Accurate quartic anharmonic force fields for and have been calculated using the CCSD(T) method and basis sets of spdf quality. Based on the ab initio force field with a minor empirical adjustment, the vibrational energy levels of these two molecules and their isotopomers are calculated by means of high order Canonical Van Vleck Perturbation Theory (CVPT) based on curvilinear coordinates. The calculated energies agree very well with the experimental data. The full quadratic force field of is further refined to the experimental data. The symmetrization of the Cartesian basis for arbitrary combination bands of group molecules is discussed using the circular promotion operator for the doubly degenerate modes, together with tabulated vector coupling coefficients. The extraction of the spectroscopic constants from our second order transformed Hamiltonian in curvilinear coordinates is discussed, and compared to a similar procedure in rectilinear coordinates.
REFERENCES
1.
Kirk–Othmer Encyclopedia of Chemical Technology, 4th ed., edited by R. E. Kirk, D. F. Othmer, and J. I. Kroschwitz (Wiley, New York, 1998).
2.
H.-G.
Mack
and H.
Oberhammer
, J. Chem. Phys.
87
, 2158
(1987
), and references therein.3.
J.-H.
Kim
, S.-H.
Seo
, S.-M.
Yun
, H.-Y.
Chang
, K.-M.
Lee
, and C.-K.
Choi
, J. Electrochem. Soc.
143
, 2990
(1996
), and references therein.4.
5.
P. G. M.
Sebel
, L. J. F.
Hermans
, and H. C. W.
Beijerinck
, J. Vac. Sci. Technol. A
17
, 755
(1999
);see also
T.
Lagarde
, J.
Pelletier
, and Y.
Arnal
, J. Vac. Sci. Technol. A
17
, 118
(1999
).6.
P.
Francis
, C.
Chaffin
, A.
Maciejewski
, and C.
Oppenheimer
, Geophys. Res. Lett.
23
, 249
(1996
).7.
K.
Tanaka
, S.
Isomura
, H.
Kaetsu
, Y.
Yatsurugi
, M.
Hashimoto
, K.
Togashi
, and S.
Arai
, Bull. Chem. Soc. Jpn.
69
, 493
(1996
).8.
A.
Maki
, E. K.
Plyler
, and R.
Thibault
, J. Chem. Phys.
37
, 1899
(1960
);9.
L. H.
Jones
, B. J.
Krohn
, and R. C.
Kennedy
, J. Mol. Spectrosc.
70
, 288
(1978
).10.
L. H.
Jones
, C.
Kennedy
, and S.
Ekberg
, J. Chem. Phys.
69
, 833
(1978
).11.
A. C.
Jeannotte
II, D.
Legler
, and J.
Overend
, Spectrochim. Acta A
29
, 1915
(1973
).12.
13.
P.
Esherick
, A.
Owyoung
, and C. W.
Patterson
, J. Mol. Spectrosc.
86
, 250
(1981
).14.
15.
A.
Tabyaoui
, B.
Lavorel
, R.
Saint-Loup
, and M.
Rötger
, J. Raman Spectrosc.
25
, 255
(1994
).16.
C. W.
Patterson
, R. S.
McDowell
, N. G.
Nereson
, R. F.
Begley
, H. W.
Galbraith
, and B. J.
Krohn
, J. Mol. Spectrosc.
80
, 71
(1980
).17.
18.
G.
Tarrago
, G.
Poussigue
, M.
Dang-Nhu
, and J.
Kauppinen
, J. Mol. Spectrosc.
86
, 232
(1981
).19.
R. S.
McDowell
, M. J.
Reisfeld
, H. W.
Galbraith
, B. J.
Krohn
, H.
Flicker
, R. C.
Kennedy
, J. P.
Aldridge
, and N. G.
Nereson
, J. Mol. Spectrosc.
83
, 440
(1980
).20.
21.
M.
Dang-Nhu
, G.
Graner
, and G.
Guelachvili
, J. Mol. Spectrosc.
85
, 358
(1981
).22.
23.
T.
Gabard
, A.
Nikitin
, J. P.
Champion
, G.
Pierre
, and A. S.
Pine
, J. Mol. Spectrosc.
170
, 431
(1995
).24.
25.
26.
27.
A. C.
Jeannotte
II, C.
Marcott
, and J.
Overend
, J. Chem. Phys.
68
, 2076
(1978
).28.
29.
30.
31.
V. G.
Tyuterev
, Y. L.
Babikov
, S. A.
Tashkun
, V. I.
Perevalov
, A.
Nikitin
, J. P.
Champion
, C.
Wenger
, G.
Pierre
, J. C.
Hilico
, and M.
Loëte
, J. Quant. Spectrosc. Radiat. Transf.
52
, 459
(1994
) based on Ref. 24.32.
W.
Maring
, J. P.
Toennies
, R. G.
Wang
, and H. B.
Levene
, J. Chem. Phys.
103
, 1333
(1995
).33.
R. K. Heenan, Ph.D. thesis, University of Reading, UK, 1979.
34.
35.
R. S.
McDowell
, M. J.
Reisfeld
, C. W.
Patterson
, B. J.
Krohn
, M. C.
Vasquez
, and G. A.
Laguna
, J. Chem. Phys.
77
, 4337
(1982
).36.
X.-W.
Hou
, S.-H.
Dong
, M.
Xie
, and Z.-Q.
Ma
, Chem. Phys. Lett.
283
, 174
(1998
).37.
X.-W.
Hou
, M.
Xie
, S.-H.
Dong
, and Z.-Q.
Ma
, Ann. Phys. (N.Y.)
263
, 340
(1998
).38.
39.
40.
41.
L.
Jörissen
, H.
Prinz
, W. A.
Kreiner
, C.
Wenger
, G.
Pierre
, G.
Magerl
, and W.
Schupita
, Can. J. Phys.
67
, 532
(1989
).42.
J.
Breidung
, J.
Demaison
, L.
Margules
, and W.
Thiel
, Chem. Phys. Lett.
313
, 713
(1999
).43.
J. M. L.
Martin
and P. R.
Taylor
, J. Phys. Chem. A
103
, 4427
(1999
).44.
45.
T. J.
Lee
, J. M. L.
Martin
, and P. R.
Taylor
, J. Chem. Phys.
102
, 254
(1995
).46.
S.
Carter
, H. M.
Shnider
, and J. M.
Bowman
, J. Chem. Phys.
110
, 8417
(1999
).47.
E.
Venuti
, L.
Halonen
, and R. G. Della
Valle
, J. Chem. Phys.
110
, 7339
(1999
).48.
49.
H.-J. Werner and P. J. Knowles, MOLPRO 97.3, a package of ab initio programs, with contributions from J. Almlöf, R. D. Amos, A. Berning, D. L. Cooper, M. J. O. Deegan, A. J. Dobbyn, F. Eckert, S. T. Elbert, C. Hampel, R. Lindh, A. W. Lloyd, W. Meyer, A. Nicklass, K. A. Peterson, R. M. Pitzer, A. J. Stone, P. R. Taylor, M. E. Mura, P. Pulay, M. Schütz, H. Stoll, and T. Thorsteinsson.
50.
G. D.
Purvis
III and R. J.
Bartlett
, J. Chem. Phys.
76
, 1910
(1982
).51.
K.
Raghavachari
, G. W.
Trucks
, J. A.
Pople
, and M.
Head-Gordon
, Chem. Phys. Lett.
157
, 479
(1989
).52.
P. J.
Knowles
, C.
Hampel
, and H. J.
Werner
, J. Chem. Phys.
99
, 5219
(1993
).53.
T. J. Lee and G. E. Scuseria, in Quantum Mechanical Electronic Structure Calculations With Chemical Accuracy, edited by S. R. Langhoff (Kluwer Academic, Dordrecht, 1995).
54.
55.
D. Papoušek and M. R. Aliev, Molecular Vibrational-Rotational Spectra (Elsevier Science, New York, 1982).
56.
A. Willetts, J. F. Gaw, W. H. Green Jr., and N. C. Handy, SPECTRO 1.0, a second-order rovibrational perturbation theory program, University Chemical Laboratory, Cambridge, UK, 1989.
57.
J. F. Gaw, A. Willetts, W. H. Green, and N. C. Handy, in Advances in Molecular Vibrations and Collision Dynamics, edited by J. M. Bowman (JAI, Greenwich, 1990).
58.
D. P.
Hodgkinson
, R. K.
Heenan
, A. R.
Hoy
, and A. G.
Robiette
, Mol. Phys.
48
, 193
(1983
).59.
This is done fairly trivially by taking apart the compound fractions in Eq. (3.20) of Ref. 58, then inserting a test that skips the appropriate one among the four affected terms if the respective denominator corresponds to the resonant interaction. Alternatively, the reciprocal denominators may be precomputed and stored in a three-dimensional array, and any that correspond to resonant interactions set to zero before the actual spectroscopy routines are entered, similar to
J. M. L.
Martin
and P. R.
Taylor
, Spectrochim. Acta A
53
, 1039
(1997
).60.
61.
62.
63.
64.
J. M. L.
Martin
, Spectrochim. Acta A
55
, 709
(1999
) (special issue, “Theoretical spectroscopy: State of the science”).65.
R. A.
Kendall
, T. H.
Dunning
, Jr., and R. J.
Harrison
, J. Chem. Phys.
96
, 6796
(1992
).66.
J. M. L.
Martin
and P. R.
Taylor
, Chem. Phys. Lett.
225
, 473
(1994
).67.
J. M. L.
Martin
, J. P.
François
, and R.
Gijbels
, J. Phys. Chem.
98
, 11394
(1994
).68.
69.
J. M. L.
Martin
, K. K.
Baldridge
, and T. J.
Lee
, Mol. Phys.
97
, 945
(1999
).70.
71.
72.
73.
R. G.
Della Valle
, L.
Halonen
, and E.
Venuti
, J. Comput. Chem.
20
, 1716
(1999
).74.
75.
76.
J. S. Griffith, The Theory of Transition-Metal Ions (Cambridge University Press, Cambridge, 1961), Table A20 of Appendix 2.
77.
78.
L. Pauling and E. B. Wilson, Introduction to Quantum Mechanics with Applications to Chemistry (Dover, New York, 1935).
79.
80.
C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics (Wiley, New York, 1977), Vol. 1, pp. 727–741.
81.
Y.
Pak
, E. L.
Sibert
III, and R. C.
Woods
, J. Chem. Phys.
107
, 1717
(1997
).82.
MAPLE V, Release 4, Waterloo Maple Software, Waterloo, Ontario, 1981–1994.
83.
84.
Z.-Q.
Ma
, X.-W.
Hou
, and M.
Xie
, Phys. Rev. A
53
, 2173
(1996
).85.
A.
Frank
, R.
Lemus
, F.
Pérez-Bernal
, and R.
Bijker
, J. Mol. Spectrosc.
196
, 329
(1999
).86.
87.
88.
89.
90.
91.
I. M.
Mills
, Mol. Phys.
1
, 107
(1958
), Fig. 1 of this work is inconsistent with its definition of symmetry coordinates.92.
A. G.
Robiette
, D. L.
Gray
, and F. W.
Birss
, Mol. Phys.
32
, 1591
(1976
).93.
94.
95.
A. B.
McCoy
, D. C.
Burleigh
, and E. L.
Sibert
, J. Chem. Phys.
95
, 7449
(1991
).96.
K. L.
Mardis
and E. L.
Sibert
, J. Mol. Spectrosc.
187
, 167
(1998
).
This content is only available via PDF.
© 2000 American Institute of Physics.
2000
American Institute of Physics
You do not currently have access to this content.
