Skip to main content

Advertisement

SpringerLink
Log in

Pauling bond strength, bond length and electron density distribution

  • Original Paper
  • Published:
Physics and Chemistry of Minerals Aims and scope Submit manuscript

Abstract

The power law regression equation, <R(M–O)> = 1.46(<ρ(r c)>/r)−0.19, relating the average experimental bond lengths, <R(M–O)>, to the average accumulation of the electron density at the bond critical point, <ρ(r c)>, between bonded pairs of metal and oxygen atoms (r is the row number of the M atom), determined at ambient conditions for oxide crystals, is similar to the regression equation R(M–O) = 1.41(ρ(r c)/r)−0.21 determined for three perovskite crystals at pressures as high as 80 GPa. The pair are also comparable with the equation <R(M–O)> = 1.43(<s>/r)−0.21 determined for oxide crystals at ambient conditions and <R(M–O)> = 1.39(<s>/r)−0.22 determined for geometry-optimized hydroxyacid molecules that relate the geometry-optimized bond lengths to the average Pauling bond strength, <s>, for the M–O bonded interactions. On the basis of the correspondence between the equations relating <ρ(r c)> and <s> with bond length, it seems plausible that the Pauling bond strength might serve a rough estimate of the accumulation of the electron density between M–O bonded pairs of atoms. Similar expressions, relating bond length and bond strength hold for fluoride, nitride and sulfide molecules and crystals. The similarity of the expressions for the crystals and molecules is compelling evidence that molecular and crystalline M–O bonded interactions are intrinsically related. The value of <ρ(r c)> = r[(1.41)/<R(M–O)>]4.76 determined for the average bond length for a given coordination polyhedron closely matches the Pauling’s electrostatic bond strength reaching each the coordinating anions of the coordinated polyhedron. Despite the relative simplicity of the expression, it appears to be more general in its application in that it holds for the bulk of the M–O bonded pairs of atoms of the periodic table.

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
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Alkorta I, Rozas I, Elguero J (1998) Bond length electron density relationships: from covalent bonds to hydrogen bond interactions. Struct Chem 9(4):243–247

    Article  Google Scholar 

  • Altermatt D, Brown ID (1985) The automatic searching for chemical bonds in inorganic crystal structures. Acta Crystallogr B 41:240–244

    Article  Google Scholar 

  • Bader RFW (1990) Atoms in molecules. Oxford Science Publications, Oxford

    Google Scholar 

  • Bader RFW (2009) Bond paths are not chemical bonds. J Phys Chem A 113(38):10391–10396

    Article  Google Scholar 

  • Bartelmehs KL, Gibbs GV, Boisen MB (1989) Bond-length and bonded-radii variations in sulfide molecules and crystals containing main-group elements; a comparison with oxides. Am Mineral 74(5–6):620–626

    Google Scholar 

  • Baur WH (1970) Bond length variation and distorted coordination polyhedra in inorganic crystals. Transactions of the american crystallographic association, 6, pp 129–154. American Crystallographic Association

    Google Scholar 

  • Boisen MB, Gibbs GV, Zhang ZG (1988) Resonance bond numbers: a graph-theoretic study of bond length variations in silicate crystals. Phys Chem Minerals 15(4):409–415

    Article  Google Scholar 

  • Bragg WL (1937) Atomic structure of minerals. Cornell University Press, Ithaca

    Google Scholar 

  • Brown ID (2002) Topology and chemistry. Struct Chem 13(3–4):339–355

    Article  Google Scholar 

  • Brown ID, Shannon RD (1973) Empirical bond-strength-bond-length curves for oxides. Acta Crystallogr A 29(3):266–282

    Article  Google Scholar 

  • Buterakos LA, Gibbs GV, Boisen MB (1992) Bond length variation in hydronitride molecules and nitride crystals. Phys Chem Minerals 19(2):127–132

    Article  Google Scholar 

  • Byström A, Wilhelmi KA (1951) The crystal structure of (NH4)2Cr2O7. Acta Chem Scand 5:1003–1010

    Article  Google Scholar 

  • Castillo N, Robertson KN, Choi SC, Boyd RJ, Knop O (2008) Bond length and the electron density at the bond critical point: X–X, Z–Z, and C–Z bonds (X = Li–F, Z = Na–Cl). J Comput Chem 29(3):367–379

    Article  Google Scholar 

  • Clark JR, Appleman DE, Papike JJ (1969) Crystal-chemical characterization of clinopyroxenes based on eight new refinements. In: Papike JJ (ed) Msa special paper no. 2, pp 31–50

  • Demaison J, Császár AG (2012) Equilibrium co bond lengths. J Mol Struct 1023:7–14

    Article  Google Scholar 

  • Donnay G, Allmann R (1970) How to recognize O2−, OH−, and H2O in crystal structures determined by x-ray. Am Mineral 55:1003–1015

    Google Scholar 

  • Downs RT, Gibbs GV, Boisen MB Jr, Rosso KM (2002) A comparison of procrystal and ab initio model representations of the electron-density distributions of minerals. Phys Chem Minerals 29(5):369–385

    Article  Google Scholar 

  • Gatti C (1997) Topond96 user’s manual. CNR-CSRSRC, Milano

    Google Scholar 

  • Gibbs GV (1982) Molecules as models for bonding in silicates. Am Mineral 67(5–6):421–450

    Google Scholar 

  • 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. In: Cygan RT, Kubicki JD (eds) Molecular modeling theory: applications in the geosciences, 42. Mineralogical Society of America, Washington, DC, pp 345–381

    Google Scholar 

  • Gibbs GV, Cox DF, Rosso KM (2004) A connection between empirical bond strength and the localization of the electron density at the bond critical points of the Si-O bonds in silicates. J Phys Chem A 108(38):7643–7645

    Article  Google Scholar 

  • 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 Minerals 32(2):114–125

    Article  Google Scholar 

  • Gibbs GV, Downs RT, Cox DF, Ross NL, Prewitt CT, Rosso KM, Lippmann T, Kirfel A (2008a) Bonded interactions and the crystal chemistry of minerals: A review. Z Kristallogr 223:1–40

    Article  Google Scholar 

  • Gibbs GV, Downs RT, Cox DF, Rosso KM, Ross NL, Kirfel A, Lippmann T, Morgenroth W, Crawford TD (2008b) Experimental bond critical point and local energy density properties determined for Mn–O, Fe–O, and Co–O bonded interactions for tephroite, Mn2SiO4, fayalite, Fe2SiO4, and Co2SiO4 olivine and selected organic metal complexes: Comparison with properties calculated for non-transition and transition metal m-o bonded interactions for silicates and oxides. J Phys Chem A 112(37):8811–8823

    Article  Google Scholar 

  • Gibbs GV, Finger LW, Boisen MB (1987) Molecular mimicry of the bond length-bond strength variations in oxide crystals. Phys Chem Minerals 14(4):327–331

    Article  Google Scholar 

  • Gibbs GV, Ross NL, Cox DF, Rosso KM, Iversen BB, Spackman MA (2013) Bonded radii and the contraction of the electron density of the oxygen atom by bonded interactions. J Phys Chem A 117(7):1632–1640

    Article  Google Scholar 

  • Gibbs GV, Spackman MA, Boisen MB (1992) Bonded and promolecule radii for molecules and crystals. Am Mineral 77(7–8):741–750

    Google Scholar 

  • Gibbs GV, Wang D, Hin C, Ross NL, Cox DF, Crawford TD, Spackman MA, Angel RJ (2012) Properties of atoms under pressure: bonded interactions of the atoms in three perovskites. J Chem Phys 137(16):164313

    Article  Google Scholar 

  • Gibbs GV, Whitten AE, Spackman MA, Stimpfl M, Downs RT, Carducci MD (2003) An exploration of theoretical and experimental electron density distributions and Si O bonded interactions for the silica polymorph coesite. J Phys Chem B 107(47):12996–13006

    Article  Google Scholar 

  • Hoffmann R (1988) Solids and surfaces: a chemist’s view of bonding in extended structures. VCH Publishers, Inc., New York, p 142

    Google Scholar 

  • Knop O, Boyd RJ, Choi SC (1988) S–S bond lengths, or can a bond length be estimated from a single parameter. J Am Chem Soc 110(22):7299–7301

    Article  Google Scholar 

  • Nicoll JS, Gibbs GV, Boisen MB, Downs RT, Bartelmehs KL (1994) Bond length and radii variations in fluoride and oxide molecules and crystals. Phys Chem Minerals 20(8):617–624

    Article  Google Scholar 

  • Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. Oxford University Press, Oxford, p 333

    Google Scholar 

  • Pauling L (1929) The principles determining the crystal structure of complex ionic crystals. J Am Chem Soc 51:1010–1026

    Article  Google Scholar 

  • Pauling L (1947) Atomic radii and interatomic distances in metals. J Am Chem Soc 69(3):542–553

    Article  Google Scholar 

  • Pauling L (1948) The modern theory of valency. J Chem Soc (Resumed) 0(0):1461–1467

    Article  Google Scholar 

  • Pauling L (1960) The nature of the chemical bond and the structure of molecules and crystals: an introduction to modern structural chemistry. Cornell University Press, Ithaca

    Google Scholar 

  • Saunders VR, Dovesi R, Roetti C, Causa M, Harrison NM, Orlando R, Apra E (1998) Crystal98 user’s manual. University of Torino, Torino

    Google Scholar 

  • Shannon RD (1976) Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr A 32(5):751–767

    Article  Google Scholar 

  • Shannon RD, Prewitt CT (1969) Effective ionic radii in oxides and fluorides. Acta Cryst B25:925–946

    Article  Google Scholar 

  • Slater JC (1965) Quantum theory of molecules and solids: symmetry and energy bands in crystals. McGraw Hill, Inc., New York

    Google Scholar 

  • Smith JV (1953) Reexamination of the crystal structure of melilite. Am Mineral 38:643–661

    Google Scholar 

  • Smith VH, Absar I (1977) Basic concepts of quantum chemistry for electron density studies. Isr J Chem 16(2–3):87–102

    Article  Google Scholar 

  • Wang W-P, Parr RG (1977) Statistical atomic models with piecewise exponentially decaying electron densities. Phys Rev A 16(3):891

    Article  Google Scholar 

  • Zachariasen WH (1954) Crystal chemical studies of the 5f-series of elements. XXIII. On the crystal chemistry of uranyl compounds and of related compounds of transuranic elements. Acta Crystallogr 7:795–799

    Article  Google Scholar 

  • Zachariasen WH, Plettinger HA (1959) Crystal chemical studies of the 5f-series of elements. XXV. The crystal structure of sodium uranyl acetate. Acta Crystallogr 12:526–530

    Article  Google Scholar 

Download references

Acknowledgments

The work was supported in part by the National Science Foundation and the U.S. Department of Energy through grants to N.L.R. (Grant Nos. EAR-0738692 and EAR-1118691) and D.F.C. (Grant No. DEFG02-97ER14751). K.M.R. acknowledges support from US Department of Energy (DOE), Office of Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division. The bulk of this study was supported by a Virginia Tech University Distinguished Professor Virginia Travel Grant to G.V.G. together with a Jack Phillips Bequeath for generous support during his visit and collaboration with Mark Spackman at the School of Chemistry and Biochemistry, University of Western Australia in Australia and travel support from the Danish National Research Foundation for his visit and to participate in a symposium at the Department of Chemistry, Aarhus University in Denmark and his collaboration with Bo Iversen. G.V.G. also wishes to thank Prof. Vladimir Tsirelson, Head of the Quantum Chemistry Department at the Mendeleev University of Chemical Technology, Miusskaya, Moscow, Russia for bringing to his attention that the electron density distribution between the bonded carbon atoms of diamond is consistent with a power law rather than a exponential law relationship. Finally, we wish to thank the two reviewers of the manuscript who made a number of very important suggestions that definitely improved the manuscript. We are particularly grateful to Frank Hawthorne for suggesting a number of important changes in the text. The paper reads much better because of the reviewer’s efforts and suggestions.

Author information

Authors and Affiliations

  1. Department of Geosciences, Virginia Tech, Blacksburg, VA, 24061, USA

    G. V. Gibbs & N. L. Ross

  2. Department of Materials Science and Engineering, Virginia Tech, Blacksburg, VA, 24061, USA

    G. V. Gibbs

  3. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    G. V. Gibbs

  4. Department of Chemical Engineering, Virginia Tech, Blacksburg, VA, 24061, USA

    D. F. Cox

  5. Physical Sciences Division, Pacific Northwest National Laboratories, Richland, WA, 99352, USA

    K. M. Rosso

  6. Center for Materials Crystallography, Department of Chemistry and iNANO, Aarhus University, 8000, Aarhus, Denmark

    B. B. Iversen

  7. School of Chemistry and Biochemistry, University of Western Australia, Crawley, WA, 6009, Australia

    M. A. Spackman

Authors
  1. G. V. Gibbs
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. L. Ross
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. F. Cox
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. M. Rosso
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. B. B. Iversen
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M. A. Spackman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. V. Gibbs.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gibbs, G.V., Ross, N.L., Cox, D.F. et al. Pauling bond strength, bond length and electron density distribution. Phys Chem Minerals 41, 17–25 (2014). https://doi.org/10.1007/s00269-013-0619-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00269-013-0619-z

Keywords

Search

Navigation