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On the non-existence of parallel universes in chemistry

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Abstract

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.

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References

  • 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 

  • 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 

  • Bader, R.F.W.: Vibrationally induced perturbations in molecular electron distributions. Can. J. Chem. 40, 1164–1175 (1962)

    Google Scholar 

  • 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)

  • Bader, R.F.W.: Atoms in molecules: a quantum theory. Oxford University Press, Oxford UK (1990)

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • Bader, R.F.W.: The quantum mechanical basis of conceptual chemistry. Monatshefte für Chemie 136, 819–854 (2005)

    Google Scholar 

  • Bader, R.F.W.: Pauli repulsions exist only in the mind of the beholder. Chem. Eur. J. 12, 2896–2901 (2006a)

    Google Scholar 

  • Bader, R.F.W.: Comment on: revisiting the variational derivation of QTAIM. Chem. Phys. Lett. 426, 226–228 (2006b)

    Google Scholar 

  • 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 

  • Bader, R.F.W.: Nearsightedness as seen by a physicist and a chemist. J. Phys. Chem. A 112, 13717–13728 (2008)

    Google Scholar 

  • Bader, R.F.W.: Bond paths are not chemical bonds. J. Phys. Chem. A 113, 10391–10396 (2009a)

    Google Scholar 

  • Bader, R.F.W.: Bond paths are not chemical bonds. J. Phys. Chem. A 113, 10391–10396 (2009b)

    Google Scholar 

  • Bader, R.F.W.: Definition of molecular structure: by choice or by observation. J. Phys. Chem. A 114, 7431–7444 (2010a)

    Google Scholar 

  • Bader, R.F.W.: Density in density functional theory. J. Mol. Struct. (THEOCHEM) 943, 2–18 (2010b)

    Google Scholar 

  • 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 

  • Bader, R.F.W., Bayles, D.: Properties of atoms in molecules: group additivity. J. Phys. Chem. A 104, 5579–5589 (2000)

    Google Scholar 

  • 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 

  • Bader, R.F.W., Cortés-Guzmán, F.: The Virial Field and Transferability in DNA Base-Pairing. Wiley-VCH, 2009 (2009)

    Google Scholar 

  • 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 

  • Bader, R.F.W., Essén, H.: The characterization of atomic interactions. J. Chem. Phys. 80, 1943–1960 (1984)

    Google Scholar 

  • 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 

  • Bader, R.F.W., Keith, T.A.: Properties of atoms in molecules: magnetic susceptibilities. J. Chem. Phys. 99, 3683–3693 (1993)

    Google Scholar 

  • 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 

  • Bader, R.F.W., Nguyen-Dang, T.T.: Theory of atoms in molecules—Dalton revisited. Ad. Quantum Chem. 14, 63–124 (1981)

    Google Scholar 

  • 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 

  • 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 www.chemistry.mcmaster.ca/faculty/bader/aim/

  • Bader, R.F.W.: Atoms in molecules, In: Encyclopedia of Computational Chemistry. Wiley, Chichester (1998)

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • Bethe, H.: New York Times Obituary. March 18 (2005)

  • 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 

  • 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)

  • 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 

  • 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 

  • 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)

  • 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 

  • 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 

  • 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 

  • Collard, K., Hall, G.G.: Orthogonal trajectories of the electron density. Int. J. Quantum Chem. 12, 623 (1977)

    Google Scholar 

  • Coppens, P.: X-Ray Charge Densities and Chemical Bonding. Oxford University Press, Oxford (1997)

    Google Scholar 

  • Coppens, P.: Charge densitiers come of age. Angew. Chem. Int. Ed. 44, 6810–6811 (2005)

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • Cremer, D., Childs, R.F., Kraka, E.: Cyclopropyl homoconjugation, homoaromaticity and homoantiaromaticity—theoretical aspects and analysis. Wiley, New York (1995)

    Google Scholar 

  • Dalton, J.: New System of Chemical Philosophy. 1808. Manchester, facsimile edition. Dawson, London (1808)

    Google Scholar 

  • Dirac, P.A.M.: The Principles of Quantum Mechanics. Oxford University Press, Oxford (1958)

    Google Scholar 

  • Dirac, P.A.M. The Lagrangian in quantum mechanics. Physik. Zeits. Sowjetunion 3, 64 (1933)

    Google Scholar 

  • Ditchfield, R.: A gauge-invariant LCAO method for NMR chemical shifts. Mol. Phys. 27, 789 (1974)

    Google Scholar 

  • Ehrenfest, P.: Bemerkumg űber die angemaherte gű ltigkeit der klassischen mechanic immerhalb der quanten mechanic. Z. Phys. 45, 455 (1927)

    Google Scholar 

  • 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 

  • Feynman, R.P.: Forces in molecules. Phys. Rev. 56, 340–343 (1939)

    Google Scholar 

  • Feynman, R.P.: Space-time approach to non-relativistic quantum mechanics. Rev. Mod. Phys. 20, 367–387 (1948)

    Google Scholar 

  • 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 

  • 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 

  • Fradera, X., Austen, M.A., Bader, R.F.W.: The Lewis model and beyond. J. Phys. Chem. A 103, 304–314 (1999)

    Google Scholar 

  • Frenking, G.: Chemical bonding and molecular geometry. Angew. Chem. Int. Ed. 42, 143–147 (2003)

    Google Scholar 

  • Gatti, C.: Chemical bonding in crystals: new directions. Z. Kristallogr. 220, 399–457 (2005)

    Google Scholar 

  • Gell-Mann, M.: Dick Feynman—the guy in the office down the hall. Phys. Today 42, 50 (1989)

    Google Scholar 

  • 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 

  • Gillespie, R.J.: Molecular Geometry. Van Nostrand Reinhold, London (1972)

    Google Scholar 

  • 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 

  • Gleick, J.: Genius: The Life and Science of Richard Feynman. Vintage Books, New York (1992)

    Google Scholar 

  • Goddard, W.A., Wilson, C.W.: Theor. Chim. Acta 26, 195, 211 (1972)

    Google Scholar 

  • Heitler, W., London, F.: Interaction between neutral atoms and homopolar binding according to quantum mechanics. Z. Physik 44, 455 (1927)

    Google Scholar 

  • Hellmann, H., Khimiya, K.: German manuscript translated into Russian by Golovin, J., Tunitskij, N., Kovner, M. ONTI, Moscow and Leningrad (1937)

  • Hellmann, H.: Einführung in die Quantumchemie. Deauticke, Vienna (1937b)

    Google Scholar 

  • Hernández-Trujillo, J., Cortés-Guzmán, F., Fang, D.C., Bader, R.F.W.: Forces in molecules. Faraday Discuss. 135, 79–95 (2007)

    Google Scholar 

  • Herzberg, G.: Molecular Spectra and Molecular Structure. I. D. Van Nostrand Co. Inc., New York (1950)

    Google Scholar 

  • Hohenberg, P., Kohn, W.: Inhomogeneous electron gas. Phys. Rev. B136, 864–865 (1964)

    Google Scholar 

  • Hund, F.: On the interpretation of molecular spectra. Z. Phys. 43, 805 (1927)

    Google Scholar 

  • 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 

  • 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 

  • Keith, T.A., Bader, R.F.W.: Topological analysis of magnetically induced molecular current distributions. J. Chem. Phys. 99, 3669–3682 (1993b)

    Google Scholar 

  • Keith, T.A., Bader, R.F.W.: Properties of atoms in molecules: nuclear magnetic shielding. Can. J. Chem. 74, 185–200 (1996)

    Google Scholar 

  • Kingsforf-Adaboh, R., et al.: Topological analysis of DL-arginine monohydrate at 100 K. Z. Kristallogr. 217, 168–173 (2002)

    Google Scholar 

  • Kohn, W., Sham, L.J.: Self-consistent equations including exchange and correlation. Phys. Rev. A 140, 1133 (1965)

    Google Scholar 

  • Kutzelnigg, W.: The physical mechanism of the chemical bond. Angew. Chem. Int. Ed. 12, 546–562 (1973)

    Google Scholar 

  • Kutzelnigg, W.: Theory of magnetic susceptibilities and NMR chemical shifts in terms of localized quantities. Israel J. Chem. 19, 193–200 (1980)

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • Morokuma, K.: Molecular orbital studies of hydrogen bonds. III. J. Chem. Phys. 55, 1236–1244 (1971)

    Google Scholar 

  • 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 

  • Mulliken, R.S.: The assignmant of quantum numbers for electrons in molecules. Phys. Rev. 32, 186 (1928)

    Google Scholar 

  • Mulliken, R.S.: Interpretation of band spectra. Parts I, IIa and IIb. Rev. Mod. Phys. 2, 60–115 (1930)

    Google Scholar 

  • Mulliken, R.S.: Interpretation of band spectra. Part IIc. empirical bond types. Rev. Mod. Phys. 3, 89–155 (1931)

    Google Scholar 

  • 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)

  • 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 

  • Ruedenberg, K.: The physical nature of the chemical bond. Rev. Mod. Phys. 34, 326–376 (1962)

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • Scherer, W. et al.: Molecular recognition in the solid state. Chem. Commun. 635 (2000)

  • Schöllkopf, W., Toennies, J.P.: transmission grating determ of He dimer. Science 266, 1345 (1994)

    Google Scholar 

  • Schrödinger, E.: Quantization as a problem of proper values (part I). Ann. D. Phys. 79, 361 (1926)

    Google Scholar 

  • Schrödinger, E.: Quantization as a problem of proper values (part IV) Schroedinger. Ann. d. Physik 81, 109 (1926)

    Google Scholar 

  • 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. Karachalios

  • Schwinger, J.: The theory of quantized fields. Phys. Rev. 82, 914–927 (1951)

    Google Scholar 

  • Shaik, S.: The Lewis legacy: the chemical bond—a territory and heartland of chemistry. J. Comput. Chem. 28, 51–61 (2007)

    Google Scholar 

  • Slater, J.C.: The virial and molecular structure. J. Chem. Phys. 1, 687 (1933)

    Google Scholar 

  • Slater, J.C.: Quantum theory of molecules and solids. I. McGraw-Hill, New York (1963)

    Google Scholar 

  • Slater, J.C.: Hellmann-Feynman and virial theorems in the X-alpha method. J. Chem. Phys. 57, 2389 (1972)

    Google Scholar 

  • Spackman, M.A.: Charge densities from x-ray diffraction data. R. Soc. Chem. Ann. Rep C 94, 183–198 (1998)

    Google Scholar 

  • 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 

  • Thom, R.: Structural Stability and Morphogenesis. W. A. Benjamin, Reading (1975)

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • Woodward, R.B., Hoffmann, R.H.: The conservation of orbital symmetry. Verlag Chemie, Weinheim (1970)

    Google Scholar 

  • 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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Acknowledgments

I wish to thank Professor R. Hoffmann for permission to reproduce his personal correspondence given in the opening paragraph. I am indebted to Professor Vladimir Tsirelson of The Mendeleev University of Chemical Technology, Moscow, for obtaining a copy of Hellmann’s original book printed in Russian, “Kvantovaya Khimiya” (Moscow, 1936) and for his assistance in translating the relevant portions dealing with the virial and ‘Hellmann–Feynman’ theorems. (The Russian version is apparently difficult to access in the west.) I also wish to acknowledge the assistance of Mr. Ivan Vinogradov and Mr. Pavel Kulikov of Professor Ayers’ group at McMaster University, in assisting in the translation of the Russian version of Hellmann’s book. The book was originally written in German and translated into Russian by three PhD students after Professor Hellmann fled to Russia in 1934 to escape the Nazis, where, unfortunately he was later shot as a German spy in 1938.

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Bader, R.F.W. On the non-existence of parallel universes in chemistry. Found Chem 13, 11–37 (2011). https://doi.org/10.1007/s10698-011-9106-0

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