Skip to main content

Shape entropy’s response to molecular ionization

Journal of Molecular Modeling volume 19, pages 1677–1683 (2013)Cite this article

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

In this work we define a shape entropy by calculating the Shannon’s entropy of the shape function. This shape entropy and its linear response to the change in the total number of electrons of the molecule are explored as descriptors of bonding properties. Calculations on selected molecular systems were performed. According to these, shape entropy properly describes electron delocalization while its linear response to ionization predicts changes in bonding patterns. The derivative of the shape entropy proposed turned out to be fully determined by the shape function and the Fukui function.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

References

  1. Gagliardi L, Roos BO (2007) Multiconfigurational quantum chemical methods for molecular systems containing actinides. Chem Soc Rev 36:893–903

    Article  CAS  Google Scholar 

  2. Roos BO, Borin AC, Gagliardi L (2007) The maximum multiplicity of the covalent chemical bond. Angew Chem Int Ed 46:1469–1472

    Article  CAS  Google Scholar 

  3. Bader R (1994) Atoms in Molecules: a quantum theory. Oxford Univ. Press, Oxford

    Google Scholar 

  4. Tognetti V, Joubert L, Cortona P, Adamo C (2009) Toward a combined DFT/QTAIM description of agostic bonds: the critical case of a Nb(III) complex. J Phys Chem A 113:12322–12327

    Article  CAS  Google Scholar 

  5. Nalewajski RF (2006) Information theory of molecular systems. Elsevier, Cambridge

  6. Ihara S (1993) Information theory for continuous systems. World Scientific, Singapore

    Book  Google Scholar 

  7. Hocker D, Li X, Iyengar SS (2011) Shannon entropy based time-dependent deterministic sampling for efficient on-the-fly quantum dynamics and electronic structure. J Chem Theory Comput 7:256–268

    Article  CAS  Google Scholar 

  8. Sagar RP, Hô M (2008) Shannon entropies of atomic basins and electron correlation effects. J Mex Chem Soc 52:60–66

    CAS  Google Scholar 

  9. Corzo HH, Laguna HG, Sagar RP (2012) Localization phenomena in a cyclic box. J Math Chem 50:233–248

    Article  CAS  Google Scholar 

  10. Noorizadeh S, Shakerzadeh E (2010) Shannon entropy as a new measure of aromaticity, Shannon aromaticity. Phys Chem Chem Phys 12:4742–4749

    Article  CAS  Google Scholar 

  11. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(379–423):623–656

    Google Scholar 

  12. Cover TM, Thomas JA (2006) Elements of information theory. Wiley, New York

    Google Scholar 

  13. El Saddik A, Orozco M, Asfaw Y, Shirmohammadi S, Adler A (2007) A novel biometric system for identification and verification of haptic users. IEEE Trans Instrum Meas 56:895–906

    Article  Google Scholar 

  14. Moddemeijer R (1989) On estimation of entropy and mutual information of continuous distributions. Signal Process 16:233–248

    Article  Google Scholar 

  15. Gadre SR, Sears SB, Chakravorty SJ, Bendale RD (1985) Some novel characteristics of atomic information entropies. Phys Rev A 32:2602–2606

    Article  CAS  Google Scholar 

  16. Hô MH, Sagar RP, Pérez-Jordá JM, Smith VH, Esquivel RO (1994) A numerical study of molecular information entropies. Chem Phys Lett 219:15–20

    Article  Google Scholar 

  17. Hô MH, Sagar RP, Smith VH, Esquivel RO (1994) Atomic information entropies beyond the Hartree-Fock limit. J Phys B Atomic Mol Opt Phys 27:5149–5157

    Article  Google Scholar 

  18. Hô MH, Sagar RP, Weaver DF, Smith VH (1995) An investigation of the dependence of Shannon-information entropies and distance measures on molecular-geometry. Int J Quantum Chem S29:109–115

    Article  Google Scholar 

  19. Esquivel RO, Rodríguez AL, Sagar RP, Hô MH, Smith VH (1996) Physical interpretation of information entropy: numerical evidence of the Collins conjecture. Phys Rev A 54:259–265

    Article  CAS  Google Scholar 

  20. Ramírez JC, Soriano C, Esquivel RO, Sagar RP, Hô MH, Smith VH (1997) Jaynes information entropy of small molecules: numerical evidence of the Collins conjecture. Phys Rev A 56:4477–4482

    Article  Google Scholar 

  21. Hô M, Smith VH, Weaver DF, Gatti C, Sagar RP, Esquivel RO (1998) Molecular similarity based on information entropies and distances. J Chem Phys 108:5469–5475

    Article  Google Scholar 

  22. Hô M, Weaver DF, Smith VH, Sagar RP, Esquivel RO, Yamamoto S (1998) An information entropic study of correlated densities of the water molecule. J Chem Phys 109:10620–10627

    Article  Google Scholar 

  23. Chattaraj PK, Chamorro E, Fuentealba P (1999) Chemical bonding and reactivity: a local thermodynamic viewpoint. Chem Phys Lett 314:114–121

    Article  CAS  Google Scholar 

  24. Nalewajski RF, Parr RG (2000) Information theory, atoms in molecules, and molecular similarity. Proc Natl Acad Sci 97:8879–8882

    Article  CAS  Google Scholar 

  25. Nalewajski RF (2002) Applications of the information theory to problems of molecular electronic structure and chemical reactivity. Int J Mol Sci 3:237–259

    Article  CAS  Google Scholar 

  26. Ayers PW (2000) Atoms in molecules, an axiomatic approach. I. Maximum transferability. J Chem Phys 113:10886–10898

    Article  CAS  Google Scholar 

  27. Parr RG, Ayers PW, Nalewajski RF (2005) What is an atom in a molecule? J Phys Chem A 109:3957–3959

    Article  CAS  Google Scholar 

  28. Ghiringhelli LM, Delle Site L, Mosna RA, Hamilton IP (2010) Information-theoretic approach to kinetic-energy functionals: the nearly uniform electron gas. J Math Chem 48:78–82

    Article  CAS  Google Scholar 

  29. Ghiringhelli LM, Hamilton IP, Delle Site L (2010) Interacting electrons, spin statistics, and information theory. J Chem Phys 132:014106

    Article  CAS  Google Scholar 

  30. Parr RG, Bartolotti LJ (1983) Some remarks on the density functional theory of few-electron systems. J Phys Chem 87:2810–2815

    Article  CAS  Google Scholar 

  31. Cedillo A (1994) A new representation for ground-states and its Legendre transforms. Int J Quantum Chem Symp 28:231–240

    Article  CAS  Google Scholar 

  32. Baekelandt BG, Cedillo A, Parr RG (1995) Reactivity indexes and fluctuation formulas in density-functional theory—isomorphic ensembles and a new measure of local hardness. J Chem Phys 103:8548–8556

    Article  CAS  Google Scholar 

  33. Ayers PW, De Proft F, Geerlings P (2007) A comparison of the utility of the shape function and electron density for predicting periodic properties: atomic ionization potentials. Phys Rev A 75:012508

    Article  Google Scholar 

  34. De Proft F, Ayers PW, Sen K, Geerlings P (2004) On the importance of the “density per particle” (shape function) in the density functional theory. J Chem Phys 120:9969–9973

    Article  Google Scholar 

  35. Ayers PW (2006) Information theory, the shape function, and the Hirshfeld atom. Theor Chem Accounts 115:370–378

    Article  CAS  Google Scholar 

  36. Ayers PW (2000) Density per particle as a descriptor of coulombic systems. Proc Natl Acad Sci 97:1959–1964

    Article  CAS  Google Scholar 

  37. Ayers PW, Cedillo A (2009) The shape function. In: Chattaraj PK (ed) Chemical reactivity theory: a density functional view. Taylor and Francis, Boca Raton, p 269

    Google Scholar 

  38. Parr RG, Yang WT (1984) Density-functional approach to the frontier-electron theory of chemical reactivity. J Am Chem Soc 106:4049

    Article  CAS  Google Scholar 

  39. Fuentealba P, Florez E, Tiznado W (2010) Topological analysis of the Fukui function. J Chem Theory Comput 6:1470–1478

    Article  CAS  Google Scholar 

  40. Cardenas C, Tiznado W, Ayers PW, Fuentealba P (2011) The Fukui potential and the capacity of charge and the global hardness of atoms. J Phys Chem A 115:2325–2331

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  42. 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 

  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. Ayers PW, Levy M (2000) Perspective on “Density functional approach to the frontier-electron theory of chemical reactivity” by Parr RG, Yang W (1984). Theor Chem Account 103:353–360

    Article  CAS  Google Scholar 

  45. Ayers PW, Yang WT, Bartolotti LJ (2009) Fukui function. In: Chattaraj PK (ed) Chemical reactivity theory: A density functional view. CRC Press, Boca Raton, pp 255–267

    Google Scholar 

  46. Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:A1133–A1138

    Article  Google Scholar 

  47. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864–B871

    Article  Google Scholar 

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

    Google Scholar 

  49. Yang W, Parr RG, Pucci R (1984) Electron density, Kohn–Sham frontier orbitals, and Fukui functions. J Chem Phys 81:2862–2863

    Article  CAS  Google Scholar 

  50. Michalak A, De Proft F, Geerlings P, Nalewajski RF (1999) Fukui functions from the relaxed Kohn-Sham orbitals. J Phys Chem A 103:762–771

    Article  CAS  Google Scholar 

  51. Balawender R, Geerlings P (2005) DFT-based chemical reactivity indices in the Hartree Fock method. II. Hardness and Fukui function. J Chem Phys 123:124103

    Article  Google Scholar 

  52. Flores-Moreno R, Köster AM (2008) Auxiliary density perturbation theory. J Chem Phys 128:134105

    Article  Google Scholar 

  53. Flores-Moreno R, Melin J, Ortiz JV, Merino G (2008) Efficient calculation of analytic Fukui functions. J Chem Phys 129:224105

    Article  Google Scholar 

  54. Flores-Moreno R (2010) Symmetry conservation in Fukui functions. J Chem Theory Comput 6:48

    Article  CAS  Google Scholar 

  55. Yang W, Cohen AJ, De Proft F, Geerlings P (2012) Analytical evaluation of Fukui functions and real-space linear response function. J Chem Phys 136:144110

    Article  Google Scholar 

  56. Dirac PAM (1928) The quantum theory of the electron. Proc R Soc Lond A 117:610–624

    Article  Google Scholar 

  57. 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

    Article  CAS  Google Scholar 

  58. Godbout N, Salahub DR, Andzelm J, Wimmer E (1992) Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I: boron through neon, optimization technique and validation. Can J Phys 70:560–571

    CAS  Google Scholar 

  59. Andzelm J, Radzio E, Salahub DR (1985) Compact basis sets for LCAO-LSD calculations. Part I: method and bases for Sc to Zn. J Comput Chem 6:520–532

    Article  CAS  Google Scholar 

  60. Andzelm J, Russo N, Salahub DR (1987) Ground and excited states of group IVA diatomics from local-spin-density calculations: model potentials for Si, Ge, and Sn. J Chem Phys 87:6562

    Article  CAS  Google Scholar 

  61. Köster AM, Geudtner G, Calaminici P, Casida ME, Domínguez VD, Flores-Moreno R, Gamboa GU, Goursot A, Heine T, Ipatov A, Janetzko F, del Campo JM, Reveles JU, Vela A, Zuñiga-Gutierrez B, Salahub DR (2011) deMon2k, Version 3, The deMon developers, Cinvestav, México City. http://www.demon-software.com

  62. Flores-Moreno R, Pineda-Urbina K, Gómez-Sandoval Z (2012) Sinapsis, Version XII-V, Sinapsis developers, Guadalajara. http://sinapsis.sourceforge.net

Download references

Acknowledgments

This work was financially supported by the CONACyT (CB 2009: 127362, CB 2008: 105721). KPU gratefully acknowledges CONACyT fellowship 229123. RDGM acknowledges support from the Mazda Foundation for Art and Science.

Author information

Authors and Affiliations

  1. Facultad de Ciencias Químicas, Universidad de Colima, Carretera Colima-Coquimatlán Km. 9, Coquimatlán, Colima Col., C.P. 28400, Mexico

    K. Pineda-Urbina & Z. Gómez-Sandoval

  2. Departamento de Física, Universidad Nacional de Colombia, Bogota D.C., Colombia

    R. D. Guerrero

  3. Departamento de Química, Universidad Nacional de Colombia, Bogota D.C., Colombia

    A. Reyes

  4. Departamento de Química, Universidad de Guadalajara, Blvd. Marcelino García Barragán 1421, Guadalajara, Jalisco, C.P. 44430, Mexico

    R. Flores-Moreno

Authors
  1. K. Pineda-Urbina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. D. Guerrero
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Reyes
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Z. Gómez-Sandoval
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. R. Flores-Moreno
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Flores-Moreno.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Pineda-Urbina, K., Guerrero, R.D., Reyes, A. et al. Shape entropy’s response to molecular ionization. J Mol Model 19, 1677–1683 (2013). https://doi.org/10.1007/s00894-012-1725-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00894-012-1725-4

Keywords

  • Electron delocalization
  • Fukui function
  • Shannon’s entropy
  • Shape function