Physics and Chemistry of Minerals

, Volume 32, Issue 3, pp 208–221 | Cite as

A mapping of the electron localization function for earth materials

  • G. V. Gibbs
  • D. F. Cox
  • N. L. Ross
  • T. D. Crawford
  • J. B. Burt
  • K. M. Rosso
Original papers


The electron localization function, ELF, generated for a number of geometry-optimized earth materials, provides a graphical representation of the spatial localization of the probability electron density distribution as embodied in domains ascribed to localized bond and lone pair electrons. The lone pair domains, displayed by the silica polymorphs quartz, coesite and cristobalite, are typically banana-shaped and oriented perpendicular to the plane of the SiOSi angle at ~0.60 Å from the O atom on the reflex side of the angle. With decreasing angle, the domains increase in magnitude, indicating an increase in the nucleophilic character of the O atom, rendering it more susceptible to potential electrophilic attack. The Laplacian isosurface maps of the experimental and theoretical electron density distribution for coesite substantiates the increase in the size of the domain with decreasing angle. Bond pair domains are displayed along each of the SiO bond vectors as discrete concave hemispherically-shaped domains at ~0.70 Å from the O atom. For more closed-shell ionic bonded interactions, the bond and lone pair domains are often coalesced, resulting in concave hemispherical toroidal-shaped domains with local maxima centered along the bond vectors. As the shared covalent character of the bonded interactions increases, the bond and lone pair domains are better developed as discrete domains. ELF isosurface maps generated for the earth materials tremolite, diopside, talc and dickite display banana-shaped lone pair domains associated with the bridging O atoms of SiOSi angles and concave hemispherical toroidal bond pair domains associated with the nonbridging ones. The lone pair domains in dickite and talc provide a basis for understanding the bonded interactions between the adjacent neutral layers. Maps were also generated for beryl, cordierite, quartz, low albite, forsterite, wadeite, åkermanite, pectolite, periclase, hurlbutite, thortveitite and vanthoffite. Strategies are reviewed for finding potential H docking sites in the silica polymorphs and related materials. As observed in an earlier study, the ELF is capable of generating bond and lone pair domains that are similar in number and arrangement to those provided by Laplacian and deformation electron density distributions. The formation of the bond and lone pair domains in the silica polymorphs and the progressive decrease in the SiO length as the value of the electron density at the bond critical point increases indicates that the SiO bonded interaction has a substantial component of covalent character.


Silica Tremolite Diopside Talc Dickite Pectolite Forsterite Hydrogen bonding SiO bond 


  1. Bader RFW, MacDougall PJ, Lau CDH (1984) Bonded and nonbonded charge concentrations and their relation to molecular geometry and reactivity. J Amer Chem Soc 106:1594–1605CrossRefGoogle Scholar
  2. Bader RFW, Essén H (1984) The characterizations of atomic interactions. J Chem Phys 80:1943–1960Google Scholar
  3. Bader RFW, MacDougall PJ (1985) Toward a theory of chemical reactivity based on charge density. J Amer Chem Soc 107:6788–6795CrossRefGoogle Scholar
  4. Bader RFW, Gillespie RJ, MacDougall PJ (1988) A physical basis for the VSEPR model of molecular geometry. J Amer Chem Soc 110:7329–7336CrossRefGoogle Scholar
  5. Bader RFW (1990) Atoms in molecules. Oxford Science Publications Oxford, pp 1–438Google Scholar
  6. Bader RFW, Johnson S, Tang TH, Popelier PLA (1996) The electron pair. J Phys Chem 100:15398–15415CrossRefGoogle Scholar
  7. Bader RFW (1998) A bond path: a universal indicator of bonded interactions. J Phys Chem 100:15398-15415CrossRefGoogle Scholar
  8. Becke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and molecular systems. J Chem Phys 92:5397–5403CrossRefGoogle Scholar
  9. Boily JF (2003) AIM and ELF analyses and Gas phase acidities of some main group oxyanions (H2XO4, X = Cl, S, P, Si and Br, Se, As, Ge). J Phys Chem A 107:4276–4285CrossRefGoogle Scholar
  10. Bragg WL, Claringbull GF, Taylor WH (1965) Crystal structures of minerals. Cornell University Press, Ithaca, pp 1–409Google Scholar
  11. Brown GE, Gibbs GV (1969) The nature and variation in length of the Si-O and Al-O bonds in framework silicates. Amer Mineral 54:1044–1061Google Scholar
  12. Burdett JK, McCormick TA (1998) Electron localization in molecules and solids: The meaning of ELF. J Phys Chem A 102:6366–6372CrossRefGoogle Scholar
  13. Chesnut DB (2000) An electron localization function study of the lone pair. J Phys Chem A 104:11644–11650CrossRefGoogle Scholar
  14. Dera P, Prewitt CT, Stefanie J, Bish DL, Johnston CT (2003) Pressure–controlled polytypism in hydrous layered materials. Amer Mineral 88:1428–1435Google Scholar
  15. Downs JW (1995) The electron density distribution of coesite. J Phys Chem 99:6849–6856CrossRefGoogle Scholar
  16. Gibbs GV, Downs JW, Boisen MB Jr (1994) The elusive SiO bond vol 29: reviews in Mineralogy. Mineralogical Society of America pp 331–368Google Scholar
  17. Gibbs GV, Rosso KM, Teter DM Boisen MB, Bukowinski MST (1999) Model structures and properties of the electron density distribution for low quartz at pressure: a study of the SiO bond. J Mole Struct 485:13–25CrossRefGoogle Scholar
  18. Gibbs GV, Boisen MB, Rosso KM, Teter DM, Bukowinski MST (2000) Model structures and electron density distributions of the silica polymorph coesite at pressure: An assessment of OO bonded interactions. J Phys Chem B 104:10534–10542CrossRefGoogle Scholar
  19. Gibbs GV, Boisen MB, Beverly LL, Rosso KM (2001) A computational quantum chemical study of the bonded interactions in earth materials and structurally and chemically related molecules, Molecular modeling theory: applications in the geosciences. Reviews in Mineralogy and Geochemistry, vol 42, (eds) Cygan RT, Kubicki JD, Series Ed. J.J. Rosso Mineralogical Society of America, Washington, DC 345–382Google Scholar
  20. Gibbs GV, Cox DF, Crawford TD, Boisen MB, Lim M (2002) A mapping of the electron localization function for the silica polymorphs: evidence for domains of electron pairs and sites of potential electrophilic attack. Phys Chem Miner 29:307–318CrossRefGoogle Scholar
  21. Gibbs GV, Cox DF, Boisen MB, Downs RT, Ross NL (2003a) The electron localization function: a tool for locating favorable proton docking sites in the silica polymorphs. Phys Chem Miner 30:305–316Google Scholar
  22. Gibbs GV, Whitten EW, Spackman MA, Stimp M, Downs RT, Carducci MD (2003b) An exploration of theoretical and experimental electron density distributions and SiO bonded interactions for the silica polymorph coesite. J Phys Chem B 108:12996–13006CrossRefGoogle Scholar
  23. Gibbs GV, Cox DF, Ross NL (2004a) A modelling of the structure and favorable H-docking sites and defects for the high pressure silica polymorphs stishovite. Phys Chem Miner 31:232–239CrossRefGoogle Scholar
  24. Gibbs GV, Cox DF, Rosso KM (2004b) A connection between empirical bond strength and the localization of the electron density at the bond critical points of the SiO bonds in silicates. J Phys Chem A 108:7643–7645CrossRefGoogle Scholar
  25. Gibbs GV, Cox DF, Rosso KM, Kirfel A, Lippmann T, Blaha P, Schwarz K (2005) Experimental and theoretical bond critical point properties for model electron density distributions for earth materials. Phys Chem Miner (in press)Google Scholar
  26. Gillespie RJ (1970) The valence - shell electron pair model of molecular geometry. J Chem Edu 47:18–23Google Scholar
  27. Gillespie RJ, Johnson SA (1997) Study of bond angles and bond lengths in disiloxane and related molecules in terms of the topology of the electron density and its Laplacian. Inorg Chem 36:3031-3039CrossRefPubMedGoogle Scholar
  28. Jeffrey GA (1997) An introduction to hydrogen bonding. Oxford University Press, New York, pp 1–303Google Scholar
  29. Kihara K (1990) An X-ray study of the temperature dependence of the quartz structure natural, T=298 K. Eur J Mineral 2:63–77Google Scholar
  30. Kirfel A, Krane HG, Blaha P, Scwartz K, Lippmann T (2001) Electron density distribution in stishovite, SiO2: a high energy synchrotron radiation study. Acta Crystallogr A 57:663–677CrossRefPubMedGoogle Scholar
  31. Kirfel A, Lippmann T, Blaha P, Schwarz K, Cox DF, Rosso KM, Gibbs GV (in press) Electron density distribution and bond critical point properties for forsterite, Mg2SiO4, determined with high energy synchrotron radiation data. Phys Chem MinerGoogle Scholar
  32. Koch-Müller M, Fei Y, Hauri E, Liu Z (2001) Location and qualitative analysis of OH in coesite. Phys Chem Miner 28:693–705CrossRefGoogle Scholar
  33. Kresse G, Furthmüller J (1999) Vienna Ab-initio simulation package. Technische Universität Wien, Wien 1:1–120Google Scholar
  34. Kresse G, Hafner J (1953) Ab initio molecular dynamics for liquid metals. Phys Rev B 47:558–561CrossRefGoogle Scholar
  35. Kresse G, Hafner J (1994) Ab initio molecular-dynamics simulation of the liquid-metal amorphous-semiconductor transition in germanium. Phys Rev B 49:14251–14269CrossRefGoogle Scholar
  36. Kresse G, Furthmüller J (1996b) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54:11169–11186Google Scholar
  37. Lewis GN (1966) Valence and the structure of atoms and molecules. Dover Press, New YorkGoogle Scholar
  38. Monkhorst HJ, Pack JD (1976) Special points for Brillouin zone integrations. Phys Rev B 13:5188–5192CrossRefGoogle Scholar
  39. Pauling L (1960) The nature of the chemical bond, 3rd edn. Cornell University Press, IthacaGoogle Scholar
  40. Pawley AR, McMillian PF, Holloway JR (1963) Hydrogen in stishovite with impurities for mantle water content. Struct Chem 261:1024–1026Google Scholar
  41. Prewitt CT (1967) Refinement of the structure of pectolite, Ca2NaHSi3O9. Zeits Krist 125:298–316Google Scholar
  42. Savin A, Becke AD, Flad J, Nesper R, Preuss H, von Scnering HG (1991) A new look at electron localization. Angew Chem Ind Ed Engl 30:409–412CrossRefGoogle Scholar
  43. Savin A, Jepsen O, Flad J, Andersen OK, Preuss H, von Scnering HG (1992) Electron localization in solid state structures of the elements: the diamond structure. Angew Chem Ind Ed Engl 31:187–188CrossRefGoogle Scholar
  44. Savin A, Nesper R, Wengert S, Fässler TF (1997) ELF: The electron localization function. Angew Chem Ind Ed Engl 36:1808–1832CrossRefGoogle Scholar
  45. Silvi B, Savin A (1994) Classification of chemical bonds based on topological analysis of electron localization functions. Nature Lond 371:683–686CrossRefGoogle Scholar
  46. Silvi B, Savin A, Wagner FR (1997) The nature of silicon oxygen bonds in silica polymorphs. In: Silvi B, D’Arco P (eds) Modeling of minerals and silicated materials. Kluwer Academic Publishers, Dortrecht, pp 179–199Google Scholar
  47. Slater JC (1964) Atomic radii in crystals. J Chem Phys 41:3199-3204CrossRefGoogle Scholar
  48. Smyth JR, Swope RJ, Pawley AR (1995) H in rutile type compounds: II Crystal chemistry of Al substitutions in H–bearing stishovite. Amer Mineral 80:454–4560Google Scholar
  49. Takéuchi Y, Kudoh Y (1977) Hydrogen bonding and cation ordering in Magnet Cove pectolite. Zeits Krist 146:281–292Google Scholar
  50. Terriberry TB, Cox DF, Bowman DA (2002) A tool for the interactive 3D visualization of electronic structure in molecules and solids. Comput Chem 26:313–319CrossRefPubMedGoogle Scholar
  51. Trout BL, Parrinello M (1999) Analysis of the dissolution of H2O using first-principles molecular dynamics. J Phys Chem B 103:7340–7345CrossRefGoogle Scholar
  52. Vanderbilt D (1990) Soft self–consistent psuedopotentials in a generalized eigenvalue formalism. Phys Rev B 41:7892–7895CrossRefGoogle Scholar
  53. Warren BE (1927) The structure of tremolite, H2Ca2Mg5(SiO3)8. Zeits Krist 72:42–57Google Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • G. V. Gibbs
    • 1
  • D. F. Cox
    • 2
  • N. L. Ross
    • 3
  • T. D. Crawford
    • 4
  • J. B. Burt
    • 3
  • K. M. Rosso
    • 5
  1. 1.Departments of Geosciences, Materials Science and Engineering and MathematicsVirginia TechBlacksburgUSA
  2. 2.Department of Chemical EngineeringVirginia TechBlacksburgUSA
  3. 3.Department of GeosciencesVirginia TechBlacksburgUSA
  4. 4.Department of ChemistryVirginia TechBlacksburgUSA
  5. 5.W.R.Wiley Environmental Molecular Sciences LaboratoryPacific Northwest National LaboratoryRichland

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