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Beyond the orthodox QTAIM: motivations, current status, prospects and challenges

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Foundations of Chemistry Aims and scope Submit manuscript

“There must be chemistry in all these wave functions because we live in one world only”

Paul Popelier (Popelier 2000).

Abstract

Recently, the author of this paper and his research team have extended the orthodox quantum theory of atoms in molecules (QTAIM) to a novel paradigm called the two-component QTAIM (TC-QTAIM). This extended framework enables one to incorporate nuclear dynamics into the AIM analysis as well as performing AIM analysis of the exotic species; positronic and muonic species are a few examples. In present paper, this framework has been reviewed, providing some computational examples with particular emphasis on origins and applications, in a non-technical language. The main questions, enigmas and basic ideas that finally yielded the TC-QTAIM are considered in chronological order to help the reader comprehend the intuition behind the math. Finally, it is demonstrated that the TC-QTAIM and its more refined versions are able to tackle problems inaccessible to the orthodox QTAIM.

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References

  • Alexander, M.H.: Chemical kinetics under test. Science 331, 411–412 (2011)

    Article  Google Scholar 

  • Bader, R.F.W.: Atoms in Molecules: A Quantum Theory. Oxford University Press, Oxford (1990)

    Google Scholar 

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

    Article  Google Scholar 

  • Baer, M.: Beyond Born–Oppenhiemer. Wiley, New Jersey (2006)

    Google Scholar 

  • Born, M., Oppenheimer, R.: Zur Quantentheorie der Molekeln. Ann. Phys. 84, 457–484 (1927)

    Article  Google Scholar 

  • Cafiero, M., Adamowicz, L.: Non-Born–Oppenhiemer calculations of the ground state of H3. Int. J. Quantum Chem. 107, 2679–2686 (2007)

    Article  Google Scholar 

  • Cafiero, M., Adamowicz, L.: Molecular structure in non-Born–Oppenhiemer quantum mechanics. Chem. Phys. Lett. 387, 136–141 (2004)

    Article  Google Scholar 

  • Cafiero, M., Bubin, S., Adamowicz, L.: Non-Born–Oppenhiemer calculations of atoms and molecules. Phys. Chem. Chem. Phys. 5, 1491–1501 (2003)

    Article  Google Scholar 

  • Capitani, J.F., Nalewajski, R.F., Parr, R.G.: Non-Born–Oppenhiemer density functional theory of molecular systems. J. Chem. Phy. 76, 568–573 (1982)

    Article  Google Scholar 

  • Collard, K., Hall, G.G.: Orthogonal trajectories of the electron density. Int. J. Quantum Chem. 12, 623–637 (1977)

    Article  Google Scholar 

  • Eremets, M.I., Troyan, I.A.: Conductive dense hydrogen. Nat. Mater. 10, 927–931 (2011)

    Article  Google Scholar 

  • Espinosa-García, J.: Theoretical rate constants and kinetic isotope effects in the reaction of the methane with H, D, T, and Mu atoms. Phys. Chem. Chem. Phys. 10, 1277–1284 (2008)

    Article  Google Scholar 

  • Fillaux, F., Nicolaï, B.: Proton transfer in malonaldehyde: from reaction path to Schrödinger’s Cat. Chem. Phys. Lett. 415, 357–361 (2005)

    Article  Google Scholar 

  • Fleming, D.G., Arseneau, D.J., Sukhorukov, O., Brewer, J.H., Mielke, S.L., Schatz, G.C., Garrett, B.C., Peterson, K.A., Truhlar, D.G.: Kinetic isotope effects for the reactions of muonic helium and muonium with H2. Science 331, 448–450 (2011a)

    Article  Google Scholar 

  • Fleming, D.G., Arseneau, D.J., Sukhorukov, O., Brewer, J.H., Mielke, S.L., Truhlar, D.G., Schatz, G.C., Garrett, B.C., Peterson, K.A.: Kinetics of the reaction of the heaviest hydrogen atom with H2, the 4Heμ + H2 → 4HeμH + H reaction: experiments, accurate quantal calculations, and variational transition state theory, including kinetic isotope effects for a factor of 36.1 in isotopic mass. J. Chem. Phys. 331, 448–450 (2011b)

    Google Scholar 

  • Gatti, C., Macchi, P.: Modern Charge-Density Analysis. Springer, New York (2012)

    Book  Google Scholar 

  • Goli, M., Shahbazian, S.: The quantum theory of atoms in positronic molecules: a case study on diatomic species. Int. J. Quantum Chem. 111, 1982–1998 (2011a)

    Article  Google Scholar 

  • Goli, M., Shahbazian, S.: Atoms in molecules: beyond Born–Oppenheimer paradigm. Theor. Chem. Acc. 129, 235–245 (2011b)

    Article  Google Scholar 

  • Goli, M., Shahbazian, S.: The two-component quantum theory of atoms in molecules (TC-QTAIM): foundations. Theor. Chem. Acc. 131(1–19), 1208 (2012)

    Article  Google Scholar 

  • Goncharov, A.F., Crowhurst, J.: Proton delocalization under extreme condition of high pressure and temperature. Phase Transit. 80, 1051–1072 (2007)

    Article  Google Scholar 

  • Helgaker, T., Jørgenson, P., Olsen, J.: Molecular Electronic-Structure Theory. Wiley, New York (2000)

    Google Scholar 

  • Heidar Zadeh, F., Shahbazian, S.: The quantum theory of atoms in positronic molecules: the subsystem variational procedure. Int. J. Quantum Chem. 111, 1999–2013 (2011)

    Article  Google Scholar 

  • Ishimoto, T., Tachikawa, M., Nagashima, U.: Review of multicomponent molecular orbital method for direct treatment of nuclear quantum effect. Int. J. Quantum Chem. 109, 2677–2694 (2009)

    Article  Google Scholar 

  • Jean, Y.C., Mallon, P.E., Schrader, D.M.: Principles and Applications of Positron & Positronium Chemistry. World Scientific, New Jersey (2003)

    Book  Google Scholar 

  • Khanna, M.P.: Introduction to Particle Physics. PHI Learning, New Delhi (2009)

    Google Scholar 

  • Klug, D.D., Yao, Y.: Metallization of solid hydrogen: the challenge and possible solutions. Phys. Chem. Chem. Phys. 13, 16999–17006 (2011)

    Article  Google Scholar 

  • Levine, I.N.: Quantum Chemistry. Prentice-Hall, New Delhi (2000)

    Google Scholar 

  • Mao, H.-K., Hemley, R.J.: Ultrahigh-pressure transitions in solid hydrogen. Rev. Mod. Phys. 66, 671–692 (1994)

    Article  Google Scholar 

  • Mátyus, E., Hutter, J., Müller-Herold, U., Reiher, M.: On the emergence of molecular structure. Phys. Rev. A 83, 052512 (2011)

    Article  Google Scholar 

  • Mátyus, E., Reiher, M.: Extracting elements of molecular structure from the all-particle wave function. J. Chem. Phys. 135, 204302 (2011)

    Article  Google Scholar 

  • Matta, C.F., Boyd, R.J.: The Quantum Theory of Atoms in Molecules: From Solid State to DNA and Drug Design. Wiley, Weinheim (2007)

    Book  Google Scholar 

  • Nagamine, K.: Introductory Muon Science. Cambridge University Press, Cambridge (2003)

    Book  Google Scholar 

  • Nakai, H.: Nuclear orbital plus moeluclar orbital theory: simultaneous determination of nuclear and electronic wave functions without Born-Oppenheimer approximation. Int. J. Quantum Chem. 107, 2849–2869 (2007)

    Article  Google Scholar 

  • Nasertayoob, P., Goli, M., Shahbazian, S.: Toward a regional quantum description of the positronic systems: primary considerations. Int. J. Quantum Chem. 111, 1970–1981 (2011)

    Article  Google Scholar 

  • Nasertayoob, P., Shahbazian, S.: The topological analysis of electronic charge densities: a reassessment of foundations. J. Mol. Struct. (Thoechem) 869, 53–58 (2008)

    Article  Google Scholar 

  • Nasertayoob, P., Shahbazian, S.: Revisiting the foundations of the quantum theory of atoms in molecules (QTAIM): the subsystem variational procedure and the finite nuclear models. Int. J. Quantum Chem. 110, 1188–1196 (2010)

    Google Scholar 

  • Parr, R.G., Yang, W.: Density-Functional Theory of Atoms and Molecules. Oxford University Press, Oxford (1989)

    Google Scholar 

  • Popelier, P.: Atoms in Molecules: An Introduction. Prentice Hall, London (2000)

    Google Scholar 

  • Popelier, P.: Solving The Schrödinger Equation: Has Everything Been Tried? Imperial College Press, London (2011)

    Book  Google Scholar 

  • Primas H. (1982) Chemistry, quantum mechanics and reductionism. In: Lecture Notes in Chemistry, vol. 24. Springer, Berlin

  • Shahbazian, S., Zahedi, M.: The role of observables and non-observables in chemistry: a critique to chemical language. Found. Chem. 8, 37–52 (2006)

    Article  Google Scholar 

  • Shahbazian, S., Zahedi, M.: Letter to the editor: the concept of chemical bond—some like it fuzzy but others concrete. Found. Chem. 9, 85–95 (2007)

    Article  Google Scholar 

  • Strasburger, K.: Binding energy, structure, and annihilation properties of the positron-LiH molecules complex, studied with explicitly correlated Gaussian functions. J. Chem. Phys. 111, 10555–10558 (1999)

    Article  Google Scholar 

  • Sutcliffe, B.T.: The decoupling of electronic and nuclear motions in the isolated molecular Schrödinger Hamiltonian. Adv. Chem. Phys. 114, 1–121 (2000)

    Article  Google Scholar 

  • Sutcliffe, B.T., Woolley, R.G.: Molecular structure calculations with clamping the nuclei. Phys. Chem. Chem. Phys. 7, 3664–3676 (2005a)

    Article  Google Scholar 

  • Sutcliffe, B.T., Woolley, R.G.: Comment on “Molecular structure in non-Born–Oppenhiemer quantum mechanics”. Chem. Phys. Lett. 408, 445–447 (2005b)

    Article  Google Scholar 

  • Walker, D.C.: Leptons in chemistry. Acc. Chem. Res. 18, 167–173 (1986)

    Article  Google Scholar 

  • Weininger, S.J.: The molecular structure conundrum: can classical chemistry be reduced to quantum chemistry. J. Chem. Educ. 61, 939–944 (1984)

    Article  Google Scholar 

  • Wiberg, K.B., Hadad, C.M., Breneman, C.M., Laidig, K.E., Murcko, M.A., LePage, T.J.: The responses of electrons to structural changes. Science 252, 1266–1272 (1991)

    Article  Google Scholar 

  • Woolley, R.G.: Quantum theory and molecular structure. Adv. Phys. 25, 27–52 (1976)

    Article  Google Scholar 

  • Woolley, R.G.: Must a molecule have a shape? J. Am. Chem. Soc. 100, 1073–1078 (1978)

    Article  Google Scholar 

  • Woolley, R.G.: The molecular structure conundrum. J. Chem. Educ. 62, 1082–1084 (1985)

    Article  Google Scholar 

  • Woolley, R.G.: Molecular shapes and molecular structures. Chem. Phys. Lett. 125, 200–205 (1986)

    Article  Google Scholar 

Download references

Acknowledgments

The author is grateful to Dr. Cherif Matta, Dr. Paul Ayers, Miss. Farnaz Heidar Zadeh, Dr. Cina Foroutan-Nejad and Mr. Mohammad Goli for detailed reading of a previous draft and their fruitful comments and suggestions. The author is also indebted to his current Ph.D student Mohammad Goli for his dedicated work and outstanding contributions.

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Authors and Affiliations

  1. Department of Chemistry, Faculty of Sciences, Shahid Beheshti University, G.C., Evin, P.O. Box 19395-4716, 19839, Tehran, Iran

    Shant Shahbazian

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  1. Shant Shahbazian
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Correspondence to Shant Shahbazian.

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This paper is dedicated to the memory of Prof. Richard F. W. Bader (1931–2012), a true genius and one of giants of theoretical chemistry.

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Shahbazian, S. Beyond the orthodox QTAIM: motivations, current status, prospects and challenges. Found Chem 15, 287–302 (2013). https://doi.org/10.1007/s10698-012-9170-0

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