In a previous article we have introduced an alternative perturbation scheme to the traditional one starting from the harmonic oscillator, rigid rotator Hamiltonian, to find approximate solutions of the spectral problem for rotation-vibration molecular Hamiltonians. The convergence of our method for the methane vibrational ground state rotational energy levels was quicker than that of the traditional method, as expected, and our predictions were quantitative. In this second article, we study the convergence of the ab initio calculation of effective dipole moments for methane within the same theoretical frame. The first order of perturbation when applied to the electric dipole moment operator of a spherical top gives the expression used in previous spectroscopic studies. Higher orders of perturbation give corrections corresponding to higher centrifugal distortion contributions and are calculated accurately for the first time. Two potential energy surfaces of the literature have been used for solving the anharmonic vibrational problem by means of the vibrational mean field configuration interaction approach. Two corresponding dipole moment surfaces were calculated in this work at a high level of theory. The predicted intensities agree better with recent experimental values than their empirical fit. This suggests that our ab initio dipole moment surface and effective dipole moment operator are both highly accurate.

1.
P.
Cassam-Chenaï
and
J.
Liévin
,
Int. J. Quantum Chem.
93
,
245
264
(
2003
).
2.
J. K. G.
Watson
,
Mol. Phys.
15
,
479
490
(
1968
).
3.
J. K. G.
Watson
,
Mol. Phys.
19
,
465
487
(
1970
).
4.
C.
Eckart
,
Phys. Rev.
47
,
552
(
1935
).
5.
H. H.
Nielsen
,
Phys. Rev.
60
,
794
(
1941
).
6.
I. M.
Mills
, in
Molecular Spectroscopy: Modern Reseach
, edited by
K. Narahari
Rao
and
C. W.
Mathews
(
Acadmic
,
New York
,
1972
), pp.
115
140
.
7.
M. R.
Aliev
and
J. K. G.
Watson
, in
Molecular Spectroscopy: Modern Reseach
, edited by
K. Narahari
Rao
(
Academic
,
Orlando, FL
,
1985
), Vol.
3
, pp.
1
67
.
8.
P.
Cassam-Chenaï
,
Y.
Bouret
,
M.
Rey
,
S. A.
Tashkun
,
A. V.
Nikitin
, and
Vl. G.
Tyuterev
,
Int. J. Quantum. Chem.
112
,
2201
2220
(
2012
).
9.
P.
Cassam-Chenaï
,
J. Quant. Spectrosc. Radiat. Transf.
82
,
251
277
(
2003
).
10.
L. S.
Rothman
,
I. E.
Gordon
,
A.
Barbe
,
D.
Chris Benner
,
P. F.
Bernath
,
M.
Birk
,
V.
Boudon
,
L. R.
Brown
,
A.
Campargue
,
J.-P.
Champion
,
K.
Chance
,
L. H.
Coudert
,
V.
Dana
,
V. M.
Devi
,
S.
Fally
,
J.-M.
Flaud
,
R. R.
Gamache
,
A.
Goldmanm
,
D.
Jacquemart
,
I.
Kleiner
,
N.
Lacome
,
W. J.
Lafferty
,
J.-Y.
Mandin
,
S. T.
Massie
,
S. N.
Mikhailenko
,
C. E.
Miller
,
N.
Moazzen-Ahmadi
,
O. V.
Naumenko
,
A. V.
Nikitin
,
J.
Orphal
,
V. I.
Perevalov
,
A.
Perrin
,
A.
Predoi-Cross
,
C. P.
Rinsland
,
M.
Rotger
,
M.
Šimečkovà
,
M. A. H.
Smith
,
K.
Sung
,
S. A.
Tashkun
,
J.
Tennyson
,
R. A.
Toth
,
A. C.
Vandaele
, and
J.
Vander Auwera
,
J. Quant. Spectrosc. Radiat. Transf.
110
,
533
572
(
2009
).
11.
I.
Ozier
,
Phys. Rev. Lett.
27
,
1329
(
1971
).
12.
P.
Cassam-Chenaï
,
J. Math. Chem.
49
,
821
(
2011
).
13.
P.
Cassam-Chenaï
and
J.
Liévin
,
J. Comput. Chem.
27
,
627
640
(
2006
).
14.
S.
Albert
,
S.
Bauerecker
,
V.
Boudon
,
L. R.
Brown
,
J.-P.
Champion
,
M.
Lote
,
A.
Nikitin
, and
M.
Quack
,
Chem. Phys.
356
,
131
(
2009
).
15.
V.
Boudon
,
O.
Pirali
,
P.
Roy
,
J.-B.
Brubach
,
L.
Manceron
, and
J.
Vander Auwera
,
J. Quant. Spectrosc. Radiat. Transf.
111
,
1117
(
2010
).
16.
E. H.
Wishnow
,
G. S.
Orton
,
I.
Ozier
, and
H. P.
Gush
,
J. Quant. Spectrosc. Radiat. Transf.
103
,
102
(
2007
).
17.
D. L.
Gray
and
A. G.
Robiette
,
Mol. Phys.
37
,
1901
(
1979
).
18.
S.
Brodersen
and
J.-E.
Lolck
,
J. Mol. Spectrosc.
126
,
405
426
(
1987
).
19.
X.-G.
Wang
and
E. L.
Sibert
 III
,
J. Chem. Phys.
111
,
4510
(
1999
).
20.
E.
Venuti
,
L.
Halonen
, and
R. G.
Della Valle
,
J. Chem. Phys.
110
,
7339
(
1999
).
21.
J.
Tennyson
and
J.
Xie
, in
Rovibrational Bound States in Polyatomic Molecules
, edited by
M. M.
Law
,
I. A.
Atkinson
, and
J. M.
Hutson
(
CCP6
,
Daresbury
,
1999
), pp.
5
12
.
22.
S.
Carter
,
H. M.
Shnider
, and
J. M.
Bowman
,
J. Phys. Chem.
110
,
8417
(
1999
).
23.
S.
Carter
and
J. M.
Bowman
,
J. Phys. Chem. A
104
,
2355
(
2000
).
24.
D. W.
Schwenke
and
H.
Partridge
,
Spectrochim. Acta A
57
,
887
(
2001
).
25.
X. G.
Wang
and
E. L.
Sibert
,
Spectrochim. Acta A
58
,
863
(
2002
).
26.
D. W.
Schwenke
,
Spectrochim. Acta A
58
,
849
861
(
2002
).
27.
H.-G.
Yu
,
J. Chem. Phys.
121
,
6334
(
2004
).
28.
X. G.
Wang
and
T.
Carrington
,
J. Chem. Phys.
121
,
2937
(
2004
).
29.
J.
Wu
,
X.
Huang
,
S.
Carter
, and
J. M.
Bowman
,
Chem. Phys. Lett.
426
,
285
(
2006
).
30.
E.
Mátyus
,
J.
Šimunek
, and
A. G.
Császár
,
J. Chem. Phys.
131
,
074106
(
2009
).
31.
R.
Signorell
,
R.
Marquardt
,
M.
Quack
, and
M. A.
Suhm
,
Mol. Phys.
89
,
297
(
1996
).
32.
D.
Klein
,
J. Chem. Phys.
61
,
786
(
1974
).
33.
Yu. S.
Makushkin
and
Vl. G.
Tyuterev
,
Perturbation Methods and Effective Hamiltonians in Molecular Spectroscopy
(
Nauka
,
Novosibirsk
,
1984
) [in Russian].
34.
J. K. G.
Watson
,
Mol. Phys.
103
,
3283
(
2005
).
35.
J.
des Cloizeaux
,
Nucl. Phys.
20
,
321
(
1960
).
36.
C.
Soliverez
,
J. Phys. C: Solid State Phys.
2
,
2161
(
1969
).
37.
J. H.
Van Vleck
,
Phys. Rev.
33
,
467
(
1929
).
38.
E. C.
Kemble
,
Fundamentals of Quantum Mechanics
(
Dover
,
New York
,
1937
), p.
395
.
39.
H.
Primas
,
Rev. Mod. Phys.
35
,
710
(
1963
).
40.
L. N.
Buleavski
,
Zh. Eksp. Teor. Fiz.
51
,
230
(
1966
)
L. N.
Buleavski
, [
Sov. Phys. JETP
24
,
154
(
1967
)].
41.
M.
Born
and
J. R.
Oppenheimer
,
Ann. Phys.
84
,
457
(
1927
).
42.
H.-J.
Werner
,
P. J.
Knowles
,
R.
Lindh
,
F. R.
Manby
,
M.
Schütz
 et al, MOLPRO, version 2009.1, a package of ab initio programs,
2009
, see http://www.molpro.net.
43.
T. J.
Lee
,
J. M. L.
Martin
, and
P. R.
Taylor
,
J. Chem. Phys.
102
,
254
(
1995
).
44.
G. D.
Purvis
 III
,
R. J.
Bartlett
,
J. Chem. Phys.
76
,
1910
(
1982
).
45.
K.
Raghavachari
,
G. W.
Trucks
,
J. A.
Pople
, and
M.
Head-Gordon
,
Chem. Phys. Lett.
157
,
479
(
1989
).
46.
T. H.
Dunning
,
J. Chem. Phys.
90
,
1007
(
1989
).
47.
A. V.
Nikitin
,
M.
Rey
, and
Vl. G.
Tyuterev
,
Chem. Phys. Lett.
501
,
179
(
2011
).
48.
R. A.
Kendall
and
T. H.
Dunning
 Jr.
,
J. Chem. Phys.
96
,
6796
(
1992
).
49.
D. E.
Woon
and
T. H.
Dunning
 Jr.
,
J. Chem. Phys.
103
,
4572
(
1995
).
50.
H.-J.
Werner
and
P. J.
Knowles
,
J. Chem. Phys.
89
,
5803
(
1988
).
51.
P. J.
Knowles
and
H.-J.
Werner
,
Chem. Phys. Lett.
115
,
259
(
1985
).
52.
See supplementary material at http://dx.doi.org/10.1063/1.4705278 for the convergence of the equilibrium CH distance of methane, of the quartic force constants of modes 3 and 4, and of the non-zero first order derivatives of the electric dipole moment z-component with orbital basis set; for the grid point coordinates together with the values of the z-component, electric, dipole moment; and for the Q-branch and R-branch of methane main isotopologue up to J = 30.
53.
S. R.
Langhoff
and
E. R.
Davidson
,
Int. J. Quantum Chem.
8
,
62
(
1974
).
54.
L.
McMurchie
,
S.
Elbert
,
S.
Langhoff
,
E. R.
Davidson
,
D.
Feller
,
R.
Cave
,
D.
Rawlings
,
R.
Frey
,
R.
Daasch
,
L.
Nitchie
,
P.
Phillips
,
K.
Iberle
, and
C.
Jackels
, “
MELDF-X
,” The University of Washington, Indiana University, and the Environmental Molecular Sciences Laboratory,
1993
.
55.
M.
Loete
,
Can. J. Phys.
66
,
17
(
1988
).
56.
A.
Mourbat
,
A.
Aboumajd
, and
M.
Loete
,
J. Mol. Spectrosc.
190
,
198
(
1998
).
57.
H.
Hollenstein
,
R. R.
Marquardt
,
M.
Quack
, and
M. A.
Suhm
,
J. Chem. Phys.
101
,
3588
(
1994
).
58.
I. A.
Mills
,
Mol. Phys.
1
,
107
(
1958
).
59.
D.
Bégué
,
C.
Pouchan
,
N.
Gohaud
,
P.
Cassam-Chenaï
, and
J.
Liévin
,
J. Chem. Phys.
127
,
164115
164124
(
2007
).
60.
P.
Cassam-Chenaï
,
Y.
Scribano
, and
J.
Liévin
,
Chem. Phys. Lett.
466
,
16
(
2008
).
61.
B.
Maessen
and
M.
Wolfsberg
,
J. Phys. Chem.
89
,
3876
(
1985
).
62.
C. L.
Chen
,
B.
Maessen
, and
M.
Wolfsberg
,
J. Chem. Phys.
83
,
1795
(
1985
).
63.
J.
Tennyson
,
Comput. Phys. Rep.
4
,
1
(
1986
).
64.
S.
Carter
and
N. C.
Handy
,
Comput. Phys. Rep.
5
,
115
172
(
1986
).
65.
Z.
Bačić
and
J. C.
Light
,
Annu. Rev. Phys. Chem.
40
,
469
(
1989
).
66.
J. M.
Bowman
and
B.
Gazdy
,
J. Chem. Phys.
94
,
454
(
1991
).
67.
W. H.
Shaffer
,
J. Mol. Spectrosc.
1
,
69
(
1957
).
68.
I.
Ozier
and
A.
Rosenberg
,
J. Chem. Phys.
69
,
5203
(
1978
).
69.
K.
Fox
,
Phys. Rev. Lett.
27
,
233
(
1971
).
70.
J. K. G.
Watson
,
J. Mol. Spectrosc.
40
,
536
(
1971
).
71.
V. M.
Mikhailov
,
M. V.
Mikhailova
, and
M. A.
Smirnov
, in
7th International Symposium on Atmospheric and Ocean Optics
, edited by
G. G.
Matvienko
and
M. V.
Panchenko
[
Proc. SPIE
4341
,
55
(
2000
)].
72.
I.
Ozier
,
A.
Rosenberg
, and
D. B.
Litvin
,
J. Mol. Spectrosc.
58
,
39
(
1975
).
73.
W. H.
Shaffer
and
J. D.
Louck
,
J. Mol. Spectrosc.
3
,
123
(
1959
).
74.
L. S.
Rothman
,
J.
Schroeder
,
A.
McCann
,
R. R.
Gamache
,
R. B.
Wattson
,
J.-M.
Flaud
,
A.
Perrin
,
V.
Dana
,
J.-Y.
Mandin
,
A.
Goldman
,
S.
Massie
,
P.
Varanasi
, and
K.
Yoshino
,
J. Quant. Spectrosc. Radiat. Transf.
60
,
665
(
1998
), see http://www.hitran.com.
75.
J.
Fisher
 et al,
J. Quant. Spectrosc. Radiat. Transf.
82
,
401
412
(
2003
).
76.
C.
Wenger
,
J. P.
Champion
, and
V.
Boudon
,
J. Quant. Spectrosc. Radiat. Transf.
109
,
2697
2706
(
2008
), see http://icb.u-bourgogne.fr/JSP/TIPS.jsp.
77.
A.
Chakraborty
,
D. G.
Truhlar
,
J. M.
Bowman
, and
S.
Carter
,
J. Chem. Phys.
121
,
2071
(
2004
);
[PubMed]
A.
Chakraborty
,
D. G.
Truhlar
,
J. M.
Bowman
, and
S.
Carter
, erratum,
J. Chem. Phys.
135
,
119904
(
2011
).
78.
E. B.
Wilson
 Jr.
,
J. Chem. Phys.
3
,
276
285
(
1935
).
79.
A. J.
Dorney
and
J. K. G.
Watson
,
J. Mol. Spectrosc.
42
,
135
148
(
1972
).
80.
B.
Bobin
and
J. C.
Hilico
,
J. Phys.
36
,
225
(
1975
).
81.
V.
Boudon
, private communication (circa 18 November
2011
).
82.
C.
Wenger
and
J. P.
Champion
,
J. Quant. Spectrosc. Radiat. Transf.
59
,
471
480
(
1998
).
83.
E.
Lellouch
,
P.
Hartogh
,
H.
Feuchtgruber
,
B.
Vandenbussche
,
T.
de Graauw
,
R.
Moreno
,
C.
Jarchow
,
T.
Cavalié
,
G.
Orton
,
M.
Banaszkiewicz
,
M. I.
Blecka
,
D.
Bockelée-Morvan
,
J.
Crovisier
,
T.
Encrenaz
,
T.
Fulton
,
M.
Küppers
,
L. M.
Lara
,
D. C.
Lis
,
A. S.
Medvedev
,
M.
Rengel
,
H.
Sagawa
,
B.
Swinyard
,
S.
Szutowicz
,
F.
Bensch
,
E.
Bergin
,
F.
Billebaud
,
N.
Biver
,
G. A.
Blake
,
J. A. D. L.
Blommaert
,
J.
Cernicharo
,
R.
Courtin
,
G. R.
Davis
,
L.
Decin
,
P.
Encrenaz
,
A.
Gonzalez
,
E.
Jehin
,
M.
Kidger
,
D.
Naylor
,
G.
Portyankina
,
R.
Schieder
,
S.
Sidher
,
N.
Thomas
,
M.
de Val-Borro
,
E.
Verdugo
,
C.
Waelkens
,
H.
Walker
,
H.
Aarts
,
C.
Comito
,
J. H.
Kawamura
,
A.
Maestrini
,
T.
Peacocke
,
R.
Teipen
,
T.
Tils
, and
K.
Wildeman
,
Astron. Astrophys.
518
,
L152
(
2010
).

Supplementary Material

You do not currently have access to this content.