19 September 1997
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 276 (1997) 224-232
Conformation selective electronic excitation of iodocyclohexane and Franck-Condon region photodissociation dynamics from emission spectroscopy Xuming Zheng, David Lee Phillips * Department of Chemistry, Universityof Hong Kong, PokfulamRoad, Hong Kong, Hong Kong Received 18 June 1997; in final form 18 June 1997
Abstract Conformation selective resonance emission spectra are reported for gas-phase iodocyclohexane with excitation wavelengths of 199.8 and 204.2 run. These spectra reveal seven Franck-Condon active vibrational modes for the axial conformation and eleven Franck-Condon vibrations for the equatorial conformation, and indicate that the initial dynamics on the B- and C-states have a complex multidimensional character with contributions from the CCC, CCH and HCI bending motions, torsional motions, and C-I, C-C, and C - H stretching motions for both conformations. The resonance emission spectra are generally consistent with the previously reported assignments of the far ultraviolet absorption spectra. © 1997 Elsevier Science B.V.
1. Introduction Iodocyclohexane exists in two chair conformations (axial and equatorial forms) which coexist in equilibrium at room temperature [1]. The equatorial conformation of iodocyclohexane has a larger population than the axial conformation at room temperature due to steric interactions [1,2]. IR/NMR studies have shown that the equatorial conformation (eqCtH11I) is more stable than the axial conformation (ax-C6HHI) by AG° -- 0.61 kcal/mol [3]. The equatorial and axial conformations also have different C-I bond lengths with the axial C-I bond 0.0050.012 ,~ longer than the equatorial C-I bond length as determined from both microwave spectroscopy
* Correspondingauthor.
experiments [4] and molecular mechanics calculations [5]. Recent time-of-flight translational spectroscopy experiments [6] measured the translational energy distributions of I and I * fragments produced from A-band photodissociation of iodocyclohexane, and found that the axial conformation receives 6.0 + 0.8 kcal/mol more translational energy than the fragments from the equatorial conformation photodissodation [6]. This implies that the cyclohexyl radical fragment from A-band photodissociation of the equatorial conformation has more internal excitation than the cyclohexyl radical fragment produced from A-band photodissociation of the axial conformation of iodocyclohexane. EI-Sayed and co-workers concluded from this study [6] that the ground state of the cyclohexyl radical has the hydrogen atom at the radical center in the equatorial position, which is in agreement with the results of MM2 calculations [7].
0009-2614/97/$17.00 © 1997 Elsevier Science B.V. All tights reserved. PII S0009-2614(97)00837-3
X. Zheng, D. Lee Phillips/Chemical Physics Letters 276 (1997) 224-232
Iodocyclohexane is one of a few examples where two conformations have sufficiently different electronic transition frequencies so as to allow ultraviolet absorption spectroscopy to distinguish between electronic excitation of each conformation [8]. The Rydberg-like B and C absorption bands between 48,000 and 53,000 cm -~ in the far ultraviolet absorption spectrum of gas-phase iodocyclohexane have been tentatively assigned to four electronic transitions to two electronic excited states of the axial and equatorial conformations of iodocyclohexane (ax-B, eq-B, ax-C, and eq-C) [8]. In this Letter we report conformation selective electronic excitation of iodocyclohexane in the B, C Rydberg-like states and emission spectra in order to further investigate the absorption spectral assignments to electronic transitions of the axial and equatorial conformations of iodocyclohexane, and to investigate the nature of the Franck-Condon region of the B, C Rydberg states.
2. Experiment Iodocyclobexane was purchased from Aldrich Chemical Company and used as received for the emission experiments. The emission spectroscopy experimental apparatus has been described previously [10-12]. The laser excitation frequencies for the emission spectroscopy experiments (199.8 and 204.2 nm) were generated by hydrogen Raman shifting the fourth and third harmonics of a Nd:YAG laser (Spectra-Physics GCR-150-10). A stream of dry nitrogen gas was passed through a reservoir filled with gas and liquid iodocyclobexane in order to carry some gas-phase iodocyclohexane sample out through a pipette nozzle where the excitation laser beam excites the sample. The excitation laser beam was not noticeably attenuated after passing through the sample region and reabsorption of the emission light was minimal. The emission light was collected in a 90° geometry by an ellipsoidal mirror and imaged through a polarization scrambler and onto the entrance slit of a 0.5 m spectrograph equipped with a 1200 groove/nun grating blazed at 250 nm. The spectrograph grating dispersed the emission light onto a liquid nitrogen cooled CCD detector and the signal was collected ~ 200-300 s before being read-
225
out to a computer. About 30-60 of these readouts were added together to obtain the emission spectra. Raman peaks of nitrogen and oxygen as well as some mercury emission peaks were used to calibrate the wavenumber shifts from the excitation frequency for the gas-phase iodocyclohexane spectra. The channel to channel variations of the detection system were corrected for using spectra taken of an intensity calibrated deuterium lamp (Optronics). The emission peak intensities were found by fitting sections of the spectrum with a sum of Lorentzians and a baseline.
3. Results and discussion Fig. 1 displays the geometries of the axial and equatorial conformations of iodocyclohexane. Fig. 2 shows the absorption spectrum of gas-phase iodocyclohexane in the 193-210 nm region. Two excitation wavelengths (199.8 and 204.2 nm) for the resonance emission experiments are shown above the absorption spectrum. The absorption spectrum in Fig. 2 is similar to that reported previously by Boschi and Salahub [8]. The region between 199 and 205 nm is composed mainly of four major peaks tentatively assigned to the axial B-state, the axial C-state, the equatorial B-state, and the equatorial C-state. The 199.8 nm excitation wavelength is in resonance primarily with the equatorial C-state with some contribution from the partially overlapped equatorial Bstate while the 204.2 nm excitation wavelength is in resonance primarily with the axial B-state with some contribution from the partially overlapped axial Cstate. Thus the 199.8 nm light predominantly excites the equatorial conformation of iodocyclobexane while the 204.2 nm light predominantly excites the axial conformation of iodocyclohexane.
I
Axial
Equatorial
Fig. I. Geometries of axial and equatorial conformations of iodocyclohexane.
226
X. Zheng, D. Lee Phillips/Chemical Physics Letters 276 (1997) 224-232
Boschi and Salahub [8] also observed some vibrational progressions in the far ultraviolet absorption spectrum of the B- and C-states of iodocyclohexane which they tentatively assigned to progressions in a 'probable C - H deformation' vibration and a C - I stretch vibration. Progressions due to the 'probable C - H deformation' in the equatorial B- and C-states are found with ~ 1030 and ~ 1060 c m - i spacing, respectively, and in the axial B- and C-states with spacing of 1007 and 998 cm - j , respectively, in the absorption spectrum. Additional vibrational progressions assigned to the nominal C - I stretch were observed with spacing of 410, 405, 565, and 570 cm -I for the axial B-state, axial C-state, equatorial B-state, and equatorial C-state, respectively. Boschi and Salahub [8] noted that the excited state frequency for the C - I stretch vibration is lowered more for the axial conformation than the equatorial conformation, and this suggests that a larger increase of the C - I bond length in the axial B- and C-states compared to the equatorial B- and C-states. It is interesting to note that the major geometry changes in the B and C excited states are very similar to one another (axial B-state with axial C-state and equatorial B-state with equatorial C-state). While the far ultraviolet absorption spectrum of iodocyclohexane has some vibronic structure, the absorption bands are relatively diffuse and this makes it difficult to obtain a good vibrational mode specific characterization of the excited state potential energy surfaces. Our resonance emission experiments should provide much more detail
5
l [
199.8 nm
g3
195
200 205 Wavelength ( n m )
21o
Fig. 2. Far ultraviolet absorption spectrum of iodocyclohexane with the two excitation wavelengths (199.8 and 204.2 nm) for the emission experiments indicated above the absorption spectrum.
FT-IR
FT-Raman
_,g, ¢/I r-
t,-
m/gu
0
500
1000
1500
2000
Raman Shift ( cm -1) Fig. 3. Comparison of emission spectra of gas-phase iodocyclohexane (excitation wavelengths of 199.8, 204.2, and 223.1 nm) with FT-Raman and FT-IR spectra of liquid iodocyclohexane.
about the excited state structure of the axial and equatorial forms of the B and C excited states of iodocyclohexane. Fig. 3 shows an overview of the 199.8, 204.2, and 223.1 nm resonance emission spectra of gas-phase iodocyclohexane. Fig. 3 also displays a 199.8 nm resonance emission spectrum of iodocyclohexane in cyclohexane solution as well as FT-IR and FT-Raman spectra of neat liquid iodocyclohexane. Figs. 4 and 5 show expanded views of the 199.8 and 204.2 nm resonance emission spectra with tentative assignments shown above the larger peaks. Table 1 gives the tentative peak assignments and relative peak intensities for the gas-phase 199.8, 204.2, and 223.1 nm resonance emission spectra of iodocyclohexane and the FT-Raman spectrum of neat liquid iodocyclohexane. The F r - R a m a n and resonance emission spectra features were assigned based on previously published Raman and IR vibrational spectra as well as a normal coordinate analysis [9]. Our FT-Raman
X. Zheng, D. Lee Phillips / Chemical Physics Letters 276 (1997) 224-232
spectrum in Fig. 3 agrees very well with the Raman spectra previously taken of neat iodocyelohexane [9]. The 199.8 and 204.2 nm resonance emission spectra of gas-phase iodocyclohexane are significantly different from one another in both peak positions and relative intensities. Almost all of the peaks in the 199.8 nm spectrum can be assigned to equatorial vibrational features and the peaks in the 204.2 nm spectrum can be assigned to axial vibrational features. The gas-phase vibrational frequencies are generally 20-30 cm-I higher for the equatorial conformation peaks than the corresponding neat liquid peaks while the gas-phase vibrational frequencies for the axial conformation peaks are generally 5-15 cm -I higher than the corresponding neat liquid peaks. Solvation tends to lower the vibrational frequencies of both equatorial and axial conformations of iodocyclohexane. Solvation also significantly
®
broadens the absorption spectrum so as to remove most of the vibrational structure. Thus excitation at 199.8 and 204.2 nm of iodocyclohexane in cyclohexane solution results in excitation of both equatorial and axial conformations at the same time. Comparison of the 199.8 nm iodocyclohexane in cyclohexane solution resonance emission spectrum with the 199.8 and 204.2 nm gas-phase spectra shown in Fig. 3 reveals that the solution-phase spectrum is more complex and appears to have features that are a mixture of the peaks appearing in the gas-phase equatorial 199.8 nm and axial 204.2 nm resonance emission spectra. The 199.8 nm resonance emission spectrum shown in Fig. 4 has most of its intensity tentatively assigned to the fundamentals, overtones and combination bands of the following equatorial Franck-Condon active vibrations (with major internal coordinate con-
%
I
i:r:i
0
,
,
,
t
1000
.
.
.
.
i :: :: :: :: :: °
'i ii
:i .
,
227
!
2000
,
.
.
.
i
-ll
.
',
~i
i
3000
1.,
i
'
'
i
,,
,
i
i
i
4000
Raman Shift ( cm -1 ) Fig. 4. Expanded view of 199.8 nm emission spectrum of gas-phase iodocyclohexane with tentative peak assignments shown above the spectrum.
228
X. Zheng, D. Lee Phillips / Chemical Physics Letters 276 (1997) 224-232
tributions in parentheses): ='27 (CCI bend and CCC bend), ='26 (CI stretch), ='25 (CCC bend, torsion), ='24 (CCC bend), ='22 (C-I stretch), //19/44 (CC stretch and CCH bend), ='is (CCC bend and CCH bend), ='16 (CCH bend and I-ICI bend), v15 (HCI bend), ='14/3s (CCH bend), and v2/1 (CH stretch). These eleven Franck-Condon active modes give rise to many combination bands and/or overtones (some of which overlap and are unresolved in our spectrum) and this leads to a fairly complex 199.8 nm resonance emission spectrum. The significant amount of intensity appearing in the overtones and combination bands of the eleven Franck-Condon active vibrations in the 199.8 nm resonance emission spectrum suggests that the equatorial C (B) excited state(s) change their geometry(ies) in the Franck-Condon region mostly along a complex multidimensional surface with contributions from the CCC, CCH, and
,~ tD
i*=
~
--®
HCI bending motions, torsional motions, and C-I, C-C, and C - H stretching motions. The 204.2 nm resonance emission spectrum displayed in Fig. 5 has most of its intensity tentatively assigned to fundamentals, overtones, and combination bands of the following vibrations: v26 (CCI bend, CCC bend, and torsion), ='25 (CCC bend and torsion), ='23 (CCC bend, CCH bend, and CI stretch), 1/17/42 (C-C stretch and CCH bend), ;'15 (HCI bend), ='14 (CCH bend), and ='1 (C-H stretch). The large amount of intensity in the overtones and combination bands of these seven Franck-Condon active vibrations suggests that the axial B (C) excited state(s) change their geometry(ies) primarily along a multidimensional surface with contributions from CCC, CCH, and HCI bending motions, and torsional motion as well as the C-I, C-C, and C - H stretching motions.
: *=
:
:
*= -
i# it==
::
I
0
I
I
.-:
I
:
I
1000
I
I
'
'
I
2000
ix=o:: A
a
3000
4000
R a m a n Shift ( c m "1 ) Fig. 5. Expanded view of 204.2 nm emission spectrumof gas-phase iodocyclohexanewith tentative peak assignments shown abovethe spectrum.
X. Zheng, D. Lee Phillips / Chemical Physics Letters 276 (1997) 224-232
229
Table l lodocyciohexane gas-phase emission peak intensities and assignments based on eomparision to previous Raman and IR spectra for liquid iodocyclohexane Raman shifts ( c m - t) and intensities
Peak assignment a
P27 a (At) /,,27 e (At)
/148 a (A") //4s • (A") v26 • (At) /126 a (At) v25 e (At) /125 a (At) v24 e (At)
199.8 n m
Raman shift
Raman shift b
Int. c
141
397
257
1219
b c c I, ¢ bccl/ccc
121 W 132 w
/1c-J b c c l / c c o r~ bcc c , % bcc c , ¢ bccc
175 197 222 238 320 359 421
//24/46 a /123 a
FT-Raman
vw w sh vs sh w m w
351 454
204.2 nm
223.1 nm
Raman shift b
Int. c
131
327
242
428
362
bCCC/CCH, V c _ x
Int. ~
229
570
229
320 362
12 28
491
1769
445 495
117 125
660
263
678 726 825
113
874
201
807 848 878
39 35 41
962
46 994
62
1031
40
1100
61
1179
100
1258
80
1338
76
354 1029
446 m
(At)
Raman shift b
4 8 0 sh
(2/126 ~) /12~ ~
(At)
/122 a (,~) v22 e (At) 3/,,26 a
v2,
o/a
V2o e/a
494 m 639 w sh 654 s
vC_l
(~) (At)
805m 843 m 864 w 884 w
ViOl4 4 a (At) Vl9/4 4 ~ ( ~ ) 2 !123 a Vl 8 e (At)
bCCC/CCH
vls " (At) vl7 " (At) //17/42 a
//C-C" b c c H
v42 ~ ( R ) v41 ~ (At') vt5 ~ (At) Vl 5 e (At) //14 a (,~) Vl 4 e / v 3 S e
btlct bncl bCCH
v3s a (A") v37 e (A") v36 a (A") vl 2 • (At)
bcc H, 2 " 6 8 1
988 1005 1020 1028 1047 1073 1094 1166 1173 1246 1254 1268 1297 1320 1331
m vw mw wsh vw vw w sh m m sh w sh m
/'12 e//2V22 e /1|6 e + //'~6 e
/114 //14/38 e + /126 •
115
681
1347
815
194
886
426
1008
264
1119 1200
a+
41
1030
201
1184
706
1261
521
433 539
1280
164
1350
334
1348 sh 1420 sh 1443m
v,o ~ (At) v3_, a (At,) (major) v 9 e/v~2 ~ (minor) i/14/38 e ..1_ /127 e e . t. e /~15 //26
568
1420
58
1519
138
//26
1366
208
1481
80
X. Zheng, D. Lee Phillips / Chemical Physics Letters 276 (1997) 224-232
230 Table 1 (continued) Peak assignment a
Raman shifts (cm- ') and intensities
V14/38 e q_ /'25 • e.[_ e /"12 //26 //18
e
-I- /'22
a+
//14
e
a..[.
1/15 e
e
•
q- //22
//23
199.8 nm
Raman shift
Raman shift b
204.2 nm Int. c
1608
35
1668
43
a a
//14 a + 2 v 2 6
/'16 -1- /'22 /'14/38 e - l - 2 / ' 2 6 /'15
//25
Fl'-Raman
a
1776
77
1854
100
1932
40
2001
66
//14/38 e .~. /'22 e Vl 4 a . l _ 2 v 2 5
2//17/42 a 2088
/'14/38 e -t" //22 e q.. 1/27 • e _ t_ e /'15 /'19/44 //14 a + / / 1 9 / 4 4
a
//15 a"1-//17/42
a
2/,16 e
e+
//18
Int. c
shift b
1623
79
1670 1736
63 30
1810
18
1886
15
e . t_
//26
2053
90
2118 2192
31 67
2266
30
2339
100
2422
70
2522
55
2595
25
2874
15
2972
77
8.5
2194
46
2271
30
2348
64
2434 2511
45 33
2587
16
2653
17
e
I,,14 a..~. /"17/42 a
//12
Raman
1979
a
2Vl8 e/3/'22 e e.~. e //16 /'19/44 e _ I. e !/12 I'22
/'14/38 e-1"/'18
223.1 nm Int. c
•
e
//14/38 e "4- //22
Raman shift b
e 2vl5
e
a
2/'22 e + / ' i s • 1/14 a.~_ /'15 a Vl 6 e + 2 / ' 2 2
e
1,15 e_1_2/'22
e 21/14 a
1/14/38 e ..4. 2 V22 e
a
/'14
"[- 1/35
a
4//22 e 2Pl8
e .4. //22 e
2851
//14/38 e .~. 2/,.22 e + i,.26 e e /'2/I //14/38 e + !/25 e + //26 e 1'12 e + 2 / ' 2 6 e
2/'14
8.4
a_l_ V25 a
2954
29
//14/38 e .~ //18 • + //22 e 1/15 • _]. //16 e q_ 1/22 e a
/'1
3010
3//1 s • 1,18 e -I- 3/)22 •
3//17/42 ;',6 e + 31/22 e
6.8
a
3088
3094
I0
7.4
2866 2940
90 128
X. Zheng, D. Lee Phillips / Chemical Physics Letters 276 (1997) 224-232
231
Table I (continued) Peak assignment a
Raman shifts ( c m - I ) and intensities FT-Raman Raman shift
Vl 5 e + 3/)22 e /)15 a + 2/)17/42
204.2 n m
Raman shift b
Int. c
3168
12
a
/)14 a + 2/)17/42
a
3194
6.1
3265
8.8
3335
4.5
Raman shift b
Int. c
3288
/)14/38 e q_ 2/)18 e ¢ .4. //25 c
2ul5 a + /)17/42 a /)12 e 4- 2/)18 e
3371
7.9
3508 3590
5.2 12
/)14 a +/)15 a + /)17/42 a /)15 e + /)2/I
Raman shift b
223.1 nm Int. c
3242
/)14/38 e .4_ 3/)22 e
/)2/I
199.8 nm
/)18 e + 2 / ) 2 2
e
e .1_ /)22 e
3431
14
/)14/38 e _~ //18 e .]_ 2/)22 e
/)t4 a + 2/)15 a 2/)14 a + / ) 1 5 a vl6 ~ + 4v22 ~ vl 5 e + 4 v 2 2 e
3597 3666 3744 3825
4.7 3.8
4049
5.0
4147
7.3
4253 4271
1.6 1.9
/)1 a -I'- /)17/42 a
/)2/I ~ + /)t6 e /)1 a + / ) , 5 a /)2/I ~ +/)15 e ut a + v t 4 a /)2/I
e "4- /)14/38 e
/)2/t ~ + /)12 ¢
8.7 6.3
4009
13
4137
16
4213
8.9
a Peak assignments based on Raman and IR spectra reported in reference [9]. For most fundamental features the internal coordinate motions making significant contributions to the normal coordinate vibration are given next to the peak assignment (based on normal coordinate calculations of reference [9]). Symbols used are b = bend for three subscript atoms, v = stretch for two subscript atoms, ¢ = torsional motion as described in [9]. The symmetry of the fundamental peaks (P/ or ,a/') are also indicated next to the peak assignment. b Estimated uncertainties are about 5 e r a - t for the emission peak positions. ¢ The relative intensities are based on integrated areas of the peaks. Estimated uncertainties are + 10% for peaks above 100, + 2 0 % for peaks between 30 and 100, and + 3 0 % for peaks below 30. Intensities for the F T - R a m a n spectrum are given qualitatively next to the Raman shifts with symbols of vw = very weak, w = weak, m = medium, s = strong, vs = very strong, sh = shoulder of nearby peak.
It is interesting that the same types of vibrational motions (CCC, CCH, and HCI bending motions, and torsional motion as well as both the C-l, C-C, and C - H stretching motions) contribute to the excited state Franck-Condon region for both the equatorial (predominantly C-state at 199.8 nm) and axial (predominantly B-state at 204.2 nm) conformations. However, the relative intensities of the peak progressions are substantially different for the equatorial and axial conformations. This could indicate that the Band C-states are very different from one another though this appears unlikely since the B- and C-states have very similar absorption spectra in the gas phase [8]. It is more likely due to a combination of differ-
ent normal coordinate descriptions of the two conformations and/or the excited state surfaces are different for the equatorial and axial conformations. In order to sort the relative contributions from these two effects, a more quantitative investigation using simulations of the emission spectra and the normal coordinate descriptions is required. The axial B-state resonance emission spectrum (204.2 nm) has only seven Franck-Condon active modes compared to eleven modes for the equatorial C-state resonance emission spectrum (199.8 nm). This appears to imply that the initial Franck-Condon region dynamics are spread around more vibrational motions in the equatorial conformation than in the
232
X. Zheng, D. Lee Phillips/Chemical Physics Letters 276 (1997) 224-232
axial conformation. The C-H stretch vibrational mode is noticeably more active in the axial B-state resonance emission spectrum (204.2 nm) than in the equatorial C-state resonance emission spectrum (199.8 nm) and this indicates the C-H bond length changes more in the initial Franck-Condon region for the axial B-state. Both the axial and equatorial conformation resonance emission spectra have a large degree of Franck-Condon activity in vibrational modes whose fundamentals are in the 1000-1300 cm -1 region (axial //14, ]717/42' and //15, and the equatorial //18, //16, //15, //14/38' and //12) which involve mainly CCH and HCI bending motions as well as some C-C stretch motion. These modes also roughly correspond to the 'CH deformation' vibrational spacing observed in the far ultraviolet absorption spectrum by Boschi and Salahub [8]. There are several low frequency modes in the 200-700 cmregion that are Franck-Condon active in both axial and equatorial conformation resonance emission spectra, and these vibrational progressions likely correspond mainly to the 'C-I' stretch progressions in the far ultraviolet absorption spectrum [8]. Our resonance emission spectra are generally consistent with the basic assignments of the far ultraviolet absorption transitions to axial and equatorial conformations of iodocyclohexane by Boschi and Salahub [8]. The resonance emission spectra also show the relatively complex multidimensional nature of the equatorial and axial conformation Franck-Condon region dynamics of the B, C excited states of gas-phase iodocylohexane. It would be very interesting for conformation selective molecular beam experiments and/or vibrational mode specific spectroscopic studies of the photofragments to be carried out on the Band C-states of gas-phase iodocyclohexane in order to investigate the energy disposal of the different conformations of iodocyclohexane and compare this to the initial dynamics on the B, C Rydberg states found from our resonance emission spectra. It would also be very helpful for more detailed emission studies which examine the depolarization ratio as the excitation wavelength is tuned over the absorption
bands similar to investigations carded out previously on iodomethane [13-19]. This would help provide a more complete picture of the B, C state photodissociation reactions for iodocyclohexane.
Acknowledgements This work was supported by grants from the Committee on Research and Conference Grants (CRCG), the Research Grants Council (RGC) of Hong Kong, the Hung Hing Ying Physical Sciences Research Fund and the Large Items of Equipment Allocation 1993-94 from the University of Hong Kong.
References [1] J. McMurray, Organic Chemistry, Brooks-Cole, Belmont, CA, 1984. [2] H. Hart, G.J. Karabatsos, Advances in Alicyclic Chemistry, voi. 3, Academic Press, New York, 1971. [3] D.E. Bugay, C.H. Bushweller, C.T. Danhey, S. Hoogasian, J.A. Blersch, W.R. Leenstra, J. Phys. Chem. 93 (1989) 3908. [4] D. Damiani, F. Scappini, W. Caminati, G. Corbelli, J. Mol. Spectrosc. 100 (1983) 36. [5] A.Y. Meyer, J. Mol. Struct. THEOCHEM 94 (1983) 95. [6] J.E. Freitas, H.J. Hwang, A.B. Ticknor, M.A. E1-Sayed, Chem. Phys. Lett. 183 (1991) 165. [7] M.R. Imam, N.L. Allinger, J. Mol. Struct. 126 (1985) 345. [8] R.A. Boschi, D.R. Salahub, Mol. Phys. 24 (1972) 735. [9] T. Woldbaek, Acta Chem. Scand. A 36 (1982) 641. [10] W.M. Kwok, D.L. Phillips, Chem. Phys. Lett. 235 (1995) 260. [11] W.M. Kwok, D.L. Phillips, J. Chem. Phys. 104 (1996) 2529. [12] S.-Q. Man, W.M. Kwok, A.E. Johnson, D.L. Phillips, J. Chem. Phys. 105 (1996) 5842. [13] K. Lao, M.D. Person, T. Chou, L.J. Butler, J. Chem. Phys. 89 (1988) 3463. [14] Y.C. Chung, L.D. Ziegler, J. Chem. Phys. 88 (1988) 7287. [15] L.D. Ziegler, Y.C. Chung, P. Wang, Y.P. Zhang, J. Chem. Phys. 90 (1989) 4125. [16] P.G. Wang, Y.P. Zhang, C.J. Ruggles, L.D. Ziegler, J. Chem. Phys. 92 (1990) 2806. [17] P.G. Wang, L.D. Ziegler, J. Chem. Phys. 95 (1991) 288. [18] L.D. Ziegler, Acc. Chem. Res. 27 (1993) 1. [19] R. Fan, T. Kalbfleisch, L.D. Ziegler, J. Chem. Phys. 104 (1996) 3886.