Journal of Mathematical Chemistry

, Volume 51, Issue 5, pp 1293–1299 | Cite as

A comparison of efficiency and accuracy of two-electron integrals calculation between two methods in multi-configuration time-dependent hartree fock frame

Original Paper


An approach to the evaluation of the two-electron repulsion integrals exactly in sine finite basis representation is proposed. The two-electron coulomb potential integrals are calculated respectively in sine finite basis representation by using two-fold Gaussian quadrature rules and in discrete variable representation by using the natural potential expansion of coulomb potential \(r_{12} \). The efficiency and accuracy of two methods to calculate the two-electron repulsion integrals are compared. Some demonstrative calculations indicate that both the two ways are effective methods to do two-electron integrals calculations in the multi-configuration time-dependent hartree fock (MCTDHF) frame. By using the method to calculate the two-electron integrals in sine FBR, the working equations of MCTDHF are propagated in imaginary time. The ground state energy of helium atom obtained in the imaginary propagation is close to the Full Configuration interaction energy calculated by Molpro.


MCTDHF Two electrons integrals Finite basis representation Discrete variable representation Gaussian quadrature integrals  Nature potential approximation 



This work was supported by the NSF of China (NSFC) (Grant No. 10974198).


  1. 1.
    E. Runge, E.K.U. Gross, Phy. Rev. Lett. 52, 997 (1984)CrossRefGoogle Scholar
  2. 2.
    F. Calvayrac, P.G. Reinhard, E. Suraud, C.A. Ullrich, Phys. Rep. 337, 493 (2000)CrossRefGoogle Scholar
  3. 3.
    K.C. Kulander, Phys. Rev. A 36, 2726 (1987)CrossRefGoogle Scholar
  4. 4.
    M.S. Pindzola, P. Gavras, T.W. Gorczyca, Phys. Rev. A 51, 3999 (1995)CrossRefGoogle Scholar
  5. 5.
    T. Klamroth, Phys. Rev. B 68, 245421 (2003)CrossRefGoogle Scholar
  6. 6.
    J. Zanghellini, M. Kitzler, C. Fabian, T. Brabec, A. Scrinzi, Laser Phys. 13, 1064 (2003)Google Scholar
  7. 7.
    J. Zanghellini, M. Kitzler, T. Brabec, A. Scrnzi, J. Phys. B At. Mol. Opt. Phys. 37, 763 (2004)CrossRefGoogle Scholar
  8. 8.
    J. Caillat, J. Zhanghellini, M. Kitzler, O. Koch, W. Kreuzer, A. Scrinzi, Phys. Rev. A 71, 012712 (2005)CrossRefGoogle Scholar
  9. 9.
    T. Kato, H. Kono, Chem. Phys. Lett. 392, 533 (2004)CrossRefGoogle Scholar
  10. 10.
    T. Kato, K. Yamanouchi, J. Chem. Phys. 131, 164118 (2009)CrossRefGoogle Scholar
  11. 11.
    M. Nest, T. Klamroth, P. Saalfrank, J. Chem. Phys. 122, 124102 (2005)CrossRefGoogle Scholar
  12. 12.
    M. Nest, T. Klamroth, Phys. Rev. A 72, 012710 (2005)CrossRefGoogle Scholar
  13. 13.
    M. Nest, J. Theor. Comput. Chem 6, 563 (2007)CrossRefGoogle Scholar
  14. 14.
    M. Nest, J. Chem. Phys. 472, 171 (2009)Google Scholar
  15. 15.
    M. Nest, R. Padmanaban, P. Saalfrank, J. Chem. Phys. 126, 124106 (2007)CrossRefGoogle Scholar
  16. 16.
    H.D. Meyer, U. Manthe, L.S. Cederbaum, Chem. Phys. Lett. 165, 73 (1990)CrossRefGoogle Scholar
  17. 17.
    M.H. Beck, A. Jackle, G.A. Worth, H.D. Meyer, Phys. Rep. 324, 1 (2000)CrossRefGoogle Scholar
  18. 18.
    M. Nest, H.D. Meyer, J. Chem. Phys. 119, 24 (2003)CrossRefGoogle Scholar
  19. 19.
    H.D. Meyer, G.A. Worth, Theor. Chem. Acc. 109, 251 (2003)CrossRefGoogle Scholar
  20. 20.
    W. Li, W. Xu, Mol. Phys. 111, 119 (2013)Google Scholar
  21. 21.
    A.Szabo, N.S. Ostlund, Modern Quantum Chemistry, Mineola, New YorkGoogle Scholar
  22. 22.
    H.J. Werner, P.J. Konwles, R.D. Amos, A. Berning, D.L. Cooper, M.J.O. Deegan, A.J. Dobbyn, F. Eckert, C. Hampel, T. Leininger, R. Lindh, A.W. Lloyd, 245 W. Meyer, M.E. Mura, A. Nickla, P. Palmieri, K. Peterson, R. Pitzer, P. Pulay, G. Rauhut, M. Schfltz, H. Stoll, A.J. Stone, T. Thoresteinsson, MOLPRO 2010, a package of ab initio programs, see

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.State key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical PhysicsChinese Academy of ScienceDalianChina
  2. 2.Xinjiang Institute of Engineering, UrumqiXinjiangChina

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