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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
C.M. Marian, Wiley Interdiscip. Rev. Comput. Molecular Sci. 2, 187–203 (2012)
Y. Imamura, M. Kamiya, T. Nakajima, Chem. Phys. Lett. 635, 152–156 (2015)
Y. Imamura, M. Kamiya, T. Nakajima, Chem. Phys. Lett. 648, 60–65 (2016)
M.E. Casida, M. Huix-Rotllant, Ann. Rev. Phys. Chem. 63, 287–323 (2012)
C. Adamo, D. Jacquemin, Chem. Soc. Rev. 42, 845–856 (2013)
A.D. Laurent, D. Jacquemin, Int. J. Quantum Chem. 113, 2019–2039 (2013)
H. Weiss, R. Ahlrichs, M. Häser, J. Chem. Phys. 99, 1262–1270 (1993)
R. Bauernschmitt, R. Ahlrichs, Chem. Phys. Lett. 256, 454–464 (1996)
R.E. Stratmann, G.E. Scuseria, M.J. Frisch, J. Chem. Phys. 109, 8218–8224 (1998)
P. Norman, D.M. Bishop, H.J. Aa. Jensen, J. Oddershede, J. Chem. Phys. 115, 10323–10334
K. Kristensen, J. Kauczor, T. Kjærgaard, P. Jørgensen, J. Chem. Phys. 131, 044112 (2009)
M. Douglas, N.M. Kroll, Ann. Phys. (NY) 82, 89 (1974)
B.A. Hess, Phys. Rev. A 32, 756 (1985)
B.A. Hess, Phys. Rev. A 33, 3742 (1986)
L.E. McMurchie, E.R. Davidson, J. Comput. Phys. 44, 289–301 (1981)
R.M. Pitzer, N.W. Winter, Int. J. Quantum Chem. 40, 773–780 (1991)
P. Norman, B. Schimmelpfennig, K. Ruud, H.J. Aa. Jensen, H. Ågren, J. Chem. Phys. 116, 6914–6923 (2002)
P. Salek, T. Helgaker, T. Saue, Chem. Phys. 311, 187–201 (2005)
R. Bast, T. Saue, J. Henriksson, P. Norman, J. Chem. Phys. 130, 024109 (2009)
F. Wang, T. Ziegler, J. Chem. Phys. 121, 12191–12196 (2004)
J. Gao, W. Zou, W. Liu, Y. Xiao, D. Peng, B. Song, C. Liu, J. Chem. Phys. 123, 054102 (2005)
F. Wang, T. Ziegler, J. Chem. Phys. 122, 074109 (2005)
A. Nakata, T. Tsuneda, K. Hirao, J. Chem. Phys. 135, 224106 (2011)
S. Hirata, M. Head-Gordon, Chem. Phys. Lett. 314, 291–299 (1999)
R. Bast, H.J.A. Jensen, T. Saue, Int. J. Quantum Chem. 109, 2091–2112 (2009)
T. Nakajima, M. Katouda, M. Kamiya, Y. Nakatsuka, Int. J. Quantum Chem. 115, 349–359 (2015)
SymPy: Python library for symbolic mathematics. http://sympy.org
J.A. Pople, R. Krishnan, H.B. Schlegel, J.S. Binkley, Int. J. Quantum Chem. 16, 225–241 (1979)
P. Pulay, J. Chem. Phys. 78, 5043–5051 (1983)
H. Sekino, R.J. Bartlett, J. Chem. Phys. 84, 2726–2733 (1986)
E.R. Davidson, J. Comput. Phys. 17, 87–94 (1975)
K. Hirao, H. Nakatsuji, J. Comput. Phys. 45, 246–254 (1982)
J. Olsen, H.J. Aa. Jensen, P. Jørgensen, J. Comput. Phys. 74, 265–282 (1988)
R. Bast, U. Ekstrom, B. Gao, T. Helgaker, K. Ruud, A.J. Thorvaldsen, Phys. Chem. Chem. Phys. 13, 2627–2651 (2011)
L. Nordström, D.J. Singh, Phys. Rev. Lett. 76, 4420–4423 (1996)
T. Oda, A. Pasquarello, R. Car, Phys. Rev. Lett. 80, 3622–3625 (1998)
S. Yamanaka, D. Yamaki, Y. Shigeta, H. Nagao, Y. Yoshioka, N. Suzuki, K. Yamaguchi, Int. J. Quantum Chem. 80, 664–671 (2000)
P. Kurz, F. Förster, L. Nordström, G. Bihlmayer, S. Blügel, Phys. Rev. B 69, 024415 (2004)
J.E. Peralta, G.E. Scuseria, J. Chem. Phys. 120, 5875–5881 (2004)
J.E. Peralta, G.E. Scuseria, M.J. Frisch, Phys. Rev. B 75, 125119 (2007)
M.K. Armbruster, F. Weigend, C. van Wullen, W. Klopper, Phys. Chem. Chem. Phys. 10, 1748–1756 (2008)
G. Scalmani, M.J. Frisch, J. Chem. Theor. Comput. 8, 2193–2196 (2012)
H. Sekino, J. Phys. Chem. A 104, 4685–4689 (2000)
R.J. Harrison, J. Comput. Chem. 25, 328–334 (2004)
S. Hirata, M. Head-Gordon, R.J. Bartlett, J. Chem. Phys. 111, 10774–10786 (1999)
R. Strange, F.R. Manby, P.J. Knowles, Comput. Phys. Commun. 136, 310–318 (2001)
P. Sałek, A. Hesselmann, J. Comput. Chem. 28, 2569–2575 (2007)
U. Ekström, L. Visscher, R. Bast, A.J. Thorvaldsen, K. Ruud, J. Chem. Theor. Comput. 6, 1971–1980 (2010)
J.P. Perdew, Burke K., Ernzerhof M., Phys. Rev. Lett. 77, 3865 (1996)
J.C. Slater, Phys. Rev. 81, 385 (1951)
S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58, 1200 (1980)
A.D. Becke, Phys. Rev. A 38, 3098 (1988)
C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37, 785 (1988)
A.D. Becke, J. Chem. Phys. 98, 5648 (1993)
H. Iikura, T. Tsuneda, T. Yanai, K. Hirao, J. Chem. Phys. 115, 3540 (2001)
T. Yanai, D.P. Tew, N.C. Handy, Chem. Phys. Lett. 393, 51–57 (2004)
V. Kellö, A.J. Sadlej, Theor. Chim. Acta. 94, 93–104 (1996)
A.J. Sadlej, Collect. Czech. Chem. Commun. 53, 1995 (1988)
S. Kirpekar, J. Oddershede, Jensen HJrA. J. Chem. Phys. 103, 2983–2990 (1995)
O.A. Vydrov, J. Heyd, A.V. Krukau, G.E. Scuseria, W.K, J. SL., J Chem. Phys. 125, 074106 (2006)
O.A. Vydrov, G.E. Scuseria, J. Chem. Phys. 125, 234109 (2006)
O.A. Vydrov, G.E. Scuseria, J.P. Perdew, J. Chem. Phys. 126, 154109 (2007)
T. Pluta, A.J. Sadlej, Chem. Phys. Lett. 297, 391–401 (1998)
T. Nakajima, K. Hirao, M. Douglas, N.M. Kroll, J. Chem. Phys. 113, 7786–7789 (2000)
J.C. Boettger, Phys. Rev. B 62, 7809–7815 (2000)
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
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-981-10-5651-2_10
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-5650-5
Online ISBN: 978-981-10-5651-2
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)