Vapor phase room temperature overtone spectra of cyclohexane are measured with conventional near infrared spectroscopy for the lower overtones, ΔvCH=2–4, and with intracavity dye laser photoacoustic spectroscopy for the higher overtones, ΔvCH=5–7. The relative intensity of the axial to equatorial peak is explained in terms of the local mode model of harmonically coupled anharmonic oscillators, where all modes but the two CH‐stretching modes are neglected. The dipole moment function is expanded in the two CH‐stretching coordinates, where the expansion coefficients are determined from abinitio molecular orbital calculations. This simple calculation, which contains no adjustable parameters, can account very well for the observed relative intensity of axial and equatorial pure local mode peaks in the overtone spectra from ΔvCH=3–7. We also investigate different ways of obtaining the dipole moment derivatives, and find that a fourth order series expansion around the equilibrium geometry is a good approximation when calculating the relevant matrix elements.

1.
H. M.
Pickett
and
H. L.
Strauss
,
J. Chem. Phys.
55
,
324
(
1971
).
2.
B. R.
Henry
,
I.-F.
Hung
,
R. A.
MacPhail
, and
H. L.
Strauss
,
J. Am. Chem. Soc.
102
,
515
(
1980
).
3.
J. S.
Wong
,
R. A.
MacPhail
,
C. B.
Moore
, and
H. L.
Strauss
,
J. Phys. Chem.
86
,
1478
(
1982
).
4.
M. S.
Burberry
,
J. A.
Morrell
,
A. C.
Albrecht
, and
R. L.
Swofford
,
J. Chem. Phys.
70
,
5522
(
1979
).
5.
H. L.
Fang
and
R. L.
Swofford
,
J. Chem. Phys.
73
,
2607
(
1980
).
6.
R. J.
Hayward
and
B. R.
Henry
,
J. Mol. Spectrosc.
57
,
221
(
1975
).
7.
B. R.
Henry
,
Acc. Chem. Res.
10
,
207
(
1977
).
8.
I. A.
Watson
,
B. R.
Henry
, and
I. G.
Ross
,
Spectrochim. Acta, Part A
37
,
857
(
1981
).
9.
O. S.
Mortensen
,
B. R.
Henry
, and
M. A.
Mohammadi
,
J. Chem. Phys.
75
,
4800
(
1981
).
10.
M. S.
Child
and
R. T.
Lawton
,
Faraday Discuss. Chem. Soc.
71
,
273
(
1981
).
11.
B. R. Henry, Vibrational Spectra and Structure, edited by J. R. Durig (Elsevier, Amsterdam, 1981), Vol. 10, pp. 269–319.
12.
M. L.
Sage
and
J.
Jortner
,
Adv. Chem. Phys.
47
,
293
(
1981
).
13.
B. R.
Henry
,
A. W.
Tarr
,
O. S.
Mortensen
,
W. F.
Murphy
, and
D. A. C.
Compton
,
J. Chem. Phys.
79
,
2583
(
1983
).
14.
M. S.
Child
and
L.
Halonen
,
Adv. Chem. Phys.
57
,
1
(
1984
).
15.
M. S.
Child
,
Acc. Chem. Res.
18
,
45
(
1985
).
16.
B. R.
Henry
,
Acc. Chem. Res.
20
,
429
(
1987
).
17.
M. K.
Ahmed
and
B. R.
Henry
,
J. Phys. Chem.
91
,
3741
(
1987
).
18.
M. K.
Ahmed
and
B. R.
Henry
,
J. Phys. Chem.
91
,
5194
(
1987
).
19.
I.
Schek
,
J.
Jortner
, and
M. L.
Sage
,
Chem. Phys. Lett.
64
,
209
(
1979
).
20.
M. L.
Sage
,
J. Chem. Phys.
80
,
2872
(
1984
).
21.
M.
Lewerenz
and
M.
Quack
,
Chem. Phys. Lett.
123
,
197
(
1986
).
22.
H.-R.
Dübal
,
T.-K.
Ha
,
M.
Lewerenz
, and
M.
Quack
,
J. Chem. Phys.
91
,
6698
(
1989
).
23.
O. S.
Mortensen
,
M. K.
Ahmed
,
B. R.
Henry
, and
A. W.
Tarr
,
J. Chem. Phys.
82.
,
3903
(
1985
).
24.
A. W.
Tarr
,
D. J.
Swanton
, and
B. R.
Henry
,
J. Chem. Phys.
85
,
3463
(
1986
).
25.
L. A.
Findsen
,
H. L.
Fang
,
R. L.
Swofford
, and
R. R.
Birge
,
J. Chem. Phys.
84
,
16
(
1986
).
26.
A. W.
Tarr
and
F.
Zerbetto
,
Chem. Phys. Lett.
154
,
273
(
1989
).
27.
K. K.
Lehmann
and
A. M.
Smith
,
J. Chem. Phys.
93
,
6140
(
1990
).
28.
H. G.
Kjaergaard
,
H.
Yu
,
B. J.
Schattka
,
B. R.
Henry
, and
A. W.
Tarr
,
J. Chem. Phys.
93
,
6239
(
1990
).
29.
A. M.
Smith
,
W.
Klemperer
, and
K. K.
Lehmann
,
J. Chem. Phys.
94
,
5040
(
1991
).
30.
H. G.
Kjaergaard
,
B. R.
Henry
, and
A. W.
Tarr
,
J. Chem. Phys.
94
,
5844
(
1991
).
31.
H. G.
Kjaergaard
,
J. D.
Goddard
, and
B. R.
Henry
,
J. Chem. Phys.
95
,
5556
(
1991
).
32.
R.
Mecke
,
Z. Elektrochem.
54
,
38
(
1950
).
33.
B. R.
Henry
and
M. G.
Sowa
,
Prog. Anal. Spectrosc.
12
,
349
(
1989
).
34.
A. M.
Smith
,
U. G.
Jo/rgensen
, and
K. K.
Lehmann
,
J. Chem. Phys.
87
,
5649
(
1987
).
35.
J.-Y.
Mandin
,
J.-P.
Chevillard
,
C.
Camy-Peyret
,
J.-M.
Flaud
, and
J.
Brault
,
J. Mol. Spectrosc.
116
,
167
(
1986
).
36.
H. D.
Babcock
and
L.
Herzberg
,
Astrophys. J.
108
,
167
(
1948
).
37.
Spectra Calc is a commercially available product from Galactic Industries Corporation. Marquardt’s nonlinear least-squares fitting algorithm is used;
D. W.
Marquardt
,
J. Soc. Ind. Appl. Math.
11
,
431
(
1963
).
38.
P. W. Atkins, Molecular Quantum Mechanics, 2nd ed. (Oxford University, Oxford, 1983).
39.
H. G.
Kjaergaard
and
O. S.
Mortensen
,
Chem. Phys.
138
,
237
(
1989
).
40.
E. B. Wilson, J. C. Decius, and P. C. Cross, Molecular Vibrations (McGraw-Hill, New York, 1955).
41.
A. Messiah, Quantum Mechanics (Wiley, New York, 1961), Vol. 1.
42.
G. W. King, Spectroscopy and Molecular Structure (Holt, Rinehart, and Winston, New York, 1964), p. 332.
43.
W. B.
Olson
,
R. H.
Hunt
,
B. W.
Young
,
A. G.
Maki
, and
J. W.
Brault
,
J. Mol. Spectrosc.
127
,
12
(
1988
).
44.
C.
Douketis
and
J. P.
Reilly
,
J. Chem. Phys.
91
,
5239
(
1989
).
45.
GAUSSIAN 90, Revision F. M. J. Frisch, M. Head-Gordon, G. W. Trucks, J. B. Foresman, H. B. Schlegel, K. Raghavachari, M. Robb, J. S. Binkley, C. Gonzalez, D. J. Defrees, D. J. Fox, R. A. Whiteside, R. Seeger, C. F. Melius, J. Baker, R. L. Martin, L. R. Kahn, J. J. P. Stewart, S. Topiol, and J. A. Pople (Gaussian Inc., Pittsburgh, PA, 1990).
46.
S. Wolfram, Mathematica: A System for Doing Mathematics by Computer (Addison-Wesley, Reading, 1988).
47.
W. H. Press, B. F. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University, Cambridge, 1988).
48.
M. L.
Sage
,
Chem. Phys.
35
,
375
(
1978
).
49.
O.
Bastiansen
,
L.
Fernholt
,
H. M.
Seip
,
H.
Kambara
, and
K.
Kuchitsu
,
J. Mol. Struct.
18
,
163
(
1973
).
50.
J. D.
Ewbank
,
G.
Kirsch
, and
L.
Schäfer
,
J. Mol. Struct.
31
,
39
(
1976
).
51.
K. B.
Wiberg
,
V. A.
Walters
, and
W. P.
Dailey
,
J. Am. Chem. Soc.
107
,
4860
(
1985
).
52.
W. J. Hehre, L. Radom, P. v. R. Schleyer, and J. A. Pople, Ab initio Molecular Orbital Theory (Wiley, New York, 1986), and references therein.
53.
K. B.
Wiberg
and
A.
Shrake
,
Spectrochim. Acta, Part A
27
,
1139
(
1971
).
54.
K. B.
Wiberg
and
A.
Shrake
,
Spectrochim. Acta, Part A
29
,
567
,
583
(
1973
).
55.
J. W.
Perry
,
D. J.
Moll
,
A.
Kuppermann
, and
A. H.
Zewail
,
J. Chem. Phys.
82
,
1195
(
1985
).
56.
G.
Longhi
,
G.
Zerbi
,
L.
Ricard
, and
S.
Abbate
,
J. Chem. Phys.
88
,
6733
(
1988
).
57.
T.
Carrington
, Jr.
,
J. Chem. Phys.
86
,
2207
(
1987
).
58.
M. L.
Sage
,
J. Phys. Chem.
83
,
1455
(
1979
).
59.
H.-R.
Dübal
and
F. F.
Crim
,
J. Chem. Phys.
83
,
3863
(
1985
).
60.
J. S.
Wong
and
C. B.
Moore
,
J. Chem. Phys.
77
,
603
(
1982
).
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