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Advances in the Theory of Quantum Systems in Chemistry and Physics pp 139–171Cite as

Atomic Density Functions: Atomic Physics Calculations Analyzed with Methods from Quantum Chemistry

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Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 22))

Abstract

This contribution reviews a selection of findings on atomic density functions and discusses ways for reading chemical information from them. First an expression for the density function for atoms in the multi-configuration Hartree–Fock scheme is established. The spherical harmonic content of the density function and ways to restore the spherical symmetry in a general open-shell case are treated. The evaluation of the density function is illustrated in a few examples. In the second part of the paper, atomic density functions are analyzed using quantum similarity measures. The comparison of atomic density functions is shown to be useful to obtain physical and chemical information. Finally, concepts from information theory are introduced and adopted for the comparison of density functions. In particular, based on the Kullback–Leibler form, a functional is constructed that reveals the periodicity in Mendeleev’s table. Finally a quantum similarity measure is constructed, based on the integrand of the Kullback–Leibler expression and the periodicity is regained in a different way.

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References

  1. Hohenberg P, Kohn W (1964) Phys Rev B 136(3B):B864

    Google Scholar 

  2. Fischer CF, Tachiev G, Gaigalas G, Godefroid MR (2007) Comput Phys Commun 176(8):559

    Article  Google Scholar 

  3. Borgoo A, Scharf O, Gaigalas G, Godefroid M (2010) Comput Phys Commun 181(2):426. doi:10.1016/j.cpc.2009.10.014. URL http://www.sciencedirect.com/science/article/B6TJ5-4XG3SF0-1/2/d040eb496c97b1d109b779bede692437

    Google Scholar 

  4. Desclaux JP (1975) Comput Phys Commun 9(1):31

    Article  Google Scholar 

  5. Carbó R, Leyda L, Arnau M (1980) Int J Quantum Chem 17(6):1185

    Article  Google Scholar 

  6. Borgoo A, Godefroid M, Sen KD, De Proft F, Geerlings P (2004) Chem Phys Lett 399(4-6):363

    Article  CAS  Google Scholar 

  7. Borgoo A, Godefroid M, Indelicato P, De Proft F, Geerlings P (2007) J Chem Phys 126(4):044102

    Article  CAS  Google Scholar 

  8. Kullback S, Leibler RA (1951) Ann Math Stat 22(1):79. URL http://www.jstor.org/stable/2236703

    Google Scholar 

  9. Hibbert A, Glass R, Fisher CF (1991) Comput Phys Commun 64(3):455

    Article  CAS  Google Scholar 

  10. McWeeny R (1992) Methods of molecular quantum mechanics. Academic, London

    Google Scholar 

  11. Helgaker T, Jorgensen P, Olsen J (2000) Molecular electronic structure theory. Wiley, Chichester

    Google Scholar 

  12. Davidson ER (1976) Reduced density matrices in quantum mechanics. Academic, New York

    Google Scholar 

  13. Cowan R (1981) The theory of atomic structure and spectra. Los Alamos Series in Basic and Aplied Sciences. University of California Press

    Google Scholar 

  14. Fertig HA, Kohn W (2000) Phys Rev A 62(5):052511

    Article  Google Scholar 

  15. Slater J (1930) Phys Rev 35:210

    Article  Google Scholar 

  16. Hartree D (1957) The calculation of atomic structures. Wiley, New York

    Google Scholar 

  17. Fischer CF (1977) The Hartree-Fock method for atoms. A numerical approach. Wiley, New York

    Google Scholar 

  18. Varshalovich D, Moskalev A, Khersonskii V (1988) Quantum theory of angular momentum. World Scientific, Singapore

    Book  Google Scholar 

  19. Unsöld A (1927) Ann Phys 82:355

    Article  Google Scholar 

  20. Judd B (1967) Second quantization and atomic spectroscopy. The Johns Hopkins Press, Baltimore

    Google Scholar 

  21. Olsen J, Godefroid MR, Jönsson P, Malmqvist PA, Fischer CF (1995) Phys Rev E 52(4):4499. doi:10.1103/PhysRevE.52.4499

    Article  CAS  Google Scholar 

  22. Gaigalas G, Fritzsche S, Grant, IP (2001) Comput Phys Commun 139(3):263

    Article  CAS  Google Scholar 

  23. Carette T, Drag C, Scharf O, Blondel C, Delsart C, Froese Fischer C, Godefroid M (2010) Phys Rev A 81:042522. doi:10.1103/PhysRevA.81.042522

    Google Scholar 

  24. Indelicato P (1995) Phys Rev A 51(2):1132

    Article  CAS  Google Scholar 

  25. Indelicato P (1996) Phys Rev Lett 77(16):3323

    Article  CAS  Google Scholar 

  26. Grant I (1996) In: Drake G (ed) Atom, molecular ant optical physics. AIP, New York

    Google Scholar 

  27. Desclaux J (1993) In: Clementi E (ed) Methods and techniques in computational chemistry - vol. A: small systems of METTEC, Stef, Cagliari, p. 253

    Google Scholar 

  28. Parr RG, Bartolotti LJ (1983) J Phys Chem 87(15):2810

    Article  CAS  Google Scholar 

  29. Ayers PW (2000) Proc Natl Acad Sci U S A 97(5):1959

    Article  CAS  Google Scholar 

  30. Kato T (1957) Commun Pure Appl Math 10(2):151

    Article  Google Scholar 

  31. Geerlings P, Boon, G, Van Alsenoy C, De Proft F (2005) Int J Quantum Chem 101(6):722

    Article  CAS  Google Scholar 

  32. Geerlings P, De Proft F, Ayers P (2007) In: Toro Labbé A (ed) Theoretical aspects of chemical reactivity, Elsevier, Amsterdam

    Google Scholar 

  33. Chattaraj P (ed) (2009) Chemical reactivity theory; a density functional view. CRC/Taylor & Francis Group, Boca Raton

    Google Scholar 

  34. Rouvray D (1995) In: Sen K (ed) Topics in current chemistry, vol 173. Springer, Berlin/New York, p. 2

    Google Scholar 

  35. Patai S (ed) (1992) The chemistry of functional groups. Interscience Pubishers, London

    Google Scholar 

  36. Bultinck P, De Winter H, Langeneaker W (2003) Computation medicinal chemistry for drug discovery. Decker Inc., New York

    Google Scholar 

  37. Bultinck P, Girones X, Carbó-Dorca R (2005) Rev Comput Chem 21:127

    Article  CAS  Google Scholar 

  38. Boon G, De Proft F, Langenaeker W, Geerlings P (1998) Chem Phys Lett 295(1–2):122

    Article  CAS  Google Scholar 

  39. Boon G, Langenaeker W, De Proft F, De Winter H, Tollenaere JP, Geerlings P (2001) J Phys Chem A 105(38):8805

    Article  CAS  Google Scholar 

  40. Geerlings P, De Proft F, Langenaeker W (2003) Chem. Rev. 103(5):1793

    Article  CAS  Google Scholar 

  41. Boon G, Van Alsenoy C, De Proft F, Bultinck P, Geerlings P (2003) J Phys Chem A 107(50):11120

    Article  CAS  Google Scholar 

  42. Janssens S, Boon G, Geerlings P (2006) J Phys Chem A 110(29):9267

    Article  CAS  Google Scholar 

  43. Janssens S, Van Alsenoy C, Geerlings P (2007) J Phys Chem A 111(16):3143

    Article  CAS  Google Scholar 

  44. Sola M, Mestres J, Oliva JM, Duran M, Carbó R (1996) Int J Quantum Chem 58(4):361

    Article  CAS  Google Scholar 

  45. Robert D, Carbó-Dorca R (2000) Int J Quantum Chem 77(3):685

    Article  CAS  Google Scholar 

  46. Burke VM, Grant IP (1967) Proc Phys Soc Lond 90(2):297

    Article  CAS  Google Scholar 

  47. Desclaux JP (2002) The relativistic electronic structure theory book. Theoretical and computational chemistry, vol 11. Elsevier, Amsterdam

    Google Scholar 

  48. Geerlings P, De Proft F (2008) Phys Chem Chem Phys 10(21):3028

    Article  CAS  Google Scholar 

  49. Shannon S (1948) Bell Syst Tech 27:379

    Article  Google Scholar 

  50. Jaynes ET (1957) Phys Rev 106(4):620

    Article  Google Scholar 

  51. Jaynes ET (1957) Phys Rev 108(2):171

    Article  Google Scholar 

  52. Ben-Naim A (2008) Farewell to entropy: statistical thermodynamics based on information. World Scientific Publishing Co. Pte. Ltd., Singapore

    Book  Google Scholar 

  53. Levine RD (1978) Annu Rev Phys Chem 29:59

    Article  CAS  Google Scholar 

  54. Sears SB, Parr RG, Dinur U (1980) Israel J Chem 19(1–4):165

    CAS  Google Scholar 

  55. Gadre S (2002) In: Sen K (ed) Reviews of modern quantum chemistry, vol 1. World Scientific Publishing Co., Singapore, pp. 108–147

    Google Scholar 

  56. Catalan RG, Garay J, Lopez-Ruiz R (2002) Phys Rev E 66(1):011102

    Article  Google Scholar 

  57. Mathai A (1975) Basic concepts in information theory and statistics axiomatic foundations and applications. Wiley Eastern, New Delhi

    Google Scholar 

  58. Ash R (1967) Information theory. Interscience Publishers, New York

    Google Scholar 

  59. Kinchin A (1957) Mathematical foundations of information theory. Dover, New York

    Google Scholar 

  60. Lin J (1991) IEEE Trans Inf Theory 37(1):145

    Article  Google Scholar 

  61. Majtey A, Lamberti PW, Martin MT, Plastino A (2005) Eur Phys J D 32(3):413

    Article  CAS  Google Scholar 

  62. Chatzisavvas KC, Moustakidis CC, Panos CP (2005) J Chem Phys 123(17):174111

    Article  Google Scholar 

  63. Sanderson RT (1951) Science 114:670

    Article  CAS  Google Scholar 

  64. Geerlings P, Borgoo A (2011) Phys Chem Chem Phys 13(3):911

    Article  CAS  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Chemistry, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium

    Alex Borgoo & Paul Geerlings

  2. Service de Chimie quantique et Photophysique CP160/09, Université Libre de Bruxelles, 50, av. F.D. Roosevelt, B-1050, Bruxelles, Belgium

    Michel R. Godefroid

Authors
  1. Alex Borgoo
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  2. Michel R. Godefroid
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  3. Paul Geerlings
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Editor information

Editors and Affiliations

  1. , LASMEA, Clermont University, avenue des Landais 24, Aubiere Cedex, 63177, France

    Philip E. Hoggan

  2. Dept. Quantum Chemistry, Uppsala University, Uppsala, Sweden

    Erkki J. Brändas

  3. Labo. Chimie Physique, CNRS, rue Pierre et Marie Curie 11, Paris, 75005, France

    Jean Maruani

  4. Dept. Chemistry, Michigan State University, Chemistry Building, East Lansing, 48824, Michigan, USA

    Piotr Piecuch

  5. Inst. Matemáticas y Física, Fundamental (IMAFF), CSIC Madrid, C/ Serrano 123, Madrid, 28006, Spain

    Gerardo Delgado-Barrio

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Borgoo, A., Godefroid, M.R., Geerlings, P. (2012). Atomic Density Functions: Atomic Physics Calculations Analyzed with Methods from Quantum Chemistry. In: Hoggan, P., Brändas, E., Maruani, J., Piecuch, P., Delgado-Barrio, G. (eds) Advances in the Theory of Quantum Systems in Chemistry and Physics. Progress in Theoretical Chemistry and Physics, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2076-3_9

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