Foundations of Chemistry

, Volume 13, Issue 1, pp 11–37 | Cite as

On the non-existence of parallel universes in chemistry



This treatise presents thoughts on the divide that exists in chemistry between those who seek their understanding within a universe wherein the laws of physics apply and those who prefer alternative universes wherein the laws are suspended or ‘bent’ to suit preconceived ideas. The former approach is embodied in the quantum theory of atoms in molecules (QTAIM), a theory based upon the properties of a system’s observable distribution of charge. Science is experimental observation followed by appeal to theory that, upon occasion, leads to new experiments. This is the path that led to the development of the molecular structure hypothesis—that a molecule is a collection atoms with characteristic properties linked by a network of bonds that impart a structure—a concept forged in the crucible of nineteenth century experimental chemistry. One hundred and fifty years of experimental chemistry underlie the realization that the properties of some total system are the sum of its atomic contributions. The concept of a functional group, consisting of a single atom or a linked set of atoms, with characteristic additive properties forms the cornerstone of chemical thinking of both molecules and crystals and Dalton’s atomic hypothesis has emerged as the operational theory of chemistry. We recognize the presence of a functional group in a given system and predict its effect upon the static, reactive and spectroscopic properties of the system in terms of the characteristic properties assigned to that group. QTAM gives physical substance to the concept of a functional group.


Electron density Atoms in molecules Molecular structure QTAIM 

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  1. Alvarez, S., Hoffmann, R., Mealli, C.: A bonding quandry - or - a demonstration that scientists are not born with logic. Chem. Eur. J. 15, 8358–8373 (2009)Google Scholar
  2. Bader, R.F.W.: An interpretation of potential interaction constants in terms of low-lying excited states. Mol. Phys. 3, 137–151 (1960)Google Scholar
  3. Bader, R.F.W.: Vibrationally induced perturbations in molecular electron distributions. Can. J. Chem. 40, 1164–1175 (1962)Google Scholar
  4. Bader, R.F.W.: Molecular charge distributions. Their display and use. In: Coulson, C.A., Buckingham, E.D.A. (eds.) M. T. P. International Series of Science, Theoretical Chemistry. Butterworths (1975)Google Scholar
  5. Bader, R.F.W.: Atoms in molecules: a quantum theory. Oxford University Press, Oxford UK (1990)Google Scholar
  6. Bader, R.F.W.: Principle of stationary action and the definition of a proper open system. Phys. Rev. B 49, 13348–13356 (1994)Google Scholar
  7. Bader, R.F.W.: The zero-flux surface and the topological and quantum definitions of an atom in a molecule. Theor. Chem. Acc. 105, 276–283 (2001)Google Scholar
  8. Bader, R.F.W.: A comment on”Some fundamental problems with zero-flux partitioning of electron densities”. Theor. Chem. Acc. 107, 381–382 (2002)Google Scholar
  9. Bader, R.F.W.: The quantum mechanical basis of conceptual chemistry. Monatshefte für Chemie 136, 819–854 (2005)Google Scholar
  10. Bader, R.F.W.: Pauli repulsions exist only in the mind of the beholder. Chem. Eur. J. 12, 2896–2901 (2006a)Google Scholar
  11. Bader, R.F.W.: Comment on: revisiting the variational derivation of QTAIM. Chem. Phys. Lett. 426, 226–228 (2006b)Google Scholar
  12. Bader, R.F.W.: Everyman’s derivation of the theory of an atom in a molecule. J. Phys. Chem. A 111, 7966–7972 (2007)Google Scholar
  13. Bader, R.F.W.: Nearsightedness as seen by a physicist and a chemist. J. Phys. Chem. A 112, 13717–13728 (2008)Google Scholar
  14. Bader, R.F.W.: Bond paths are not chemical bonds. J. Phys. Chem. A 113, 10391–10396 (2009a)Google Scholar
  15. Bader, R.F.W.: Bond paths are not chemical bonds. J. Phys. Chem. A 113, 10391–10396 (2009b)Google Scholar
  16. Bader, R.F.W.: Definition of molecular structure: by choice or by observation. J. Phys. Chem. A 114, 7431–7444 (2010a)Google Scholar
  17. Bader, R.F.W.: Density in density functional theory. J. Mol. Struct. (THEOCHEM) 943, 2–18 (2010b)Google Scholar
  18. Bader, R.F.W., Bandrauk, A.D.: Molecular charge distribution and chemical binding III. The isoelectronic series N2, CO, BF and C2, BeO, LiF. J. Chem. Phys. 49, 1653–1665 (1968)Google Scholar
  19. Bader, R.F.W., Bayles, D.: Properties of atoms in molecules: group additivity. J. Phys. Chem. A 104, 5579–5589 (2000)Google Scholar
  20. Bader, R.F.W., Beddall, P.M.: A virial field relationship for molecular charge distributions and a spatial partitioning of molecular properties. J. Chem. Phys. 56, 3320–3329 (1972)Google Scholar
  21. Bader, R.F.W., Cortés-Guzmán, F.: The Virial Field and Transferability in DNA Base-Pairing. Wiley-VCH, 2009 (2009)Google Scholar
  22. Bader, R.F.W., De-Cai, F.: Properties of atoms in molecules: caged atoms and the Ehrenfest force. J. Chem. Theory Comput. 1, 403–414 (2005)Google Scholar
  23. Bader, R.F.W., Essén, H.: The characterization of atomic interactions. J. Chem. Phys. 80, 1943–1960 (1984)Google Scholar
  24. Bader, R.F.W., Heard, G.L.: The mapping of the conditional pair density onto the electron density. J. Chem. Phys. 111, 8789–8798 (1999)Google Scholar
  25. Bader, R.F.W., Keith, T.A.: Properties of atoms in molecules: magnetic susceptibilities. J. Chem. Phys. 99, 3683–3693 (1993)Google Scholar
  26. Bader, R.F.W., Matta, C.F.: Atomic charges are measurable quantum expectation values: a rebuttal of criticisms of QTAIM charges. J. Phys. Chem A 108, 8385–8394 (2004)Google Scholar
  27. Bader, R.F.W., Nguyen-Dang, T.T.: Theory of atoms in molecules—Dalton revisited. Ad. Quantum Chem. 14, 63–124 (1981)Google Scholar
  28. Bader, R.F.W., Preston, H.J.T.: The kinetic energy of molecular charge distributions. Int. J. Quantum Chem. 3, 327–347 (1969)Google Scholar
  29. Bader, R.F.W.: An Introduction to the Electronic Structure of Atoms and Molecules. Clarke Irwin & Co Ltd, Toronto (1970). This book is available on line at
  30. Bader, R.F.W.: Atoms in molecules, In: Encyclopedia of Computational Chemistry. Wiley, Chichester (1998)Google Scholar
  31. Bader, R.F.W., Stephens, M.E.: Spatial Localization of the electron pair and number distributions in molecules. J. Am. Chem. Soc. 97, 7391–7399 (1975)Google Scholar
  32. Bader, R.F.W., Henneker, W.H., Cade, P.E.: Molecular charge distributions and chemical binding. J. Chem. Phys. 46, 3341–3363 (1967a)Google Scholar
  33. Bader, R.F.W., Keaveny, I., Cade, P.E.: Molecular charge distributions and chemical binding. II Second-row diatomic hydrides. J. Chem. Phys. 47, 3381–3402 (1967b)Google Scholar
  34. Bader, R.F.W., Srebrenik, S., Nguyen Dang, T.T.: Subspace quantum dynamics and the quantum action principle. J. Chem. Phys. 68, 3680–3691 (1978)Google Scholar
  35. Bader, R.F.W., Anderson, S.G., Duke, A.J.: Quantum topology of molecular charge distributions. I. J. Am. Chem. Soc. 101, 1389–1395 (1979a)Google Scholar
  36. Bader, R.F.W., Nguyen-Dang, T.T., Tal, Y.: Quantum topology of molecular charge distributions II Molecular structure and its change. J. Chem. Phys. 70, 4316–4329 (1979b)Google Scholar
  37. Bader, R.F.W., Nguyen-Dang, T.T., Tal, Y.: A topological theory of molecular structure. Rep. Prog. Phys. 44, 893–948 (1981)Google Scholar
  38. Bader, R.F.W., Slee, T.S., Cremer, D., Kraka, E.: Description of conjugation and hyperconjugation in terms of electron distributions. J. Am. Chem. Soc. 105, 5061–5068 (1983)Google Scholar
  39. Bader, R.F.W., MacDougall, P.J., Lau, C.D.H.: Bonded and nonbonded charge concentrations and their relation to molecular geometry and reactivity. J. Am. Chem. Soc. 106, 1594–1605 (1984)Google Scholar
  40. Bader, R.F.W., Carroll, M.T., Cheeseman, J.R., Chang, C.: Properties of atoms in molecules: atomic volumes. J. Am. Chem. Soc. 109, 7968–7979 (1987)Google Scholar
  41. Bader, R.F.W., Gillespie, R.J., MacDougall, P.J.: The Laplacian of the Charge Density—The Physical Basis of the VSEPR Model. VCH, New York, N. Y. (1989)Google Scholar
  42. Bader, R.F.W., Cheeseman, J.R., Laidig, K.E., Breneman, C., Wiberg, K.B.: Origin of rotation and inversion barriers. J. Am. Chem. Soc. 112, 6530–6536 (1990)Google Scholar
  43. Bader, R.F.W., Popelier, P.L.A., Keith, T.A.: Theoretical definition of a functional group and the molecular orbital paradigm. Angew. Chem. Int. Ed. Engl. 106, 647–658 (1994)Google Scholar
  44. Bader, R.F.W., Matta, C.F., Cortés-Guzmán, F.: Where to draw the line in defining molecular structure. Organometallics 23, 6253–6263 (2004)Google Scholar
  45. Bader, R.F.W., Hernández-Trujillo, J., Cortés-Guzmán, F.: Chemical bonding: from Lewis to atoms in molecules. J. Comput. Chem. 28, 4–14 (2007)Google Scholar
  46. Benabicha, F., Pichon-Pesme, V., Jelsch, C., Lecomte, C., Khmou, A.: Experimental charge density and electrostatic potential of glycyl-l-threonine dihydrate. Acata Cryst. B56, 155–165 (2000)Google Scholar
  47. Bethe, H.: New York Times Obituary. March 18 (2005)Google Scholar
  48. Bickelhaupt, F.M., Baerends, E.J.: The case for steric repulsion causing the staggered conformation in ethane. Angew. Chem. Int. Ed. 42, 4183–4188 (2003)Google Scholar
  49. Brown, E.C., Bader, R.F.W., Werstiuk, N.H.: QTAIM study of the degenerate Cope rearrangement of 1,5-hexadiene and semibullvalene. J. Chem. Phys. A 113, (2009)Google Scholar
  50. Bui, T.T.T., Dahaoui, S., Lecomte, C., Desiraju, G.R., Espinosa, E.: Nature of halogen—halogen interactions. Ange. Chem. 121, 1–5 (2009)Google Scholar
  51. Bytheway, I., Gillespie, R.J., Tang, T.-H., Bader, R.F.W.: Core distortions and geometries of the diflourides and dihydrides of Ca, Sr and Ba. Inorg. Chem. 34, 2407–2414 (1995)Google Scholar
  52. Cade, P.E., Huo, W.M.: Hartree-Fock wavefunctions for diatomic molecules: I. First- and second-row hydrides AH, AH+ and AH*. At. Data Nucl. Data Tables 12, 415–466 (1973)Google Scholar
  53. Cade, P.E., Huo, W.M.: Hartree-Fock wavefunctions for diatomic molecules: III. First-row heteronuclear systems AB, AB+, AB, AB*. At. Data Nucl. Data Tables 15, 1–39 (1975)Google Scholar
  54. Cade, P.E., Wahl, A.C.: Hartree-Fock wavefunctions for diatomic molecules: II. First-row homonuclear systems A2, A2 +, A2 and A2*. At. Data Nucl. Data Tables 13, 339–389 (1974)Google Scholar
  55. Cade, P.E., Bader, R.F.W., Henneker, W.H., Keaveny, I.: Molecular charge distributions and chemical binding IV: the second-row diatomic hydrides AH. J. Chem. Phys. 50, 5313–5333 (1969)Google Scholar
  56. Collard, K., Hall, G.G.: Orthogonal trajectories of the electron density. Int. J. Quantum Chem. 12, 623 (1977)Google Scholar
  57. Coppens, P.: X-Ray Charge Densities and Chemical Bonding. Oxford University Press, Oxford (1997)Google Scholar
  58. Coppens, P.: Charge densitiers come of age. Angew. Chem. Int. Ed. 44, 6810–6811 (2005)Google Scholar
  59. Cortés-Guzmán, F., Bader, R.F.W.: Transferability of group properties and satisfaction of the virial theorem. Chem. Phys. Lett. 379, 183–192 (2003)Google Scholar
  60. Cortés-Guzmán, F., Bader, R.F.W.: Role of functional groups in linear regression analysis of molecular properties. J. Phys. Org. Chem. 17, 95–99 (2004)Google Scholar
  61. Cortés-Guzmán, F., Bader, R.F.W.: Complementarity of QTAIM and MO theory in the study of bonding in donor-acceptor complexes. Coordination Chem. Rev. 249, 633–662 (2005)Google Scholar
  62. Cremer, D., Childs, R.F., Kraka, E.: Cyclopropyl homoconjugation, homoaromaticity and homoantiaromaticity—theoretical aspects and analysis. Wiley, New York (1995)Google Scholar
  63. Dalton, J.: New System of Chemical Philosophy. 1808. Manchester, facsimile edition. Dawson, London (1808)Google Scholar
  64. Dirac, P.A.M.: The Principles of Quantum Mechanics. Oxford University Press, Oxford (1958)Google Scholar
  65. Dirac, P.A.M. The Lagrangian in quantum mechanics. Physik. Zeits. Sowjetunion 3, 64 (1933)Google Scholar
  66. Ditchfield, R.: A gauge-invariant LCAO method for NMR chemical shifts. Mol. Phys. 27, 789 (1974)Google Scholar
  67. Ehrenfest, P.: Bemerkumg űber die angemaherte gű ltigkeit der klassischen mechanic immerhalb der quanten mechanic. Z. Phys. 45, 455 (1927)Google Scholar
  68. Feinberg, M.J., Ruedenberg, K.: Paradoxical role of kinetic energy operator in the formation of the covalent bond. J. Chem. Phys. 54, 1495–1511 (1971)Google Scholar
  69. Feynman, R.P.: Forces in molecules. Phys. Rev. 56, 340–343 (1939)Google Scholar
  70. Feynman, R.P.: Space-time approach to non-relativistic quantum mechanics. Rev. Mod. Phys. 20, 367–387 (1948)Google Scholar
  71. Flaig, R., Koritsánszky, T., Zobel, D., Luger, P.: Topological analysis of the experimental electron densities of amino acids. 1. d, l-aspartic acid. J. Am. Chem. Soc. 120, 2227–2238 (1998)Google Scholar
  72. Flaig, R., Koritsanszky, T., Dittrich, B., Wagner, A., Luger, P.: Intra-and inter-molecular topologocical properties of amino acids: a comparitive study of experimental and theoretical results. J. Am. Chem. Soc. 124, 3407–3417 (2002)Google Scholar
  73. Fradera, X., Austen, M.A., Bader, R.F.W.: The Lewis model and beyond. J. Phys. Chem. A 103, 304–314 (1999)Google Scholar
  74. Frenking, G.: Chemical bonding and molecular geometry. Angew. Chem. Int. Ed. 42, 143–147 (2003)Google Scholar
  75. Gatti, C.: Chemical bonding in crystals: new directions. Z. Kristallogr. 220, 399–457 (2005)Google Scholar
  76. Gell-Mann, M.: Dick Feynman—the guy in the office down the hall. Phys. Today 42, 50 (1989)Google Scholar
  77. Gibbs, G.V., et al.: Role of directed van der Waals bonded interactions in the determination of the structures of moelcular arsenate solids. J. Phys. Chem. A 113, 736–749 (2009)Google Scholar
  78. Gillespie, R.J.: Molecular Geometry. Van Nostrand Reinhold, London (1972)Google Scholar
  79. Gillespie, R.J., Bytheway, I., Tang, T.-H., Bader, R.F.W.: Geometry of the fluorides, oxofluorides, hydrides and methylides of vanadium (V), chromium (VI) and molybdenum (VI): understanding the geometry of some non VSEPR molecules in terms of core distortion. Inorg. Chem. 35, 3954–3963 (1996)Google Scholar
  80. Gleick, J.: Genius: The Life and Science of Richard Feynman. Vintage Books, New York (1992)Google Scholar
  81. Goddard, W.A., Wilson, C.W.: Theor. Chim. Acta 26, 195, 211 (1972)Google Scholar
  82. Heitler, W., London, F.: Interaction between neutral atoms and homopolar binding according to quantum mechanics. Z. Physik 44, 455 (1927)Google Scholar
  83. Hellmann, H., Khimiya, K.: German manuscript translated into Russian by Golovin, J., Tunitskij, N., Kovner, M. ONTI, Moscow and Leningrad (1937)Google Scholar
  84. Hellmann, H.: Einführung in die Quantumchemie. Deauticke, Vienna (1937b)Google Scholar
  85. Hernández-Trujillo, J., Cortés-Guzmán, F., Fang, D.C., Bader, R.F.W.: Forces in molecules. Faraday Discuss. 135, 79–95 (2007)Google Scholar
  86. Herzberg, G.: Molecular Spectra and Molecular Structure. I. D. Van Nostrand Co. Inc., New York (1950)Google Scholar
  87. Hohenberg, P., Kohn, W.: Inhomogeneous electron gas. Phys. Rev. B136, 864–865 (1964)Google Scholar
  88. Hund, F.: On the interpretation of molecular spectra. Z. Phys. 43, 805 (1927)Google Scholar
  89. Keith, T.A., Bader, R.F.W.: Calculation of magnetic response properties using atoms in molecules. Chem. Phys. Lett. 194, 1–8 (1992)Google Scholar
  90. Keith, T.A., Bader, R.F.W.: Calculation of magnetic response properties using a continuous set of gauge transformations. Chem. Phys. Lett. 210, 223–231 (1993a)Google Scholar
  91. Keith, T.A., Bader, R.F.W.: Topological analysis of magnetically induced molecular current distributions. J. Chem. Phys. 99, 3669–3682 (1993b)Google Scholar
  92. Keith, T.A., Bader, R.F.W.: Properties of atoms in molecules: nuclear magnetic shielding. Can. J. Chem. 74, 185–200 (1996)Google Scholar
  93. Kingsforf-Adaboh, R., et al.: Topological analysis of DL-arginine monohydrate at 100 K. Z. Kristallogr. 217, 168–173 (2002)Google Scholar
  94. Kohn, W., Sham, L.J.: Self-consistent equations including exchange and correlation. Phys. Rev. A 140, 1133 (1965)Google Scholar
  95. Kutzelnigg, W.: The physical mechanism of the chemical bond. Angew. Chem. Int. Ed. 12, 546–562 (1973)Google Scholar
  96. Kutzelnigg, W.: Theory of magnetic susceptibilities and NMR chemical shifts in terms of localized quantities. Israel J. Chem. 19, 193–200 (1980)Google Scholar
  97. London, F.: On the quantum theory of homo-polar valence numbers. Z. Phys.46, 455 (1928). From the English translation by Hinne Hettema, in Quantum Chemistry: Classic Scientific Papers. World Scientific, Hong Kong (2000)Google Scholar
  98. Luo, F., McBane, G.C., Kim, G., Giese, C.F., Gentry, R.: The weakest bond: experimental observation of helium dimer. J. Chem. Phys. 98, 3564–3567 (1993)Google Scholar
  99. MacDougall, P.J., Henze, C.E.: Indentification of molecular reactive sites with an interactive volume rendering tool. Theor. Chim. Acc. 105, 345–353 (2001)Google Scholar
  100. Matta, C.F.: Hydrogen-Hydrogen Bonding: The Non-electrostatic Limit of Closed-shell Interactions Between Two hydrogen atoms. A Critical Review. Hydrogen Bonding—New Insight, (Challenges and Advances in Computational Chemistry and Phyiscs Series). Dordrecht, Netherlands (2006)Google Scholar
  101. Matta, C.F., Bader, R.F.W.: Atoms in molecules study of genetically encoded amino acids: III. Bond and atomic properties and their correlations with experiment including mutation-induced changes in protein stability and genetic coding. Proteins 52, 360–399 (2003)Google Scholar
  102. Matta, C.F., Bader, R.F.W.: An experimentalist’s reply to “What is an atom in a molecule?”. J. Phys. Chem. A 110, 6365–6371 (2006)Google Scholar
  103. Matta, C.F., Hernández-Trujillo, J., Tang, T.-H., Bader, R.F.W.: Hydrogen-hydrogen bonding: a stabilizing interaction in molecules and crystals. Chem. Eur. J. 9, 1940–1951 (2003)Google Scholar
  104. Morokuma, K.: Molecular orbital studies of hydrogen bonds. III. J. Chem. Phys. 55, 1236–1244 (1971)Google Scholar
  105. Morokuma, K.: Why do molecules interact? The origin of electron donor-acceptor complexes, hydrogen bonding and proton affinity. Acc. Chem. Res. 10, 294–300 (1977)Google Scholar
  106. Mulliken, R.S.: The assignmant of quantum numbers for electrons in molecules. Phys. Rev. 32, 186 (1928)Google Scholar
  107. Mulliken, R.S.: Interpretation of band spectra. Parts I, IIa and IIb. Rev. Mod. Phys. 2, 60–115 (1930)Google Scholar
  108. Mulliken, R.S.: Interpretation of band spectra. Part IIc. empirical bond types. Rev. Mod. Phys. 3, 89–155 (1931)Google Scholar
  109. Palis, J., Smale, S.: Structure stability theorems. Global analysis. Proc. Sympos. Pure Math. XIV, Berkeley CF. American Math. Soc. Providence RI. pp. 223–231 (1968)Google Scholar
  110. Poater, J., Solá, M., Bickelhaupt, F.M.: Hydrogen–hydrogen bonding in planar biphenyl, predicted by AIM theory does not exist. Chem. Eur. J. 12, 2889 (2006)Google Scholar
  111. Ruedenberg, K.: The physical nature of the chemical bond. Rev. Mod. Phys. 34, 326–376 (1962)Google Scholar
  112. Ruedenberg, K., Schmidt, M.W.: Physical understanding through variational reasoning of electron sharing and covalent bonding. J. Phys. Chem. 113, 1954–1968 (2009a)Google Scholar
  113. Ruedenberg, K., Schmidt, M.W.: Physical understanding through variational reasoning: electron sharing and covalent bonding. J. Phys. Chem. A 113, 1954–1968 (2009b)Google Scholar
  114. Runtz, G.R., Bader, R.F.W., Messer, R.R.: Definition of bond paths and bond directions of the molecular charge distribution. Can. J. Chem. 55, 3040–3045 (1977)Google Scholar
  115. Salinas-Olvera, J., Gómez, R., Cortes-Guzman, F.: Structural evolution: mechanism of olefin insertion in hydroformylation reaction. J. Phys. Chem. A 112, 2906–2912 (2008)Google Scholar
  116. Scheins, S., Dittrich, B., Messerschmidt, M., Paulmann, C., Luger, P.: Atomic volumes and charges in a system with a strong hydrogen bond: l-tryptophan formic acid. Acta Cryst. B60, 184–190 (2004)Google Scholar
  117. Scherer, W. et al.: Molecular recognition in the solid state. Chem. Commun. 635 (2000)Google Scholar
  118. Schöllkopf, W., Toennies, J.P.: transmission grating determ of He dimer. Science 266, 1345 (1994)Google Scholar
  119. Schrödinger, E.: Quantization as a problem of proper values (part I). Ann. D. Phys. 79, 361 (1926)Google Scholar
  120. Schrödinger, E.: Quantization as a problem of proper values (part IV) Schroedinger. Ann. d. Physik 81, 109 (1926)Google Scholar
  121. Schwarz, W.H.E. et al.: Hans G. A. Hellmann (1903–1938) part I. Bunsen - Magazin 1, 10–21 (1999). Translation from German to English by M. Smith, W. H. E. Schwarz, J. Hinze and A. KarachaliosGoogle Scholar
  122. Schwinger, J.: The theory of quantized fields. Phys. Rev. 82, 914–927 (1951)Google Scholar
  123. Shaik, S.: The Lewis legacy: the chemical bond—a territory and heartland of chemistry. J. Comput. Chem. 28, 51–61 (2007)Google Scholar
  124. Slater, J.C.: The virial and molecular structure. J. Chem. Phys. 1, 687 (1933)Google Scholar
  125. Slater, J.C.: Quantum theory of molecules and solids. I. McGraw-Hill, New York (1963)Google Scholar
  126. Slater, J.C.: Hellmann-Feynman and virial theorems in the X-alpha method. J. Chem. Phys. 57, 2389 (1972)Google Scholar
  127. Spackman, M.A.: Charge densities from x-ray diffraction data. R. Soc. Chem. Ann. Rep C 94, 183–198 (1998)Google Scholar
  128. Srebrenik, S., Bader, R.F.W.: Towards the development of the quantum mechanics of a subspace. J. Chem. Phys. 63, 3945–3961 (1975)Google Scholar
  129. Thom, R.: Structural Stability and Morphogenesis. W. A. Benjamin, Reading (1975)Google Scholar
  130. Tsirelson, V.G., Ozerov, R.P.: Electron Density and Bonding in Crystals: Principles, Theory and X-ray Diffraction Experiments in Solid State Physics and Chemistry. Institute of Physics Publishing, Bristol (1996)Google Scholar
  131. Tsirelson, V., Zou, P.F., Bader, R.F.W.: Topological definition of crystal structure: determination of the bonded interactions in solid molecular chlorine. Acta Cryst. A 51, 143–153 (1995)Google Scholar
  132. Wang, S.-G., Qui, Y.-X., Schwarz, W.H.E.: Antibond breaking-the formation and decomposition of He@adamantane. Chem. Eur. J. 16, 9107–9116 (2010)Google Scholar
  133. Wiberg, K.B., Bader, R.F.W., Lau, C.D.H.: A theoretical analysis of hydrocarbon properties: II Additivity of groups properties and the origin of strain energy. J. Am. Chem. Soc. 109, 1001–1012 (1987)Google Scholar
  134. Wolstenholme, D.J., Cameron, T.S.: Comparative study of weak interactions in molecular crystals: H–H bonds versus hydrogen bonds. J. Phys. Chem A 110, 8970–8978 (2006)Google Scholar
  135. Woodward, R.B., Hoffmann, R.H.: The conservation of orbital symmetry. Verlag Chemie, Weinheim (1970)Google Scholar
  136. Zhang, L., Ying, F., Wu, W., Hiberty, P.C., Shaik, S.: Topology of electron charge density for chemical bonds from valence bond theory: a probe of bonding types. Chem. Eur. J. 15, 2979–2989 (2009)Google Scholar

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Authors and Affiliations

  1. 1.Department of ChemistryMcMaster UniversityHamiltonCanada

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