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Relativistic Time-Dependent Density Functional Theory for Molecular Properties

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Abstract

In this review article, we introduce the two-component relativistic time-dependent density functional theory (TDDFT) with spin–orbit interactions to calculate linear response properties and excitation energies. The approach is implemented in the NTChem program. Our implementation is based on a noncollinear exchange–correlation potential presented by Wang et al. In addition, various DFT functionals including the range-separated hybrid functionals have been derived and implemented with the aid of a newly developed computerized symbolic algebra system. The two-component relativistic TDDFT with spin–orbit interactions was successfully applied to the calculation of the frequency-dependent polarizabilities of SnH4 and PbH4 molecules containing heavy atoms and the excitation spectra of a HI molecule.

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References

  1. C.M. Marian, Wiley Interdiscip. Rev. Comput. Molecular Sci. 2, 187–203 (2012)

    Article  CAS  Google Scholar 

  2. Y. Imamura, M. Kamiya, T. Nakajima, Chem. Phys. Lett. 635, 152–156 (2015)

    Article  CAS  Google Scholar 

  3. Y. Imamura, M. Kamiya, T. Nakajima, Chem. Phys. Lett. 648, 60–65 (2016)

    Article  CAS  Google Scholar 

  4. M.E. Casida, M. Huix-Rotllant, Ann. Rev. Phys. Chem. 63, 287–323 (2012)

    Article  CAS  Google Scholar 

  5. C. Adamo, D. Jacquemin, Chem. Soc. Rev. 42, 845–856 (2013)

    Article  CAS  Google Scholar 

  6. A.D. Laurent, D. Jacquemin, Int. J. Quantum Chem. 113, 2019–2039 (2013)

    Article  CAS  Google Scholar 

  7. H. Weiss, R. Ahlrichs, M. Häser, J. Chem. Phys. 99, 1262–1270 (1993)

    Article  CAS  Google Scholar 

  8. R. Bauernschmitt, R. Ahlrichs, Chem. Phys. Lett. 256, 454–464 (1996)

    Article  CAS  Google Scholar 

  9. R.E. Stratmann, G.E. Scuseria, M.J. Frisch, J. Chem. Phys. 109, 8218–8224 (1998)

    Article  CAS  Google Scholar 

  10. P. Norman, D.M. Bishop, H.J. Aa. Jensen, J. Oddershede, J. Chem. Phys. 115, 10323–10334

    Google Scholar 

  11. K. Kristensen, J. Kauczor, T. Kjærgaard, P. Jørgensen, J. Chem. Phys. 131, 044112 (2009)

    Article  Google Scholar 

  12. M. Douglas, N.M. Kroll, Ann. Phys. (NY) 82, 89 (1974)

    Article  CAS  Google Scholar 

  13. B.A. Hess, Phys. Rev. A 32, 756 (1985)

    Article  CAS  Google Scholar 

  14. B.A. Hess, Phys. Rev. A 33, 3742 (1986)

    Article  CAS  Google Scholar 

  15. L.E. McMurchie, E.R. Davidson, J. Comput. Phys. 44, 289–301 (1981)

    Article  Google Scholar 

  16. R.M. Pitzer, N.W. Winter, Int. J. Quantum Chem. 40, 773–780 (1991)

    Article  CAS  Google Scholar 

  17. P. Norman, B. Schimmelpfennig, K. Ruud, H.J. Aa. Jensen, H. Ågren, J. Chem. Phys. 116, 6914–6923 (2002)

    Google Scholar 

  18. P. Salek, T. Helgaker, T. Saue, Chem. Phys. 311, 187–201 (2005)

    Article  CAS  Google Scholar 

  19. R. Bast, T. Saue, J. Henriksson, P. Norman, J. Chem. Phys. 130, 024109 (2009)

    Article  Google Scholar 

  20. F. Wang, T. Ziegler, J. Chem. Phys. 121, 12191–12196 (2004)

    Article  CAS  Google Scholar 

  21. J. Gao, W. Zou, W. Liu, Y. Xiao, D. Peng, B. Song, C. Liu, J. Chem. Phys. 123, 054102 (2005)

    Article  Google Scholar 

  22. F. Wang, T. Ziegler, J. Chem. Phys. 122, 074109 (2005)

    Article  Google Scholar 

  23. A. Nakata, T. Tsuneda, K. Hirao, J. Chem. Phys. 135, 224106 (2011)

    Article  Google Scholar 

  24. S. Hirata, M. Head-Gordon, Chem. Phys. Lett. 314, 291–299 (1999)

    Article  CAS  Google Scholar 

  25. R. Bast, H.J.A. Jensen, T. Saue, Int. J. Quantum Chem. 109, 2091–2112 (2009)

    Article  CAS  Google Scholar 

  26. T. Nakajima, M. Katouda, M. Kamiya, Y. Nakatsuka, Int. J. Quantum Chem. 115, 349–359 (2015)

    Article  CAS  Google Scholar 

  27. SymPy: Python library for symbolic mathematics. http://sympy.org

  28. J.A. Pople, R. Krishnan, H.B. Schlegel, J.S. Binkley, Int. J. Quantum Chem. 16, 225–241 (1979)

    Article  Google Scholar 

  29. P. Pulay, J. Chem. Phys. 78, 5043–5051 (1983)

    Article  CAS  Google Scholar 

  30. H. Sekino, R.J. Bartlett, J. Chem. Phys. 84, 2726–2733 (1986)

    Article  CAS  Google Scholar 

  31. E.R. Davidson, J. Comput. Phys. 17, 87–94 (1975)

    Article  Google Scholar 

  32. K. Hirao, H. Nakatsuji, J. Comput. Phys. 45, 246–254 (1982)

    Article  Google Scholar 

  33. J. Olsen, H.J. Aa. Jensen, P. Jørgensen, J. Comput. Phys. 74, 265–282 (1988)

    Google Scholar 

  34. R. Bast, U. Ekstrom, B. Gao, T. Helgaker, K. Ruud, A.J. Thorvaldsen, Phys. Chem. Chem. Phys. 13, 2627–2651 (2011)

    Article  CAS  Google Scholar 

  35. L. Nordström, D.J. Singh, Phys. Rev. Lett. 76, 4420–4423 (1996)

    Article  Google Scholar 

  36. T. Oda, A. Pasquarello, R. Car, Phys. Rev. Lett. 80, 3622–3625 (1998)

    Article  CAS  Google Scholar 

  37. S. Yamanaka, D. Yamaki, Y. Shigeta, H. Nagao, Y. Yoshioka, N. Suzuki, K. Yamaguchi, Int. J. Quantum Chem. 80, 664–671 (2000)

    Article  CAS  Google Scholar 

  38. P. Kurz, F. Förster, L. Nordström, G. Bihlmayer, S. Blügel, Phys. Rev. B 69, 024415 (2004)

    Article  Google Scholar 

  39. J.E. Peralta, G.E. Scuseria, J. Chem. Phys. 120, 5875–5881 (2004)

    Article  CAS  Google Scholar 

  40. J.E. Peralta, G.E. Scuseria, M.J. Frisch, Phys. Rev. B 75, 125119 (2007)

    Article  Google Scholar 

  41. M.K. Armbruster, F. Weigend, C. van Wullen, W. Klopper, Phys. Chem. Chem. Phys. 10, 1748–1756 (2008)

    Article  CAS  Google Scholar 

  42. G. Scalmani, M.J. Frisch, J. Chem. Theor. Comput. 8, 2193–2196 (2012)

    Article  CAS  Google Scholar 

  43. H. Sekino, J. Phys. Chem. A 104, 4685–4689 (2000)

    Article  CAS  Google Scholar 

  44. R.J. Harrison, J. Comput. Chem. 25, 328–334 (2004)

    Article  CAS  Google Scholar 

  45. S. Hirata, M. Head-Gordon, R.J. Bartlett, J. Chem. Phys. 111, 10774–10786 (1999)

    Article  CAS  Google Scholar 

  46. R. Strange, F.R. Manby, P.J. Knowles, Comput. Phys. Commun. 136, 310–318 (2001)

    Article  CAS  Google Scholar 

  47. P. Sałek, A. Hesselmann, J. Comput. Chem. 28, 2569–2575 (2007)

    Article  Google Scholar 

  48. U. Ekström, L. Visscher, R. Bast, A.J. Thorvaldsen, K. Ruud, J. Chem. Theor. Comput. 6, 1971–1980 (2010)

    Article  Google Scholar 

  49. J.P. Perdew, Burke K., Ernzerhof M., Phys. Rev. Lett. 77, 3865 (1996)

    Google Scholar 

  50. J.C. Slater, Phys. Rev. 81, 385 (1951)

    Article  CAS  Google Scholar 

  51. S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58, 1200 (1980)

    Article  CAS  Google Scholar 

  52. A.D. Becke, Phys. Rev. A 38, 3098 (1988)

    Article  CAS  Google Scholar 

  53. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37, 785 (1988)

    Article  CAS  Google Scholar 

  54. A.D. Becke, J. Chem. Phys. 98, 5648 (1993)

    Article  CAS  Google Scholar 

  55. H. Iikura, T. Tsuneda, T. Yanai, K. Hirao, J. Chem. Phys. 115, 3540 (2001)

    Article  CAS  Google Scholar 

  56. T. Yanai, D.P. Tew, N.C. Handy, Chem. Phys. Lett. 393, 51–57 (2004)

    Article  CAS  Google Scholar 

  57. V. Kellö, A.J. Sadlej, Theor. Chim. Acta. 94, 93–104 (1996)

    Google Scholar 

  58. A.J. Sadlej, Collect. Czech. Chem. Commun. 53, 1995 (1988)

    Article  CAS  Google Scholar 

  59. S. Kirpekar, J. Oddershede, Jensen HJrA. J. Chem. Phys. 103, 2983–2990 (1995)

    Article  CAS  Google Scholar 

  60. O.A. Vydrov, J. Heyd, A.V. Krukau, G.E. Scuseria, W.K, J. SL., J Chem. Phys. 125, 074106 (2006)

    Google Scholar 

  61. O.A. Vydrov, G.E. Scuseria, J. Chem. Phys. 125, 234109 (2006)

    Article  Google Scholar 

  62. O.A. Vydrov, G.E. Scuseria, J.P. Perdew, J. Chem. Phys. 126, 154109 (2007)

    Article  Google Scholar 

  63. T. Pluta, A.J. Sadlej, Chem. Phys. Lett. 297, 391–401 (1998)

    Article  CAS  Google Scholar 

  64. T. Nakajima, K. Hirao, M. Douglas, N.M. Kroll, J. Chem. Phys. 113, 7786–7789 (2000)

    Article  CAS  Google Scholar 

  65. J.C. Boettger, Phys. Rev. B 62, 7809–7815 (2000)

    Article  CAS  Google Scholar 

Download references

Acknowledgements

This work was supported by the Next-Generation Supercomputer project (the K computer project) and the FLAGSHIP2020 project within the priority study5 (Development of new fundamental technologies for high-efficiency energy creation, conversion/storage, and use) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. This work was also supported by FOCUS Establishing Supercomputing Center of Excellence.

Author information

Authors and Affiliations

  1. Faculty of Regional Studies, Gifu University, 1-1, Yanagido, Gifu, 501-1193, Japan

    Muneaki Kamiya

  2. RIKEN Advanced Institute for Computational Science, 7-1-26, Minatojima-Minami-Machi, Chuo-ku, Kobe, 650-0047, Japan

    Muneaki Kamiya & Takahito Nakajima

Authors
  1. Muneaki Kamiya
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  2. Takahito Nakajima
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Correspondence to Takahito Nakajima .

Editor information

Editors and Affiliations

  1. Jagiellonian University, Kraków, Poland

    Marek J. Wójcik

  2. Quantum Chemistry Research Institute, Nishikyo-ku, Kyoto, Japan

    Hiroshi Nakatsuji

  3. University of California, Santa Barbara, California, USA

    Bernard Kirtman

  4. School of Science and Technology, Kwansei Gakuin University, Sanda, Japan

    Yukihiro Ozaki

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Kamiya, M., Nakajima, T. (2018). Relativistic Time-Dependent Density Functional Theory for Molecular Properties. In: Wójcik, M., Nakatsuji, H., Kirtman, B., Ozaki, Y. (eds) Frontiers of Quantum Chemistry. Springer, Singapore. https://doi.org/10.1007/978-981-10-5651-2_10

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