An analytical expression is found for the accurate ab initio potential energy curve of the fluorine molecule that has been determined in the preceding two papers. With it, the vibrational and rotational energy levels of F2 are calculated using the discrete variable representation. The comparison of this theoretical spectrum with the experimental spectrum, which had been measured earlier using high-resolution electronic spectroscopy, yields a mean absolute deviation of about 5cm1 over the 22 levels. The dissociation energy with respect to the lowest vibrational energy is calculated within 30cm1 of the experimental value of 12953±8cm1. The reported agreement of the theoretical spectrum and dissociation energy with experiment is contingent upon the inclusion of the effects of core-generated electron correlation, spin-orbit coupling, and scalar relativity. The Dunham analysis [Phys. Rev.41, 721 (1932)] of the spectrum is found to be very accurate. New values are given for the spectroscopic constants.

1.
L.
Bytautas
,
T.
Nagata
,
M. S.
Gordon
, and
K.
Ruedenberg
J. Chem. Phys.
127
,
164317
(
2007
).
2.
L.
Bytautas
,
N.
Matsunaga
,
T.
Nagata
,
M. S.
Gordon
, and
K.
Ruedenberg
,
J. Chem. Phys.
127
,
204301
(
2007
).
3.
M.
Born
and
J. R.
Oppenheimer
,
Ann. Phys.
84
,
457
(
1927
).
4.
P. G.
Mezey
,
Potential Energy Hypersurfaces
(
Elsevier
,
New York
,
1979
).
5.
J. N.
Murrell
,
S.
Carter
,
S. C.
Farantos
,
P.
Huxley
, and
A. J. C.
Varandas
,
Molecular Potential Energy Surfaces
(
Wiley
,
New York
,
1984
).
6.
P.
Pechukas
,
J. Chem. Phys.
64
,
1516
(
1976
).
7.
P. G.
Mezey
,
J. Am. Chem. Soc.
112
,
3791
(
1990
).
8.
L. J.
Schaad
and
J.
Hu
,
J. Am. Chem. Soc.
120
,
1571
(
1998
).
9.
L.
Bytautas
and
D. J.
Klein
,
Int. J. Quantum Chem.
70
,
205
(
1998
).
10.
H.
Eyring
,
J. Chem. Phys.
3
,
107
(
1935
).
11.
E.
Wigner
,
J. Chem. Phys.
5
,
720
(
1937
).
12.
W. H.
Miller
,
Acc. Chem. Res.
9
,
306
(
1976
).
13.
D. G.
Truhlar
,
Annu. Rev. Phys. Chem.
35
,
159
(
1984
).
14.
T.
Komatsuzaki
and
R. S.
Berry
,
Proc. Natl. Acad. Sci. U.S.A.
98
,
7666
(
2001
).
15.
E.
Pollak
and
P.
Talkner
,
Chaos
15
,
026116
(
2005
).
16.
K. M.
Kuhler
,
D. G.
Truhlar
, and
A. D.
Isaacson
,
J. Chem. Phys.
104
,
4664
(
1996
).
17.
B.
Njegic
and
M. S.
Gordon
,
J. Chem. Phys.
125
,
224102
(
2006
).
18.
J. M.
Bowman
,
J. Chem. Phys.
68
,
608
(
1978
).
19.
R. A.
Marcus
,
J. Chem. Phys.
41
,
610
(
1964
).
20.
D. K.
Hoffman
,
R. S.
Nord
, and
K.
Ruedenberg
,
Theor. Chim. Acta
69
,
265
(
1986
).
21.
D. J.
Wales
,
Int. J. Mod. Phys. B
19
,
2877
(
2005
).
22.
J. A.
Pople
,
Rev. Mod. Phys.
71
,
1267
(
1999
).
23.
R. J.
Le Roy
,
Mol. Spectrosc. (Chem. Soc., London)
1
,
113
(
1973
).
24.
W. T.
Zemke
,
W. C.
Stwalley
,
J. A.
Coxon
, and
P. G.
Hajigeorgiou
,
Chem. Phys. Lett.
177
,
412
(
1991
).
25.
Z.
Xie
,
B. J.
Braams
, and
J. M.
Bowman
,
J. Chem. Phys.
122
,
224307
(
2005
).
26.
J.
Brandão
,
C.
Mogo
, and
B. C.
Silva
,
J. Chem. Phys.
121
,
8861
(
2004
).
27.
A. J. C.
Varandas
and
P.
Piecuch
,
Chem. Phys. Lett.
430
,
448
(
2006
).
28.
R.
Rydberg
,
Z. Phys.
73
,
376
(
1931
);
A. L. G.
Rees
,
Proc. Phys. Soc. London
59
,
998
(
1947
).
29.
J.
Tellinghuisen
,
J. Mol. Spectrosc.
44
,
194
(
1972
);
J.
Tellinghuisen
,
Comput. Phys. Commun.
6
,
221
(
1973
);
J. E.
Blackwood
,
G. A.
Robinson
, and
M. R. H.
Rudge
,
J. Phys. B
33
,
1185
(
2000
).
30.
R. J.
Le Roy
,
Y.
Huang
, and
C.
Jary
,
J. Chem. Phys.
125
,
164310
(
2006
).
31.
32.
Y. P.
Varshni
,
Rev. Mod. Phys.
29
,
664
(
1957
).
33.
A. A.
Zavitsas
,
J. Am. Chem. Soc.
113
,
4755
(
1991
).
34.
K. P.
Huber
and
G.
Herzberg
,
Constants of Diatomic Molecules
,
Molecular Spectra and Molecular Structure
Vol.
IV
(
Van Nostrand Reinhold Company
,
New York
,
1979
).
35.
J. F.
Ogilvie
,
The Vibrational and Rotational Spectrometry of Diatomic Molecules
(
Academic Press
,
New York
,
1998
).
36.
W.
Kołos
and
L.
Wolniewicz
,
J. Mol. Spectrosc.
54
,
303
(
1975
).
37.
R. E.
Moss
and
L.
Valenzano
,
Mol. Phys.
101
,
2635
(
2003
).
38.
J.
Carbonell
,
R.
Lazauskas
,
D.
Delande
,
L.
Hilico
, and
S.
Kilic
,
Europhys. Lett.
64
,
316
(
2003
).
39.
J. M.
Taylor
,
Z.-C.
Yan
,
A.
Dalgarno
, and
J. F.
Babb
,
Mol. Phys.
97
,
25
(
1999
).
40.
R.
Jaquet
,
W.
Cencek
,
W.
Kutzelnigg
, and
J.
Rychlewski
,
J. Chem. Phys.
108
,
2837
(
1998
).
41.
O. L.
Polyansky
and
J.
Tennyson
,
J. Chem. Phys.
110
,
5056
(
1999
).
42.
S.
Bubin
and
L.
Adamowicz
,
J. Chem. Phys.
125
,
064309
(
2006
).
43.
S.
Bubin
,
L.
Adamowicz
, and
M.
Molski
,
J. Chem. Phys.
123
,
134310
(
2005
).
44.
J. M. L.
Martin
,
Chem. Phys. Lett.
303
,
399
(
1999
).
45.
R. J.
Gdanitz
,
Chem. Phys. Lett.
312
,
578
(
1999
).
46.
O. L.
Polyansky
,
A. G.
Császár
,
S. V.
Shirin
,
N. F.
Zobov
,
P.
Barletta
,
J.
Tennyson
,
D. W.
Schwenke
, and
P. J.
Knowles
,
Science
299
,
539
(
2003
).
47.
P.
Piecuch
,
S. A.
Kucharski
,
V.
Špirko
, and
K.
Kowalski
,
J. Chem. Phys.
115
,
5796
(
2001
).
48.
X.
Li
and
J.
Paldus
,
J. Chem. Phys.
117
,
1941
(
2002
).
49.
H.
Müller
,
R.
Franke
,
S.
Vogtner
,
R.
Jaquet
, and
W.
Kutzelnigg
,
Theor. Chem. Acc.
100
,
85
(
1998
).
50.
W.
Cardoen
and
R. J.
Gdanitz
,
J. Chem. Phys.
123
,
024304
(
2005
).
51.
W. D.
Laidig
,
P.
Saxe
, and
R. J.
Bartlett
,
J. Chem. Phys.
86
,
887
(
1987
).
52.
X.
Li
and
J.
Paldus
,
J. Chem. Phys.
113
,
9966
(
2000
).
53.
M.
Nooijen
and
R. J.
Le Roy
,
J. Mol. Struct.: THEOCHEM
768
,
25
(
2006
).
54.
R. J.
Gdanitz
,
Chem. Phys. Lett.
283
,
253
(
1998
).
55.
C.
Angeli
,
C. J.
Calzado
,
R.
Cimiraglia
, and
J.-P.
Malrieu
,
J. Chem. Phys.
124
,
234109
(
2006
).
56.
C.
Angeli
,
R.
Cimiraglia
, and
J.-P.
Malrieu
,
Chem. Phys. Lett.
317
,
472
(
2000
).
57.
A. D.
McLean
,
B.
Liu
, and
G. S.
Chandler
,
J. Chem. Phys.
97
,
8459
(
1992
).
58.
T. A.
Ruden
,
T.
Helgaker
,
P.
Jørgensen
, and
J.
Olsen
,
J. Chem. Phys.
121
,
5874
(
2004
).
59.
M.
Heckert
,
M.
Kállay
,
D. P.
Tew
,
W.
Klopper
, and
J.
Gauss
,
J. Chem. Phys.
125
,
044108
(
2006
).
60.
G. E.
Scuseria
and
H. F.
Schaefer
 III
,
Chem. Phys. Lett.
148
,
205
(
1988
).
61.
K. A.
Peterson
,
R. A.
Kendall
, and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
99
,
9790
(
1993
).
62.
J. D.
Watts
and
R. J.
Bartlett
,
J. Chem. Phys.
95
,
6652
(
1991
).
63.
A. L.
Wulfov
,
Chem. Phys. Lett.
263
,
79
(
1996
).
64.
J.
Mášik
,
I.
Hubač
, and
P.
Mach
,
J. Chem. Phys.
108
,
6571
(
1998
).
65.
O.
Živný
and
J.
Czernek
,
Chem. Phys. Lett.
308
,
165
(
1999
).
66.
67.
U.
Louderaj
,
M. K.
Harbola
, and
N.
Sathyamurthy
,
Chem. Phys. Lett.
366
,
88
(
2002
).
68.
R.
Baer
and
D.
Neuhauser
,
Phys. Rev. Lett.
94
,
043002
(
2005
).
69.
H.-J.
Werner
and
P. J.
Knowles
,
Theor. Chim. Acta
78
,
175
(
1990
).
70.
C.
Hampel
,
K. A.
Peterson
, and
H.-J.
Werner
,
Chem. Phys. Lett.
190
,
1
(
1992
).
71.
72.
J.
Sánchez-Marín
,
I.
Nebot-Gil
,
D.
Maynau
, and
J. P.
Malrieu
,
Theor. Chim. Acta
92
,
241
(
1995
).
73.
X.
Li
and
J.
Paldus
,
J. Chem. Phys.
124
,
174101
(
2006
).
74.
K. A.
Peterson
,
A. K.
Wilson
,
D. E.
Woon
, and
T. H.
Dunning
, Jr.
,
Theor. Chem. Acc.
97
,
251
(
1997
).
75.
F. A.
Evangelista
,
W. D.
Allen
, and
H. F.
Schaefer
 III
,
J. Chem. Phys.
127
,
024102
(
2007
).
76.
M.
Urban
and
J.
Noga
,
Mol. Phys.
38
,
1621
(
1979
);
M.
Urban
,
J.
Noga
, and
V.
Kellö
,
Theor. Chim. Acta
62
,
549
(
1983
).
77.
J.
Pittner
,
J.
Šmydke
,
P.
Čársky
, and
I.
Hubač
,
J. Mol. Struct.: THEOCHEM
547
,
239
(
2001
).
78.
H.
Moriyama
,
Y.
Wasada-Tsutsui
,
M.
Sekiya
, and
H.
Tatewaki
,
J. Chem. Phys.
118
,
5413
(
2003
).
79.
G.
Das
and
A. C.
Wahl
,
J. Chem. Phys.
56
,
3532
(
1972
).
80.
K.
Jankowski
,
R.
Becherer
,
P.
Scharf
,
H.
Schiffer
, and
R.
Ahlrichs
,
J. Chem. Phys.
82
,
1413
(
1985
).
81.
D. C.
Cartwright
and
P. J.
Hay
,
Chem. Phys.
114
,
305
(
1987
).
82.
J.-P.
Daudey
,
J.-L.
Heully
, and
J.-P.
Malrieu
,
J. Chem. Phys.
99
,
1240
(
1993
).
83.
S. R.
Gwaltney
,
C. D.
Sherrill
,
M.
Head-Gordon
, and
A. I.
Krylov
,
J. Chem. Phys.
113
,
3548
(
2000
).
84.
V.
Sychrovský
,
P.
Čársky
, and
H.
Lischka
,
Int. J. Quantum Chem.
76
,
185
(
2000
).
85.
K.
Kowalski
and
P.
Piecuch
,
Chem. Phys. Lett.
344
,
165
(
2001
).
86.
A. I.
Krylov
and
C. D.
Sherrill
,
J. Chem. Phys.
116
,
3194
(
2002
).
87.
K.
Kowalski
,
J. Chem. Phys.
123
,
014102
(
2005
).
88.
L.
Meissner
,
J.
Gryniaków
, and
I.
Hubač
,
Mol. Phys.
103
,
2173
(
2005
).
89.
P.
Piecuch
,
M.
Włoch
,
J. R.
Gour
, and
A.
Kinal
,
Chem. Phys. Lett.
418
,
467
(
2006
).
90.
M.
Włoch
,
M. D.
Lodriguito
,
P.
Piecuch
, and
J. R.
Gour
,
Mol. Phys.
104
,
2149
(
2006
).
91.
M.
Musiał
and
R. J.
Bartlett
,
J. Chem. Phys.
122
,
224102
(
2005
);
[PubMed]
R. J.
Bartlett
and
M.
Musiał
,
J. Chem. Phys.
125
,
204105
(
2006
).
[PubMed]
92.
V. V.
Ivanov
,
L.
Adamowicz
, and
D. I.
Lyakh
,
Int. J. Quantum Chem.
106
,
2875
(
2006
).
93.
X.
Li
and
J.
Paldus
,
J. Chem. Phys.
125
,
164107
(
2006
).
94.
J.
Yang
,
Y.
Hao
,
J.
Li
,
C.
Zhou
, and
Y.
Mo
,
J. Chem. Phys.
122
,
134308
(
2005
).
95.
E. A.
Colbourn
,
M.
Dagenais
,
A. E.
Douglas
, and
J. W.
Raymonda
,
Can. J. Phys.
54
,
1343
(
1976
).
96.
Potential Energy Surfaces: Proceedings of the Mariapfarr Workshop in Theoretical Chemistry
,
Lecture Notes in Chemistry
Vol.
71
, edited by
A. F.
Sax
(
Springer
,
New York
,
1999
);
N.
Sathyamurthy
,
Comput. Phys. Rep.
3
,
1
(
1985
);
D.
Steele
,
E. R.
Lippincott
, and
T.
Vanderslice
,
Rev. Mod. Phys.
34
,
239
(
1962
).
97.
R. D.
Bardo
and
K.
Ruedenberg
,
J. Chem. Phys.
59
,
5956
(
1973
).
98.
D. F.
Feller
and
K.
Ruedenberg
,
Theor. Chim. Acta
52
,
231
(
1979
).
99.
M. W.
Schmidt
and
K.
Ruedenberg
,
J. Chem. Phys.
71
,
3951
(
1979
).
100.
R. C.
Raffenetti
,
J. Chem. Phys.
59
,
5936
(
1973
).
101.
R. C.
Raffenetti
and
K.
Ruedenberg
, “
Even-tempered exponential representations of atomic self-consistent-field wavefunctions
,” USAEC Research and Development Report No. 1S 3195 (
Ames Laboratory, USAEC, Iowa State University
, Ames, IA,
1973
).
102.
X.
Chu
and
A.
Dalgarno
,
J. Chem. Phys.
121
,
4083
(
2004
).
103.
See, e.g.,
L.
Pauling
and
E. B.
Wilson
,
Introduction to Quantum Mechanics
(
McGraw-Hill
,
New York
,
1935
).
104.
National Institute of Standards and Technology
, Physics Laboratory, Physical Reference Data, Atomic Weights and Isotopic Compositions (
2005
);
105.
Z.
Bacic
and
J. C.
Light
,
J. Chem. Phys.
85
,
4594
(
1986
).
106.
J. C.
Light
,
I. P.
Hamilton
, and
J. V.
Lill
,
J. Chem. Phys.
82
,
1400
(
1985
).
107.
D. T.
Colbert
and
W. H.
Miller
,
J. Chem. Phys.
96
,
1982
(
1992
).
108.
B. S.
Garbow
,
J. M.
Boyle
,
J. J.
Dongarra
, and
C. B.
Moler
,
EISPACK Guide Extension Lecture Notes in Computer Science
(
Springer-Verlag
,
New York
,
1977
), Vol.
51
;
109.
110.
G.
Herzberg
,
Spectra of Diatomic Molecules
,
Molecular Spectra and Molecular Structure
Vol.
I
(
Krieger
,
Malabar
,
1989
).
111.
D. K. W.
Mok
,
R.
Neumann
, and
N. C.
Handy
,
J. Phys. Chem.
100
,
6225
(
1996
).
112.
R. Z.
Martínez
,
D.
Bermejo
,
J.
Santos
, and
P.
Cancio
,
J. Mol. Spectrosc.
168
,
343
(
1994
).
113.
H. G. M.
Edwards
,
D. A.
Long
, and
R.
Love
, in
Advances in Raman Spectroscopy
, edited by
J. P.
Mathieu
(
Heyden
,
London
,
1972
), Vol.
1
, pp.
514
515
.
114.
W.
Stricker
and
I. G.
Hochenbleicher
,
Z. Naturforsch. A
28
,
27
(
1973
).
115.
J.
Berkowitz
,
W. A.
Chupka
,
P. M.
Guyon
,
J. H.
Holloway
, and
R.
Spohr
,
J. Chem. Phys.
54
,
5165
(
1971
).
116.
J. G.
Stamper
and
R. F.
Barrow
,
Trans. Faraday Soc.
54
,
1952
(
1958
).
117.
H. G. M.
Edwards
,
E. A. M.
Good
, and
D. A.
Long
,
J. Chem. Soc., Faraday Trans. 2
72
,
984
(
1976
).
118.
H. H.
Claassen
,
H.
Selig
, and
J.
Shamir
,
Appl. Spectrosc.
23
,
8
(
1969
).
119.
D.
Andrychuk
,
Can. J. Phys.
29
,
151
(
1951
).
120.
G. V.
Calder
and
K.
Ruedenberg
,
J. Chem. Phys.
49
,
5399
(
1968
).
121.
F.
Pawłowski
,
P.
Jørgensen
,
J.
Olsen
,
F.
Hegelund
,
T.
Helgaker
,
J.
Gauss
,
K. L.
Bak
, and
J. F.
Stanton
,
J. Chem. Phys.
116
,
6482
(
2002
).
122.
L.
Bytautas
and
K.
Ruedenberg
,
J. Chem. Phys.
121
,
10905
(
2004
).
123.
L.
Bytautas
and
K.
Ruedenberg
,
J. Chem. Phys.
121
,
10919
(
2004
).
124.
L.
Bytautas
and
K.
Ruedenberg
,
J. Chem. Phys.
121
,
10852
(
2004
).
125.
L.
Bytautas
and
K.
Ruedenberg
,
J. Chem. Phys.
122
,
154110
(
2005
).
126.
L.
Bytautas
and
K.
Ruedenberg
,
J. Chem. Phys.
124
,
174304
(
2006
).
127.
S.
Hirata
,
T.
Yanai
,
R. J.
Harrison
,
M.
Kamiya
, and
P.-D.
Fan
,
J. Chem. Phys.
126
,
024104
(
2007
).
128.
A. J. C.
Varandas
,
Chem. Phys. Lett.
443
,
398
(
2007
).
You do not currently have access to this content.