Skip to main content
SpringerLink
Log in

The two-component quantum theory of atoms in molecules (TC-QTAIM): the unified theory of localization/delocalization of electrons, nuclei, and exotic elementary particles

  • Regular Article
  • Published:
Theoretical Chemistry Accounts Aims and scope Submit manuscript

Abstract

In this contribution, pursuing our research program by extending the atoms in molecules analysis into unorthodox domains, another key ingredient of the two-component quantum theory of atoms in molecules (TC-QTAIM) namely the theory of localization/delocalization of quantum particles, is disclosed. The unified proposed scheme is able not only to deal with the localization/delocalization of electrons in/between atomic basins, but also to treat nuclei as well as exotic particles such as positrons and muons equally. Based on the general reduced second-order density matrices for indistinguishable quantum particles, the quantum fluctuations of atomic basins are introduced and then used as a gauge to quantitate the localization/delocalization introducing proper indexes. The explicit mass dependence of the proposed indexes is demonstrated, and it is shown that a single localization/delocalization index is capable of being used for all kind of quantum particles regardless of their masses or charge content. For various non-Born–Oppenhiemer (non-BO) wavefunctions, including Hartree product as well as singlet and triplet determinants, the indices are calculated and then employed to rationalize the localization/delocalization of particles in a series of four-body model systems consist of two electrons and two positively charged particles with variable mass. The ab initio FV-MC_MO derived non-BO wavefunctions for the four-body series are used for a comprehensive computational TC-QTAIM analysis, including topological analysis as well as basin integrations, in a wide mass region, m = 10m e  − 1013 m e (m e stands for electron mass), disclosing various traits in these series of species that are unique to the TC-QTAIM. On the other hand, it is demonstrated that in the large mass extreme, the TC-QTAIM analysis reduces to the one performed within context of the orthodox QTAIM with two clamped positive particles revealing the fact that the TC-QTAIM encompasses the orthodox QTAIM as an asymptote. Finally, it is concluded that the proposed localization/delocalization scheme is capable of quantitating quantum tunneling of nuclei for systems containing delocalized protons. Such capability promises novel applications for the TC-QTAIM as well as its extended multi-component version (MC-QTAIM) introduced recently.

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
Fig. 5

Similar content being viewed by others

References

  1. Ramberg PJ (2003) Chemical structure, spatial arrangement: the early history of stereochemistry, 1874–1914. Ashgate Publishing Company, Burlington

    Google Scholar 

  2. Shahbazian Sh (2013) Found Chem 15:327

    Article  Google Scholar 

  3. Shahbazian Sh (2013) Found Chem. doi:10.1007/s10698-013-9187-z

    Google Scholar 

  4. Shahbazian Sh (2011) Int J Quantum Chem 111:4497

    Article  CAS  Google Scholar 

  5. Bader RFW (1990) Atoms in molecules: a quantum theory. Oxford University Press, Oxford

    Google Scholar 

  6. Popelier PLA (2000) Atoms in molecules an introduction. Pearson, London

    Google Scholar 

  7. Matta C, Boyd RJ (2007) Quantum theory of atoms in molecules: from solid state to DNA and drug design. Wiley-VCH, Weinheim

    Book  Google Scholar 

  8. Goli M, Shahbazian Sh (2011) Theor Chem Acc 129:235

    Article  CAS  Google Scholar 

  9. Goli M, Shahbazian Sh (2012) Theor Chem Acc 131:1208

    Article  Google Scholar 

  10. Goli M, Shahbazian Sh (2013) Theor Chem Acc 132:1362

    Article  Google Scholar 

  11. Shahbazian Sh (2013) Found Chem 15:287

    Article  CAS  Google Scholar 

  12. Nasertayoob P, Goli M, Shahbazian Sh (2011) Int J Quantum Chem 111:1970

    Article  CAS  Google Scholar 

  13. Goli M, Shahbazian Sh (2011) Int J Quantum Chem 111:1982

    Article  CAS  Google Scholar 

  14. Heidar Zadeh F, Shahbazian S (2011) Int J Quantum Chem 111:1999

    Article  Google Scholar 

  15. Wolfsberg M, Alexander Van Hook W, Paneth P, Rebelo LPN (2010) Isotope effects in the chemical, geological and bio sciences. Springer, New York

    Google Scholar 

  16. Goli M, Shahbazian Sh (2013) Theor Chem Acc 132:1365

    Article  Google Scholar 

  17. Lampert MA (1958) Phys Rev Lett 1:450

    Article  CAS  Google Scholar 

  18. Sharma RR (1968) Phys Rev 170:770

    Article  CAS  Google Scholar 

  19. Wehner RK (1969) Solid State Commun 7:457

    Article  CAS  Google Scholar 

  20. Adamowski J, Bednarek S, Suffczynski M (1971) Solid State Commun 9:2037

    Article  CAS  Google Scholar 

  21. Akimoto O, Hanamura E (1972) Solid State Commun 10:253

    Article  CAS  Google Scholar 

  22. Brinkman WF, Rice TM, Bell B (1973) Phys Rev B 8:1579

    Google Scholar 

  23. Lee MA, Vashista P, Kalla RK (1983) Phys Rev Lett 51:2422

    Article  CAS  Google Scholar 

  24. Abdel-Raouf MA, El-Gogary MMH, Salehy SA (1998) J Phys B: At Mol Opt Phys 31:1911

    Article  CAS  Google Scholar 

  25. Varga K, Usukura J, Suzuki Y (1998) Phys Rev Lett 80:1876

    Article  CAS  Google Scholar 

  26. Usukura J, Suzuki Y, Varga K (1999) Phys Rev B 59:5652

    Article  CAS  Google Scholar 

  27. Armour EAG, Richrad J-M, Varga K (2004) Phys Rep 413:1

    Article  Google Scholar 

  28. Jensen AS, Riisager K, Fedorov DV, Garrido E (2004) Rev Mod Phys 76:215

    Article  CAS  Google Scholar 

  29. Mitroy J (2005) Phys Rev Lett 94:033402

    Article  CAS  Google Scholar 

  30. Rolim F, Braga JP, Mohallem JR (2000) Chem Phys Lett 332:139

    Article  CAS  Google Scholar 

  31. Mohallem JR, Rolim F, Goncalves CP (2004) J Phys B: At Mol Opt Phys 37:1045

    Article  CAS  Google Scholar 

  32. Rolim F, Moreira T, Mohallem JR (2004) Brazil J Phys 34:1197

    Article  CAS  Google Scholar 

  33. Rolim F, Mohallem JR (2005) Acta Phys Pol, A 107:661

    CAS  Google Scholar 

  34. Mátyus E, Hutter J, Müller-Herold U, Reiher M (2011) Phys Rev A 83:052512

    Article  Google Scholar 

  35. Mátyus E, Hutter J, Müller-Herold U, Reiher M (2011) J Chem Phys 135:204302

    Article  Google Scholar 

  36. Mátyus E, Reiher M (2012) J Chem Phys 137:024104

    Article  Google Scholar 

  37. Bader RFW, Stephens ME (1974) Chem Phys Lett 26:445

    Article  CAS  Google Scholar 

  38. Daudel R, Bader RFW, Stephens ME, Borrett DS (1974) Can J Chem 52:1310

    Article  CAS  Google Scholar 

  39. Bader RFW, Stephens ME (1975) J Am Chem Soc 97:7391

    Article  CAS  Google Scholar 

  40. Bader RFW, Streitwieser A, Neuhaus A, Laidig KE, Speers P (1996) J Am Chem Soc 118:4959

    Article  CAS  Google Scholar 

  41. Bader RFW, Johnson S, Tang T-H, Popelier PLA (1996) J Phys Chem 100:15398

    Article  CAS  Google Scholar 

  42. Gillespie RJ, Bayles D, Platts J, Heard GL, Bader RFW (1998) J Phys Chem A 102:3407

    Article  CAS  Google Scholar 

  43. Fradera X, Austen M, Bader RFW (1999) J Phys Chem A 103:304

    Article  CAS  Google Scholar 

  44. Bader RFW, Heard GL (1999) J Chem Phys 111:8789

    Article  CAS  Google Scholar 

  45. Anderson JSM, Ayers PW, Rodriguez Hernandez JI (2010) J Phys Chem A 114:8884

    Article  CAS  Google Scholar 

  46. Bader RFW, Popelier PLA (1993) Int J Quantum Chem 45:189

    Article  CAS  Google Scholar 

  47. Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. Oxford University Press, New York

    Google Scholar 

  48. McQuarrie DA (2000) Statistical thermodynamics. University Science Books, California

    Google Scholar 

  49. Benjamin A, Hammes-Schiffer S (2010) J Chem Phys 132:084110

    Article  Google Scholar 

  50. Buijse MA, Baerends EJ (1995) In: Ellis DE (ed) Density functional theory of molecules, clusters and solids. Kluwer Academic Publishers, Netherlands, pp 1–46

    Google Scholar 

  51. Udagawa T, Tachikawa M (2009) Multi-component molecular orbital theory. Nova Science Publishers, New York

    Google Scholar 

  52. Ishimoto T, Tachikawa M, Nagashima U (2009) Int J Quantum Chem 109:2677

    Article  CAS  Google Scholar 

  53. Bochevarov AD, Valeev EF, Sherrill CD (2004) Mol Phys 102:111

    Article  CAS  Google Scholar 

  54. Tachikawa M, Osamura Y (2000) Theor Chem Acc 104:29

    Article  CAS  Google Scholar 

  55. Joypazadeh H, Shahbazian Sh (2013) Found Chem. doi:10.1007/s10698-013-9186-0

    Google Scholar 

  56. Bader RFW, Carroll MT, Cheeseman JR, Chang C (1987) J Am Chem Chem 109:7968

    Article  CAS  Google Scholar 

  57. Swalina C, Pak MV, Chakraborty A, Hammes-Schiffer S (2006) J Phys Chem A 110:9983

    Article  CAS  Google Scholar 

  58. Chakraborty A, Pak MV, Hammes-Schiffer S (2008) J Chem Phys 129:014101

    Article  Google Scholar 

  59. Pak MV, Chakraborty A, Hammes-Schiffer S (2009) J Phys Chem A 113:4004

    Article  CAS  Google Scholar 

  60. Swalina C, Pak MV, Hammes-Schiffer S (2012) J Chem Phys 136:164105

    Article  Google Scholar 

  61. Scuseria GE (1993) Nature 366:512

    Article  Google Scholar 

  62. Marx D, Parrinello M (1995) Nature 375:216

    Article  CAS  Google Scholar 

  63. Boo DW, Liu ZF, Suits AG, Tse JS, Lee YT (1995) Science 269:57

    Article  CAS  Google Scholar 

  64. White ET, Tang J, Oka T (1999) Science 284:135

    Article  CAS  Google Scholar 

  65. Marx D, Parrinello M (1999) Science 284:59

    Article  CAS  Google Scholar 

  66. Schreiner PR (2000) Angew Chem Int Ed 39:3239

    Article  CAS  Google Scholar 

  67. Asvany O, Kumar PP, Redlich B, Hegemann I, Schlemmer S, Marx D (2005) Science 309:1219

    Article  CAS  Google Scholar 

  68. Huang X, McCoy AB, Bowman JM, Johnson LM, Savage C, Dong F, Nesbitt DJ (2006) Science 311:60

    Article  CAS  Google Scholar 

  69. Ivanov SD, Asvany O, Witt A, Hugo E, Mathias G, Redlich B, Marx D, Schlemmer S (2010) Nature Chem 2:298

    Article  CAS  Google Scholar 

  70. Hoshino M, Nishizawa H, Nakai H (2011) J Chem Phys 135:024111

    Article  Google Scholar 

  71. Nishizawa H, Hoshino M, Imamura Y, Nakai H (2012) Chem Phys Lett 521:142

    Article  CAS  Google Scholar 

  72. Nishizawa H, Imamura Y, Ikabata Y, Nakai H (2012) Chem Phys Lett 533:100

    Article  CAS  Google Scholar 

  73. Sirjoosingh A, Pak MV, Hammes-Schiffer S (2012) J Chem Phys 136:174114

    Article  Google Scholar 

  74. Aguirre N, Villarreal P, Delgado-Barrio G, Posada E, Reyes A, Biczysko M, Mitrushchenkov AO, de Lara-Castells MP (2013) J Chem Phys 138:184113

    Article  Google Scholar 

  75. Diaz-Tinoco M, Romero J, Ortiz JV, Reyes A, Flores-Moreno R (2013) J Chem Phys 138:194108

    Article  Google Scholar 

  76. Sirjoosingh A, Pak MV, Swalina C, Hammes-Schiffer S (2013) J Chem Phys 139:034102

    Article  Google Scholar 

  77. Sirjoosingh A, Pak MV, Swalina C, Hammes-Schiffer S (2013) J Chem Phys 139:034103

    Article  Google Scholar 

  78. Fleming DG, Areseneau DJ, Sukhorukov O, Brewer JH, Mielke SL, Schatz GC, Peterson KA, Truhlar DG (2011) Science 331:448

    Article  CAS  Google Scholar 

  79. Moncada F, Cruz D, Reyes A (2012) Chem Phys Lett 539–540:209

    Article  Google Scholar 

  80. Moncada F, Cruz D, Reyes A (2013) Chem Phys Lett 570:16

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The authors are grateful to the Research Council of Shahid Beheshti Univestity (SBU) for their financial support. The authors are grateful to Masume Gharabaghi and Shahin Sowlati for their detailed reading of a previous draft of paper and helpful suggestions.

Author information

Authors and Affiliations

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

    Mohammad Goli & Shant Shahbazian

Authors
  1. Mohammad Goli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shant Shahbazian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shant Shahbazian.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOC 481 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goli, M., Shahbazian, S. The two-component quantum theory of atoms in molecules (TC-QTAIM): the unified theory of localization/delocalization of electrons, nuclei, and exotic elementary particles. Theor Chem Acc 132, 1410 (2013). https://doi.org/10.1007/s00214-013-1410-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00214-013-1410-4

Keywords

Search

Navigation