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Finite element density functional calculations for light molecules using a cusp factor to mitigate the Coulomb potential

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Abstract

Finite element calculations have been performed in Cartesian coordinates using the density functional approach for a number of small molecules. In order to aid convergence of the orbitals and total energies a suitable cusp factor was employed, such that the resulting effective potential is non-singular at all nuclei. The resulting total energies and densities were compared with those obtained using the Gaussian basis set package NWChem [M. Valiev et al., Comput. Phys. Commun. 181, 1477 (2010)] and excellent agreement was found.

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References

  1. M. Valiev, E.J. Bylaska, N. Govind, K. Kowalski, T.P. Straatsma, H.J.J. Van Dam, D. Wang, J. Nieplocha, E. Apra, T.L. Windus, W.A. de Jong, Comput. Phys. Commun. 181, 1477 (2010)

    Article  ADS  Google Scholar 

  2. W.J. Hehre, R.F. Stewart, J.A. Pople, J. Chem. Phys. 51, 2657 (1969)

    Article  ADS  Google Scholar 

  3. G. te Velde, F.M. Bickelhaupt, E.J. Baerends, C. Fonseca Guerra, S.J.A. van Gisbergen, J.G. Snijders, T. Ziegler, J. Comput. Chem. 22, 931 (2001)

    Article  Google Scholar 

  4. V. Blum, R. Gehrke, F. Hanke, P. Havu, V. Havu, X. Ren, K. Reuter, M. Scheffler, Comput. Phys. Commun. 180, 2175 (2009)

    Article  ADS  Google Scholar 

  5. R. Alizadegan, K.J. Hsia, T.J. Martinez, J. Chem. Phys. 132, 034101 (2010)

    Article  ADS  Google Scholar 

  6. M. Braun, J. Comput. Appl. Math. 270, 100 (2014)

    Article  MathSciNet  Google Scholar 

  7. P. Blaha, K. Schwarz, G.K.H Madsen, D. Vasnicka, J. Luitz,WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Technical University Vienna, Austria, 2001)

  8. M. Braun, K.O. Obodo, Comput. Math. Appl. 74, 35 (2017)

    Article  MathSciNet  Google Scholar 

  9. A. Castro, H. Appel, M. Oliveira, C.A. Rozzi, L.F.X. Andrade, M.A.L. Marques, E. Gross, A. Rubio, Phys. Status Solidi B 243, 2465 (2006)

    Article  ADS  Google Scholar 

  10. S. Ghosh, P. Suryanarayana, Comput. Phys. Commun. 212, 03 (2016)

    Google Scholar 

  11. J.J. Mortensen, L.B. Hansen, K.W. Jacobsen, Phys. Rev. B 71, 035109 (2005)

    Article  ADS  Google Scholar 

  12. M. Braun, J. Comput. Appl. Math. 236, 4840 (2012)

    Article  Google Scholar 

  13. C. Geuzaine, J.-F. Remacle, Int. J. Numer. Methods Eng. 79, 1309 (2009)

    Article  Google Scholar 

  14. S. Lehtola, C. Steigemann, M.J.T. Oliveira, M.A.L. Marques, SoftwareX 7, 1 (2018)

    Article  ADS  Google Scholar 

  15. M.S. Alnæs, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M.E. Rognes, G.N. Wells, The FEniCS project version 1.5, inArchive of Numerical Software (2015), Vol. 3

  16. O. Čertík, J.E. Pask, J. Vackář, Comput. Phys. Commun. 184, 1777 (2013)

    Article  ADS  Google Scholar 

  17. P. Pulay, Chem. Phys. Lett. 73, 393 (1980)

    Article  ADS  Google Scholar 

  18. G. Strang, G.J. Fix, An Analysis of the Finite Element Method, Prentice-Hall series in automatic computation (Prentice-Hall, Upper Saddle River, New Jersey, USA, 1973)

  19. P.A.M. Dirac, Math. Proc. Cambridge Philos. Soc. 26, 376 (1930)

    Article  ADS  Google Scholar 

  20. J.P. Perdew, Y. Wang, Phys. Rev. B 45, 13244 (1992)

    Article  ADS  Google Scholar 

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Correspondence to Moritz Braun.

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Braun, M., Obodo, K.O. Finite element density functional calculations for light molecules using a cusp factor to mitigate the Coulomb potential. Eur. Phys. J. B 92, 230 (2019). https://doi.org/10.1140/epjb/e2019-100310-6

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  • DOI: https://doi.org/10.1140/epjb/e2019-100310-6

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