Progress in Hylleraas-CI Calculations on Boron

  • María Belén RUIZ
Part of the Progress in Theoretical Chemistry and Physics book series (PTCP, volume 22)


Preliminary results on Hylleraas-Configuration Interaction calculations of the boron atom ground state are presented. The wave function consists of a 954 term Configuration Interaction part and 192 configurations including all interelectronic distances. An energy value of − 24. 64815076 a.u. was been obtained with a minimal orbital basis [4s3p2d]. Calculations with more configurations are in progress. Correct description of the electronic cusp is important, as discussed and the most recent benchmark calculations in the field are concisely reviewed. The computational techniques for matrix element evaluation are described. Those employed for the B atom can be readily used for C and N atoms, and further for the highly accurate calculation of the nonrelativistic energy of second row elements.


Configuration Interaction Boron Neutron Capture Therapy Configuration Interaction Calculation Nonrelativistic Energy Wave Function Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I would like to thank Philip E. Hoggan for the invitation to contribute to these Proceedings. I am indebted to James Sims for interesting discussions about the Hy-CI method, and for providing highly accurate results of three- and four-electron integrals to test the program code. The high precision Vkl, Condon and Shortley coefficients and triangle integral programs of James Sims and Stanley Hagstrom are greatly acknowledged. I would like to thank very much Carlos Bunge for helpful advice on the CI method. It is a pleasant duty to acknowledge Peter Otto for advising in efficient Fortran programming and for supporting this project. Finally, I am indebted to the anonymous Referee for the careful revision, valuable comments and insights.


  1. 1.
    Almora-Díaz CX, Bunge CF (2010) Int J Quantum Chem 10:2982–2988CrossRefGoogle Scholar
  2. 2.
    Aquino N, Garza J, Flores-Riveros A, Rivas-Silva JF, Sen KD (2006) J Chem Phys 124:054311CrossRefGoogle Scholar
  3. 3.
    Bailey DH High-precision software directory. Available at: Accessed 10 Aug 2011
  4. 4.
    Barrois R, Lüchow A, Kleindienst H (1997) Int J Quantum Chem 62:77CrossRefGoogle Scholar
  5. 5.
    Brown RE (1967) PhD. thesis, Department of Chemistry, Indiana University, USAGoogle Scholar
  6. 6.
    Brown MD, Trail JR, López Ríos P, Needs RJ (2007) J Chem Phys 126:224110Google Scholar
  7. 7.
    Bubin S, Stanke M, Adamowicz L (2009) J Chem Phys 131:044128CrossRefGoogle Scholar
  8. 8.
    Budzinski J (2004) Int J Quantum Chem 97:832CrossRefGoogle Scholar
  9. 9.
    Bunge CF (2010) Theor Chem Acc 126:139CrossRefGoogle Scholar
  10. 10.
    Büsse G, Kleindienst H, Lüchow A (1998) Int J Quantum Chem 66:241CrossRefGoogle Scholar
  11. 11.
    Cencek W, Rychlewski J (1993) J Chem Phys 98:1252CrossRefGoogle Scholar
  12. 12.
    Cencek W, Szalewicz K (2008) Int J Quantum Chem 108:2191CrossRefGoogle Scholar
  13. 13.
    Chakravorty SJ, Gwaltney SR, Davidson ER, Parpia FA, Fischer CF (1993) Phys Rev A 47:3649CrossRefGoogle Scholar
  14. 14.
    Clary DC (1977) Mol Phys 34:793CrossRefGoogle Scholar
  15. 15.
    Clary DC, Handy NC (1976) Phys Rev A 14:1607CrossRefGoogle Scholar
  16. 16.
    Condon EU, Shortley GH (1967) The theory of atomic spectra. Cambridge University Press, Cambridge, MAGoogle Scholar
  17. 17.
    Drake GWF (1999) Phys Scripta T83:83CrossRefGoogle Scholar
  18. 18.
    Feller D, Davidson ER (1988) J Chem Phys 88:7580CrossRefGoogle Scholar
  19. 19.
    Fischer CF Personal communicationGoogle Scholar
  20. 20.
    Frankowski K, Pekeris CL (1966) Phys Rev 146:46CrossRefGoogle Scholar
  21. 21.
    Frolov AM, Ruiz MB (2010) Phys Rev A 82:042511CrossRefGoogle Scholar
  22. 22.
    Gálvez FJ, Buendía E, Sarsa A (2005) J Chem Phys 122:154307CrossRefGoogle Scholar
  23. 23.
    Gdanitz RJ (1998) J Chem Phys 109:9795CrossRefGoogle Scholar
  24. 24.
    Hill RN (1985) J Chem Phys 83:1173CrossRefGoogle Scholar
  25. 25.
    Hoggan PE, Ruiz MB, Özdogan T (2011) Molecular integrals over slater-type orbitals. From pioneers to recent progress. In: Putz MV (ed) Quantum frontiers of atoms and molecules. Nova Publishing Inc., New York, pp 61–89Google Scholar
  26. 26.
    Hylleraas EA (1929) Z Phys 54:347CrossRefGoogle Scholar
  27. 27.
    James HM, Coolidge AS (1936) Phys Rev 49:688CrossRefGoogle Scholar
  28. 28.
    Jönsson P, Froese Fischer C (1994) Phys Rev A 50:3080Google Scholar
  29. 29.
    Kato T (1957) Commun Pure Appl Math 10:151CrossRefGoogle Scholar
  30. 30.
    King FW (1999) Adv Mol Opt Phys 40:57CrossRefGoogle Scholar
  31. 31.
    kleindienst H, Büsse G, Lüchow A (1995) Int J Quantum Chem 53:575Google Scholar
  32. 32.
    Klopper W, Bachorz RA, Tew DP, Hättig C (2010) Phys Rev A 81:022503CrossRefGoogle Scholar
  33. 33.
    Komasa J personal communicationGoogle Scholar
  34. 34.
    Kutzelnigg W (1985) Theor Chim Acta 86:445CrossRefGoogle Scholar
  35. 35.
    Kutzelnigg W, Morgan JD III (1992) J Chem Phys 96:4484CrossRefGoogle Scholar
  36. 36.
    Kurokawa Y, Nakashima H, Nakatsuji H (2005) Phys Rev A 72:062502CrossRefGoogle Scholar
  37. 37.
    MAPLE 9 Release by Waterloo Maple Inc. Copyright 2003Google Scholar
  38. 38.
    Mayer I (1991) Personal communication. HONDO-8, from MOTECC-91, contributed and documented by M. Dupuis and A. Farazdel, IBM Corporation Center for Scientific & Engineering Computations, Kingston, NY. Knowles PJ, Handy NC Chem Phys Lett 111:315 (1984); Comput Phys Commun 54:75 (1989)Google Scholar
  39. 39.
    Meyer H, Müller T, Schweig A (1995) Chem Phys 191:213CrossRefGoogle Scholar
  40. 40.
    Merckens H-P (2002) Eigenwertberechnungen an angeregten 1 S-Zuständen des Berylliumatoms, Thesis, Düsseldorf, GermanyGoogle Scholar
  41. 41.
    Mohr PJ, Taylor BN, Newell DB (2008) CODATA Recommended values of the fundamental physical constants: 2006. Rev Mod Phys 80:633–730CrossRefGoogle Scholar
  42. 42.
    Nakashima H, Nakatsuji H (2008) J Chem Phys 128:154107CrossRefGoogle Scholar
  43. 43.
    Nakashima H, Hijikata Y, Nakatsuji H (2008) J Chem Phys 128:154108CrossRefGoogle Scholar
  44. 44.
    Pachucki K (2010) Phys Rev A 82:032509CrossRefGoogle Scholar
  45. 45.
    Preiskorn A, Frey D, Lie GC, Clementi E (1991) In: Clementi E (ed) Modern techniques in computational chemistry: MOTECC-91. ESCOM Science Publishers, Leiden, Chapter 13Google Scholar
  46. 46.
    Przybytek M, Cencek W, Komasa J, Lach G, Jeziorski B, Szalewicz K (2010) Phys Rev Lett 104:183003CrossRefGoogle Scholar
  47. 47.
    Puchalski M, Kedziera D, Pachucki K (2009) Phys Rev A 80:032521CrossRefGoogle Scholar
  48. 48.
    Ruiz MB (2009) J Math Chem 46:24CrossRefGoogle Scholar
  49. 49.
    Ruiz MB (2009) J Math Chem 46:1322CrossRefGoogle Scholar
  50. 50.
    Ruiz MB (2005) Int J Quantum Chem 100:246CrossRefGoogle Scholar
  51. 51.
    Ruiz MB, Peuker K (2008) In: Ozdogan T, Ruiz MB Recent advances in computational chemistry: molecular integrals over slater orbitals. Transworld Research Network, Kerala, pp 99–144Google Scholar
  52. 52.
    Ruiz MB, Rojas M (2003) Comput Methods Sci Technol 9(1–2):101Google Scholar
  53. 53.
    Ruiz MB, Rojas M, Chicón G, Otto P (2010) Int J Quantum Chem 111, 1921 (2011)Google Scholar
  54. 54.
    Sasaki F, Yoshimine M (1974) Phys Rev A 9:17CrossRefGoogle Scholar
  55. 55.
    Schaefer HF, Harris FE (1968) Phys Rev 167:67CrossRefGoogle Scholar
  56. 56.
    Schwartz C (1962) Phys Rev 126:1015CrossRefGoogle Scholar
  57. 57.
    Schwartz C (2006) Int J Mod Phys E15:877; e-Print arXiv:physics/0208004; Updated results in e-Print math-phys/0605018Google Scholar
  58. 58.
    Sharkey KL, Bubin S, Adamowicz L (2010) J Chem Phys 132:184106CrossRefGoogle Scholar
  59. 59.
    Sims JS, Hagstrom SA (1971) J Chem Phys 55:4699CrossRefGoogle Scholar
  60. 60.
    Sims JS, Hagstrom SA (1971) Phys Rev A 4:908CrossRefGoogle Scholar
  61. 61.
    Sims JS, Hagstrom SA (2002) Int J Quantum Chem 90:1600CrossRefGoogle Scholar
  62. 62.
    Sims JS, Hagstrom SA (2004) J Phys B: At Mol Opt Phys 37:1519CrossRefGoogle Scholar
  63. 63.
    Sims JS, Hagstrom SA (2006) J Chem Phys 124:094101CrossRefGoogle Scholar
  64. 64.
    Sims JS, Hagstrom SA (2009) Phys Rev A 80:052507CrossRefGoogle Scholar
  65. 65.
    Sims JS, Hagstrom SA (2011) Phys Rev A 83:032512CrossRefGoogle Scholar
  66. 66.
    Stanke M, Komasa J, Bubin S, Adamowitz L (2009) Phys Rev A 80:022514CrossRefGoogle Scholar
  67. 67.
    Stevenson R (1965) Multiplet structure of atoms and molecules. W.B. Saunders Company, Philadelphia & LondonGoogle Scholar
  68. 68.
    Walsh P, Borowitz S (1960) Phys Rev 119:1274CrossRefGoogle Scholar
  69. 69.
    Weiss AW (1961) Phys Rev 122:1826CrossRefGoogle Scholar
  70. 70.
    Weiss AW (1969) Phys Rev 188:119CrossRefGoogle Scholar
  71. 71.
    Woznicki W (1971) In: Jucys A (ed) Theory of electronic shells in atoms and molecules. Mintis, Vilnius, p 103Google Scholar
  72. 72.
    Zhou BL, Zhu JM, Yan ZC (2006) Phys Rev A 73:064503CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • María Belén RUIZ
    • 1
  1. 1.Department of Theoretical Chemistry of the Friedrich-Alexander-UniversityErlangen-NürnberErlangenGermany

Personalised recommendations