Advertisement

New advances in conceptual-DFT: an alternative way to calculate the Fukui function and dual descriptor

  • Jesús Sánchez-MárquezEmail author
Original Paper
  • 64 Downloads

Abstract

An alternative way of calculating the Fukui function and the partial derivative of second order of the electronic density with respect to the number of electrons N is presented, the new formulas agree with the usual ones but only in cases without degeneracy. The new operative formulas are more general than the previous ones and are the right ones for those problematic cases where one or both of the frontier molecular orbitals are degenerate. Finally, we present a new way of applying the finite difference approximation that leads to more realistic results than the usual formulas.

Graphical abstract

A new way of calculating the Fukui function is presented that results in a new operative formula of the function. It has also been obtained the partial derivative of second order of the electronic density with respect to the number of electrons N, and it agree with the usual formula of the dual descriptor function but only in cases without degeneration.

Keywords

Reactivity descriptors Fukui function Dual descriptor Finite difference approximation UCA-FUKUI software Conceptual DFT 

Notes

Acknowledgment

Calculations were performed through CICA (Centro Informático Científico de Andalucía).

Supplementary material

894_2019_4000_MOESM1_ESM.doc (750 kb)
ESM 1 (DOC 749 kb)

References

  1. 1.
    Yang WT, Parr RG, Pucci R (1984) Electron density, Kohn-sham frontier orbitals, and Fukui functions. J Chem Phys 81:2862–2863CrossRefGoogle Scholar
  2. 2.
    Par RG, Yang W (1984) Density functional approach to the frontier-electron theory of chemical reactivity. J Am Chem Soc 106:4049CrossRefGoogle Scholar
  3. 3.
    Ayers PW, Levy M (2000) Density functional approach to the frontierelectron theory of chemical reactivity. Theor Chem Accounts 103:353CrossRefGoogle Scholar
  4. 4.
    Ayers PW, Yang WT, Bartolotti LJ (2009) The Fukui function. In: Chattaraj PK (ed) Chemical reactivity theory: a density functional view. CRC, Boca Raton, p 255Google Scholar
  5. 5.
    Yang W, Parr RG (1985) Hardness, softness, and the Fukui function in the electronic theory of metals and catalysis. Proc Natl Acad Sci USA 82:6723CrossRefGoogle Scholar
  6. 6.
    Chandra AK, Nguyen MT (2008) Fukui function and local softness. In: Chattaraj PK (ed) Chemical reactivity theory: a density-functional view. Taylor and Francis, New York, pp 163–178Google Scholar
  7. 7.
    Geerlings P, Proft FD, Langenaeker W (2003) Conceptual density functional theory. Chem Rev 103:1793–1874CrossRefGoogle Scholar
  8. 8.
    Parr R, Yang W (1989) Density-functional theory of atoms and molecules. Oxford University Press, OxfordGoogle Scholar
  9. 9.
    Perdew JP, Parr RG, Levy M, Balduz JL (1982) Density-functional theory for fractional particle number: derivative discontinuities of the energy. Phys Rev Lett 49:1691–1694CrossRefGoogle Scholar
  10. 10.
    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 84:5172–5175CrossRefGoogle Scholar
  11. 11.
    Ayers PW (2008) The continuity of the energy and other molecular properties with respect to the number of electrons. J Math Chem 43:285–303CrossRefGoogle Scholar
  12. 12.
    Gázquez JL (2009) Chemical reactivity concepts in density functional theory. In: Chattaraj PK (ed) Chemical reactivity theory: A density functional view. CRC, Boca Raton, p 7Google Scholar
  13. 13.
    Morell C, Gázquez JL, Vela A, Guegan F, Chermette H (2014) Revisiting electroaccepting and electrodonating powers: proposals for local electrophilicity and local nucleophilicity descriptors. Phys Chem Chem Phys 16:26832CrossRefGoogle Scholar
  14. 14.
    Robles A, Franco-Pérez M, Gázquez JL, Cárdenas C, Fuentealba P (2018) Local electrophilicity. J Mol Model 24:245CrossRefGoogle Scholar
  15. 15.
    Morell C, Grand A, Toro-Labbe A (2005) New dual descriptor for chemical reactivity. J Phys Chem A 109:205–212CrossRefGoogle Scholar
  16. 16.
    Morell C, Grand A, Toro-Labbe A (2006) Theoretical support for using the Δf(r) descriptor. Chem Phys Lett 425:342–346CrossRefGoogle Scholar
  17. 17.
    De Proft F, Ayers PW, Fias S, Geerlings P (2006) Woodward-Hoffmann rules in density functional theory: initial hardness response. J Chem Phys 125:214101–214109CrossRefGoogle Scholar
  18. 18.
    Ayers PW, Morell C, De Proft F, Geerlings P (2007) Understanding the Woodward–Hoffmann rules by using changes in Electron density. Chem Eur J 13:8240–8247CrossRefGoogle Scholar
  19. 19.
    Cárdenas AC, Ayers PW, Cedillo A (2011) Reactivity indicators for degenerate states in the density-functional theoretic chemical reactivity theory. J Chem Phys 134:174103–13CrossRefGoogle Scholar
  20. 20.
    Bultinck P, Cardenas C, Fuentealba P, Johnson PA, Ayers PW (2013) Atomic charges and the electrostatic potential are ill-defined in degenerate ground states. J Chem Theory Comp 9:4779–4788CrossRefGoogle Scholar
  21. 21.
    Bultinck P, Cardenas C, Fuentealba P, Johnson PA, Ayers PW (2014) How to compute the Fukui matrix and function for systems with (quasi-)degenerate states. J Chem Theory Comp 10:202–210CrossRefGoogle Scholar
  22. 22.
    Bultinck P, Jayatilaka D, Cardenas C (2015) A problematic issue for atoms in molecules: impact of (quasi-)degenerate states on quantum theory atoms in molecules and Hirshfeld-I properties. Comput Theor Chem 1053:106–111CrossRefGoogle Scholar
  23. 23.
    Martínez-Araya JI (2016) A generalized operational formula based on Total electronic densities to obtain 3D pictures of the dual descriptor to reveal nucleophilic and electrophilic sites accurately on closed-Shell molecules. J Comput Chem 37:2279–2303CrossRefGoogle Scholar
  24. 24.
    Martínez-Araya JI (2015) Why is the dual descriptor a more accurate local reactivity descriptor than Fukui functions? J Math Chem 53:451–465CrossRefGoogle Scholar
  25. 25.
    Becke AD (1993) Density-functional thermochemistry. III the role of exact exchange. J Chem Phys 98:5648–5652CrossRefGoogle Scholar
  26. 26.
    Frisch MJ, Pople JA, Binkley JS (1984) Self-consistent molecular orbital methods. 25. Supplementary functions for gaussian basis sets. J Chem Phys 80:3265–3269CrossRefGoogle Scholar
  27. 27.
    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, Izmaylov 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.02. Gaussian, Inc., Wallingford CTGoogle Scholar
  28. 28.
    Sánchez-Márquez J, Zorrilla D, Sánchez-Coronilla AM, de los Santos D, Navas J, Fernández-Lorenzo C, Alcántara R, Martín-Calleja J (2014) Introducing UCA-FUKUI software: reactivity-index calculations. J Mol Model 20:2492CrossRefGoogle Scholar
  29. 29.
    Bultinck P et al (2007) Critical thoughts on computing atom condensed Fukui functions. J Chem Phys 127:034102–034111CrossRefGoogle Scholar
  30. 30.
    Nalewajski RF, Parr RG (2000) Information theory, atoms in molecules, and molecular similarity. Proc Natl Acad Sci USA 97:8879–8882CrossRefGoogle Scholar
  31. 31.
    Heidar-Zadeh F, Ayers PW, Verstraelen T, Vinogradov I, Vöhringer-Martinez E, Bultinck P (2018) Information-theoretic approaches to atoms-in-molecules: Hirshfeld family of partitioning schemes. J Phys Chem A 122:4219–4245CrossRefGoogle Scholar
  32. 32.
    Roy RK, Pal S, Hirao K (1999) On non-negativity of Fukui function indices. J Chem Phys 110:8236–8245CrossRefGoogle Scholar
  33. 33.
    Yang WT, Mortier WJ (1986) The use of global and local molecular parameters for the analysis of the gas-phase basicity of amines. J Am Chem Soc 108:5708–5711CrossRefGoogle Scholar
  34. 34.
    Hirshfeld FL (1977) Bonded-atom fragments for describing molecular charge densities. Theor Chem Accounts 44:129–138CrossRefGoogle Scholar
  35. 35.
    Ritchie JP (1985) Electron density distribution analysis for nitromethane, nitromethide, and nitramide. J Am Chem Soc 107:1829–1837CrossRefGoogle Scholar
  36. 36.
    Ritchie JP, Bachrach SM (1987) Some methods and applications of electron density distribution analysis. J Comp Chem 8:499–509CrossRefGoogle Scholar
  37. 37.
    Mulliken RS (1955) Electronic population analysis on LCAO–MO molecular wave functions I. J Chem Phys 23:1833CrossRefGoogle Scholar
  38. 38.
    Reed AE, Weinhold F (1983) Natural bond orbital analysis of near-Hartree-Fock water dimer. J Chem Phys 78:4066CrossRefGoogle Scholar
  39. 39.
    Reed AE, Weinstock RB, Weinhold F (1985) Natural population analysis. J Chem Phys 83:735CrossRefGoogle Scholar
  40. 40.
    Reed AE, Weinhold F (1985) Natural localized molecular orbitals. J Chem Phys 83:1736CrossRefGoogle Scholar
  41. 41.
    Orozco-Valencia U, Gazquez JL, Vela A (2018) Global and local charge transfer in electron donor-acceptor complexes. J Mol Model 24:250CrossRefGoogle Scholar
  42. 42.
    Orozco-Valencia U, Gazquez JL, Vela A (2018) Role of reaction conditions in the global and local two parabolas charge transfer model. J Phys Chem A 122:1796–1806CrossRefGoogle Scholar
  43. 43.
    Parr RG, Pearson RG (1983) Absolute hardness: companion parameter to absolute electronegativity. J Am Chem Soc 105:7512–7516CrossRefGoogle Scholar
  44. 44.
    Parr RG, Bartolotti LJ (1982) On the geometric mean principle for electronegativity equalization. J Am Chem Soc 104:3801–3803CrossRefGoogle Scholar
  45. 45.
    Heidar-Zadeh F (2016) When is the Fukui function not normalized? The danger of inconsistent energy interpolation models in density functional theory. J Chem Theory Comp. 12:5777–5787CrossRefGoogle Scholar
  46. 46.
    Heidar-Zadeh F, Richer M, Fias S, Miranda-Quintana RA, Chan M, Franco-Pérez M, González-Espinoza CE, Kim TD, Lanssens C, Patel AHG, Yang XD, Vöhringer-Martinez E, Cárdenas C, Verstraelen T, Ayers PW (2016) Chem Phys Lett 660:307–312CrossRefGoogle Scholar
  47. 47.
    Franco-Perez M, Gá́zquez JL, Ayers PW, Vela A (2018) Thermodynamic justification for the parabolic model for reactivity indicators with respect to Electron number and a rigorous definition for the Electrophilicity: the essential role played by the electronic entropy. J Chem Theory Comp 14:597–606CrossRefGoogle Scholar
  48. 48.
    Dennington R, Keith T, Millam J (2009) Gauss View 5.0. Semichem Inc, Shawnee Mission, KS 7Google Scholar
  49. 49.
    Bader RFW (1990) Atoms in molecules: a quantum theory. Oxford University Press, OxfordGoogle Scholar
  50. 50.
    Matta CF, Boyd RJ (2007) The quantum theory of atoms in molecules: from solid state to DNA and drug design. WILEY-VCH, WeinhamCrossRefGoogle Scholar
  51. 51.
    Bader RFW (2005) The quantum mechanical basis for conceptual chemistry. Monatsh Chem 136:819–854CrossRefGoogle Scholar
  52. 52.
    Montgomery JA, Frisch MJ, Ochterski JW, Petersson GA (1999) A complete basis set model chemistry. VI. Use of density functional geometries and frequencies. J Chem Phys 110:2822CrossRefGoogle Scholar
  53. 53.
    Montgomery JA, Frisch MJ, Ochterski JW, Petersson GA (2000) A complete basis set model chemistry. VII. Use of the minimum population localization method. J Chem Phys 112:6532CrossRefGoogle Scholar
  54. 54.
    Sánchez-Márquez J (2016) Introducing new reactivity descriptors: “bond reactivity indices.” comparison of the new definitions and atomic reactivity indices. J Chem Phys 145:194105–194112CrossRefGoogle Scholar
  55. 55.
    Sánchez-Márquez J, Zorrilla D, García V, Fernández M (2018) Introducing a new bond reactivity index: Philicities for natural bond orbitals. J Mol Model 24:25CrossRefGoogle Scholar
  56. 56.
    Sánchez-Márquez J, Zorrilla D, García V, Fernández M (2018) Introducing a new methodology for the calculation of local philicity and multiphilic descriptor: an alternative to the finite difference approximation. Mol Phys 116:1737–1748CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de Química-Física, Facultad de Ciencias, Campus Universitario Río San PedroUniversidad de CádizPuerto RealSpain

Personalised recommendations