An efficient perturbational treatment of spin-orbit coupling within the framework of high-level multi-reference techniques has been implemented in the most recent version of the Columbus quantum chemistry package, extending the existing fully variational two-component (2c) multi-reference configuration interaction singles and doubles (MRCISD) method. The proposed scheme follows related implementations of quasi-degenerate perturbation theory (QDPT) model space techniques. Our model space is built either from uncontracted, large-scale scalar relativistic MRCISD wavefunctions or based on the scalar-relativistic solutions of the linear-response-theory-based multi-configurational averaged quadratic coupled cluster method (LRT-MRAQCC). The latter approach allows for a consistent, approximatively size-consistent and size-extensive treatment of spin-orbit coupling. The approach is described in detail and compared to a number of related techniques. The inherent accuracy of the QDPT approach is validated by comparing cuts of the potential energy surfaces of acrolein and its S, Se, and Te analoga with the corresponding data obtained from matching fully variational spin-orbit MRCISD calculations. The conceptual availability of approximate analytic gradients with respect to geometrical displacements is an attractive feature of the 2c-QDPT-MRCISD and 2c-QDPT-LRT-MRAQCC methods for structure optimization and ab inito molecular dynamics simulations.

1.
P.
Pyykkö
,
Chem. Rev.
88
(
3
),
563
594
(
1988
).
2.
M.
Reiher
,
Theor. Chem. Acc.
116
(
1
),
241
252
(
2006
).
3.
F.
Neese
,
T.
Petrenko
,
D.
Ganyushin
, and
G.
Olbrich
,
Coord. Chem. Rev.
251
(
3–4
),
288
327
(
2007
).
4.
C. M.
Marian
,
WIREs: Comput. Mol. Sci.
2
(
2
),
187
203
(
2012
).
5.
B. A.
Hess
in
Encyclopedia of Computational Chemistry
, edited by
P.
von Rague Schleyer
(
Wiley
,
Chichester
,
1998
), p.
2499
.
6.
W. H. E.
Schwarz
, in
Relativistic Methods for Chemists
, edited by
M.
Barysz
and
Y.
Ishikawa
(
Springer
,
Dordrecht
,
2010
), p.
1
.
7.
Relativistic Effects in Chemistry. Part B: Applications
, edited by
K.
Balasubramanian
(
Wiley
,
New York
,
1997
).
8.
Relativistic Effects in Heavy-Element Chemistry and Physics
,
Series in Theoretical Chemistry
Vol.
12
, edited by
B. A.
Hess
(
Wiley
,
Chichester, UK
,
2002
).
9.
N. J.
Turro
,
J. C.
Scaiano
, and
V.
Ramamurthy
,
Principles of Molecular Photochemistry: An Introduction
(
University Science Books
,
Sausalito, CA
,
2009
).
10.
M.
Klessinger
and
J.
Michl
,
Excited States and Photochemistry of Organic Molecules
(
VCH Publishers, Inc.
,
New York
,
1995
).
11.
R. S.
Minns
,
D. S. N.
Parker
,
T. J.
Penfold
,
G. A.
Worth
, and
H. H.
Fielding
,
Phys. Chem. Chem. Phys.
12
(
48
),
15607
15615
(
2010
).
12.
T. J.
Penfold
,
R.
Spesyvtsev
,
O. M.
Kirkby
,
R. S.
Minns
,
D. S. N.
Parker
,
H. H.
Fielding
, and
G. A.
Worth
,
J. Chem. Phys.
137
(
20
),
204310
(
2012
).
13.
C. E.
Crespo-Hernández
,
G.
Burdzinski
, and
R.
Arce
,
J. Phys. Chem. A
112
(
28
),
6313
6319
(
2008
).
14.
R. A.
Vogt
,
C.
Reichardt
, and
C. E.
Crespo-Hernández
,
J. Phys. Chem.
117
(
30
),
6580
6588
(
2013
).
15.
C. E.
Crespo-Hernández
,
B.
Cohen
,
P. M.
Hare
, and
B.
Kohler
,
Chem. Rev.
104
(
4
),
1977
2020
(
2004
).
16.
M.
Richter
,
P.
Marquetand
,
J.
González-Vázquez
,
I.
Sola
, and
L.
González
,
J. Phys. Chem. Lett.
3
,
3090
3095
(
2012
).
17.
S.
Mai
,
P.
Marquetand
,
M.
Richter
,
J.
González-Vázquez
, and
L.
González
,
ChemPhysChem
14
,
2920
2931
(
2013
).
18.
L.
Martínez-Fernández
,
I.
Corral
,
G.
Granucci
, and
M.
Persico
,
Chem. Sci.
5
,
1336
(
2014
).
19.
S.
Mai
,
P.
Marquetand
, and
L.
González
,
J. Chem. Phys.
140
,
204302
(
2014
).
20.
C. A.
Mead
,
J. Chem. Phys.
70
,
2276
(
1979
).
21.
S.
Matsika
and
D. R.
Yarkony
,
J. Chem. Phys.
115
,
2038
(
2001
).
22.
S.
Matsika
and
D. R.
Yarkony
,
J. Chem. Phys.
115
,
5066
(
2001
).
23.
S.
Matsika
and
D. R.
Yarkony
,
J. Chem. Phys.
116
,
2825
(
2002
).
24.
B. O.
Roos
and
P.-Å.
Malmqvist
,
Phys. Chem. Chem. Phys.
6
(
11
),
2919
2927
(
2004
).
25.
P. A. M.
Dirac
,
Proc. R. Soc. London, Ser. A
117
(
778
),
610
624
(
1928
).
26.
G.
Breit
,
Phys. Rev.
34
(
4
),
553
573
(
1929
).
27.
W.
Pauli
, Jr.
,
Z. Phys.
43
(
9–10
),
601
623
(
1927
).
28.
H. A.
Bethe
and
E. E.
Salpeter
,
Quantum Mechanics of One- and Two-Electron Atoms
(
Springer
,
Berlin
,
1957
).
29.
T.
Fleig
,
Chem. Phys.
395
(
0
),
2
15
(
2012
).
30.
K. G.
Dyall
and
K.
Fægri
, Jr.
,
Introduction to Relativistic Quantum Chemistry
(
Oxford University Press
,
2007
).
31.
I. P.
Grant
, and
H. M.
Quiney
, in
Relativistic Electronic Structure Theory. Part 1: Fundamentals
, edited by
P.
Schwerdtfeger
(
Elsevier
,
Amsterdam
,
2002
), p.
107
.
32.
T.
Saue
,
K.
Faegri
,
T.
Helgaker
, and
O.
Gropen
,
Mol. Phys.
91
,
937
(
1997
).
33.
S.
Knecht
,
H. J. A.
Jensen
, and
T.
Fleig
,
J. Chem. Phys.
132
,
014108
(
2010
).
34.
J.
Thyssen
,
T.
Fleig
, and
H. J. A.
Jensen
,
J. Chem. Phys.
129
,
034109
(
2008
).
35.
L. K.
Sørensen
,
S.
Knecht
,
T.
Fleig
, and
C. M.
Marian
,
J. Phys. Chem. A
113
,
12607
12614
(
2009
).
36.
T.
Fleig
,
L. K.
Sørensen
, and
J.
Olsen
,
Theor. Chem. Acc.
118
,
347
(
2007
).
37.
E.
Eliav
, and
U.
Kaldor
, in
Recent Progress in Coupled Cluster Methods
, edited by
P.
Carsky
,
J.
Paldus
, and
J.
Pittner
(
Springer
,
Dordrecht
,
2010
), p.
113
.
38.
E.
Engel
in
Relativistic Electronic Structure Theory. Part 1: Fundamentals
, edited by
P.
Schwerdtfeger
(
Elsevier
,
Amsterdam
,
2002
), p.
523
.
39.
T.
Saue
and
T.
Helgaker
,
J. Comput. Chem.
23
,
814
(
2002
).
40.
T.
Nakajima
and
K.
Hirao
,
Chem. Rev.
112
,
385
(
2012
).
41.
E.
van Lenthe
,
R.
van Leeuwen
,
E. J.
Baerends
, and
J. G.
Snijders
,
Int. J. Quantum Chem.
57
,
281
(
1996
).
42.
B. A.
Hess
,
Phys. Rev. A
33
(
6
),
3742
3748
(
1986
).
43.
T.
Fleig
,
J.
Olsen
, and
C. M.
Marian
,
J. Chem. Phys.
114
(
11
),
4775
4790
(
2001
).
44.
D.
Ganyushin
and
F.
Neese
,
J. Chem. Phys.
138
(
10
),
104113
(
2013
).
45.
H.-S.
Lee
,
Y.-K.
Han
,
M. C.
Kim
,
C.
Bae
, and
Y. S.
Lee
,
Chem. Phys. Lett.
293
(
1–2
),
97
102
(
1998
).
46.
M. K.
Armbruster
,
F.
Weigend
,
C.
van Wullen
, and
W.
Klopper
,
Phys. Chem. Chem. Phys.
10
,
1748
1756
(
2008
).
47.
F.
Wang
and
T.
Ziegler
,
J. Chem. Phys.
123
(
15
),
154102
(
2005
).
48.
P.
Romaniello
and
P. L.
de Boeij
,
J. Chem. Phys.
127
(
17
),
174111
(
2007
).
49.
F.
Franco de Carvalho
,
B. F. E.
Curchod
,
T. J.
Penfold
, and
I.
Tavernelli
,
J. Chem. Phys.
140
(
14
),
144103
(
2014
).
50.
M.
Dolg
and
X.
Cao
,
Chem. Rev.
112
(
1
),
403
480
(
2012
).
51.
B. A.
Hess
, and
C. M.
Marian
, in
Computational Molecular Spectroscopy
, edited by
P.
Jensen
and
P. R.
Bunker
(
John Wiley and Sons, Inc.
,
Sussex
,
2000
), pp.
152
278
.
52.
H.
Lischka
,
T.
Müller
,
P. G.
Szalay
,
I.
Shavitt
,
R. M.
Pitzer
, and
R.
Shepard
,
WIREs: Comput. Mol. Sci.
1
,
191
199
(
2011
).
53.
H.
Lischka
,
R.
Shepard
,
R. M.
Pitzer
,
I.
Shavitt
,
M.
Dallos
,
T.
Müller
,
P. G.
Szalay
,
M.
Seth
,
G. S.
Kedziora
,
S.
Yabushita
, and
Z.
Zhang
,
Phys. Chem. Chem. Phys.
3
(
5
),
664
673
(
2001
).
54.
H.
Lischka
,
R.
Shepard
,
I.
Shavitt
,
R. M.
Pitzer
,
M.
Dallos
,
T.
Müller
,
P. G.
Szalay
,
F. B.
Brown
,
R.
Ahlrichs
,
H. J.
Böhm
,
A.
Chang
,
D. C.
Comeau
,
R.
Gdanitz
,
H.
Dachsel
,
C.
Ehrhardt
,
M.
Ernzerhof
,
P.
Höchtl
,
S.
Irle
,
G.
Kedziora
,
T.
Kovar
,
V.
Parasuk
,
M. J. M.
Pepper
,
P.
Scharf
,
H.
Schiffer
,
M.
Schindler
,
M.
Schüler
,
M.
Seth
,
E. A.
Stahlberg
,
J.-G.
Zhao
,
S.
Yabushita
,
Z.
Zhang
,
M.
Barbatti
,
S.
Matsika
,
M.
Schuurmann
,
D. R.
Yarkony
,
S. R.
Brozell
,
E. V.
Beck
,
J.-P.
Blaudeau
,
M.
Ruckenbauer
,
B.
Sellner
,
F.
Plasser
, and
J. J.
Szymczak
, Columbus, an ab initio electronic structure program, release 7.0,
2012
.
55.
P. G.
Szalay
,
T.
Müller
, and
H.
Lischka
,
Phys. Chem. Chem. Phys.
2
,
2067
2073
(
2000
).
56.
I.
Shavitt
,
Lecture Notes in Chemistry
(
Springer-Verlag
,
Berlin
,
1981
), Vol.
22
, pp.
51
99
.
57.
S.
Yabushita
,
Z.
Zhang
, and
R. M.
Pitzer
,
J. Phys. Chem. A
103
(
29
),
5791
5800
(
1999
).
58.
M.
Dolg
, in
Theoretical and Computational Chemistry
, edited by
P.
Schwerdtfeger
(
Elsevier Science B.V.
,
Amsterdam
,
2002
), Vol.
11
.
59.
W. C.
Ermler
,
R. B.
Ross
, and
P. A.
Christiansen
,
Advances in Quantum Chemistry
(
Academic Press
,
1988
), Vol.
19
, pp.
139
182
.
60.
P. A.
Christiansen
,
Y. S.
Lee
, and
K. S.
Pitzer
,
J. Chem. Phys.
71
(
11
),
4445
4450
(
1979
).
61.
S.
Huzinaga
,
L.
Seijo
,
Z.
Barandiaran
, and
M.
Klobukowski
,
J. Chem. Phys.
86
(
4
),
2132
2145
(
1987
).
62.
M.
Klobukowski
,
S.
Huzinaga
, and
Y.
Sakai
, in
Computational Chemistry: Review of Current Trends
, edited by
J.
Leszczynski
(
World Scientific
,
Singapore
,
1999
), Vol.
3
, p.
49
.
63.
A.
Wolf
,
M.
Reiher
, and
B. A.
Hess
,
J. Chem. Phys.
117
(
20
),
9215
9226
(
2002
).
64.
B.
Schimmelpfennig
, “
Atomic spin-orbit mean-field integral program AMFI
,”
1996
.
65.
R.
Samzow
and
B. A.
Hess
,
Chem. Phys. Lett.
184
(
5–6
),
491
496
(
1991
).
66.
B. A.
Heß
,
C. M.
Marian
,
U.
Wahlgren
, and
O.
Gropen
,
Chem. Phys. Lett.
251
(
5–6
),
365
371
(
1996
).
67.
O.
Christiansen
,
J.
Gauss
, and
B.
Schimmelpfennig
,
Phys. Chem. Chem. Phys.
2
,
965
971
(
2000
).
68.
B. O.
Roos
, in
Methods of Electronic Structure Theory
, edited by
I. H. F.
Schaefer
(
Plenum
,
New York
,
1977
), p.
277
.
69.
T.
Saue
,
L.
Visscher
,
H. J. A.
Jensen
,
R.
Bast
,
K. G.
Dyall
,
U.
Ekstrm
,
E.
Eliav
,
T.
Enevoldsen
,
T.
Fleig
,
A. S. P.
Gomes
,
J.
Henrikson
,
M.
Ilias
,
C. R.
Jacob
,
S.
Knecht
,
H. S.
Nataraj
,
P.
Norman
,
J.
Olsen
,
M.
Pernpointner
,
K.
Ruud
,
B.
Schimmelpfennig
,
J.
Sikkema
,
A.
Thorvaldsen
,
J.
Thyssen
,
S.
Villaume
, and
S.
Yamamoto
, DIRAC, a relativistic ab initio electronic structure program, release DIRAC11,
2011
, see http://dirac.chem.vu.nl.
70.
V.
Vallet
,
L.
Maron
,
C.
Teichteil
, and
J.-P.
Flament
,
J. Chem. Phys.
113
(
4
),
1391
1402
(
2000
).
71.
M.
Kleinschmidt
,
J.
Tatchen
, and
C. M.
Marian
,
J. Chem. Phys.
124
(
12
),
124101
(
2006
).
72.
R. J.
Buenker
,
A. B.
Alekseyev
,
H.-P.
Liebermann
,
R.
Lingott
, and
G.
Hirsch
,
J. Chem. Phys.
108
(
9
),
3400
3408
(
1998
).
73.
P. A.
Christiansen
,
K.
Balasubramanian
, and
K. S.
Pitzer
,
J. Chem. Phys.
76
(
10
),
5087
5092
(
1982
).
74.
R. M.
Pitzer
and
N. W.
Winter
,
J. Phys. Chem.
92
(
11
),
3061
3063
(
1988
).
75.
P. G.
Szalay
,
T.
Müller
,
G.
Gidofalvi
,
H.
Lischka
, and
R.
Shepard
,
Chem. Rev.
112
(
1
),
108
181
(
2012
).
76.
T.
Müller
,
J. Phys. Chem. A
113
,
12729
(
2009
).
77.
V.
Vallet
,
L.
Maron
,
C.
Teichteil
, and
J.-P.
Flament
,
J. Chem. Phys.
113
,
1391
(
2000
).
78.
F.
Neese
,
WIREs: Comput. Mol. Sci.
2
(
1
),
73
78
(
2012
).
79.
P.-A.
Malmqvist
,
B. O.
Roos
, and
B.
Schimmelpfennig
,
Chem. Phys. Lett.
357
,
230
(
2002
).
80.
A.
Berning
,
M.
Schweizer
,
H.
Werner
,
P. J.
Knowles
, and
P.
Palmieri
,
Mol. Phys.
98
(
21
),
1823
1833
(
2000
).
81.
P. G.
Szalay
and
R. J.
Bartlett
,
Chem. Phys. Lett.
214
(
5
),
481
488
(
1993
).
82.
P. G.
Szalay
in
Recent Advances in Coupled-Cluster Methods
, edited by
R. B.
Bartlett
(
World Scientific
,
Singapore
,
1997
), p.
81
.
83.
R. M.
Pitzer
and
N. W.
Winter
,
Int. J. Quantum Chem.
40
(
6
),
773
780
(
1991
).
84.
F.
Aquilante
,
L.
De Vico
,
N.
Ferré
,
G.
Ghigo
,
P.-Å.
Malmqvist
,
P.
Neogrády
,
T. B.
Pedersen
,
M.
Pitoňák
,
M.
Reiher
,
B. O.
Roos
,
L.
Serrano-Andrés
,
M.
Urban
,
V.
Veryazov
, and
R.
Lindh
,
J. Comput. Chem.
31
(
1
),
224
247
(
2010
).
85.
A.
Messiah
,
Quantum Mechanics
(
Dover
,
Minneola
,
1999
).
86.
A. D.
Walsh
,
Trans. Faraday Soc.
41
,
498
505
(
1945
).
87.
M.
Reguero
,
M.
Olivucci
,
F.
Bernardi
, and
M. A.
Robb
,
J. Am. Chem. Soc.
116
(
5
),
2103
2114
(
1994
).
88.
M. A.
El-Sayed
,
J. Chem. Phys.
38
(
12
),
2834
2838
(
1963
).
89.
M.
Richter
,
P.
Marquetand
,
J.
González-Vázquez
,
I.
Sola
, and
L.
González
,
J. Chem. Theory Comput.
7
(
5
),
1253
1258
(
2011
).
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