Skip to main content
SpringerLink
Log in

Localization-Delocalization Matrices and Electron Density-Weighted Adjacency/Connectivity Matrices: A Bridge Between the Quantum Theory of Atoms in Molecules and Chemical Graph Theory

  • Chapter
  • First Online:
Applications of Topological Methods in Molecular Chemistry

Part of the book series: Challenges and Advances in Computational Chemistry and Physics ((COCH,volume 22))

Abstract

Chemical graph theory (CGT) starts by defining matrices that represent the molecular graph then proceed to extract numbering-independent matrix invariants to be used as molecular descriptors in empirical quantitative structure to activity (or property) relationships (QSAR/QSPR). Two proposed matrix representations of molecular structure are presented in this chapter as alternatives to simple connectivity molecular graphs. Firstly, it is proposed to use a more “nuanced” connectivity matrix by weighing the “ones” entered in a CGT molecular graph matrix by the bond critical point electron densities associated with each bond path to yield what we term the “electron density-weighted adjacency/connectivity matrices (EDWAM/EDWCM)”. In a second approach, it is proposed to use the localization and delocalization indices of the quantum theory of atoms in molecules (QTAIM) to construct a richer representation of the molecular graph, a “fuzzy” graph, whereby an edge exists between any two atoms (measured by the delocalization index between them) whether they share a bond path or not. Such a fuzzy graph is represented by what we term “electron localization-delocalization matrix (LDM)”. We show that the LDM representations of a series of molecules provide a powerful tool for robust QSAR/QSPR modeling.

The development of chemistry has both led to, and been made possible by, the evolution of certain primary concepts. These concepts, without which there would be neither correlation nor prediction of the observations of descriptive chemistry, are: (1) the existence of atoms of functional groupings of atoms in molecules as evidenced by characteristic sets of properties; (2) the concept of bonding; and (3) the associated concepts of molecular structure and molecular shape. These concepts logically (but not historically) are consequences of fundamental topological properties of the charge distribution (electronic and nuclear) in a molecular system. In terms of the Born-Oppenheimer approximation the electronic distribution ρ( r ) is the scalar field defined in the real three-dimensional space with Euclidean metric. The universal topological properties of ρ( r ) are characterized by its gradient field ∇ ρ( r ) [1].

I.S. Dmitriev (1981)

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 349.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 449.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 449.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Dmitriev IS (1981) Molecules without chemical bonds (English Translation). Mir Publishers, Moscow

    Google Scholar 

  2. Balaban AT (1976) Chemical applications of graph theory. Academic Press, New York

    Google Scholar 

  3. Balaban AT (1985) Applications of graph theory in chemistry. J Chem Inf Comput Sci 25:334–343

    Article  CAS  Google Scholar 

  4. Hall LH, Kier LB (1976) Molecular connectivity in chemistry and drug research. Academic Press, Boston

    Google Scholar 

  5. Bonchev D, Rouvray DH (1991) Chemical graph theory: introduction and fundamentals. OPA, Amsterdam

    Google Scholar 

  6. Balasubramanian K (1994) Integration of graph theory and quantum chemistry for structure-activity relationship. SAR & QSAR Eviron Res 2:59–77

    Article  CAS  Google Scholar 

  7. Diudea MD, Gutman I, Lorentz J (1999) Molecular topology. Nova Science Publishers Inc, Hauppauge NY

    Google Scholar 

  8. Janezić D, Milicević A, Nikolić S, Trinajstić N (2007) Graph theoretical matrices in chemistry. In: Mathematical chemistry monographs, vol 3. University of Kragujevac, Kragujevac

    Google Scholar 

  9. Todeschini R, Consonni V (2009) Molecular descriptors for chemoinformatics, 2nd Edn, vols. I and II). Wiley-VCH Weinheim, Weinheim

    Google Scholar 

  10. Bader RFW (1990) Atoms in molecules: a quantum theory. Oxford University Press, Oxford

    Google Scholar 

  11. Popelier PLA (2000) Atoms in molecules: an introduction. Prentice Hall, London

    Book  Google Scholar 

  12. Matta CF, Boyd RJ (eds) (2007) The quantum theory of atoms in molecules: from solid state to DNA and drug design. Wiley-VCH, Weinheim

    Google Scholar 

  13. Bader RFW (1998) A bond path: a universal indicator of bonded interactions. J Phys Chem A 102:7314–7323

    Article  CAS  Google Scholar 

  14. Bader RFW (2009) Bond paths are not chemical bonds. J Phys Chem A 113:10391–10396

    Article  CAS  Google Scholar 

  15. Martín-Pendás A, Francisco E, Blanco MA, Gatti C (2007) Bond paths as privileged exchange channels. Chem Eur J 13:9362–9371

    Google Scholar 

  16. Runtz GR, Bader RFW, Messer RR (1977) Definition of bond paths and bond directions in terms of the molecular charge distribution. Can J Chem 55:3040–3045

    Article  CAS  Google Scholar 

  17. Keith TA, Bader RFW, Aray Y (1996) Structural homeomorphism between the electron density and the virial field. Int J Quantum Chem 57:183–198

    Article  CAS  Google Scholar 

  18. Keith TA (2015) AIMAll/AIMStudio. http://aim.tkgristmill.com/

  19. Fradera X, Austen MA, Bader RFW (1999) The Lewis model and beyond. J Phys Chem A 103:304–314

    Article  CAS  Google Scholar 

  20. Matta CF (2014) Modeling biophysical and biological properties from the characteristics of the molecular electron density, electron localization and delocalization matrices, and the electrostatic potential. J Comput Chem 35:1165–1198

    Article  CAS  Google Scholar 

  21. Sumar I, Ayers PW, Matta CF (2014) Electron localization and delocalization matrices in the prediction of pK a’s and UV-wavelengths of maximum absorbance of p-benzoic acids and the definition of super-atoms in molecules. Chem Phys Lett 612:190–197

    Article  CAS  Google Scholar 

  22. Timm MJ, Matta CF, Massa L, Huang L (2014) The localization-delocalization matrix and the electron density-weighted connectivity matrix of a finite graphene flake reconstructed from kernel fragments. J Phys Chem A 118:11304–11316

    Article  CAS  Google Scholar 

  23. Matta CF (2014) Localization-delocalization matrices and electron density-weighted adjacency matrices: new electronic fingerprinting tools for medicinal computational chemistry. Future Med Chem 6:1475–1479

    Article  CAS  Google Scholar 

  24. Dittrich B, Matta CF (2014) Contributions of charge-density research to medicinal chemistry. Int U Cryst J (IUCrJ) 1:457–469

    Article  CAS  Google Scholar 

  25. Sumar I, Cook R, Ayers PW, Matta CF (2015) AIMLDM: a program to generate and analyze electron localization–delocalization matrices (LDMs). Comput Theor Chem 1070:55–67

    Article  CAS  Google Scholar 

  26. White D, Wilson RC (2008) Parts-based generative models for graphs. In: 19th International Conference on Pattern Recognition (ICPR 2008), pp 1–4

    Google Scholar 

  27. Pye CC, Poirier RA (1998) Graphical approach for defining natural internal coordinates. J Comput Chem 19:504–511

    Article  CAS  Google Scholar 

  28. Pye CC (1997) Applications of optimization to quantum chemistry, PhD Thesis. Memorial University of Newfoundland, Saint John’s (NF), Canada

    Google Scholar 

  29. Müller AMK (1984) Explicit approximate relation between reduced two- and one-particle density matrices. Phys Lett A 105:446–452

    Article  Google Scholar 

  30. Massa L (2014) Personal communication

    Google Scholar 

  31. Picard RR, Cook RD (1984) Cross-validation of regression models. J Am Stat Assoc 79:575–583

    Article  Google Scholar 

  32. Lide DR (2007–2008) CRC handbook of chemistry and physics, 88th Edn. CRC Press

    Google Scholar 

  33. Lide DR (2006) CRC handbook of chemistry and physics, 87th Edn. CRC Press

    Google Scholar 

  34. Jover J, Bosque R, Sales J (2008) QSPR prediction of pK a for benzoic acids in different solvents. QSAR Combin Sci 27:563–581

    Article  CAS  Google Scholar 

  35. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev B 136:864–871

    Article  Google Scholar 

  36. Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. Oxford University Press, Oxford

    Google Scholar 

  37. Guo H-B, He F, Gu B, Liang L, Smith JC (2012) Time-dependent density functional theory assessment of UV absorption of benzoic acid derivatives. J Phys Chem A 116:11870–11879

    Article  CAS  Google Scholar 

  38. Pavia DL, Lampman GM, Kriz GS, Vyvyan JR (2009) Introduction to spectroscopy, 4th edn. Brooks/Cole Cengage Learning, Belmont, CA, USA

    Google Scholar 

  39. Kamath BV, Mehta JD, Bafna SL (1975) Ultraviolet absorption spectra: some substituted benzoic acids. J Appl Chem Biotechnol 25:743–751

    Article  CAS  Google Scholar 

  40. Krygowski TM, Szatylowicz H, Stasyuk OA, Dominikowska J, Palusiak M (2014) Aromaticity from the viewpoint of molecular geometry: application to planar systems. Chem Rev 114:6383–6422

    Article  CAS  Google Scholar 

  41. Krygowski TM, Stepien BT (2005) σ- and π-electron delocalization: focus on substituent effects. Chem Rev 105:3482–3512

    Article  CAS  Google Scholar 

  42. Krygowski TM, Cyranski MK (2001) Structural aspect of aromaticity. Chem Rev 101:1385–1419

    Article  CAS  Google Scholar 

  43. Kruszewski J, Krygowski TM (1972) Definition of aromaticity basing on the harmonic oscillator model. Tetrahedron Lett 3839–3842

    Google Scholar 

  44. Chen Z, Wannere CS, Corminboeuf C, Puchta R, Schleyer PvR (2005) Nucleus-independent chemical shifts (NICS) as an aromaticity criterion. Chem Rev 105:3842–3888

    Article  CAS  Google Scholar 

  45. Schleyer PvR, Manoharan M, Wang Z-X, Kiran B, Jiao H, Puchta R, Hommes NJRVE (2001) Dissected nucleus-independent chemical shift analysis of π-aromaticity and antiaromaticity. Org Lett 3:2465–2468

    Google Scholar 

  46. Schleyer PvR, Maerker C, Dransfeld A, Jiao H, Hommes NJRVE (1996) Nucleus-Independent chemical shifts: a simple and efficient aromaticity probe. J Am Chem Soc 118:6317–6318

    Google Scholar 

  47. Memory JD, Wilson NK (1982) NMR of aromatic compounds. Wiley, New York

    Google Scholar 

  48. Mitchell RH (2001) Measuring aromaticity by NMR. Chem Rev 101:1301–1315

    Article  CAS  Google Scholar 

  49. Gomes JANF, Mallion RB (2001) Aromaticity and ring currents. Chem Rev 101:1349–1383

    Article  CAS  Google Scholar 

  50. Keith TA, Bader RFW (1993) Topological analysis of magnetically induced molecular current distributions. J Chem Phys 99:3669–3682

    Article  CAS  Google Scholar 

  51. Keith TA, Bader RFW (1996) Use of electron charge and current distributions in the determination of atomic contributions to magnetic properties. Int J Quantum Chem 60:373–379

    Article  Google Scholar 

  52. Badger GM (1969) Aromatic character and aromaticity. Cambridge University Press, Cambridge

    Google Scholar 

  53. Slayden SW, Liebman JF (2001) The energetics of aromatic hydrocarbons: an experimental thermochemical perspective. Chem Rev 101:1541–1566

    Article  CAS  Google Scholar 

  54. Cyranski MK (2005) Energetic aspects of cyclic & σ-electron delocalization: Evaluation of the methods of estimating aromatic stabilization energies. Chem Rev 105:3773–3811

    Article  CAS  Google Scholar 

  55. Sivaramakrishnan R, Tranter RS, Brezinsky K (2005) Ring conserved isodesmic reactions: a new method for estimating the heats of formation of aromatics and PAHs. J Phys Chem A 109:1621–1628

    Article  CAS  Google Scholar 

  56. Poater J, Fradera X, Duran M, Solà M (2003) The delocalization index as an electronic aromaticity criterion: application to a series of planar polycyclic aromatic hydrocarbons. Chem Eur J 9:400–406

    Article  CAS  Google Scholar 

  57. Poater J, Fradera X, Duran M, Solà M (2003) An insight into local aromaticities of polycyclic aromatic hydrocarbons and fullerenes. Chem Eur J 9:1113–1122

    Article  CAS  Google Scholar 

  58. Matta CF, Hernández-Trujillo J (2005) Bonding in polycyclic aromatic hydrocarbons in terms of the the electron density and of electron delocalization. J Phys Chem A 107:7496–7504 (Correction: J Phys Chem A (2005) 109:10798)

    Google Scholar 

  59. Matito E, Duran M, Solà M (2005) The aromatic fluctuation index (FLU): a new aromaticity index based on electron delocalization. J Chem Phys 122:014109

    Article  Google Scholar 

  60. Poater J, Duran M, Solà M, Silvi B (2005) Theoretical evaluation of electron delocalization in aromatic molecules by means of atoms in molecules (AIM) and electron localization function (ELF) topological approaches. Chem Rev 105:3911–3947

    Article  CAS  Google Scholar 

  61. Portella G, Poater J, Bofill JM, Alemany P, Solà M (2005) Local aromaticity of [n]acenes, [n]phenacenes, and [n]helicenes (n = 1–9). J Org Chem 70:2509–2521

    Article  CAS  Google Scholar 

  62. Matito E, Poater J, Solà M (2007) Aromaticity analyses by means of the quantum theory of atoms in molecules. In: Matta CF (ed) The quantum theory of atoms in molecules: from solid state to DNA and drug design. Wiley-VCH, Weinheim, pp 399–423

    Chapter  Google Scholar 

  63. Firme CI, Galembeck SE, Antunes OAC, Esteves PM (2007) Density, degeneracy, delocalization-based index of aromaticity (D3BIA). J Braz Chem Soc 18:1397–1404

    Article  CAS  Google Scholar 

  64. Howard ST, Krygowski TM (1997) Benzenoid hydrocarbon aromaticity in terms of charge density descriptors. Can J Chem 75:1174–1181

    Article  CAS  Google Scholar 

  65. Suresh CH, Gadre SR (1999) Clar’s aromatic sextet theory revisited via molecular electrostatic potential topography. J Org Chem 64:2505–2512

    Article  CAS  Google Scholar 

  66. Cyranski MK, Stepien BT, Krygowski TM (2000) Global and local aromaticities of linear and angular polyacenes. Tetrahedron 56:9663–9667

    Article  CAS  Google Scholar 

  67. Palusiak M, Krygowski TM (2007) Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings. Chem Eur J 13:7996–8006

    Article  CAS  Google Scholar 

  68. Mandado M, Gonzalez Moa MJ, Mosquera RA (2008) Aromaticity: exploring basic chemical concepts with the quantum theory of atoms in molecules. Nova Science Publishers, Inc., New York

    Google Scholar 

  69. Ebrahimi AA, Ghiasi R, Foroutan-Nejad C (2010) Topological characteristics of the ring critical points and the aromaticity of groups IIIA to VIA hetero-benzenes. J Mol Struct (THEOCHEM) 941:47–52

    Article  CAS  Google Scholar 

  70. Nigam S, Majumder C (2011) Aromaticity: from benzene to atomic clusters. In: Aromaticity and metal clusters. Chattaraj PK (Ed.), CRC Press, New York

    Google Scholar 

  71. Krygowski TM, Ciesielski A, Bird CW, Kotschy A (1995) Aromatic character of the benzene ring present in various topological environments in benzenoid hydrocarbons. Nonequivalence of indices of aromaticity. J Chem Inf Comput Sci 35:203–210

    Article  CAS  Google Scholar 

  72. Sumar I, Cook R, Ayers PW, Matta CF (2016) Aromaticity of rings-in-molecules (RIMs) from electron localization-delocalization matrices (LDMs). Phys Scripta 91:013001 (pp 13)

    Google Scholar 

  73. Cook R, Sumar I, Ayers PW, Matta CF (2015) Aromaticity of rings-in-molecules (RIMs) from electron localization-delocalization matrices (LDMs) from self-organized maps. In preparation

    Google Scholar 

  74. Mager PP (1984) Multidimensional pharmacochemistry: design of safer drugs. Academic Press Inc, London

    Google Scholar 

  75. Kier LB, Hall LH, Frazer JW (1991) An index of electrotopological state for atoms in molecules. J Math Chem 7:229–241

    Article  CAS  Google Scholar 

  76. Attwood TK, Parry-Smith DJ (1999) Introduction to bioinformatics. Prentice Hall, London

    Google Scholar 

  77. Doucet J-P, Weber J (1996) Computer-aided molecular design: theory and applications. Academic Press, ltd, London

    Google Scholar 

  78. Carbó R, Leyda L, Arnau M (1980) How similar is a molecule to another? an electron density measure of similarity between two molecular structures. Int J Quantum Chem 17:1185–1189

    Article  Google Scholar 

  79. Carbó-Dorca R, Mezey PGE (1996) Advances in molecular similarity, vol 1. Jai Press Inc, London

    Google Scholar 

  80. Carbó-Dorca R, Mezey PGE (1998) Advances in molecular similarity, vol 2. Jai Press Inc, London

    Google Scholar 

  81. Carbó-Dorca R, Robert D, Amat L, Gironés X,  Besalú E (2000) Molecular quantum similarity in QSAR and drug design. Springer, Berlin

    Google Scholar 

  82. Bonaccorsi R, Scrocco E, Tomasi J (1970) Molecular SCF calculations for the ground state of some three-membered ring molecules: (CH2)3, (CH2)2NH, (CH2)2NH2 +, (CH2)2O, (CH2)2S, (CH)2CH2, and N2CH2. J Chem Phys 52:5270–5284

    Article  CAS  Google Scholar 

  83. Petrongolo C, Tomasi J (1975) The use of electrostatic molecular potential in quantum pharmacology. 1. Ab initio results. Int J Quantum Chem Quantum Biol Symp 2:181–190

    Google Scholar 

  84. Bonaccorsi R, Scrocco E, Tomasi J (1976) Group contributions to electrostatic molecular potential. J Am Chem Soc 98:4049–4054

    Article  CAS  Google Scholar 

  85. Tomasi J (1981) Use of the electrostatic potential as a guide to understanding molecular properties. In: Truhlar DG, Politzer P (eds) Chemical applications of atomic and molecular electrostatic potentials. reactivity, structure, scattering, and energetics of organic, inorganic, and biological systems. Plenum Press, New York

    Google Scholar 

  86. Tomasi J, Cappelli C, Mennucci B, Cammi R (2010) From molecular electrostatic potentials to solvations models and ending with biomolecular photophysical processes. In: Matta CF (ed) Quantum biochemistry: electronic structure and biological activity, vol 1. Wiley-VCH, Weinheim, pp 131–170

    Chapter  Google Scholar 

  87. Truhlar DG, Politzer P (eds) (1981) Chemical applications of atomic and molecular electrostatic potentials. reactivity, structure, scattering, and energetics of organic, inorganic, and biological systems. Plenum Press, New York

    Google Scholar 

  88. Murray JS, Politzer P (1998) Electrostatic potentials: chemical applications. In: Schleyer PvR (ed) Encyclopedia of computational chemistry. Wiley, Chichester, UK

    Google Scholar 

  89. Politzer P, Murray JS (2007) Molecular electrostatic potentials and chemical reactivity. Reviews in computational chemistry. Wiley, Hoboken, NJ

    Google Scholar 

  90. Gadre SR, Kulkarni SA, Suresh CH, Shrivastava IH (1995) Basis set dependence of molecular electrostatic potential topography: a case study of substituted benzenes. Chem Phys Lett 239:273–281

    Article  CAS  Google Scholar 

  91. Suresh CH, Gadre SR (1998) Novel electrostatic approach to substituent constants: doubly substituted benzenes. J Am Chem Soc 120:7049–7055

    Article  CAS  Google Scholar 

  92. Gadre SR (1999) Topography of atomic and molecular scalar fields. Computational chemistry: reviews of current trends. World Scientific, Singapore, pp 1–53

    Google Scholar 

  93. Gadre SR, Shirsat RN (2000) Electrostatics of atoms and molecules. Universities Press, Hyderabad

    Google Scholar 

  94. Roy D, Balanarayan P, Gadre SR (2008) An appraisal of Poincaré-Hopf relation and application to topography of molecular electrostatic potentials. J Chem Phys 129:174103

    Article  CAS  Google Scholar 

  95. Cook R (2015) (in preparation)

    Google Scholar 

  96. Babić-Samardzija K, Lupu C, Hackerman N, Barron AR, Luttge A (2005) Inhibitive properties and surface morphology of a group of heterocyclic diazoles as inhibitors for acidic iron corrosion. Langmuir 21:12187–12196

    Google Scholar 

  97. Popelier PLA (2010) Developing Quantum Topological Molecular Similarity (QTMS). In: Matta CF (ed) Quantum biochemistry: electronic structure and biological activity. Wiley-VCH, Weinheim, pp 669–691

    Google Scholar 

  98. Harding AP, Wedge DC, Popelier PLA (2009) pK a prediction from “quantum chemical topology” descriptors. J Chem Inf Mod 49:1914–1924

    Article  CAS  Google Scholar 

  99. Popelier PLA, Chaudry UA, Smith PJ (2002) Quantum topological molecular similarity. Part 5. Further development with an application to the toxicity of polychlorinated dibenzo-p-dioxins (PCDDs). J Chem Soc Perkin Trans 2:1231–1237

    Article  Google Scholar 

  100. O’Brien SE, Popelier PLA (2002) Quantum topological molecular similarity. Part 4. A QSAR study of cell growth inhibitory properties of substituted (E)-1-phenylbut-1-en-3-ones. J Chem Soc Perkin Trans 2:478–483

    Article  Google Scholar 

  101. O’Brien SE, Popelier PLA (2001) Quantum molecular similarity. 3. QTMS descriptors. J Chem Inf Comput Sci 41:764–775

    Article  Google Scholar 

  102. O’Brien SE, Popelier PLA (1999) Quantum molecular similarity. Part 2: the relation between properties in BCP space and bond length. Can J Chem 77:28–36

    Article  Google Scholar 

  103. Popelier PLA (1999) Quantum molecular similarity. 1. BCP space. J Phys Chem A 103:2883–2890

    Article  CAS  Google Scholar 

  104. Cook R,. Sumar I, Ayers PW, Matta CF (2016) Electron localization-delocalization matrices (LDMs): theory and applications. Springer

    Google Scholar 

Download references

Acknowledgments

The authors thank Dr. Todd A. Keith, Professor Lou Massa, Dr. Nenad Trinajstić, Dr. Sonja Nikolić, and Mr. Matthew J. Timm for helpful discussions. Financial support of this work was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC), Canada Foundation for Innovation (CFI), Saint Mary’s University, McMaster University, and Mount Saint Vincent University.

Author information

Authors and Affiliations

  1. Department of Chemistry and Physics, Mount Saint Vincent University, Halifax, NS, B3M 2J6, Canada

    Chérif F. Matta & Ismat Sumar

  2. Department of Chemistry, Dalhousie University, Halifax, NS, B3H 4J3, Canada

    Chérif F. Matta

  3. Department of Chemistry, Saint Mary’s University, Halifax, NS, B3H 3C3, Canada

    Chérif F. Matta & Ismat Sumar

  4. Department of Chemistry, McMaster University, Hamilton, ON, L8S 4L8, Canada

    Ismat Sumar & Paul W. Ayers

  5. TDA Research, Inc, 12345 W. 52nd Ave, Wheat Ridge, CO, 80033, USA

    Ronald Cook

Authors
  1. Chérif F. Matta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ismat Sumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ronald Cook
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Paul W. Ayers
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Chérif F. Matta , Ronald Cook or Paul W. Ayers .

Editor information

Editors and Affiliations

  1. LCC-CNRS, Toulouse, France

    Remi Chauvin

  2. LCC-CNRS, Toulouse, France

    Christine Lepetit

  3. Théorique, UMR 761, Laboratoire de Chimie, Paris, France

    Bernard Silvi

  4. CNRS/UPM, MONARIS UMR 8233 (LADIR + LM2N), Paris, France

    Esmail Alikhani

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Matta, C.F., Sumar, I., Cook, R., Ayers, P.W. (2016). Localization-Delocalization Matrices and Electron Density-Weighted Adjacency/Connectivity Matrices: A Bridge Between the Quantum Theory of Atoms in Molecules and Chemical Graph Theory. In: Chauvin, R., Lepetit, C., Silvi, B., Alikhani, E. (eds) Applications of Topological Methods in Molecular Chemistry. Challenges and Advances in Computational Chemistry and Physics, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-29022-5_3

Download citation

Publish with us

Policies and ethics

Search

Navigation