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.
REFERENCES
1.
M.
Douglas
and N. M.
Kroll
, Ann. Phys.
82
, 89
(1974
).2.
B. A.
Hess
, Phys. Rev. A
32
, 756
(1985
).3.
B. A.
Hess
, Phys. Rev. A
33
, 3742
(1986
).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
).18.
K. G.
Dyall
, Int. J. Quantum Chem.
78
, 412
(2000
).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.
J. D.
Talman
, Phys. Rev. Lett.
57
, 1091
(1986
).39.
W.
Kutzelnigg
, Chem. Phys.
225
, 203
(1997
).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.
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.
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
).© 2009 American Institute of Physics.
2009
American Institute of Physics
You do not currently have access to this content.