The authors report the implementation of a simple one-step method for obtaining an infinite-order two-component (IOTC) relativistic Hamiltonian using matrix algebra. They apply the IOTC Hamiltonian to calculations of excitation and ionization energies as well as electric and magnetic properties of the radon atom. The results are compared to corresponding calculations using identical basis sets and based on the four-component Dirac-Coulomb Hamiltonian as well as Douglas-Kroll-Hess and zeroth-order regular approximation Hamiltonians, all implemented in the DIRAC program package, thus allowing a comprehensive comparison of relativistic Hamiltonians within the finite basis approximation.
REFERENCES
1.
P.
Pyykkö
, Chem. Rev. (Washington, D.C.)
88
, 563
(1988
).2.
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
.3.
L.
Visscher
, J. Comput. Chem.
23
, 759
(2002
).4.
T.
Saue
, K.
Fegri
, T.
Helgaker
, and O.
Gropen
, Mol. Phys.
91
, 937
(1997
).5.
W. J.
Liu
, G. Y.
Hong
, D. D.
Dai
, L. M.
Li
, and M.
Dolg
, Theor. Chem. Acc.
96
, 75
(1997
).6.
S.
Varga
, E.
Engel
, W.-D.
Sepp
, and B.
Fricke
, Phys. Rev. A
59
, 4288
(1999
).7.
L.
Belpassi
, F.
Tarantelli
, A.
Sgamellotti
, and H. M.
Quiney
, J. Chem. Phys.
124
, 124104
(2006
).8.
T.
Nakajima
and K.
Hirao
, J. Chem. Phys.
121
, 3438
(2004
).9.
T.
Saue
and H. J. Aa.
Jensen
, J. Chem. Phys.
111
, 6211
(1999
).10.
L.
Visscher
, Theor. Chem. Acc.
98
, 68
(1997
).11.
J. K.
Pedersen
, Ph.D. thesis, University of Southern Denmark
, Odense, 2004
,online version: http://dirac.chem.sdu.dk/thesis/
12.
W.
Liu
and D.
Peng
, J. Chem. Phys.
125
, 044102
(2006
).13.
M.
Douglas
and N. M.
Kroll
, Ann. Phys. (N.Y.)
82
, 89
(1974
).14.
B. A.
Hess
, Phys. Rev. A
32
, 756
(1985
).15.
B. A.
Hess
, Phys. Rev. A
33
, 3742
(1986
).16.
M.
Barysz
, A. J.
Sadlej
, and J. G.
Snijders
, Int. J. Quantum Chem.
65
, 225
(1997
).17.
M.
Barysz
and A. J.
Sadlej
, J. Mol. Struct.: THEOCHEM
573
, 181
(2001
).18.
C.
Chang
, M.
Pelissier
, and P.
Durand
, Phys. Scr.
34
, 394
(1986
).19.
E.
van Lenthe
, E. J.
Baerends
, and J. G.
Snijders
, J. Chem. Phys.
101
, 9783
(1994
).20.
E.
van Lenthe
, J. G.
Snijders
, and E. J.
Baerends
, J. Chem. Phys.
105
, 6505
(1996
).21.
W.
Kutzelnigg
, Chem. Phys.
225
, 203
(1997
).22.
M.
Barysz
and A. J.
Sadlej
, J. Chem. Phys.
116
, 2696
(2002
).23.
T.
Nakajima
and K.
Hirao
, J. Chem. Phys.
113
, 7786
(2000
).24.
C.
van Wüllen
, J. Chem. Phys.
120
, 7307
(2004
).25.
M.
Reiher
and A.
Wolf
, J. Chem. Phys.
121
, 2037
(2004
).26.
M.
Reiher
and A.
Wolf
, J. Chem. Phys.
121
, 10945
(2004
).27.
K.
Dyall
, J. Chem. Phys.
106
, 9618
(1997
).28.
H. J. Aa.
Jensen
and M.
Iliaš
(unpublished).29.
M.
Iliaš
, H. J. Aa.
Jensen
, V.
Kellö
, B. O.
Roos
, and M.
Urban
, Chem. Phys. Lett.
408
, 210
(2005
).30.
W.
Kutzelnigg
and W.
Liu
, J. Chem. Phys.
123
, 241102
(2005
).31.
W.
Kutzelnigg
and W.
Liu
, Mol. Phys.
104
, 2225
(2006
).32.
D.
Kedziera
and M.
Barysz
, J. Chem. Phys.
121
, 6719
(2004
).33.
H. J. Aa.
Jensen
, T.
Saue
, L.
Visscher
et al., DIRAC04.0, a relativistic ab initio electronic structure program, 2004
(http://dirac.chem.sdu.dk).34.
T.
Saue
and T.
Helgaker
, J. Comput. Chem.
23
, 814
(2002
).35.
J. K.
Lerdahl
, T.
Saue
, and K.
Fægri
, Theor. Chem. Acc.
97
, 177
(1997
).36.
H. J. Aa.
Jensen
, K. G.
Dyall
, T.
Saue
, and K.
Fægri
, J. Chem. Phys.
104
, 4083
(1996
).37.
T.
Fleig
, J.
Olsen
, and L.
Visscher
, J. Chem. Phys.
119
, 2963
(2003
).38.
L.
Visscher
, T.
Saue
, W. C.
Nieuwpoort
, K.
Fægri
, and O.
Gropen
, J. Chem. Phys.
99
, 6704
(1993
).39.
L.
Visscher
, T. J.
Lee
, and K. G.
Dyall
, J. Chem. Phys.
105
, 8769
(1996
).40.
L.
Visscher
, E.
Eliav
, and U.
Kaldor
, J. Chem. Phys.
115
, 9720
(2001
).41.
K. G.
Dyall
, Int. J. Quantum Chem.
78
, 412
(2000
).42.
V.
Kellö
and A. J.
Sadlej
, Int. J. Quantum Chem.
68
, 159
(1998
).43.
E. J.
Baerends
, W. H. E.
Schwarz
, P.
Schwerdtfeger
, and J. G.
Snijders
, J. Phys. B
23
, 3225
(1990
).44.
T.
Saue
and H. J. Aa.
Jensen
, J. Chem. Phys.
118
, 522
(2003
).45.
P.
Norman
and H. J. Aa.
Jensen
, J. Chem. Phys.
121
, 6145
(2004
).46.
47.
P. A. M.
Dirac
, in Septiéme Conseil de Physique Solvay: Structure et Propriétés des Noyaux Atomiques
, edited by J.
Cockcroft
, F.
Chadwick
, J.
Joliot
, N.
Joliot
, N.
Bohr
, G.
Gamov
, P.
Dirac
, and W.
Heisenberg
(Gauthier-Villars
, Paris
, 1934
).48.
J.-L.
Heully
, I.
Lindgren
, E.
Lindroth
, S.
Lundqvist
, and A.-M.
Mårtensson-Pendrill
, J. Phys. B
19
, 2799
(1986
).49.
W.
Kutzelnigg
, J. Chem. Phys.
110
, 8283
(1999
).50.
W.
Kutzelnigg
, in Relativistic Electronic Structure Theory: Part 1. Fundamentals
, edited by P.
Schwerdtfeger
(Elsevier
, Amsterdam
, 2002
), p. 664
.51.
R. E.
Moss
, Advanced Molecular Quantum Mechanics
(Chapmann and Hall
, London
, 1973
).52.
E.
van Lenthe
, E. J.
Baerends
, and J. G.
Snijders
, J. Chem. Phys.
105
, 2373
(1996
).53.
K.
Dyall
, in Theoretical Chemistry and Physics of Heavy and Superheavy Elements
, edited by S.
Wilson
and U.
Kaldor
(Kluwer
, Dordrecht
, 2003
), p. 325
.54.
K. G.
Dyall
and T.
Enevoldsen
, J. Chem. Phys.
111
, 10000
(1999
).55.
W.
Kutzelnigg
, Z. Phys. D: At., Mol. Clusters
11
, 15
(1989
).56.
G.
Aucar
, T.
Saue
, H. J. Aa.
Jensen
, and L.
Visscher
, J. Chem. Phys.
110
, 6208
(1999
).57.
M.
Pecul
, T.
Saue
, K.
Ruud
, and A.
Rizzo
, J. Chem. Phys.
121
, 3051
(2004
).58.
W.
Kutzelnigg
, J. Comput. Chem.
20
, 1199
(1999
).59.
L.
Visscher
, P. J. C.
Aerts
, O.
Visser
, and W. C.
Nieuwpoort
, Int. J. Quantum Chem., Quantum Chem. Symp.
25
, 131
(1991
).60.
K. G.
Dyall
and E.
van Lenthe
, J. Chem. Phys.
111
, 1366
(1999
).61.
R.
van Leeuwen
, E.
van Lenthe
, E. J.
Baerends
, and J. G.
Snijders
, J. Chem. Phys.
101
, 1272
(1994
).62.
L.
Visscher
and T.
Saue
, J. Chem. Phys.
113
, 3996
(2000
).63.
M.
Filatov
and D.
Cremer
, J. Chem. Phys.
122
, 064104
(2004
).64.
S.
Faas
, J. G.
Snijders
, J. H.
van Lenthe
, E.
van Lenthe
, and E. J.
Baerends
, Chem. Phys. Lett.
246
, 632
(1995
).65.
L. L.
Foldy
and S. A.
Wouthuysen
, Phys. Rev.
78
, 29
(1950
).66.
67.
J. H.
Wood
and A. M.
Boring
, Phys. Rev. B
18
, 2701
(1978
).68.
S.
Komorovský
, M.
Repiský
, O. L.
Malkina
, V. G.
Malkin
, I.
Malkin
, and M.
Kaupp
, J. Chem. Phys.
124
, 084108
(2006
).69.
W.
Kutzelnigg
, Phys. Rev. A
67
, 032109
(2003
).70.
71.
M. M.
Sternheim
, Phys. Rev.
128
, 676
(1962
).72.
C.
Park
and J.
Almlöf
, Chem. Phys. Lett.
231
, 269
(1994
).73.
T.
Nakajima
and K.
Hirao
, J. Chem. Phys.
119
, 4105
(2003
).74.
K. G.
Dyall
, J. Chem. Phys.
100
, 2118
(1994
).75.
K. G.
Dyall
, Theor. Chem. Acc.
108
, 335
(2002
),the basis sets are available from the DIRAC web site http://dirac.chem.sdu.dk
76.
L.
Visscher
and K. G.
Dyall
, At. Data Nucl. Data Tables
67
, 207
(1997
),77.
78.
E.
Eliav
, M. J.
Vilkas
, Y.
Ishikawa
, and U.
Kaldor
, J. Chem. Phys.
122
, 224113
(2005
).79.
J.
Vaara
and P.
Pyykkö
, J. Chem. Phys.
118
, 2973
(2003
).80.
B. A.
Hess
, C. M.
Marian
, U.
Wahlgren
, and O.
Gropen
, Chem. Phys. Lett.
251
, 365
(1996
).81.
C. E.
Moore
, Ionization Potentials and Ionization Limits Derived From the Analyses of Optical Spectra
, Natl. Bur. Stand. Ref. Data Ser., Natl. Bur. Stand.
(U.S.) Circ. No. 467 (U.S. GPO, Washington, D.C., 1970
).82.
K. G.
Dyall
, I. P.
Grant
, C. T.
Johnson
, F. A.
Parpia
, and E. P.
Plummer
, Comput. Phys. Commun.
55
, 425
(1989
).© 2007 American Institute of Physics.
2007
American Institute of Physics
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