Heavy element compounds with high symmetries often feature both spin–orbit coupling and vibronic coupling. This is especially true for systems with tetrahedral and octahedral symmetries, whose electronic states may be threefold degenerate and experience complicated Jahn–Teller and pseudo-Jahn–Teller interactions. To accurately describe these interactions, high quality spin–orbit vibronic Hamiltonian operators are needed. In this study, we present a unified one-electron Hamiltonian formalism for spin–orbit vibronic interactions for systems in all tetrahedral and octahedral symmetries. The formalism covers all spin–orbit Jahn–Teller and pseudo-Jahn–Teller problems in the symmetries with arbitrary types and arbitrary numbers of vibrational modes and generates Hamiltonian expansion formulas of arbitrarily high order.
REFERENCES
1.
I. B.
Bersuker
and V. Z.
Polinger
, Vibronic Interactions in Molecules and Crystals
(Springer-Verlag
, 1989
).2.
Conical Intersections: Electronic Structure, Dynamics and Spectroscopy
, edited by W.
Domcke
, D. R.
Yarkony
, and H.
Köppel
(World Scientific
, New Jersey
, 2004
).3.
Conical Intersections: Theory, Computation and Experiment
, edited by W.
Domcke
, D. R.
Yarkony
, and H.
Köppel
(World Scientific
, New Jersey
, 2011
).4.
H. A.
Jahn
and E.
Teller
, Proc. R. Soc. A
161
, 220
(1937
).5.
R.
Englman
, Jahn–Teller Effect in Molecules and Crystals
(John Wiley and Sons, Ltd.
, London
, 1972
).6.
R. G.
Pearson
, Proc. Natl. Acad. Sci. U. S. A.
72
, 2104
(1975
).7.
I. B.
Bersuker
, The Jahn–Teller Effect
(Cambridge University Press
, Cambridge, UK
, 2006
).8.
The Jahn–Teller Effect and Beyond
, edited by J. E.
Boggs
and V. Z.
Polinger
(The Academy of Sciences of Moldova and The University of Texas at Austin
, 2008
).9.
U.
Öpik
and M. H. L.
Pryce
, Proc. R. Soc. A
238
, 425
(1957
).10.
I. B.
Bersuker
, Chem. Rev.
113
, 1351
(2013
).11.
T. A.
Barckholtz
and T. A.
Miller
, Int. Rev. Phys. Chem.
17
, 435
(1998
).12.
J. B.
Goodenough
, Annu. Rev. Mater. Sci.
28
, 1
(1998
).13.
I. B.
Bersuker
, Chem. Rev.
101
, 1067
(2001
).14.
B. E.
Applegate
, T. A.
Barckholtz
, and T. A.
Miller
, Chem. Soc. Rev.
32
, 38
(2003
).15.
H.
Köppel
, “Jahn–teller and pseudo-Jahn–Teller intersections: Spectroscopy and vibronic dynamics
,” in Conical Intersections: Electronic Structure, Dynamics and Spectroscopy
, edited by W.
Domcke
, D. R.
Yarkony
, and H.
Köppel
(World Scientific
, New Jersey
, 2004
), Chap. 10, pp. 429
–472
.16.
T.
Zeng
, D. G.
Fedorov
, M. W.
Schmidt
, and M.
Klobukowski
, J. Chem. Theory Comput.
7
, 2864
(2011
).17.
T.
Zeng
, D. G.
Fedorov
, M. W.
Schmidt
, and M.
Klobukowski
, J. Chem. Theory Comput.
8
, 3061
(2012
).18.
M. A.
Halcrow
, Chem. Soc. Rev.
42
, 1784
(2013
).19.
W.
Hermoso
, Y.
Liu
, and I. B.
Bersuker
, J. Chem. Theory Comput.
10
, 4377
(2014
).20.
J. M.
Clemente-Juan
, A.
Palii
, E.
Coronado
, and B.
Tsukerblat
, J. Chem. Theory Comput.
12
, 3545
(2016
).21.
I. B.
Bersuker
, Adv. Chem. Phys.
160
, 159
(2016
).22.
T.
Zeng
and P.
Goel
, J. Phys. Chem. Lett.
7
, 1351
(2016
).23.
T.
Zeng
, J. Phys. Chem. Lett.
7
, 4405
(2016
).24.
A.
Japahuge
and T.
Zeng
, ChemPlusChem
83
, 146
(2018
).25.
I.
Kim
et al, J. Chem. Theory Comput.
16
, 621
(2020
).26.
M.
Toutounji
, J. Chem. Theory Comput.
16
, 1690
(2020
).27.
I. B.
Bersuker
, Chem. Rev.
121
, 1463
(2021
).28.
29.
C. M.
Marian
, Spin-Orbit Coupling in Molecules
(Wiley-VCH
, New York
, 2001
), Vol. 17, pp. 99
–204
.30.
D. G.
Fedorov
, S.
Koseki
, M. W.
Schmidt
, and M. S.
Gordon
, Int. Rev. Phys. Chem.
22
, 551
(2003
).31.
P.
Pyykkö
, Annu. Rev. Phys. Chem.
63
, 45
(2012
).32.
T.
Zeng
, D. G.
Fedorov
, M. W.
Schmidt
, and M.
Klobukowski
, J. Chem. Phys.
134
, 214107
(2011
).33.
T.
Zeng
, D. G.
Fedorov
, and M.
Klobukowski
, J. Chem. Phys.
131
, 124109
(2009
).34.
T.
Zeng
, D. G.
Fedorov
, and M.
Klobukowski
, J. Chem. Phys.
132
, 074102
(2010
).35.
T.
Zeng
, D. G.
Fedorov
, and M.
Klobukowski
, J. Chem. Phys.
133
, 114107
(2010
).36.
T.
Zeng
, D. G.
Fedorov
, and M.
Klobukowski
, J. Chem. Phys.
134
, 024108
(2011
).37.
M.
Alessio
and A. I.
Krylov
, J. Chem. Theory Comput.
17
, 4225
(2021
).38.
D. G.
Fedorov
and M. S.
Gordon
, “Symmetry in spin–orbit coupling
,” in ACS Symposium Series
(American Chemical Society
, Washington
, 2002
), Vol. 828, pp. 276
–297
.39.
S.
Matsika
and D. R.
Yarkony
, Adv. Chem. Phys.
124
, 557
(2003
).40.
M. S.
Schuurman
, D. E.
Weinberg
, and D. R.
Yarkony
, J. Chem. Phys.
127
, 104309
(2007
).41.
S.
Marquez
, J.
Dillon
, and D. R.
Yarkony
, J. Phys. Chem. A
117
, 12002
(2013
).42.
S. V.
Streltsov
and D. I.
Khomskii
, Phys. Rev. X
10
, 031043
(2020
).43.
S. K.
Lower
and M. A.
El-Sayed
, Chem. Rev.
66
, 199
(1966
).44.
45.
P.
Pokhilko
and A. I.
Krylov
, J. Phys. Chem. Lett.
10
, 4857
(2019
).46.
H.
Köppel
, “Diabatic representation: Methods for the construction of diabatic electronic states
,” in Conical Intersections: Electronic Structure, Dynamics and Spectroscopy
, edited by W.
Domcke
, D. R.
Yarkony
, and H.
Köppel
(World Scientific
, New Jersey
, 2004
), Chap. 4, pp. 175
–204
.47.
W.
Domcke
and C.
Woywod
, Chem. Phys. Lett.
216
, 362
(1993
).48.
T.
Ichino
, J.
Gauss
, and J. F.
Stanton
, J. Chem. Phys.
130
, 174105
(2009
).49.
H.
Köppel
, J.
Gronki
, and S.
Mahapatra
, J. Chem. Phys.
115
, 2377
(2001
).50.
K.
Naskar
et al, J. Chem. Theory Comput.
16
, 1666
(2020
).51.
Z.
Yin
, B. J.
Braams
, B.
Fu
, and D. H.
Zhang
, J. Chem. Theory Comput.
17
, 1678
(2021
).52.
I. G.
Ryabinkin
, L.
Joubert-Doriol
, and A. F.
Izmaylov
, Acc. Chem. Res.
50
, 1785
(2017
).53.
L. S.
Cederbaum
, “Born–oppenheimer approximation and beyond
,” in Conical Intersections: Electronic Structure, Dynamics and Spectroscopy
, edited by W.
Domcke
, D. R.
Yarkony
, and H.
Köppel
(World Scientific
, New Jersey
, 2004
), Chap. 1, pp. 3
–40
.54.
S.
Bhattacharyya
, Z.
Dai
, and W.
Domcke
, J. Chem. Phys.
143
, 194301
(2015
).55.
W.
Eisfeld
and A.
Viel
, J. Chem. Phys.
146
, 034303
(2017
).56.
A.
Viel
and W.
Eisfeld
, J. Chem. Phys.
120
, 4603
(2004
).57.
W.
Eisfeld
and A.
Viel
, J. Chem. Phys.
122
, 204317
(2005
).58.
S.
Mahapatra
, W.
Eisfeld
, and H.
Köppel
, Chem. Phys. Lett.
441
, 7
(2007
).59.
S.
Bhattacharyya
, D.
Opalka
, L. V.
Poluyanov
, and W.
Domcke
, J. Phys.: Conf. Ser.
428
, 012015
(2013
).60.
S.
Bhattacharyya
, D.
Opalka
, L. V.
Poluyanov
, and W.
Domcke
, J. Phys. Chem. A
118
, 11962
(2014
).61.
W.
Eisfeld
, O.
Vieuxmaire
, and A.
Viel
, J. Chem. Phys.
140
, 224109
(2014
).62.
T.
Codd
, M.-W.
Chen
, M.
Roudjane
, J. F.
Stanton
, and T. A.
Miller
, J. Chem. Phys.
142
, 184305
(2015
).63.
T.
Mondal
, Phys. Chem. Chem. Phys.
20
, 9401
(2018
).64.
H. K.
Tran
, J. F.
Stanton
, and T. A.
Miller
, J. Mol. Spectrosc.
343
, 102
(2018
).65.
T.
Zeng
and I.
Seidu
, Phys. Chem. Chem. Phys.
19
, 11098
(2017
).66.
R. A.
Lang
, A.
Japahuge
, and T.
Zeng
, Chem. Phys.
515
, 36
(2018
).67.
R. J.
Hickman
, R. A.
Lang
, and T.
Zeng
, Phys. Chem. Chem. Phys.
20
, 12312
(2018
).68.
I.
Seidu
et al, Phys. Chem. Chem. Phys.
21
, 8679
(2019
).69.
T.
Zeng
, R. J.
Hickman
, A.
Kadri
, and I.
Seidu
, J. Chem. Theory Comput.
13
, 5004
(2017
).70.
R. A.
Lang
, R. J.
Hickman
, and T.
Zeng
, Comput. Phys. Commun.
247
, 106946
(2020
).71.
K.
Sharma
, T. A.
Miller
, and J. F.
Stanton
, Int. Rev. Phys. Chem.
40
, 165
(2021
).72.
J.
Brown
, R. A.
Lang
, and T.
Zeng
, J. Chem. Theory Comput.
17
, 4392
(2021
).73.
W.
Moffitt
and W.
Thorson
, Phys. Rev.
108
, 1251
(1957
).74.
L. V.
Poluyanov
and W.
Domcke
, Chem. Phys.
374
, 86
(2010
).75.
L. V.
Poluyanov
and W.
Domcke
, J. Chem. Phys.
129
, 224102
(2008
).76.
L. V.
Poluyanov
and W.
Domcke
, Chem. Phys.
407
, 1
(2012
).77.
W.
Domcke
, S.
Mishra
, and L. V.
Poluyanov
, Chem. Phys.
322
, 405
(2006
).78.
W.
Domcke
, D.
Opalka
, and L. V.
Poluyanov
, J. Chem. Phys.
144
, 124101
(2016
).79.
T.
Weike
and W.
Eisfeld
, J. Chem. Phys.
144
, 104108
(2016
).80.
K.
Wang
and T.
Zeng
, Phys. Chem. Chem. Phys.
21
, 18939
(2019
).81.
J.
Brown
, E.
Pradhan
, and T.
Zeng
, J. Chem. Phys.
155
, 224108
(2021
).82.
B. A.
Hess
, C. M.
Marian
, U.
Wahlgren
, and O.
Gropen
, Chem. Phys. Lett.
251
, 365
(1996
).83.
84.
D. G.
Fedorov
and M. S.
Gordon
, J. Chem. Phys.
112
, 5611
(2000
).85.
T.
Zeng
, J. Chem. Phys.
146
, 144103
(2017
).86.
M.
Douglas
and N. M.
Kroll
, Annu. Phys.
82
, 89
(1974
).87.
B. A.
Hess
, Phys. Rev. A
33
, 3742
(1986
).88.
M.
Barysz
and A. J.
Sadlej
, J. Chem. Phys.
116
, 2696
(2002
).89.
T.
Nakajima
and K.
Hirao
, Chem. Phys. Lett.
302
, 383
(1999
).90.
© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.