Abstract
A bond path being a line of maximum electron density linking attractors of two atoms is often applied in various studies as a criterion of the existence of numerous interactions such as for example hydrogen, halogen or pnicogen bond. It covers cases of atom-atom energetically stabilized links, from weak van der Waals interactions, through stronger Lewis acid–Lewis base interactions up to covalent bonds. The location of bond paths also allows interpreting mechanisms of interactions and, in general, of chemical reactions. The Quantum Theory of Atoms in Molecules (QTAIM) results are mainly presented here; however they are supported by other approaches as, for example, the Natural Bond Orbitals (NBO) method or the σ-hole concept. The most important orbital-orbital interactions determined from the NBO method and characterizing different types of interactions are presented. The analysis of the distribution of the electron charge density is also performed here for numerous systems; this is shown that the regions of the concentration and depletion of the electron density coincide with the regions of the negative and positive regions of the electrostatic potential. The role of the analysis of the laplacian of the electron density is shown on the basis of numerous interactions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Tsirelson VG, Ozerov RP (1996) Electron density and bonding in crystals. Institute of Physics, Bristol, Philadelphia
Coppens P (1997) X-Ray charge densities and chemical bonding. Oxford University Press, IUCr
Koritszansky TS, Coppens P (2001) Chemical applications of X-ray charge density analysis. Chem Rev 101:1583–1638
Bader RFW (1985) Atoms in molecules. Acc Chem Res 18:9–15
Bader RFW (1990) Atoms in molecules, a quantum theory. Oxford University Press, Oxford
Popelier P (2000) Atoms in molecules. an introduction. Prentice Hall, Pearson Education Limited, Harlow
Matta C, Boyd RJ (ed) (2007) Quantum theory of atoms in molecules: recent progress in theory and application. Wiley-VCH
Dunitz JD (1979) X-Ray analysis and the structure of organic molecules. Cornell University Press, Ithaca, p 395
Bader RFW (1998) A bond path: a universal indicator of bonded interactions. J Phys Chem A 102:7314–7323
Bader RFW (2009) Bond paths are not chemical bonds. J Phys Chem A 113:10391–10396
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
Keith TA, Bader RFW, Aray Y (1996) Structural homeomorphism between the electron density and the virial field. Int J Quantum Chem 57:183–198
Gatti C, Cargnoni F, Bertini L (2003) Chemical information from the source function. J Comput Chem 24:422–436
Gatti C (2005) Chemical bonding in crystals: new directions. Z Kristallogr 220:399–457
Stalke D (2011) Meaningful structural descriptors from charge density. Chem Eur J 17:9264–9278
Rozas I, Alkorta I, Elguero J (2000) Behavior of ylides containing N, O, and C atoms as hydrogen bond acceptors. J Am Chem Soc 122:1154–11161
Grabowski SJ (2011) What is the covalency of hydrogen bonding? Chem Rev 11:2597–2625
Cremer D, Kraka E (1984) A description of the chemical-bond in terms of local properties of electrodensity and energy. Croat Chem Acta 57:1259–1281
Jenkins S, Morrison I (2000) The chemical character of the intermolecular bonds of seven phases of ice as revealed by ab initio calculation of electron densities. Chem Phys Lett 317:97–102
Grabowski SJ (2001) Ab initio calculations on conventional and unconventional hydrogen bonds—study of the hydrogen bond strength. J Phys Chem A 105:10739–10746
Weinhold F, Landis C (2005) Valency and bonding, a natural bond orbital donor—acceptor perspective. Cambridge University Press
Reed AE, Curtiss LA, Weinhold F (1988) Intermolecular Interactions from a natural bond orbital, donor-acceptor viewpoint. Chem Rev 88:899–926
Alabugin IV, Manoharan M, Peabody S, Weinhold F (2003) Electronic basis of improper hydrogen bonding: a subtle balance of hyperconjugation and rehybridization. J Am Chem Soc 125:5973–5987
Weinhold F, Klein R (2012) What is a hydrogen bond? mutually consistent theoretical and experimental criteria for characterizing H-bonding interactions. Mol Phys 110:565–579
Murray JS, Lane P, Politzer P (2009) Expansion of the σ-hole concept. J Mol Model 15:723–729
Politzer P, Murray JS, Clark T (2010) Halogen bonding: an electrostatically-driven highly directional noncovalent interaction. Phys Chem Chem Phys 12:7748–7758
Politzer P, Murray JS, Clark T (2013) Halogen bonding and other σ-hole interactions: a perspective. Phys Chem Chem Phys 15:11178–11189
Boys SF, Bernardi F (1970) The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors. Mol Phys 19:553–566
Nyburg SC, Faerman CH (1985) A revision of van der Waals atomic radii for molecular crystals: nitrogen, oxygen, fluorine, sulfur, chlorine, selenium, bromine, and iodine bonded to carbon. Acta Crystallogr B 41:274–279
Zordan F, Brammer L, Sherwood P (2005) Supramolecular chemistry of halogens: complementary features of inorganic (M-X) and organic (C-X’) halogens applied to M-X…X’-C halogen bond formations. J Am Chem Soc 127:5979–5989
Formigué M, Batail P (2004) Activation of hydrogen- and halogen-bonding interactions in tetrathiafulvalene-based crystalline molecular conductors. Chem Rev 104:5379–5418
Clark T, Hennemann M, Murray JS, Politzer P (2007) Halogen bonding: the σ-hole. J Mol Model 13:291–296
Clark T (2013) σ-Holes. Wires Comput Mol Sci 3:13–20
Politzer P, Murray JS, Concha MC (2007) Halogen bonding and the design of new materials: organic bromides, chlorides and perhaps even fluorides as donors. J Mol Model 13:643–650
Landrum GA, Goldberg N, Hoffmann R, Minyaev RM (1998) Intermolecular interactions between hypervalent molecules: Ph2IX and XF3 (X = Cl, Br, I) dimers. New J Chem 22:883–890
Wang W (2011) Halogen bond involving hypervalent halogen: CSD search and theoretical study. J Phys Chem A 115:9294–9299
Grabowski SJ (2014) Halogen bond with the multivalent halogen acting as the Lewis acid center. Chem Phys Lett 605–606:131–136
Weinhold F, Landis C (2005) Valency and bonding, a natural bond orbital donor—acceptor perspective. Cambridge University Press, pp 275–306
Pimentel GC (1951) The bonding of trihalide and bifluoride ions by the molecular-orbital method. J Chem Phys 19:446–448
Rundle RE (1947) Electron deficient compounds. J Am Chem Soc 69:1327–1331
Politzer P, Murray JS (2013) Halogen bonding: an interim discussion. ChemPhysChem 14:2145–2151
Bundhun A, Ramasami P, Murray JS, Politzer P (2012) Trends in σ-hole strengths and interactions of F3MX molecules (M = C, Si, Ge and X = F, Cl, Br, I). J Mol Mod 19:2739–2746
Bauzá A, Mooibroek TJ, Frontera A (2013) Tetrel-bonding interaction rediscovered supramolecular force ? Angew Chem Int Ed Engl 52:12317–12321
Mani D, Arunan E (2013) The X-C…Y (X = O/F, Y = O/S/F/Cl/Br/N/P) ‘carbon bond’ and hydrophobic interactions. Phys Chem Chem Phys 15:14377–14383
Grabowski SJ (2014) Tetrel bond—σ-hole bond as a preliminary stage of the SN2 reaction. Phys Chem Chem Phys 16:1824–1834
Sundberg MR, Uggla R, Viñas C, Teixidor F, Paavola S, Kivekäs R (2007) Nature of intramolecular interactions in hypercoordinate C-substituted 1,2-dicarba-closo-dodecaboranes with short P…P distances. Inorg Chem Commun 10:713–716
Bauer S, Tschirschwitz S, Lönnecke P, Franck R, Kirchner B, Clark ML, Hey-Hawkins E (2009) Enantiomerically Pure Bis(phosphanyl)carbaborane(12) Compounds. Eur J Inorg Chem 2776–2788
Del Bene JE, Alkorta I, Sanchez-Sanz G, Elguero J (2011) Structures, energies, bonding, and NMR properties of pnicogen complexes H2XP:NXH2 (X = H, CH3, NH2, OH, F, Cl). J Phys Chem A 115:13724–13731
Scheiner S (2011) Can two trivalent N atoms engage in a direct N…N noncovalent interaction? Chem Phys Lett 514:32–35
Grabowski SJ (2013) σ-Hole bond versus hydrogen bond: from tetravalent to pentavalent N, P, and as atoms. Chem Eur J 19:14600–14611
Sanz P, Yañez M, Mó O (2002) Competition between X…H…Y intramolecular hydrogen bonds and X…Y (X = O, S, and Y = Se, Te) chalcogen-chalcogen interactions. J Phys Chem A 106:4661–4668
Wang W, Ji B, Zhang Y (2009) Chalcogen bond: a sister noncovalent bond to halogen bond. J Phys Chem A 113:8132–8135
Alikhani E, Fuster F, Madebene B, Grabowski SJ (2014) Topological reaction sites—very strong chalcogen bonds. Phys Chem Chem Phys 16:2430–2442
Del Bene JE, Alkorta I, Sánchez-Sanz G, Elguero J (2011) 31P-31P Spin-Spin coupling constants for pnicogen homodimers. Chem Phys Lett 512:184–187
Del Bene JE, Alkorta I, Elguero J (2015) Substituent effects on the properties of pnicogen-bonded complexes H2XP:PYH2, for X, Y = F, Cl, OH, NC, CCH, CH3, CN, and H. J Phys Chem A 119:224–233
Eskandari K, Mahmoodabadi N (2013) Pnicogen bonds: a theoretical study based on the laplacian of electron density. J Phys Chem A 117:13018–13024
Eskandari K, Zariny H (2010) Halogen bonding: a lump-hole interaction. Chem Phys Lett 492:9–13
Bento AP, Solà M, Bickelhaupt FM (2005) Ab initio and DFT benchmark study for nucleophilic substitution at carbon (SN2@C) and silicon (SN2@Si). J Comput Chem 26:1497–1504
Pierrefixe SCAH, Guerra CF, Bickelhaupt FM (2008) Hypervalent silicon versus carbon: ball-in-a-box model. Chem Eur J 14:819–828
Levy CJ, Puddephatt RJ (1997) Rapid reversible oxidative addition of group 14-halide bonds to platinum(ii): rates, equilibria, and bond energies. J Am Chem Soc 119:10127–10136
Grabowski SJ (2014) Clusters of ammonium cation–hydrogen bond versus σ-hole bond. ChemPhysChem 15:876–884
Murray JS, Riley KE, Politzer P, Clark T (2010) Directional weak intermolecular interactions: σ-hole bonding. Aust J Chem 63:1598–1607
Lipkowski P, Grabowski SJ (2014) Could the lithium bond be classified as the σ-hole bond?—QTAIM and NBO analysis. Chem Phys Lett 591:113–118
Allen FH (2002) The cambridge structural database: a quarter of a million crystal structures and rising. Acta Cryst B58:380–388
http://www.ccdc.cam.ac.uk/Lists/ResourceFileList/2014_stats_entries.pdf
Domagała M, Grabowski SJ (2009) X-H…π and X-H…N hydrogen bonds—acetylene and hydrogen cyanide as proton acceptors. Chem Phys 363:42–48
Nishio M, Hirota M, Umezawa Y (1998) The CH/π interaction, evidence, nature, and consequences. Wiley-VCH, New York
Grabowski SJ, Ugalde JM (2010) Bond paths show preferable interactions: ab initio and QTAIM studies on the X-H· · ·π hydrogen bond. J Phys Chem A 114:7223–7229
Szymczak JJ, Grabowski SJ, Roszak S, Leszczynski J (2004) H…σ interactions—an ab initio and ‘atoms in molecules’ study. Chem Phys Lett 393:81–86
Grabowski SJ, Sokalski WA, Leszczynski J (2006) Can H…σ, π…H + …σ and σ…H + …σ interactions be classified as H-bonded? Chem Phys Lett 432:33–39
Grabowski SJ (2007) Hydrogen bonds with π and σ electrons as the multicenter proton acceptors: high level ab initio calculations. J Phys Chem A 111:3387–3393
Grabowski SJ (2013) Dihydrogen bond and X-H…σ interaction as sub-classes of hydrogen bond. J Phys Org Chem 26:452–459
Jucks KW, Miller RE (1987) Infrared stark spectroscopy on the hydrogen-HF binary complex. J Chem Phys 87:5629–5633
Moore DT, Miller RE (2003) Dynamics of hydrogen–HF complexes in helium nanodroplets. J Chem Phys 118:9629–9636
Moore DT, Miller RE (2003) Solvation of HF by molecular hydrogen: helium nanodroplet vibrational spectroscopy. J Phys Chem A 107:10805–10812
Moore DT, Miller RE (2004) Rotationally resolved infrared laser spectroscopy of (H2)n-HF and (D2)n-HF (n = 2-6) in helium nanodroplets. J Phys Chem A 108:1930–1937
Bieske EJ, Nizkorodov SA, Bennett FR, Maier JP (1996) The infrared spectrum of the H2–HCO1 complex. J Chem Phys 102:5152–5164
Urban J, Roszak S, Leszczynski J (2001) Shellvation of the ammonium cation by molecular hydrogen: a theoretical study. Chem Phys Lett 346:512–518
Grabowski SJ, Alkorta I, Elguero J (2013) Complexes between dihydrogen and amine, phosphine, and arsine derivatives. hydrogen bond versus pnictogen interaction. J Phys Chem A 117:3243–3251
Richardson TB, de Gala S, Crabtree RH (1995) Unconventional hydrogen bonds: intermolecular B-H…H-N interactions. J Am Chem Soc 117:12875–12876
Wessel J, Lee JC Jr, Peris E, Yap GPA, Fortin JB, Ricci JS, Sini G, Albinati A, Koetzle TF, Eisenstein O, Rheingold AL, Crabtree RH (1995) An unconventional intermolecular three-center N-H…H2Re hydrogen bond in crystalline [ReH5(PPh3)3]-indole-C6H6. Angew Chem Int Ed Engl 34:2507–2509
Crabtree RH, Siegbahn PEM, Eisenstein O, Rheingold AL, Koetzle TFA (1996) A new intermolecular interaction: unconventional hydrogen bonds with element-hydride bonds as proton acceptor. Acc Chem Res 29:348–354
Crabtree RH, Eisenstein O, Sini G, Peris E (1998) New types of hydrogen bonds. J Organomet Chem 567:7–11
Cybulski H, Pecul M, Sadlej J (2003) Characterization of dihydrogen-bonded D-H…H–A complexes on the basis of infrared and magnetic resonance spectroscopic parameters. J Chem Phys 119:5094–5104
Kubas GJ (2001) Metal dihydrogen and σ-bond complexes. Kluwer, Academic, New York
Stephan DW, Erker G (2010) Frustrated Lewis pairs: metal-free hydrogen activation and more. Angew Chem Int Ed 49:46–76
Rokob TA, Bakó I, Stirling A, Hamza A, Pápai I (2013) Reactivity models of hydrogen activation by frustrated Lewis pairs: synergistic electron transfers or polarization by electric field? J Am Chem Soc 135:4425–4437
Todd A, Keith TK (2011) AIMAll (Version 11.08.23). Gristmill Software, Overland Park KS, USA (aim.tkgristmill.com)
Acknowledgments
Financial support comes from Eusko Jaurlaritza (GIC 07/85 IT-330-07) and the Spanish Office for Scientific Research (CTQ2011-27374). Technical and human support provided by Informatikako Zerbitzu Orokora - Servicio General de Informatica de la Universidad del Pais Vasco (SGI/IZO-SGIker UPV/EHU), Ministerio de Ciencia e Innovación (MICINN), Gobierno Vasco Eusko Jaurlanitza (GV/EJ), European Social Fund (ESF) is gratefully acknowledged. The QTAIM calculations as well as the corresponding figures were performed with the use of the AIMAll program [88].
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Grabowski, S.J. (2016). What Can Be Learnt from a Location of Bond Paths and from Electron Density Distribution. 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_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-29022-5_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-29020-1
Online ISBN: 978-3-319-29022-5
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)