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Finite element method for relativistic analysis of wave functions of xenon atom

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Author Affiliations

  • 1Plasma Physics Laboratory and Interdisciplinary Research, Dakar, Senegal
  • 2Plasma Physics Laboratory and Interdisciplinary Research, Dakar, Senegal
  • 3Group of Solid Physics and Materials Sciences, Dakar, Senegal

Res. J. Engineering Sci., Volume 11, Issue (1), Pages 1-14, January,26 (2022)

Abstract

Taking into account relativistic aspect in quantum calculations, is a fundamental step towards correct modeling of systems involving heavy elements. This modeling involves an appropriate resolution of Schrödinger equation. The present study focuses on Xenon which is a heavy poly electronic atom. This is to calculate on basis of DFT, its radial wave functions for different orbitals, total energies and its effective potential in the ground state. Our motivation through this simulation is to examine the influence of relativistic effects and spin-orbit coupling on these physical grandeur. So, due to the structural complexity of the equation, we carried out the calculations implicitly by the finite element method via a program established from MATLAB software in deterministic mode. The numerical solutions obtained are based on the approximation of the local density (LDA) and that of the generalized gradient (GGA). The results obtained, allowed to describe xenon on a microscopic scale, to understand its structure and to explore the mechanisms that ensure its stability. Finally, our results are in good agreement with theoretical data found in the literature.

References

  1. Gonze, X., Beuken, J., M., Caracas, R., Detraux, F., Fuchs, M., Rignanese, G., M., Sindic, L., Verstraete, M., Zerah, G., Jollet, F., Torrent, M., Roy, A., Mikami, M., Ghosez, Ph., Raty, J., Y., and Allan., D., C. (2002)., First-principles computation of material properties: the ABINIT software project., Comp. Mat. Sci., 25, 478-492.
  2. Rama, G. (2019)., Density Functional Theory (DFT) in the study of relativistic corrections and spin-orbit coupling., Application to the electronic structure of xenon, Master
  3. Kohn, W. (1999)., Nobel Lecture: Electronic structure of matter - wave functions and density functional., Rev. Mod. Phys, 71, 1253.
  4. Adel, F. A. A. (2009)., Modeling within the DFT of the properties of electronic and magnetic structures and of chemical bonding of Intermetallic Hydrides., Thesis, University of Bordeaux I.
  5. Szabo, A and Ostlund, N. S. (1989)., Modern quantum chemistry: introduction to advanced electronic structure theory., Courier Corporation.
  6. Nadir, M. (2014)., Study of the physical properties of transition metal nanostructures: CunNim., Master
  7. Bahnes, A. (2014)., Study of two first-principle methods applied to the Heuslers., Master
  8. Nabil, B.B.E. (2013)., Ab-initio study of the structural and electronic properties of ternary alloys of zinc-based II-VI semiconductors, These De Physique Theorique, Uni. Abou Bakr Belkaïd - Tlemcen, Morocco.,
  9. Diouf, Y. (2017)., Theoretical study of the electronic structure of multielectronic atoms in the approximation of the density functional theory., Master
  10. Lamrani, F. (2015)., Modeling and simulation by DFT of the electronic magnetic and structural properties of diluted magnetic oxides., Ph.D. Thesis in computational physics, University Rabat Mohammed V, Morocco.
  11. Maylis, O. (2007)., Density Functional Theory study of electronic and magnetic properties of iron complexes., Application to Catalase and Iron-Sulfur type systems. Other, Joseph-Fourier University - Grenoble.
  12. Poree, C., & Schoenebeck, F. (2017)., A holy grail in chemistry: Computational catalyst design: Feasible or fiction?., Accounts of chemical research, 50(3), 605-608.
  13. Lehtola, S., Blockhuys, F., & Van Alsenoy, C. (2020)., An overview of self-consistent field calculations within finite basis sets., Molecules, 25(5), 1218.
  14. Diouf, Y., Talla, K., Diallo, S., and Gomis, L. (2021)., Numerical Study of Density Functional Theory of Multi-electronic Atoms: Case of Carbon and Helium., American J. of Nano. 9(1), 12-22.
  15. Shamim, M. D. and Harbola, M. K. (2010)., Application of an excited state LDA exchange energy functional for the calculation of transition energy of atoms within time independent density functional theory., J.of Phys. B: Atomic, Molecular and Optical Physics, 43(21), 1-12
  16. Jones, R. O. (2015)., Density functional theory: Its origins, rise to prominence and future., Rev. of Mod. Phys., 87(3), 897-923.
  17. Xiao, D. W., Richard, L. M., Thomas, M. H. and Gustavo, E. S. (2013)., Density Functional Theory Studies of the Electronic Structure of Solid State Actinide Oxides., Chem. Rev, 113 (2), 1063–1096.
  18. Evangelista, F. A., Shushkov, P., & Tully, J. C. (2013)., Orthogonality constrained density functional theory for electronic excited states., The Journal of Physical Chemistry A, 117(32), 7378-7392.
  19. Chloé, N. G. (2019)., Study of the electronic, magnetic and magnetocaloric properties of La2MnBO6 (B = Ni, Ru, Co, Fe) and LaAMnFeO6 (A = Ba, Sr, Ca) materials and their potential for magnetic refrigeration., Master
  20. Ravo, T. R., Raoelina, A., Hery, A. and Rakotoson, H. (2018)., Density Functional Theory and its applications in Nanotechnology., Communication made during the first international conference on Nanotechnology in Madagascar, pp 11-12.
  21. Tang, Q., Zhen, Z. and Zhongfang, C. (2015)., Innovation and discovery of graphene-like materials via density-functional theory computations., WIREs Comput Mol Sci, 5(5), 360–379.
  22. Yousef, S., James, R. C. and Suzanne, M. S. (2010)., Numerical methods for electronic structure calculations of materials., SIAM Review, 52(1), 3-54.
  23. Kohn, W. (1996)., Density Functional and Density Matrix Method Scaling Linearly with the Number of Atoms., Phys. Rev. Letters, 76(17), 3168–3171.
  24. Blackburn, S. (2013)., Analysis of the electronic properties of superconductors using the density functional theory., Thesis, University of Montreal.
  25. Dyall, K. G. and Fægri, K. (2007)., Introduction to Relativistic Quantum Chemistry., Oxford University Press
  26. Kohn, W., Becke, A. D. and Parr, R. G. (1996)., Density Functional Theory of Electronic Structure., J. Phys. Chem. 100 (31), 12974–1298.
  27. Marian, C. M. (1997)., Fine and Hyper fine Structure In Problem Solving in Computational Molecular Science., Springer, 29-35.
  28. Mouhamed, A. (2016)., Applications of ELF and QTAIM topological approaches in an almost relativistic 2-component context., Doctoral thesis, Pierre and Marie Curie University.
  29. Han, Y. K. and Lee, Y. S . (1999)., Structures of RgFn (Rg = Xe, Rn, and Element 118. n = 2, 4.) calculated by two-component spin-orbit methods., A spin-orbit induced isomer of (118) F4. J Phys Chem A, 103(8), 1104–1108.
  30. Danilo, C. (2009)., Theoretical modeling of solvated actinide spectroscopy., Theoretical modeling of actinide spectra in solution, Doctoral thesis, University of Lille 1 - Stockholm University.
  31. Zhao, M., Xu, S., Shanshan, N. and Xiangjun, C. (2017)., Relativistic and distorted wave effects on Xe 4d electron momentum distributions., Chinese Physics B, 26(9), 093103-4
  32. Bader, R. F. (1990)., Atoms in molecules: a quantum theory., Inter. series of monographs on chemistry 22.
  33. Parr, R. G. and Yang, W. (1989)., Density-Functional Theory of Atoms and Molecules., Oxford University Press.
  34. Wullen, C. V. (2010)., Relativistic density functional theory In Relativistic methods for chemists., Springer, 191-214.
  35. Sarrio, C. C., Vallet, V., Maynau, D. and Marsden, C. J. (2004)., Can density functional methods be used for open-shell actinide molecules: Comparison with multiconfigurational spin-orbit studies., J. Chem. Phys, 121(11), 5312.
  36. Hess, B. A. and Marian, C. M. (1999)., Chapter1-Relativistic effects in the calculation of clectronic energies, computational molecular spectroscopy, John Wiley & Sons, Wiley, Sussex.,
  37. Neil, B. (2003)., The Noble Gases., Chemical & Engineering News. American Chem. Soci., 81(36).
  38. Martin B. K. and Christoph, P. (2006)., Isotopic signature of atmospheric xenon released from light water reactors., J. of Envi. Radioactivity, 88(3), 215-235.
  39. Mahaffy, P. R., Niemann, H. B., Alpert, A., Atreya, S. K., Demick, J., Donahue, T. M., Harpold, D. N and . Owen, T. C. (2000)., Noble gas abundance and isotope ratios in the atmosphere of Jupiter from the Galileo Probe Mass Spectrometer., J. of Geo. Research, 105(6),‎ 15061–15072.
  40. Ramsay, W. (1902)., An Attempt to Estimate the Relative Amounts of Krypton and of Xenon in Atmospheric Air., Proceedings of the Royal Society of London, 71,‎ p p. 421–426.
  41. Owen, T., Mahaffy, P., Niemann, H. B., Atreya, S., Donahue, T., Bar-Nun, A. and De Pater, I. (1999)., A low-temperature origin for the planetesimals that formed Jupiter., Nature, 402( 6759)‎, 269–270.
  42. Elena, A., Bolotnikov, A., Doke, E. and Tadayoshi (2006)., Noble Gas Detectors., Weinheim, Wiley-VCH.
  43. Caldwell, W. A., Nguyen, J., Pfrommer, B., . Louie, S. and Jeanloz, R. (1997)., Structure, bonding and geochemistry of xenon at high pressures., Science, 277, 930–933
  44. Anderson, J.S.M. and Ayers P.W. (2011)., Quantum theory of atoms in molecules: results for the SR-ZORA Hamiltonian., J Phys Chem A., 115(45), 13001–13006
  45. Filatov, M. and Cremer, D. (2003)., On the physical meaning of the ZORA Hamiltonian., Mol Phys, 101(14), 2295–2302
  46. Matito, E., Salvador, P. and Styszynski, J. (2013)., Benchmark calculations of metal carbonyl cations: relativistic vs. electron correlation effects., Phys Chem Chem Phys, 15(46), 20080–20090.
  47. Bučinský, L., Kucková, L., Malček, M., Kožíšek, J., Biskupič, S., Jayatilaka, D., ... & Arion, V. B. (2014)., Picture change error in quasirelativistic electron/spin density, Laplacian and bond critical points., Chemical Physics, 438, 37-47.
  48. Matta, C. F. and Boyd, R. J. (2007)., An introduction to the quantum theory of atoms in molecules: from solid state to DNA and drug design. In: Matta CF, Boyd RJ (eds) The quantum theory of atoms in molecules., Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
  49. Fischer, C. F., Brage, T. and Jonsson, P. (2000)., Computational Atomic Structure: An MCHF Approach., Institute of Physics Publishing Bristol and Philadlphia.
  50. Grossetête, C. (1998)., Restricted relativity and atomic structure of matter. Ellipses.,
  51. Gomis, L. (2008)., Contribution to the study of the generalized oscillator forces in the length formulation and in the speed formulation. Application to the transitions of helium and neon., Doctoral thesis from, Cheikh Anta Diop University of Dakar.
  52. Padma, R. and Deshmukh, P. C. (1992)., Calculations of generalized oscillator strength for electron-impact excitations of krypton and xenon using a relativistic local-density potential., Phys rev, 46(5), 2513-2518.
  53. Kohn, W. and Sham, L. J. (1965). Self-Consistent Equations Including Exchange and Correlation Effects. Physi. Rev, 140 (4), 1133–A1138., undefined, undefined
  54. Dirac, P. A. M. (1930)., Note on Exchange Phenomena in the Thomas Atom., Proc. Camb. Phil. Soc. 26- 376.
  55. Dahl, J. P. and Avery, J. (1984.)., Local Density Approximations in Quantum Chemistry and Solid State., Physics, Plenum, New York.
  56. Bunge, C. F. and Barrientos, J. A. (1993)., Roothann-Hartree ground-state atomic wave functions Slater-Type orbital expansions and expectation values for Z=2-54 Atomic Data and Nuclear data Tables 53, Mexico: Instituto de Fisica, Universidad Nacional Autonoma de Mexico.,