This perspective article discusses some broadly-known and some less broadly-known consequences of Einstein's special relativity in quantum chemistry, and provides a brief outline of the theoretical methods currently in use, along with a discussion of recent developments and selected applications. The treatment of the electron correlation problem in relativistic quantum chemistry methods, and expanding the reach of the available relativistic methods to calculate all kinds of energy derivative properties, in particular spectroscopic and magnetic properties, requires on-going efforts.
REFERENCES
1.
G.
Wulfsberg
, Principles of Descriptive Inorganic Chemistry
(Brooks/Cole
, Monterey, CA
, 1987
). 2.
J. E.
Huheey
, Inorganic Chemistry. Principles of Structure and Reactivity
, 3rd ed. (Harper & Row
, New York
, 1983
). 3.
L. J.
Norrby
, J. Chem. Educ.
68
, 110
(1991
).
4.
W.
Li
and S. M.
Blinder
, J. Chem. Educ.
88
, 71
(2010
).
5.
L.
Gagliardi
and B. O.
Roos
, Nature (London)
433
, 848
(2005
).
6.
R.
Ahuja
, A.
Blomqvist
, P.
Larsson
, P.
Pyykkö
, and P.
Zaleski-Ejgierd
, Phys. Rev. Lett.
106
, 018301
(2011
).
7.
P. A. M.
Dirac
, Proc. R. Soc. London, Ser. A
123
, 714
(1929
).
8.
W. H. E.
Schwarz
, E. M.
van Wezenbeek
, E. J.
Baerends
, and J. G.
Snijders
, J. Phys. B
22
, 1515
(1989
).
9.
W.
Kołos
and L.
Wolniewicz
, J. Chem. Phys.
41
, 3663
(1964
).
10.
W.
Kołos
and L.
Wolniewicz
, J. Chem. Phys.
43
, 2429
(1965
).
11.
W.
Kołos
and L.
Wolniewicz
, J. Chem. Phys.
49
, 404
(1968
).
12.
C.
Michauk
and J.
Gauss
, J. Chem. Phys.
127
, 044106
(2007
).
13.
S.
Wang
and W. H. E.
Schwarz
, Angew. Chem., Int. Ed.
48
, 3404
(2009
).
14.
W. H. E.
Schwarz
and R. L.
Rich
, J. Chem. Educ.
87
, 435
(2010
).
15.
P.
Schwerdtfeger
, G. A.
Heath
, M.
Dolg
, and M. A.
Bennett
, J. Am. Chem. Soc.
114
, 7518
(1992
).
16.
P.
Pyykkö
, Relativistic Theory of Atoms and Molecules
, Lecture Notes in Chemistry Vol. 60
(Springer-Verlag
, Berlin
, 1993
). 17.
P.
Pyykkö
, “Effects on periodic trends
,” in The Effects of Relativity in Atoms, Molecules and Solids
(Plenum
, New York
, 1991
). 18.
P.
Pyykkö
, Chem. Rev.
88
, 563
(1988
).
19.
Y.
Nomura
, Y.
Takeuchi
, and N.
Nakagawa
, Tetrahedron Lett.
8
, 639
(1969
).
20.
C.
Marian
, “Spin-orbit coupling in molecules
,” in Reviews in Computational Chemistry
, edited by K.
Lipkowitz
and D.
Boyd
(Wiley-VCH
, Weinheim
, 2001
), Vol. 17
, pp. 99
–204
. 21.
J.
Autschbach
, “Relativistic effects on magnetic resonance parameters and other properties of inorganic molecules and metal complexes
,” in Relativistic Methods for Chemists
, edited by M.
Barysz
and Y.
Ishikawa
, Challenges and Advances in Computational Chemistry and Physics Vol. 10
(Springer
, Dordrecht
, 2010
), Chap. 12, pp. 521
–598
. 22.
P. J.
Mohr
and B. N.
Taylor
, Rev. Mod. Phys.
72
, 351
(2000
).
23.
W.
Kutzelnigg
, Chem. Phys.
395
, 16
(2012
).
24.
W.
Liu
, Mol. Phys.
108
, 1679
(2010
).
25.
P.
Pyykkö
, Chem. Rev.
112
, 371
(2012
).
26.
T.
Saue
, ChemPhysChem
12
, 3077
(2011
).
27.
T.
Fleig
, Chem. Phys.
395
, 2
(2012
).
28.
P.
Pyykkö
, Annu. Rev. Phys. Chem.
63
, 45
(2012
).
29.
R. E.
Moss
, Advanced Molecular Quantum Mechanics
(Chapman and Hall
, London
, 1973
). 30.
K.
Balasubramanian
, Relativistic Effects in Chemistry
, Part A. Theory and Techniques
(Wiley
, New York
, 1997
). 31.
K.
Balasubramanian
, Relativistic Effects in Chemistry
, Part B. Application
(Wiley
, New York
, 1997
). 32.
33.
K. G.
Dyall
and K.
Faegri
Jr., Relativistic Quantum Chemistry
(Oxford University Press
, New York
, 2007
). 34.
M.
Reiher
and A.
Wolf
, Relativistic Quantum Chemistry. The Fundamental Theory of Molecular Science
(Wiley-VCH
, Weinheim
, 2009
). 35.
Relativistic Electronic Structure Theory. Fundamentals
, Theoretical and Computational Chemistry Vol. 11
, edited by P.
Schwerdtfeger
(Elsevier
, Amsterdam
, 2002
). 36.
Relativistic Electronic Structure Theory. Part 2. Applications
, Theoretical and Computational Chemistry Vol. 14
, edited by P.
Schwerdtfeger
(Elsevier
, Amsterdam
, 2004
). 37.
Recent Advances in Relativistic Molecular Theory
, Recent Advances in Computational Chemistry Vol. 5
, edited by K.
Hirao
and Y.
Ishikawa
(World Scientific
, Singapore
, 2004
). 38.
Relativistic Effects in Heavy-Element Chemistry and Physics
, edited by B. A.
Hess
(Wiley
, Chichester
, 2003
). 39.
Theoretical Chemistry and Physics of Heavy and Superheavy Elements
, Progress in Theoretical Chemistry and Physics Vol. 11
, edited by U.
Kaldor
and S.
Wilson
(Kluwer
, Dordrecht
, 2003
). 40.
Relativistic Methods for Chemists
, Challenges and Advances in Computational Chemistry and Physics Vol. 10
, edited by M.
Barysz
and Y.
Ishikawa
(Springer
, Dordrecht
, 2010
). 41.
42.
P.
Pyykkö
and J. P.
Desclaux
, Acc. Chem. Res.
12
, 276
(1979
).
43.
K. S.
Pitzer
, Acc. Chem. Res.
12
, 271
(1979
).
44.
P. A.
Christiansen
, W. C.
Ermler
, and K. S.
Pitzer
, Ann. Rev. Phys. Chem.
36
, 407
(1985
).
45.
A. J.
Sadlej
, Methods of Relativistic Quantum Chemistry
, Lecture Notes in Chemistry II, Vol. 64
, edited by B. O.
Roos
(Springer
, Berlin
, 1994
), pp. 203
–230
. 46.
B. A.
Hess
, “Relativistic theory and applications
,” in Encyclopedia of Computational Chemistry
, edited by P.
von Ragué Schleyer
(Wiley
, Chichester
, 1998
), pp. 2499
–2508
. 47.
W. H. E.
Schwarz
, “Fundamentals of relativistic effects in chemistry
,” in The Concept of the Chemical Bond
, edited by Z. B.
Masic
(Springer-Verlag
, Berlin
, 1990
), Vol. 2
, pp. 559
–643
. 48.
M.
Reiher
and J.
Hinze
, “Four-component ab initio methods for electronic structure calculations of atoms, molecules and solids
,” in Relativistic Effects in Heavy-Element Chemistry and Physics
, edited by B. A.
Hess
(Wiley
, Chichester
, 2003
). 49.
T.
Saue
and L.
Visscher
, “Four-component electronic structure methods for molecules
,” in Theoretical Chemistry and Physics of Heavy and Superheavy Elements
, Progress in Theoretical Chemistry and Physics Vol. 11
(Kluwer
, Dordrecht
, 2003
), pp. 211
–267
. 50.
W.
Liu
, Phys. Chem. Chem. Phys.
14
, 35
(2011
).
51.
G. A.
Aucar
, T.
Saue
, L.
Visscher
, and H. J. A.
Jensen
, J. Chem. Phys.
110
, 6208
(1999
).
52.
P.
Pyykkö
, Chem. Phys.
74
, 1
(1983
).
53.
W.
Kutzelnigg
, Phys. Rev. A
67
, 032109
(2003
).
54.
Y.
Xiao
, D.
Peng
, and W.
Liu
, J. Chem. Phys.
126
, 081101
(2007
).
55.
Y.
Xiao
, W.
Liu
, L.
Cheng
, and D.
Peng
, J. Chem. Phys.
126
, 214101
(2007
).
56.
L.
Visscher
, Adv. Quantum Chem.
48
, 369
(2005
).
57.
S.
Luber
, I. M.
Ondik
, and M.
Reiher
, Chem. Phys.
356
, 205
(2009
).
58.
H. A.
Bethe
and E. E.
Salpeter
, Quantum Mechanics of One and Two Electron Atoms
(Springer-Verlag
, Berlin
, 1957
). 59.
C.
Thierfelder
and P.
Schwerdtfeger
, Phys. Rev. A
82
, 062503
(2010
).
60.
M.
Reiher
and J.
Hinze
, J. Phys. B
32
, 5489
(1999
).
61.
W. H. E.
Schwarz
and E.
Wechsel-Trakowski
, Chem. Phys. Lett.
85
, 94
(1982
).
62.
The limit c → ∞ is taken inside k for a potential that remains finite (e.g., from finite nuclei), which gives k → 1.
63.
R. E.
Stanton
and S.
Havriliak
, J. Chem. Phys.
81
, 1910
(1984
).
64.
Q.
Sun
, W.
Liu
, and W.
Kutzelnigg
, Theor. Chem. Acc.
129
, 423
(2011
).
65.
E. J.
Baerends
, W. H. E.
Schwarz
, P.
Schwerdtfeger
, and J. G.
Snijders
, J. Phys. B
23
, 3225
(1990
).
66.
L. L.
Foldy
and S. A.
Wouthuysen
, Phys. Rev.
78
, 29
(1950
).
67.
J.
Autschbach
and W. H. E.
Schwarz
, Theor. Chem. Acc.
104
, 82
(2000
).
68.
V.
Kellö
and A. J.
Sadlej
, Int. J. Quantum Chem.
68
, 159
(1998
).
69.
M.
Pernpointner
and P.
Schwerdtfeger
, Chem. Phys. Lett.
295
, 347
(1998
).
70.
R.
Mastalerz
, G.
Barone
, R.
Lindh
, and M.
Reiher
, J. Chem. Phys.
127
, 074105
(2007
).
71.
J. L.
Heully
, I.
Lindgren
, E.
Lindroth
, S.
Lundquist
, and A.-M.
Mårtenson-Pendrill
, J. Phys. B
19
, 2799
(1986
).
72.
W.
Kutzelnigg
, Z. Phys. D
15
, 27
(1990
).
73.
M.
Ilias
and T.
Saue
, J. Chem. Phys.
126
, 064102
(2007
).
74.
M.
Ilias
, H. J. Aa.
Jensen
, V.
Kello
, B. O.
Roos
, and M.
Urban
, Chem. Phys. Lett.
408
, 210
(2005
).
75.
W.
Kutzelnigg
and W.
Liu
, J. Chem. Phys.
123
, 241102
(2005
).
76.
W.
Liu
and W.
Kutzelnigg
, J. Chem. Phys.
126
, 114107
(2007
).
77.
W.
Liu
and D.
Peng
, J. Chem. Phys.
131
, 031104
(2009
).
78.
M.
Barysz
and A. J.
Sadlej
, J. Mol. Struct.: THEOCHEM
573
, 181
(2001
).
79.
M.
Barysz
and A. J.
Sadlej
, J. Chem. Phys.
116
, 2696
(2002
).
80.
D.
Kedziera
and M.
Barysz
, J. Chem. Phys.
121
, 6719
(2004
).
81.
D.
Kedziera
and M.
Barysz
, Chem. Phys. Lett.
446
, 176
(2007
).
82.
K. G.
Dyall
, J. Chem. Phys.
106
, 9618
(1997
).
83.
W.
Zou
, M.
Filatov
, and D.
Cremer
, Theor. Chem. Acc.
130
, 633
(2011
).
84.
W.
Kutzelnigg
and W.
Liu
, J. Chem. Phys.
131
, 044129
(2009
).
85.
L.
Cheng
, Y.
Xiao
, and W.
Liu
, J. Chem. Phys.
130
, 144102
(2009
).
86.
L.
Cheng
, Y.
Xiao
, and W.
Liu
, J. Chem. Phys.
131
, 244113
(2009
).
87.
L.
Cheng
and J.
Gauss
, J. Chem. Phys.
135
, 084114
(2011
).
88.
L.
Cheng
and J.
Gauss
, J. Chem. Phys.
135
, 244104
(2011
).
89.
W.
Zou
, M.
Filatov
, and D.
Cremer
, J. Chem. Phys.
134
, 244117
(2011
).
90.
W.
Kutzelnigg
, J. Comput. Chem.
20
, 1199
(1999
).
91.
S.
Komorovsky
, M.
Repisky
, O. L.
Malkina
, V. G.
Malkin
, I. M.
Ondik
, and M.
Kaupp
, J. Chem. Phys.
128
, 104101
(2008
).
92.
S.
Komorovsky
, M.
Repisky
, O. L.
Malkina
, and V. G.
Malkin
, J. Chem. Phys.
132
, 154101
(2010
).
93.
M.
Olejniczak
, R.
Bast
, T.
Saue
, and M.
Pecul
, J. Chem. Phys.
136
, 014108
(2012
).
94.
J.
Autschbach
and T.
Ziegler
, Coord. Chem. Rev.
238/239
, 83
(2003
).
95.
R. E.
Moss
and H. P.
Trivedi
, Mol. Phys.
38
, 1611
(1979
).
96.
J. D.
Morrison
and R. E.
Moss
, Mol. Phys.
41
, 491
(1980
).
97.
J.
Vaara
, P.
Manninnen
, and P.
Lantto
, “Perturbational and ECP calculation of relativistic effects in NMR shielding and spin-spin coupling
,” in Calculation of NMR and EPR Parameters. Theory and Applications
, edited by M.
Kaupp
, M.
Bühl
, and V. G.
Malkin
(Wiley-VCH
, Weinheim
, 2003
), pp. 209
–226
. 98.
P.
Manninen
, P.
Lantto
, and J.
Vaara
, J. Chem. Phys.
119
, 2623
(2003
).
99.
erratum:
P.
Manninen
, K.
Ruud
, P.
Lantto
, and J.
Vaara
, J. Chem. Phys.
124
, 149901
(2006
).
100.
C.
Chang
, M.
Pelissier
, and M.
Durand
, Phys. Scr.
34
, 394
(1986
).
101.
E.
van Lenthe
, E. J.
Baerends
, and J. G.
Snijders
, J. Chem. Phys.
99
, 4597
(1993
).
102.
The operators also differ substantially for a free particle where the ZORA operator adopts the nonrelativistic limit (assuming V = 0) but the Pauli operator retains the MV term.
103.
P.
Nichols
, N.
Govind
, E. J.
Bylaska
, and W. A.
de Jong
, J. Chem. Theory Comput.
5
, 491
(2009
).
104.
C.
van Wüllen
, J. Chem. Phys.
109
, 392
(1998
).
105.
P. H. T.
Philipsen
, E.
van Lenthe
, J. G.
Snijders
, and E. J.
Baerends
, Phys. Rev. B
56
, 13556
(1997
).
106.
E. van Lenthe,
E. J.
Baerends
, and J. G.
Snijders
, J. Chem. Phys.
101
, 9783
(1994
).
107.
K.
Dyall
and E.
van Lenthe
, J. Chem. Phys.
111
, 1366
(1999
).
108.
J.
Autschbach
and T.
Ziegler
, J. Chem. Phys.
113
, 936
(2000
).
109.
A.
Wolf
, M.
Reiher
, and B.
Hess
, “Transgressing theory boundaries: The generalized Douglas–Kroll transformation
,” in Recent Advances in Relativistic Molecular Theory
, Recent Advances in Computational Chemistry Vol. 5
, edited by K.
Hirao
and Y.
Ishikawa
(World Scientific
, Singapore
, 2004
), pp. 137
–190
. 110.
N.
Rösch
, A. V.
Matveev
, V. A.
Nasluzov
, K. M.
Neyman
, L. V.
Moskaleva
, and S.
Krüger
, “Quantum chemistry with the Douglas-Kroll-Hess approach to relativistic density functional theory: Efficient methods for molecules and materials
,” in Relativistic Electronic Structure Theory – Applications
, Theoretical and Computational Chemistry Vol. 14
, edited by P.
Schwerdtfeger
(Elsevier
, Amsterdam
, 2004
), pp. 656
–722
. 111.
B. A.
Hess
, Phys. Rev. A
33
, 3742
(1986
).
112.
A.
Wolf
, M.
Reiher
, and B. A.
Hess
, J. Chem. Phys.
117
, 9215
(2002
).
113.
R.
Samzow
, B. A.
Hess
, and G.
Jansen
, J. Chem. Phys.
96
, 1227
(1992
).
114.
T.
Nakajima
and K.
Hirao
, Chem. Phys. Lett.
302
, 383
(1999
).
115.
M.
Reiher
and A.
Wolf
, J. Chem. Phys.
121
, 10945
(2004
).
116.
D.
Peng
and K.
Hirao
, J. Chem. Phys.
130
, 044102
(2009
).
117.
D.
Peng
and M.
Reiher
, Theor. Chem. Acc.
131
(2012
).
118.
R.
Fukuda
, M.
Hada
, and H.
Nakatsuji
, J. Chem. Phys.
118
, 1015
(2003
).
119.
R.
Fukuda
, M.
Hada
, and H.
Nakatsuji
, J. Chem. Phys.
118
, 1027
(2003
).
120.
J. I.
Melo
, M. C.
Ruiz de Azúa
, J. E.
Peralta
, and G. E.
Scuseria
, J. Chem. Phys.
123
, 204112
(2005
).
121.
T.
Baba
and H.
Fukui
, Mol. Phys.
100
, 623
(2002
).
122.
K.
Kudo
and H.
Fukui
, J. Chem. Phys.
123
, 114102
(2005
).
123.
I.
Malkin
, O. L.
Malkina
, and V. G.
Malin
, Chem. Phys. Lett.
361
, 231
(2002
).
124.
A.
Rutkowski
, J. Phys. B
19
, 149
(1986
).
125.
W.
Kutzelnigg
, Z. Phys. D
11
, 15
(1989
).
126.
W.
Schwalbach
, S.
Stopkowicz
, L.
Cheng
, and J.
Gauss
, J. Chem. Phys.
135
, 194114
(2011
).
127.
A. C.
Hennum
, W.
Klopper
, and T.
Helgaker
, J. Chem. Phys.
115
, 7356
(2001
).
128.
M.
Dolg
and X.
Cao
, Chem. Rev.
112
, 403
(2011
).
129.
P.
Schwerdtfeger
, B.
Assadollahzadeh
, U.
Rohrmann
, R.
Schäfer
, and J. R.
Cheeseman
, J. Chem. Phys.
134
, 204102
(2011
).
130.
C. G.
Van
de Walle and P. E.
Blöchl
, Phys. Rev. B
47
, 4244
(1993
).
131.
C. J.
Pickard
and F.
Mauri
, Phys. Rev. B
63
, 245101
(2001
).
132.
J. E.
Harriman
, Theoretical Foundations of Electron Spin Resonance
(Academic Press
, New York
, 1978
). 133.
D.
Andrae
, Phys. Rep.
336
, 413
(2000
).
134.
J.
Autschbach
, S.
Sikierski
, P.
Schwerdtfeger
, M.
Seth
, and W. H. E.
Schwarz
, J. Comput. Chem.
23
, 804
(2002
).
135.
P.
Pyykkö
, J. G.
Snijders
, and E. J.
Baerends
, Chem. Phys. Lett.
83
, 432
(1981
).
136.
G.
Eickerling
and M.
Reiher
, J. Chem. Theory Comput.
4
, 286
(2008
).
137.
G.
Eickerling
, R.
Mastalerz
, V.
Herz
, W.
Scherer
, H.
Himmel
, and M.
Reiher
, J. Chem. Theory Comput.
3
, 2182
(2007
).
138.
J. G.
Snijders
and P.
Pyykkö
, Chem. Phys. Lett.
75
, 5
(1980
).
139.
T.
Ziegler
, J. G.
Snijders
, and E. J.
Baerends
, Chem. Phys. Lett.
75
, 1
(1980
).
140.
W. H. E.
Schwarz
, Phys. Scr.
36
, 403
(1987
).
141.
J.
Autschbach
, “Zur Berechnung relativistischer Effekte und zum Verständnis ihrer Trends bei Atomen und Molekülen
,” Ph.D. dissertation (Universität Gesamthochschule Siegen
, 1999
), see http://www.ub.uni-siegen.de/epub/diss/autschbach.htm. 142.
E.
Pahl
and P.
Schwerdtfeger
, “Mercury-from clusters to the solid
,” in Handbook of nano-Physics
, edited by K.
Sattler
(Taylor & Francis
, London
, 2010
), pp. 1
–13
. 143.
F.
Calvo
, E.
Pahl
, P.
Schwerdtfeger
, and F.
Spiegelman
, J. Chem. Theory Comput.
8
, 639
(2012
).
144.
K. E.
Saeger
and J.
Rodies
, Gold Bull.
10
, 10
(1977
).
145.
N. E.
Christensen
and B. O.
Seraphin
, Phys. Rev. B
4
, 3321
(1971
).
146.
K.
Piszczatowski
, G.
Lach
, M.
Przybytek
, J.
Komasa
, K.
Pachucki
, and B.
Jeziorski
, J. Chem. Theory Comput.
5
, 3039
(2009
).
147.
J.
Liu
, E. J.
Salumbides
, U.
Hollenstein
, J. C. J.
Koelemeij
, K. S. E.
Eikema
, W.
Ubachs
, and F.
Merkt
, J. Chem. Phys.
130
, 174306
(2009
).
148.
J.
Liu
, D.
Sprecher
, C.
Jungen
, W.
Ubachs
, and F.
Merkt
, J. Chem. Phys.
132
, 154301
(2010
).
149.
P.
Schwerdtfeger
, M.
Pernpointner
, and W.
Nazarewicz
, “Calculation of nuclear quadrupole coupling constants
,” in Calculation of NMR and EPR Parameters. Theory and Applications
, edited by M.
Kaupp
, M.
Bühl
, and V. G.
Malkin
(Wiley-VCH
, Weinheim
, 2004
), pp. 279
–291
. 150.
E.
van Lenthe
and E. J.
Baerends
, J. Chem. Phys.
112
, 8279
(2000
).
151.
F.
Aquino
, N.
Govind
, and J.
Autschbach
, J. Chem. Theory Comput.
6
, 2669
(2010
).
152.
F.
Neese
, A.
Wolf
, T.
Fleig
, M.
Reiher
, and B. A.
Hess
, J. Chem. Phys.
122
, 204107
(2005
).
153.
154.
J.
Autschbach
, Theor. Chem. Acc.
112
, 52
(2004
).
155.
J.
Autschbach
, ChemPhysChem
10
, 2274
(2009
).
156.
E.
van Lenthe
, “The ZORA equation
,” Ph.D. dissertation (Vrije Universiteit Amsterdam
, 1996
). 157.
S.
Blügel
, H.
Akai
, R.
Zeller
, and P. H.
Dederichs
, Phys. Rev. B
35
, 3271
(1987
).
158.
E.
Malkin
, I.
Malkin
, O. L.
Malkina
, V. G.
Malkin
, and M.
Kaupp
, Phys. Chem. Chem. Phys.
8
, 4079
(2006
).
159.
F.
Aquino
, B.
Pritchard
, and J.
Autschbach
, J. Chem. Theory Comput.
8
, 598
(2012
).
160.
E.
Malkin
, M.
Repisky
, S.
Komorovsky
, P.
Mach
, O. L.
Malkina
, and V. G.
Malkin
, J. Chem. Phys.
134
, 044111
(2011
).
161.
A.
Bohr
and V. F.
Weisskopf
, Phys. Rev.
77
, 94
(1950
).
162.
A.
Bohr
, Phys. Rev.
81
, 331
(1951
).
163.
J. E.
Rosenthal
and G.
Breit
, Phys. Rev.
41
, 459
(1932
).
164.
H. H.
Stroke
, R. J.
Blin-Stoyle
, and V.
Jaccarino
, Phys. Rev.
123
, 1326
(1961
).
165.
M.
Filatov
and D.
Cremer
, J. Chem. Phys.
120
, 11407
(2004
).
166.
S.
Zheng
and J.
Autschbach
, Chem.-Eur. J.
17
, 161
(2011
).
167.
S.
Moncho
and J.
Autschbach
, J. Chem. Theory Comput.
6
, 223
(2010
).
168.
169.
J.
Autschbach
and S.
Zheng
, Annu. Rep. NMR Spectrosc.
67
, 1
(2009
).
170.
M.
Kaupp
, “Relativistic effects on NMR chemical shifts
,” in Relativistic Electronic Structure Theory
, edited by P.
Schwerdtfeger
(Elsevier
, Amsterdam
, 2004
), Vol. 2
. 171.
S. K.
Wolff
and T.
Ziegler
, J. Chem. Phys.
109
, 895
(1998
).
172.
M.
Kaupp
, O. L.
Malkina
, V. G.
Malkin
, and P.
Pyykkö
, Chem.-Eur. J.
4
, 118
(1998
).
173.
P.
Hrobarik
, V.
Hrobarikova
, F.
Meier
, M.
Repisky
, S.
Komorovsky
, and M.
Kaupp
, J. Phys. Chem. A
115
, 5654
(2011
). 174.
L. A.
Truflandier
, E.
Brendler
, J.
Wagler
, and J.
Autschbach
, Angew. Chem., Int. Ed.
50
, 255
(2011
).
175.
M.
Repisky
, S.
Komorovsky
, E.
Malkin
, O. L.
Malkina
, and V. G.
Malkin
, Chem. Phys. Lett.
488
, 94
(2010
).
176.
P.
Hrobarik
, M.
Repisky
, S.
Komorovsky
, V.
Hrobarikova
, and M.
Kaupp
, Theor. Chem. Acc.
129
, 715
(2011
).
177.
H.
Bolvin
, ChemPhysChem
7
, 1575
(2006
).
178.
J.
Autschbach
and B.
Pritchard
, Theor. Chem. Acc.
129
, 453
(2011
).
179.
F.
Aquino
, N.
Govind
, and J.
Autschbach
, J. Chem. Theory Comput.
7
, 3278
(2011
).
180.
M.
Kaupp
and F. H.
Köhler
, Coord. Chem. Rev.
253
, 2376
(2009
).
181.
G. A.
Aucar
, R. H.
Romero
, and A. F.
Maldonado
, Int. Rev. Phys. Chem.
29
, 1
(2010
).
182.
A.
Bagno
and G.
Saielli
, Theor. Chem. Acc.
117
, 603
(2007
).
183.
S.
Schmitt
, P.
Jost
, and C.
van Wüllen
, J. Chem. Phys.
134
, 194113
(2011
).
184.
S.
Knecht
, S.
Fux
, R.
Meer
, L.
Visscher
, M.
Reiher
, and T.
Saue
, Theor. Chem. Acc.
129
, 631
(2011
).
185.
R.
Mastalerz
, R.
Lindh
, and M.
Reiher
, Chem. Phys. Lett.
465
, 157
(2008
).
186.
M.
Filatov
, W.
Zou
, and D.
Cremer
, J. Chem. Theory Comput.
8
, 875
(2012
).
187.
R.
Mastalerz
, P.
Widmark
, B. O.
Roos
, R.
Lindh
, and M.
Reiher
, J. Chem. Phys.
133
, 144111
(2010
).
188.
S.
Knecht
and T.
Saue
, “Nuclear size effects in rotational spectra: A tale with a twist
,” Chem. Phys.
(in press).
189.
C.
van Wüllen
, “Relativistic density functional theory
,” in Relativistic Methods for Chemists
, edited by M.
Barysz
and Y.
Ishikawa
, Challenges and Advances in Computational Chemsitry and Physics Vol. 10
(Springer
, Dordrecht
, 2010
), pp. 191
–214
. 190.
L.
Visscher
and K.
Dyall
, At. Data Nucl. Data Tables
67
, 207
(1997
).
191.
J. P.
Desclaux
, At. Data Nucl. Data Tables
12
, 311
(1973
).
192.
G.
Herzberg
, Phys. Rev. Lett.
23
, 1081
(1969
).
193.
© 2012 American Institute of Physics.
2012
American Institute of Physics
You do not currently have access to this content.