference approximations for spin-reactivity indicators and especially the spin-hardness. We derive simple approximations for these spin-reactivity indicators in terms of Kohn–Sham orbital energies and discuss their accuracy and validity. We also show that the second derivative of the energy with respect to the spin-abundance, N S  = ½M S , is nonnegative, contradicting the generally negative values obtained for one of the most popular formulas used to approximate this quantity. A new approximation for the spin-hardness is proposed and assessed based on information for spin-philicities and singlet–triplet gaps. One conclusion of our work is that the tendency in the literature to mix linear models (e.g., one-sided derivatives for chemical potentials and Fukui functions) with quadratic models (e.g., two-sided derivatives for hardnesses and dual descriptors) not only is theoretically unsound, but often leads to chemically absurd results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Geerlings P, De Proft F, Langenaeker W (2003) Conceptual density functional theory. Chem Rev 103:1793–1873

    Article  CAS  Google Scholar 

  2. Chermette H (1999) Chemical reactivity indexes in density functional theory. J Comput Chem 20:129–154

    Article  CAS  Google Scholar 

  3. Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. Oxford UP, New York

    Google Scholar 

  4. Johnson PA, Bartolotti LJ, Ayers PW, Fievez T, Geerlings P (2012) Charge density and chemical reactivity: a unified view from conceptual DFT. In: Gatti C, Macchi P (eds) Modern charge density analysis. Springer, New York, pp 715–764

    Google Scholar 

  5. Liu SB (2009) Conceptual density functional theory and some recent developments. Acta Phys Chim Sin 25:590–600

    CAS  Google Scholar 

  6. Gazquez JL (2008) Perspectives on the density functional theory of chemical reactivity. J Mex Chem Soc 52:3–10

    CAS  Google Scholar 

  7. Ayers PW, Anderson JSM, Bartolotti LJ (2005) Perturbative perspectives on the chemical reaction prediction problem. Int J Quantum Chem 101:520–534

    Article  CAS  Google Scholar 

  8. Nalewajski RF, Korchowiec J (1997) Charge sensitivity approach to electronic structure and chemical reactivity. World Scientific, Singapore

    Book  Google Scholar 

  9. Parr RG, Yang WT (1995) Density-functional theory of the electronic-structure of molecules. Annu Rev Phys Chem 46:701–728

    Article  CAS  Google Scholar 

  10. Galvan M, Vela A, Gazquez JL (1988) Chemical-reactivity in spin-polarized density functional theory. J Phys Chem 92:6470–6474

    Article  CAS  Google Scholar 

  11. Ghanty TK, Ghosh SK (1994) Spin-polarized generalization of the concepts of electronegativity and hardness and the description of chemical-binding. J Am Chem Soc 116:3943–3948

    Article  CAS  Google Scholar 

  12. Vargas R, Galvan M, Vela A (1998) Singlet–triplet gaps and spin potentials. J Phys Chem A 102:3134–3140

    Article  CAS  Google Scholar 

  13. Chan GKL (1999) A fresh look at ensembles: derivative discontinuities in density functional theory. J Chem Phys 110:4710–4723

    Article  CAS  Google Scholar 

  14. Melin J, Aparicio F, Galvan M, Fuentealba P, Contreras R (2003) Chemical reactivity in the N, N–S, nu(r) space. J Phys Chem A 107:3831–3835

    Article  CAS  Google Scholar 

  15. Perez P, Chamorro E, Ayers PW (2008) Universal mathematical identities in density functional theory: results from three different spin-resolved representations. J Chem Phys 128:204108. doi:10.1063/1.2916714

    Article  CAS  Google Scholar 

  16. Alcoba DR, Lain L, Torre A, Ona OB, Chamorro E (2013) Fukui and dual-descriptor matrices within the framework of spin-polarized density functional theory. PCCP 15(24):9594–9604. doi:10.1039/c3cp50736j

    Article  CAS  Google Scholar 

  17. Chamorro E, Perez P, Duque M, De Proft F, Geerlings P (2008) Dual descriptors within the framework of spin-polarized density functional theory. J Chem Phys 129:064117. doi:10.1063/1.2965594

    Article  CAS  Google Scholar 

  18. Fias S, Boisdenghien Z, De Proft F, Geerlings P (2014) The spin polarized linear response from density functional theory: theory and application to atoms. J Chem Phys. doi:10.1063/1.4900513

    Google Scholar 

  19. Gal T, Geerlings P (2010) Energy surface, chemical potentials, Kohn–Sham energies in spin-polarized density functional theory. J Chem Phys 133:144105. doi:10.1063/1.3467898

    Article  CAS  Google Scholar 

  20. Gal T, Geerlings P (2010) Derivative of the Lieb definition for the energy functional of density-functional theory with respect to the particle number and the spin number. Phys Rev A 81:032512. doi:10.1103/PhysRevA.81.032512

    Article  CAS  Google Scholar 

  21. Gal T, Ayers PW, De Proft F, Geerlings P (2009) Nonuniqueness of magnetic fields and energy derivatives in spin-polarized density functional theory. J Chem Phys 131:154114. doi:10.1063/1.3233717

    Article  CAS  Google Scholar 

  22. Malek AM, Balawender R (2013) Discontinuities of energy derivatives in spin-density functional theory. arXiv:13106918

  23. Perez P, Andres J, Safont VS, Tapia O, Contreras R (2002) Spin-philicity and spin-donicity as auxiliary concepts to quantify spin-catalysis phenomena. J Phys Chem A 106:5353–5357

    Article  CAS  Google Scholar 

  24. Rincon E, Perez P, Chamorro E (2007) Global and local reactivity of simple substituted nitrenes and phosphinidenes within the spin-polarized density functional theory framework. Chem Phys Lett 448:273–279

    Article  CAS  Google Scholar 

  25. Pinter B, De Proft F, Van Speybroeck V, Hemelsoet K, Waroquier M, Chamorro E, Veszpremi T, Geerlings P (2007) Spin-polarized conceptual density functional theory study of the regioselectivity in ring closures of radicals. J Org Chem 72:348–356

    Article  CAS  Google Scholar 

  26. Guerra D, Andres J, Chamorro E, Perez P (2007) Understanding the chemical reactivity of phenylhalocarbene systems: an analysis based on the spin-polarized density functional theory. Theor Chem Acc 118:325–335

    Article  CAS  Google Scholar 

  27. Chamorro E, Santos JC, Escobar CA, Perez P (2006) Electrophilicity and spin polarization of simple substituted silylenes. Chem Phys Lett 431:210–215

    Article  CAS  Google Scholar 

  28. Chamorro E, Perez P, De Proft F, Geerlings P (2006) Philicity indices within the spin-polarized density-functional theory framework. J Chem Phys 124(4):044105. doi:10.1063/1.2161187

    Article  CAS  Google Scholar 

  29. Chamorro E, De Proft F, Geerlings P (2005) Hardness and softness reactivity kernels within the spin-polarized density-functional theory. J Chem Phys 123:154104

    Article  CAS  Google Scholar 

  30. Chamorro E, De Proft F, Geerlings P (2005) Generalized nuclear Fukui functions in the framework of spin-polarized density-functional theory. J Chem Phys 123(11):084104. doi:10.1063/1.2033689

    Article  CAS  Google Scholar 

  31. Chamorro E, Perez P (2005) Condensed-to-atoms electronic Fukui functions within the framework of spin-polarized density-functional theory. J Chem Phys 123(11):114107. doi:10.1063/1.2033689

    Article  CAS  Google Scholar 

  32. Moens J, Jaque P, De Proft F, Geerlings P (2009) A new view on the spectrochemical and nephelauxetic series on the basis of spin-polarized conceptual DFT. Chem Phys Chem 10:847–854. doi:10.1002/cphc.200800864

    CAS  Google Scholar 

  33. Olah J, De Proft F, Veszpremi T, Geerlings P (2006) Relationship between electrophilicity and spin-philicity of divalent and monovalent species of group 14 and 15 elements. J Mol Struct THEOCHEM 771:135–140

    Article  CAS  Google Scholar 

  34. De Proft F, Fias S, Van Alsenoy C, Geerlings P (2005) Spin-polarized conceptual density functional theory study of the regioselectivity in the [2 + 2] photocycloaddition of enones to substituted alkenes. J Phys Chem A 109:6335–6343

    Article  CAS  Google Scholar 

  35. Pinter B, De Proft F, Veszpremi T, Geerlings P (2005) Regioselectivity in the [2 + 2] cyclo-addition reaction of triplet carbonyl compounds to substituted alkenes (Paterno–Buchi reaction): a spin-polarized conceptual DFT approach. J Chem Sci 117:561–571

    Article  CAS  Google Scholar 

  36. Olah J, De Proft F, Veszpremi T, Geerlings P (2004) Spin-philicity and spin-donicity of substituted carbenes, silylenes, germylenes, and stannylenes. J Phys Chem A 108:490–499

    Article  CAS  Google Scholar 

  37. Olah J, Veszpremi T, Nguyen MT (2005) Spin-philicity and spin-donicity of simple nitrenes and phosphinidenes. Chem Phys Lett 401:337–341

    Article  CAS  Google Scholar 

  38. Donnelly RA, Parr RG (1978) Elementary Properties of an energy functional of the first order density matrix. J Chem Phys 69:4431–4439

    Article  CAS  Google Scholar 

  39. Parr RG, Pearson RG (1983) Absolute hardness: companion parameter to absolute electronegativity. J Am Chem Soc 105:7512–7516

    Article  CAS  Google Scholar 

  40. Ayers PW (2007) The physical basis of the hard/soft acid/base principle. Faraday Discuss 135:161–190

    Article  CAS  Google Scholar 

  41. Pearson RG (2009) The hardness of closed systems. In: Chattaraj PK (ed) Chemical reactivity theory: a density functional view. CRC Press, Boca Raton, pp 155–162

    Google Scholar 

  42. Pearson RG (1997) Chemical hardness. Wiley-VCH, Weinheim

    Book  Google Scholar 

  43. Perdew JP, Parr RG, Levy M, Balduz JL Jr (1982) Density-functional theory for fractional particle number: derivative discontinuities of the energy. Phys Rev Lett 49:1691–1694

    Article  CAS  Google Scholar 

  44. Yang WT, Zhang YK, Ayers PW (2000) Degenerate ground states and fractional number of electrons in density and reduced density matrix functional theory. Phys Rev Lett 84:5172–5175

    Article  CAS  Google Scholar 

  45. Bochicchio RC, Rial D (2012) Note: energy convexity and density matrices in molecular systems. J Chem Phys 137(226101):22. doi:10.1063/1.4771955

    Google Scholar 

  46. Ayers PW (2008) The continuity of the energy and other molecular properties with respect to the number of electrons. J Math Chem 43:285–303

    Article  CAS  Google Scholar 

  47. Zhang YK, Yang WT (2000) Perspective on “Density-functional theory for fractional particle number: derivative discontinuities of the energy”. Theor Chem Acc 103:346–348

    Article  CAS  Google Scholar 

  48. Parr RG, Chattaraj PK (1991) Principle of maximum hardness. J Am Chem Soc 113:1854–1855

    Article  CAS  Google Scholar 

  49. Pearson RG (1987) Recent advances in the concept of hard and soft acids and bases. J Chem Educ 64:561–567

    Article  CAS  Google Scholar 

  50. Chattaraj PK (1996) The maximum hardness principle: an overview. Proc Indian Natl Sci Acad Part A 62:513–531

    CAS  Google Scholar 

  51. Ayers PW, Parr RG (2000) Variational principles for describing chemical reactions: the Fukui function and chemical hardness revisited. J Am Chem Soc 122:2010–2018

    Article  CAS  Google Scholar 

  52. Pearson RG, Palke WE (1992) Support for a principle of maximum hardness. J Phys Chem 96:3283–3285

    Article  CAS  Google Scholar 

  53. Chattaraj PK, PvR Schleyer (1994) An ab initio study resulting in a greater understanding of the HSAB principle. J Am Chem Soc 116:1067–1071

    Article  CAS  Google Scholar 

  54. Chattaraj PK, Lee H, Parr RG (1991) HSAB principle. J Am Chem Soc 113:1855–1856

    Article  CAS  Google Scholar 

  55. Chattaraj PK, Gomez B, Chamorro E, Santos J, Fuentealba P (2001) Scrutiny of the HSAB principle in some representative acid-base reactions. J Phys Chem A 105:8815–8820

    Article  CAS  Google Scholar 

  56. Cardenas C, Ayers PW (2013) How reliable is the hard-soft acid-base principle? An assessment from numerical simulations of electron transfer energies. PCCP 15(33):13959–13968. doi:10.1039/c3cp51134k

    Article  CAS  Google Scholar 

  57. Chattaraj PK, Ayers PW, Melin J (2007) Further links between the maximum hardness principle and the hard/soft acid/base principle: insights from hard/soft exchange reactions. PCCP 9:3853–3856

    Article  CAS  Google Scholar 

  58. Ayers PW, Parr RG, Pearson RG (2006) Elucidating the hard/soft acid/base principle: a perspective based on half-reactions. J Chem Phys 124:194107

    Article  CAS  Google Scholar 

  59. Ayers PW (2005) An elementary derivation of the hard/soft-acid/base principle. J Chem Phys 122:141102

    Article  CAS  Google Scholar 

  60. Chattaraj PK, Ayers PW (2005) The maximum hardness principle implies the hard/soft acid/base rule. J Chem Phys 123:086101

    Article  CAS  Google Scholar 

  61. Cioslowski J, Stefanov BB (1993) Electron flow and electronegativity equalization in the process of bond formation. J Chem Phys 99:5151–5162

    Article  CAS  Google Scholar 

  62. Cedillo A, Van Neck D, Bultinck P (2012) Self-consistent methods constrained to a fixed number of particles in a given fragment and its relation to the electronegativity equalization method. Theor Chem Acc 131(6):7. doi:10.1007/s00214-012-1227-6

    Article  CAS  Google Scholar 

  63. Malek A, Balawender R (2015) Revisiting the chemical reactivity indices as the state function derivatives. The role of classical chemical hardness. J Chem Phys 142:054104. doi:10.1063/1.4906555

    Article  CAS  Google Scholar 

  64. Franco-Perez M, Gazquez JL, Ayers PW, Vela A (2015) Revisiting the definition of the electronic chemical potential, chemical hardness, and softness at finite temperatures. J Chem Phys 143(15):154103. doi:10.1063/1.4932539

    Article  CAS  Google Scholar 

  65. Franco-Perez M, Ayers PW, Gazquez JL, Vela A (2015) Local and linear chemical reactivity response functions at finite temperature in density functional theory. J Chem Phys 143(24):244117. doi:10.1063/1.4938422

    Article  CAS  Google Scholar 

  66. Franco-Perez M, Gazquez JL, Vela A (2015) Electronic chemical response indexes at finite temperature in the canonical ensemble. J Chem Phys. doi:10.1063/1.4923260

    Google Scholar 

  67. Miranda-Quintana R, Ayers PW (2016) Fractional electron number, temperature, and perturbations in chemical reactions. Phys Chem Chem Phys 18:15070–15080

    Article  CAS  Google Scholar 

  68. Ayers PW (2007) On the electronegativity nonlocality paradox. Theor Chem Acc 118:371–381

    Article  CAS  Google Scholar 

  69. Noorizadeh S, Parsa H (2013) Evaluation of absolute hardness: a new approach. J Phys Chem A 117(5):939–946. doi:10.1021/jp308137w

    Article  CAS  Google Scholar 

  70. Noorizadeh S, Shakerzadeh E (2008) A new scale of electronegativity based on electrophilicity index. J Phys Chem A 112:3486–3491. doi:10.1021/jp709877h

    Article  CAS  Google Scholar 

  71. Parr RG, Bartolotti LJ (1982) On the geometric mean principle for electronegativity equalization. J Am Chem Soc 104:3801–3803

    Article  CAS  Google Scholar 

  72. Fuentealba P, Cardenas C (2013) On the exponential model for energy with respect to number of electrons. J Mol Model 19:2849–2853

    Article  Google Scholar 

  73. Fuentealba P, Parr RG (1991) Higher-order derivatives in density-functional theory, especially the hardness derivative. J Chem Phys 94:5559–5564

    Article  CAS  Google Scholar 

  74. Parr RG, Donnelly RA, Levy M, Palke WE (1978) Electronegativity: the density functional viewpoint. J Chem Phys 68:3801–3807

    Article  CAS  Google Scholar 

  75. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. PhysRev 136:B864–B871

    Google Scholar 

  76. 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 76:6062–6065

    Article  CAS  Google Scholar 

  77. Lieb EH (1983) Density functionals for Coulomb systems. Int J Quantum Chem 24:243–277

    Article  CAS  Google Scholar 

  78. Yang WT, Ayers PW, Wu Q (2004) Potential functionals: dual to density functionals and solution to the upsilon-representability problem. Phys Rev Lett 92:146404

    Article  CAS  Google Scholar 

  79. Ayers PW (2006) Axiomatic formulations of the Hohenberg-Kohn functional. Phys Rev A 73:012513

    Article  CAS  Google Scholar 

  80. Cohen AJ, Mori-Sanchez P, Yang WT (2012) Challenges for density functional theory. Chem Rev 112:289–320

    Article  CAS  Google Scholar 

  81. Almbladh CO, Von Barth U (1985) Exact results for the charge and spin-densities, exchange-correlation potentials, and density-functional eigenvalues. Phys Rev B 31:3231–3244

    Article  CAS  Google Scholar 

  82. Von Barth U, Hedin L (1972) A local exchange-correlation potential for the spin polarized case I. J Phys C 5:1629–1642

    Article  Google Scholar 

  83. Perdew JP, Zunger A (1981) Self-interaction correction to density-functional approximations for many-electron systems. Phys Rev B 23:5048–5079

    Article  CAS  Google Scholar 

  84. Capelle K, Vignale G (2002) Nonuniqueness and derivative discontinuities in density- functional theories for current-carrying and superconducting systems. Phys Rev B 65:113106

    Article  CAS  Google Scholar 

  85. Capelle K, Vignale G (2001) Nonuniqueness of the potentials of spin-density-functional theory. Phys Rev Lett 86:5546–5549

    Article  CAS  Google Scholar 

  86. Holas A, Balawender R (2006) Comment on “Legendre-transform functionals for spin-density-functional theory” [J. Chem. Phys. 124, 224108 (2006)]. J Chem Phys 125:247101

    Article  CAS  Google Scholar 

  87. Ayers PW, Yang WT (2006) Legendre-transform functionals for spin-density-functional theory. J Chem Phys 124:224108

    Article  CAS  Google Scholar 

  88. Heaton-Burgess T, Ayers PW, Yang WT (2006) Spin-potential functional formalism for current-carrying noncollinear magnetic systems. Abstracts of Papers of the American Chemical Society 231:1

  89. Ayers PW, Fuentealba P (2009) Density-functional theory with additional basic variables: extended Legendre transform. Phys Rev A 80:032510. doi:10.1103/PhysRevA.80.032510

    Article  CAS  Google Scholar 

  90. Higuchi M, Higuchi K (2004) Arbitrary choice of basic variables in density functional theory: formalism. Phys Rev B 69:035113

    Article  CAS  Google Scholar 

  91. Pan X-Y, Sahni V (2014) Comment on “Density and Physical Current Density Functional Theory”. Int J Quantum Chem 114(3):233–236. doi:10.1002/qua.24532

    Article  CAS  Google Scholar 

  92. Pan X-Y, Sahni V (2013) Reply to the comment by Vignale et al. Int J Quantum Chem 113(9):1424–1425. doi:10.1002/qua.24326

    Article  CAS  Google Scholar 

  93. Vignale G, Ullrich CA, Capelle K (2013) Comment on “density and physical current density functional theory” by Xiao-Yin Pan and Viraht Sahni. Int J Quantum Chem 113(9):1422–1423. doi:10.1002/qua.24327

    Article  CAS  Google Scholar 

  94. Pan X-Y, Sahni V (2010) Density and physical current density functional theory. Int J Quantum Chem 110(15):2833–2843. doi:10.1002/qua.22862

    Article  CAS  Google Scholar 

  95. Kohn W, Savin A, Ullrich CA (2004) Hohenberg-Kohn theory including spin magnetism and magnetic fields. Int J Quantum Chem 100(1):20–21. doi:10.1002/qua.20163

    Article  CAS  Google Scholar 

  96. Pan X-Y, Sahni V (2010) Particle number and probability density functional theory and A-representability. J Chem Phys. doi:10.1063/1.3357986

    Google Scholar 

  97. Pan X-Y, Sahni V (2012) Generalization of the Hohenberg-Kohn theorem to the presence of a magnetostatic field. J Phys Chem Solids 73(5):630–634. doi:10.1016/j.jpcs.2011.12.023

    Article  CAS  Google Scholar 

  98. Tellgren EI, Kvaal S, Helgaker T (2014) Fermion N-representability for prescribed density and paramagnetic current density. Phys Rev A. doi:10.1103/PhysRevA.89.012515

    Google Scholar 

  99. Laestadius A, Benedicks M (2014) Hohenberg-Kohn theorems in the presence of magnetic field. Int J Quantum Chem 114(12):782–795. doi:10.1002/qua.24668

    Article  CAS  Google Scholar 

  100. Pan X-Y, Sahni V (2015) Hohenberg-Kohn theorems in electrostatic and uniform magnetostatic fields. J Chem Phys. doi:10.1063/1.4934800

    Google Scholar 

  101. Eschrig H, Pickett WE (2001) Density functional theory of magnetic systems revisited. Solid State Commun 118:123–127

    Article  CAS  Google Scholar 

  102. Mori-Sanchez P, Cohen AJ, Yang WT (2009) Discontinuous nature of the exchange-correlation functional in strongly correlated systems. Phys Rev Lett 102:066403. doi:10.1103/PhysRevLett.102.066403

    Article  CAS  Google Scholar 

  103. Cohen AJ, Mori-Sanchez P, Yang WT (2008) Insights into current limitations of density functional theory. Science 321:792–794. doi:10.1126/science.1158722

    Article  CAS  Google Scholar 

  104. Cohen AJ, Mori-Sanchez P, Yang WT (2008) Fractional spins and static correlation error in density functional theory. J Chem Phys 129:121104

    Article  CAS  Google Scholar 

  105. Cuevas-Saavedra R, Chakraborty D, Rabi S, Cardenas C, Ayers PW (2012) Symmetric non local weighted density approximations from the exchange-correlation hole of the uniform electron gas. J Chem Theory Comp 8(11):4081–4093. doi:10.1021/ct300325t

    Article  CAS  Google Scholar 

  106. Garza J, Vargas R, Cedillo A, Galvan M, Chattaraj PK (2006) Comparison between the frozen core and finite differences approximations for the generalized spin-dependent global and local reactivity descriptors in small molecules. Theor Chem Acc 115:257–265

    Article  CAS  Google Scholar 

  107. Fernandez FM, Alcoba DR, Ona OB, Torre A, Lain L (2015) Electronic densities in systems with fractionally charged nuclei: a symmetry breaking study. J Math Chem 53(1):236–249. doi:10.1007/s10910-014-0424-z

    Article  CAS  Google Scholar 

  108. Cohen AJ, Mori-Sanchez P (2014) Dramatic changes in electronic structure revealed by fractionally charged nuclei. J Chem Phys. doi:10.1063/1.4858461

    Google Scholar 

  109. Savin A (1996) On degeneracy, near-degeneracy, and density functional theory. In: Seminario JM (ed) Recent developments and applications of modern density functional theory. Elsevier, New York, p 327

    Chapter  Google Scholar 

  110. Mori-Sanchez P, Cohen AJ, Yang WT (2008) Localization and delocalization errors in density functional theory and implications for band-gap prediction. Phys Rev Lett 100:146401

    Article  CAS  Google Scholar 

  111. Mori-Sanchez P, Cohen AJ, Yang WT (2006) Many-electron self-interaction error in approximate density functionals. J Chem Phys 125:201102

    Article  CAS  Google Scholar 

  112. Mori-Sanchez P, Cohen AJ (2014) The derivative discontinuity of the exchange-correlation functional. PCCP 16(28):14378–14387. doi:10.1039/c4cp01170h

    Article  CAS  Google Scholar 

  113. Johnson ER, Contreras-Garcia J (2011) Communication: a density functional with accurate fractional-charge and fractional-spin behaviour for s-electrons. J Chem Phys 135:081103. doi:10.1063/1.3630117

    Article  CAS  Google Scholar 

  114. Haunschild R, Henderson TM, Jimenez-Hoyos CA, Scuseria GE (2010) Many-electron self-interaction and spin polarization errors in local hybrid density functionals. J Chem Phys 133:134116. doi:10.1063/1.3478534

    Article  CAS  Google Scholar 

  115. Ruzsinszky A, Perdew JP, Csonka GI, Vydrov OA, Scuseria GE (2007) Density Functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H2+, He2+, LiH+, and Ne2+. J Chem Phys 126:104102

    Article  CAS  Google Scholar 

  116. Perdew JP, Ruzsinszky A, Csonka GI, Vydrov OA, Scuseria GE, Staroverov VN, Tao JM (2007) Exchange and correlation in open systems of fluctuating electron number. Phys Rev A 76:040501. doi:10.1103/Physreva.76.040501

    Article  CAS  Google Scholar 

  117. 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

    Article  CAS  Google Scholar 

  118. Ayers PW, Levy M (2014) Tight constraints on the exchange-correlation potentials of degenerate states. J Chem Phys 140(18):18a537. doi:10.1063/1.4871732

    Article  CAS  Google Scholar 

  119. Levy M, Anderson JSM, Heidar-Zadeh FH, Ayers PW (2014) Kinetic and electron-electron energies for convex sums of ground state densities with degeneracies and fractional electron number. J Chem Phys 140(18):18a538. doi:10.1063/1.4871734

    Article  CAS  Google Scholar 

  120. Savin A (2009) Is size-consistency possible with density functional approximations? Chem Phys 356:91–97. doi:10.1016/j.chemphys.2008.10.023

    Article  CAS  Google Scholar 

  121. Gori-Giorgi P, Savin A (2008) Degeneracy and size consistency in electronic density functional theory. In: Dovesi R, Orlando R, Roetti C (eds) Ab initio simulation of crystalline solids: history and prospects—contributions in honor of cesare pisani, vol 117. J Phys Conf Ser, pp 12017–12017

  122. Cohen AJ, Mori-Sanchez P, Yang WT (2009) Second-order perturbation theory with fractional charges and fractional spins. J Chem Theory Comp 5:786–792. doi:10.1021/ct8005419

    Article  CAS  Google Scholar 

  123. Mori-Sanchez P, Cohen AJ, Yang W (2012) Failure of the random-phase-approximation correlation energy. Phys Rev A. doi:10.1103/PhysRevA.85.042507

    Google Scholar 

  124. Yang W, Mori-Sanchez P, Cohen AJ (2013) Extension of many-body theory and approximate density functionals to fractional charges and fractional spins. J Chem Phys. doi:10.1063/1.4817183

    Google Scholar 

  125. van Aggelen H, Yang Y, Yang W (2013) Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random-phase approximation. Phys Rev A. doi:10.1103/PhysRevA.88.030501

    Google Scholar 

  126. Yang Y, Peng D, Davidson ER, Yang W (2015) Singlet–triplet energy gaps for diradicals from particle–particle random phase approximation. J Phys Chem A 119(20):4923–4932. doi:10.1021/jp512727a

    Article  CAS  Google Scholar 

  127. Ghanty TK, Ghosh SK (1994) A frontier orbital density-functional approach to polarizability, hardness, electronegativity, and covalent radius of atomic systems. J Am Chem Soc 116:8801–8802

    Article  CAS  Google Scholar 

  128. Zielinski F, Tognetti V, Joubert L (2012) Condensed descriptors for reactivity: a methodological study. Chem Phys Lett 527:67–72. doi:10.1016/j.cplett.2012.01.011

    Article  CAS  Google Scholar 

  129. Ayers PW, Morrison RC, Parr RG (2005) Fermi-Amaldi model for exchange-correlation: atomic excitation energies from orbital energy differences. Mol Phys 103:2061–2072

    Article  CAS  Google Scholar 

  130. Perdew JP, Levy M (1997) Comment on “Significance of the highest occupied Kohn-Sham eigenvalue”. Phys Rev B 56:16021–16028

    Article  CAS  Google Scholar 

  131. Janak JF (1978) Proof that ∂ E∂ni = ε in density-functional theory. Phys Rev B 18(12):7165–7168

    Article  CAS  Google Scholar 

  132. Harbola MK (1999) Relationship between the highest occupied Kohn-Sham orbital eigenvalue and ionization energy. Phys Rev B 60(7):4545–4550. doi:10.1103/PhysRevB.60.4545

    Article  CAS  Google Scholar 

  133. Holas A (2008) Comment on “Asymptotic form of the Kohn-Sham correlation potential”. Phys Rev A 77:026501. doi:10.1103/PhysRevA.77.026501

    Article  CAS  Google Scholar 

  134. Wu Q, Ayers PW, Yang WT (2003) Density-functional theory calculations with correct long-range potentials. J Chem Phys 119:2978–2990

    Article  CAS  Google Scholar 

  135. Della Sala F, Gorling A (2002) Asymptotic behavior of the Kohn-Sham exchange potential. Phys Rev Lett 89:033003

    Article  CAS  Google Scholar 

  136. Della Sala F, Gorling A (2002) The asymptotic region of the Kohn–Sham exchange potential in molecules. J Chem Phys 116:5374–5388

    Article  CAS  Google Scholar 

  137. Gori-Giorgi P, Gal T, Baerends EJ (2016) Asymptotic behavior of the electron density and the Kohn-Sham potential in case of a Kohn-Sham HOMO nodal plane. Mol Phys 114:1086–1097

    Article  CAS  Google Scholar 

  138. Perdew JP, Levy M (1983) Physical content of the exact Kohn–Sham orbital energies: band gaps and derivative discontinuities. Phys Rev Lett 51:1884–1887

    Article  CAS  Google Scholar 

  139. Sham LJ, Schluter M (1985) Density-functional theory of the band-gap. Phys Rev B 32(6):3883–3889

    Article  CAS  Google Scholar 

  140. Sham LJ, Schluter M (1983) Density-functional theory of the energy-gap. Phys Rev Lett 51(20):1888–1891

    Article  Google Scholar 

  141. Tozer DJ, Handy NC (1998) Improving virtual Kohn-Sham orbitals and eigenvalues: application to excitation energies and static polarizabilities. J Chem Phys 109(23):10180–10189

    Article  CAS  Google Scholar 

  142. Savin A, Umrigar CJ, Gonze X (1998) Relationship of Kohn-Sham eigenvalues to excitation energies. Chem Phys Lett 288(2–4):391–395

    Article  CAS  Google Scholar 

  143. Filippi C, Umrigar CJ, Gonze X (1997) excitation energies from density functional perturbation theory. J Chem Phys 107(23):9994–10002

    Article  CAS  Google Scholar 

  144. Baerends EJ, Gritsenko OV, van Meer R (2013) The Kohn-Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn-Sham orbital energies. PCCP 15(39):16408–16425. doi:10.1039/c3cp52547c

    Article  CAS  Google Scholar 

  145. van Meer R, Gritsenko OV, Baerends EJ (2014) Physical meaning of virtual Kohn–Sham orbitals and orbital energies: an ideal basis for the description of molecular excitations. J Chem Theory Comp 10(10):4432–4441. doi:10.1021/ct500727c

    Article  CAS  Google Scholar 

  146. Stowasser R, Hoffmann R (1999) What do the Kohn–Sham orbitals and eigenvalues mean? J Am Chem Soc 121:3414–3420

    Article  CAS  Google Scholar 

  147. Ayers PW, Day OW, Morrison RC (1998) Analysis of density functionals and their density tails in H2. Int J Quantum Chem 69:541–550

    Article  Google Scholar 

  148. Smith DW (1966) N-representabiilty problem for fermion density matrices. II. The first-order Density Matrix with N even. Phys Rev 147:896–898

    Article  CAS  Google Scholar 

  149. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Iszmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery Jr. JA, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas O, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian 09, Revision A.1. Gaussian Inc., Wallingford CT

  150. Capelle K, Vignale G, Ullrich CA (2010) Spin gaps and spin-flip energies in density-functional theory. Phys Rev B 81:125114. doi:10.1103/PhysRevB.81.125114

    Article  CAS  Google Scholar 

  151. Liu SB (2009) Electrophilicity. In: Chattaraj PK (ed) Chemical reactivity theory: a density functional view. Taylor and Francis, Boca Raton, p 179

    Google Scholar 

  152. Parr RG, von Szentpály L, Liu SB (1999) Electrophilicity index. J Am Chem Soc 121:1922–1924

    Article  CAS  Google Scholar 

  153. Chattaraj PK, Sarkar U, Roy DR (2006) Electrophilicity index. Chem Rev 106:2065–2091

    Article  CAS  Google Scholar 

  154. Chattaraj PK, Maiti B, Sarkar U (2003) Philicity: a unified treatment of chemical reactivity and selectivity. J Phys Chem A 107:4973–4975

    Article  CAS  Google Scholar 

Download references

Acknowledgments

RAMQ acknowledges support from Foreign Affairs, Trade and Development Canada in the form of an ELAP scholarship. PWA acknowledges support from NSERC and Compute Canada.

Author information

Authors and Affiliations

  1. Laboratory of Computational and Theoretical Chemistry, Faculty of Chemistry, University of Havana, Havana, Cuba

    Ramón Alain Miranda-Quintana

  2. Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON, Canada

    Ramón Alain Miranda-Quintana & Paul W. Ayers

Authors
  1. Ramón Alain Miranda-Quintana
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul W. Ayers
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paul W. Ayers.

Additional information

Published as part of the special collection of articles “Festschrift in honour of A. Vela.”

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Miranda-Quintana, R.A., Ayers, P.W. Systematic treatment of spin-reactivity indicators in conceptual density functional theory. Theor Chem Acc 135, 239 (2016). https://doi.org/10.1007/s00214-016-1995-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00214-016-1995-5

Keywords

Search

Navigation