A new approach for relativistic correlated electron structure calculations is proposed by which a transformation to a two-spinor basis is carried out after solving the four-component relativistic Hartree–Fock equations. The method is shown to be more accurate than approaches that apply an a priori transformation to a two-spinor basis. We also demonstrate how the two-component relativistic calculations with properly transformed two-electron interaction can be simulated at the four-component level by projection techniques, thus allowing an assessment of errors introduced by more approximate schemes.

1.
M.
Douglas
and
N. M.
Kroll
,
Ann. Phys.
82
,
89
(
1974
).
2.
3.
4.
C.
Chang
,
M.
Pelissier
, and
P.
Durand
,
Phys. Scr.
34
,
394
(
1986
).
5.
E.
van Lenthe
,
E. J.
Baerends
, and
J. G.
Snijders
,
J. Chem. Phys.
101
,
9783
(
1994
).
6.
E.
van Lenthe
,
J. G.
Snijders
, and
E. J.
Baerends
,
J. Chem. Phys.
105
,
6505
(
1996
).
7.
M.
Barysz
and
A. J.
Sadlej
,
J. Chem. Phys.
116
,
2696
(
2002
).
8.
A.
Wolf
,
M.
Reiher
, and
B. A.
Hess
,
J. Chem. Phys.
117
,
9215
(
2002
).
9.
M.
Filatov
and
D.
Cremer
,
J. Chem. Phys.
119
,
11526
(
2003
).
10.
K.
Dyall
,
J. Chem. Phys.
106
,
9618
(
1997
).
11.
M.
Iliaš
,
H. J. A.
Jensen
,
V.
Kellö
,
B. O.
Roos
, and
M.
Urban
,
Chem. Phys. Lett.
408
,
210
(
2005
).
12.
W.
Kutzelnigg
and
W.
Liu
,
J. Chem. Phys.
123
,
241102
(
2005
).
13.
M.
Filatov
,
J. Chem. Phys.
125
,
107101
(
2006
).
14.
W.
Kutzelnigg
and
W.
Liu
,
J. Chem. Phys.
125
,
107102
(
2006
).
15.
M.
Iliaš
and
T.
Saue
,
J. Chem. Phys.
126
,
064102
(
2007
).
16.
The generic acronym “X2C” for exact two-component Hamiltonians resulted from intensive discussions among
H. J. Aa.
Jensen
,
W.
Kutzelnigg
,
W.
Liu
,
T.
Saue
, and
L.
Visscher
during the
Twelfth International Conference on the Applications of Density Functional Theory (DFT-2007)
, Amsterdam, 26–30 August
2007
.
17.
W.
Kutzelnigg
and
W.
Liu
,
Mol. Phys.
104
,
2225
(
2006
).
19.
V.
Kellö
and
A. J.
Sadlej
,
Int. J. Quantum Chem.
68
,
159
(
1998
).
20.
E. J.
Baerends
,
W. H. E.
Schwarz
,
P.
Schwerdtfeger
, and
J. G.
Snijders
,
J. Phys. B
23
,
3225
(
1990
).
21.
C.
van Wüllen
,
J. Chem. Phys.
109
,
392
(
1998
).
22.
A.
Matveev
and
N.
Rösch
,
J. Chem. Phys.
118
,
3997
(
2003
).
23.
A. V.
Matveev
,
S.
Majumder
, and
N.
Rösch
,
J. Chem. Phys.
123
,
164104
(
2005
).
24.
C.
van Wüllen
and
C.
Michauk
,
J. Chem. Phys.
123
,
204113
(
2005
).
25.
D.
Peng
,
W.
Liu
,
Y.
Xiao
, and
L.
Cheng
,
J. Chem. Phys.
127
,
104106
(
2007
).
26.
R.
Samzow
,
B. A.
Hess
, and
G.
Jansen
,
J. Chem. Phys.
96
,
1227
(
1992
).
27.
C.
Park
and
J. E.
Almlöf
,
Chem. Phys. Lett.
231
,
269
(
1994
).
28.
T.
Nakajima
and
K.
Hirao
,
J. Chem. Phys.
119
,
4105
(
2003
).
29.
J.
Seino
and
M.
Hada
,
Chem. Phys. Lett.
461
,
327
(
2008
).
30.
B. A.
Hess
,
C. M.
Marian
,
U.
Wahlgren
, and
O.
Gropen
,
Chem. Phys. Lett.
251
,
365
(
1996
).
31.
B.
Schimmelpfennig
,
L.
Maron
,
U.
Wahlgren
,
C.
Teichteil
,
H.
Fagerli
, and
O.
Gropen
,
Chem. Phys. Lett.
286
,
267
(
1998
).
32.
M.
Born
and
J. R.
Oppenheimer
,
Ann. Phys.
389
,
457
(
1927
).
33.
J. A.
Gaunt
,
Philos. Trans. R. Soc. London
228
,
151
(
1929
).
34.
T.
Saue
and
L.
Visscher
, in
Theoretical Chemistry and Physics of Heavy and Superheavy Elements
, edited by
S.
Wilson
and
U.
Kaldor
(
Kluwer
,
Dordrecht
,
2003
), p.
211
.
35.
G. E.
Brown
and
D. G.
Ravenhall
,
Proc. R. Soc. London, Ser. A
208
,
552
(
1951
).
36.
G.
Pestka
,
M.
Bylicki
, and
J.
Karwowski
,
J. Phys. B
39
,
2979
(
2006
).
37.
M. H.
Mittleman
,
Phys. Rev. A
24
,
1167
(
1981
).
38.
39.
40.
M. J.
Esteban
,
M.
Lewin
, and
E.
Séré
,
Bull., New Ser., Am. Math. Soc.
45
,
535
(
2008
).
41.
Relativistic Electronic Structure Theory—Part 1. Fundamentals
, edited by
P.
Schwerdtfeger
(
Elsevier
,
Amsterdam
,
2002
), p.
259
.
42.
K. G.
Dyall
and
K.
Fægri
,
Theor. Chim. Acta
94
,
39
(
1996
).
43.
L.
Visscher
and
T.
Saue
,
J. Chem. Phys.
113
,
3996
(
2000
).
44.
L. L.
Foldy
and
S. A.
Wouthuysen
,
Phys. Rev.
78
,
29
(
1950
).
45.
J. -L.
Heully
,
I.
Lindgren
,
E.
Lindroth
,
S.
Lundqvist
, and
A. -M.
Mårtensson-Pendrill
,
J. Phys. B
19
,
2799
(
1986
).
46.
W.
Kutzelnigg
,
J. Chem. Phys.
110
,
8283
(
1999
).
47.
W.
Kutzelnigg
, in
Relativistic Electronic Structure Theory—Part 1. Fundamentals
, edited by
P.
Schwerdtfeger
(
Elsevier
,
Amsterdam
,
2002
), p.
664
.
48.
M.
Pernpointner
and
P.
Schwerdtfeger
,
Chem. Phys. Lett.
295
,
347
(
1998
).
49.
V.
Kellö
and
A. J.
Sadlej
,
J. Mol. Struct.: THEOCHEM
547
,
35
(
2001
).
50.
W.
Kutzelnigg
,
Int. J. Quantum Chem.
25
,
107
(
1984
).
51.
K. G.
Dyall
,
J. Chem. Phys.
100
,
2118
(
1994
).
52.
L.
Visscher
,
Theor. Chem. Acc.
98
,
68
(
1997
).
53.
L.
Visscher
,
J. Comput. Chem.
23
,
759
(
2002
).
54.
J. K.
Pedersen
, Ph.D. thesis,
University of Southern Denmark
,
2004
.
55.
T.
Saue
, Ph.D. thesis,
University of Oslo
,
1996
.
56.
W.
Liu
and
D.
Peng
,
J. Chem. Phys.
125
,
044102
(
2006
).
57.
DIRAC, a relativistic ab initio electronic structure program, release DIRAC 04.0 (
2004
), written by
H. J. Aa.
Jensen
,
T.
Saue
, and
L.
Visscher
with contributions from
V.
Bakken
,
E.
Eliav
,
T.
Enevoldsen
,
T.
Fleig
,
O.
Fossgaard
,
T.
Helgaker
,
J.
Laerdahl
,
C. V.
Larsen
,
P.
Norman
,
J.
Olsen
,
M.
Pernpointner
,
J. K.
Pedersen
,
K.
Ruud
,
P.
Salek
,
J. N. P.
van Stralen
,
J.
Thyssen
,
O.
Visser
, and
T.
Winther
, http://wiki.chem.vu.nl/dirac/index.php/Dirac_Program.
58.
L.
Visscher
and
K. G.
Dyall
,
At. Data Nucl. Data Tables
67
,
207
(
1997
);
59.
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
90
,
1007
(
1989
).
60.
R. A.
Kendall
,
T. H.
Dunning
, Jr.
, and
R. J.
Harrison
,
J. Chem. Phys.
96
,
6796
(
1992
).
61.
D. E.
Woon
and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
98
,
1358
(
1993
).
62.
K. G.
Dyall
,
Theor. Chem. Acc.
99
,
366
(
1998
);
K. G.
Dyall
,
Theor. Chem. Acc.
108
,
365
(
2002
);
K. G.
Dyall
,
Theor. Chem. Acc.
115
,
441
(R) (
2006
);
basis sets available from the DIRAC web site: http://wiki.chem.vu.nl/dirac/index.php/Dirac_Program.
63.
M.
Pernpointner
,
M.
Seth
, and
P.
Schwerdtfeger
,
J. Chem. Phys.
108
,
6722
(
1998
).
64.
V.
Kellö
and
A. J.
Sadlej
,
Phys. Rev. A
60
,
3575
(
1999
).
65.
L.
Visscher
,
E.
Eliav
, and
U.
Kaldor
,
J. Chem. Phys.
115
,
9720
(
2001
).
66.
M.
Iliaš
,
V.
Kellö
,
L.
Visscher
, and
B.
Schimmelpfennig
,
J. Chem. Phys.
115
,
9667
(
2001
).
67.
B.
Schimmelpfennig
, program AMFI, Stockholm, Sweden.
68.
C. E.
Miller
and
B. J.
Drouin
,
J. Mol. Spectrosc.
205
,
312
(
2001
).
69.
B. J.
Drouin
,
C. E.
Miller
,
E. A.
Cohen
,
G.
Wagner
, and
M.
Birk
,
J. Mol. Spectrosc.
207
,
4
(
2001
).
70.
B. J.
Drouin
,
C. E.
Miller
,
H. S. P.
Müller
, and
E. A.
Cohen
,
J. Mol. Spectrosc.
205
,
128
(
2001
).
71.
C. E.
Miller
and
E. A.
Cohen
,
J. Chem. Phys.
115
,
6459
(
2001
).
72.
K. P.
Huber
and
G.
Herzberg
,
Molecular Spectra and Molecular Structure Constants of Diatomic Molecules
(
Van Nostrand
,
New York
,
1979
).
73.
J. -L.
Heully
,
I.
Lindgren
,
E.
Lindroth
, and
A. -M.
Mårtensson-Pendrill
,
Phys. Rev. A
33
,
4426
(
1986
).
74.
M. K.
Gilles
,
M. L.
Polak
, and
W. C.
Lineberger
,
J. Chem. Phys.
96
,
8012
(
1992
).
75.
M. C.
McCarthy
,
R. W.
Field
,
R.
Engleman
, Jr.
, and
P. F.
Bemath
,
J. Mol. Spectrosc.
158
,
208
(
1993
).
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