Smith, D. D.

Zewail, A. H.

English

Caltech Authors - Main

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Characterization of vibrational overtones and "local" modes 
by emission spectroscopy 
D. D. Smith and A. H. Zewailal 
Arthur Amos Noyes Laboratory of Chemical Physics, b) California Institute of Technology, Pasadena, 
California 91125 
(Received 2 April 1979; accepted 18 April 1979) 
The concept of local modes in polyatomic molecules has 
recently been under examination, both theoretically1- 5 and 
experimentally. 4- 7 Bond locality has direct relevance to 
various interesting phenomena such as multiphoton dissoci-
ation of molecules and laser-induced chemistry. The char-
acterization of local vs normal modes in moderate -sized 
molecules has recently been addressed theoretically by 
Gelbart and his group. 1• 2 Experimentally, the question 
OVERTONE SPECTRA OF 
¢ 
'-c =O 
¢/ 
6500 6380 
4620 
4290 
-A(Al 
4600 
of local vs normal modes in liquids, 5 gases, 6 and cooled 
solids 1 has been dealt with by observing the absorption 
spectra of the different overtones. A plot of ~Ev·t, the 
energy divided by the vibrational quantum number v, vs 
v gives a straight line consistent with (but not proof of) 
the ide~ of a simple Morse oscillator. These experi-
mental results have been confined mostly to the CH 
stretch in molecules. 
4270 
FIG. 1. The overtone spectra of benzophenone in DDE at 2 K. The numbers in boxes denote the CO vibrational quantum number. 
Note the broadening and the shift of the CO and torsional bands. The v = 1 line is an uneven doublet, and relative intensities are 
resolution limited. 
540 J. Chern. Phys. 71(1). 1 Jul. 1979 0021-9606/79/01 0540-03$01.00 © 1979 American Institute of Physics 
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Letters to the Editor 541 
1670 
-
'E 
~ 
I 1650 
> 
~ 1640 
1630 
1620 
1610 
1600 
18 
~ 
I 14 
E 
u 
::::. 10 
<J 
6 
2 
A= 1670±5cm-1 
B = -12.5±1.5cm-1 
2 3 
? 
• 
• 
• 6.11 vs Energy 
0 2 4 6 8 
Energy (cm-1 x 10-3) 
4 5 6 
v-
FIG. 2. A plot of AE v -! vs v for benzophenone (CO stretch) 
in DDE at 2 K. The straight line is a linear least squares fit 
(see also footnote 9). The point for v = 1 seems to be at lower 
AEv-1 than predicted by the best straight-line fit. However, 
our uncertainty at the moment is large. The insert is a plot 
of the apparent width, .O.IJ, vs the energy of excitation. The 
6477 cm-1 point is uncertain because of spectral overlap, and 
the width of v = 1 includes the ·shoulder. 
In this Communication, we use emission spectros-
copy instead of absorption, as used in all previous 
work, and we explore a different type of molecule 
that may be useful for detailed theoretical inspec-
tion. The idea is quite simple-using a high-sen-
sitivity spectrophotometer (e. g., one that utilizes 
photon counting) one scans the optical emission spec-
trum (say, the singlet-triplet transition) that has ground 
state vibrational overtones as final states. Knowing the 
energy of the 0, 0 transition, one can deduce the energy 
of the mode as a function of v along with the anharmo-
nicity and transition linewidths. Because we are using 
the 'emission and not the absorption (which requires long 
path lengths and/or dense media), several advantages 
can be realized. First, mixed crystals at low tempera-
tures (or molecules in molecular beam nozzle sources) 
can be studied with very small concentrations (10-4-10-6 
mol/mol) thus avoiding possible intermolecular pertur-
bations (or in the case of a beam, collisional effects). 
Second, polarization techniques can be used to assign 
bands. Third, measurement of linewidths can be done 
easily, since the v transitions will be in the visible, as 
opposed to absorption measurements where IR detection 
is required in the low energy region. The method, how-
ever, relies on a finite and useful value for the Franck-
Condon factor between the upper vibronic state and the 
ground one. 
The system studied here is benzophenone isolated in 
4, 4' -dibromodiphenyl ether at approximately 2 K. 
These mixed crystals exhibit a "clean" spectra consist-
ing of a carbonyl (CO) progression together with (pre-
sumably) torsional modes of the two phenyls. The v = 1 
and 2 transitions of the carbonyl moeity have been char-
acterized before. 8 The crystals were grown from the 
melt by standard Bridgman techniques. The details of 
the spectrophotometer will be published elsewhere. All 
the work reported here utilizes the phosphorescence . 
Figure 1 displays the overtone spectra of the benzo-
phenone CO stretch at 2 K. (The detection sensitivity 
was enhanced approximately 104 to observe v = 5; but 
note that the concentration of benzophenone was only 
about 10·1 M.) From the spectra we have learned sev-
eral things; (a) When ~E v·1 vs v is plotted for the CO 
overtones, we obtain a nearly straight line (see Fig. 2); 
(b) as one goes to higher overtones of CO, the apparent 
linewidth increases. In fact at v = 5, all lines (CO and 
torsional) overlap, yielding a much broader resonance 
(CO width greater than 20 cm-1); (c) the torsional pro-
gression exhibits a similar trend in linewidth with in-
creasing quantum number. 
From the plot of ~E v -1 vs v, we find a fundamental 
frequency of 1670 ± 5 cm-1 and an anharmonicity constant 
of - 12. 5 ± 1. 5 em -t. 9 These data raise an interesting 
point. Probably due to the electronic excitation being 
highly localized on the CO, 8 the progression in the 
ground state appears to have the nature of a "local" mode 
with appreciable diagonal anharmonicity. This suggests 
that the extent to which these modes couple to other 
modes should be evident from the line broadening as v 
increases. For v = 5, an experimental estimate of the 
linewidth will be on the order of 50 cm-1• 10 It is perhaps 
accidental that this width is approximately half that of 
the naphthalene (100 cm-1) v = 5 transition of the CH 
stretch and that the ratio of the CH stretch frequency to 
the CO frequency is 1. 85. In benzophenone, the tor-
sional mode may prove to be the accepting mode for en-
ergy relaxation. This would be an example of vibra-
tional relaxation due to the forces imposed on the CO by 
the neighboring CC bonds. As suggested by Shobatake 
et al., 11 this kind of interaction yields .a relaxation rate 
linear in v (see Fig. 2). However, one must first dem-
onstrate the homogeneity of the overtone resonances and 
measure the contribution of pure dephasing to the line-
'width before deducing the energy relaxation rate ac-
curately from the line shape. 12 
In conclusion, by using simple optical techniques 
one can obtain the widths, the anharmonicity, and the 
energies of the high energy overtones. Comparison be-
tween absorption and emission data on linewidths and 
energies will be extremely important tests for current 
theoretical work. Finally, benzophenone offers an op-
portunity to unravel some of the "local" mode relaxation 
processes because of the apparent "two mode spectra" 
of the matrix-isolated molecule. Extension of these 
ideas to CH modes and to molecules in beams will be 
reported later. Similar to emission, Raman scattering 
into overtones should also be feasible. 
J. Chern. Phys., Vol. 71, No. 1, 1 July 1979 
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542 Letters to the Editor 
This work was supported by a grant from the National 
Science Foundation. 
a> Alfred P. Sloan Fellow. 
b>contribution No. 5998. 
1M. Elert, P. Stannard, and W. Gelbart, J. Chern. Phys. 67, 
5395 (1977). 
2W. M. Gelbart, P. Stannard, and M. Elert, Int. J. Quantum 
Chern. 14, (1978). 
3P. Nagy and W. Hase, Chem. Phys. Lett. 54, 73 (1978). 
4B. R. Henry, Ace Chern. Res. 10, 207 (1977). 
5A. Albrecht, in Advances in Laser Chemistry, edited by A. H. 
Zewail, Springer series in Chemical Physics 3 (Springer-
Verlag, Berlin, 1978), p. 235; and references therein. 
6K. V. Reddy, R. G. Bray, and M. J. Berry in Ref. 5, p. 48. 
7J. W. Perry and A. H. Zewail, J. Chern. Phys. 70, 582 
(1979). 
8A. H. Zewail, Ph. D. thesis, University of Pennsylvania, 
Philadelphia, PA; R. M. Hochstrasser, G. W. Scott, and 
A. H. Zewail, Mol. Phys. 36, 475 (1978). 
3From another set of data we obtained 1672 ±6 cm-1 and -14 
± 2 cm-1. These uncertainties are due to the broadening of the 
high-energy overtones and the error in the baselines. 
10G. W. Robinson in Proceedings of R. A. Welch Conference 
on Chemical Research Vol. XIX, Photon Chemistry, Houston, 
1975. The author mentioned that high energy CH modes were 
observed in benzene at long wavelengths from the singlet-
triplet origin. He estimated the relaxation time to be 10 ps. 
11 K. Shobatake, S. A. Rice, andY. T. Lee, J. Chem. Phys. 
59, 2483 (1973); see also D. Micha, Chem. Phys. Lett. 46, 
188 (1977). The idea for the v-linear dependence arose dur-
ing a conversation with ProfessorS. Rice. 
12D. D. Smith and A. H. Zewail {to be published). 
How symmetric stretch excitation in a triatomic molecule 
can be more efficient than asymmetric stretch excitation in 
enhancing reaction rates in atom plus triatom reactions 
George C. Schatz 
Department of Chemistry, Northwestern University, Evanston, Illinois 60201 
(Received 26 February 1979; accepted 24 April 1979) 
We shall show how excitation in the symmetric stretch 
mode of a linear triatomic molecule can more efficiently 
lower the reaction threshold (and hence the activation 
energy) for many atom plus triatom reactions of the 
type A +BCD- AB +CD than a comparable amount of 
excitation in the asymmetric stretch, even though the 
transition state geometry is such that the BC bond is ex-
tended and the CD bond contracted. This effect will be 
illustrated using trajectory results for a collinear model 
of oep) + cs2- cs +so. 
The influence of reagent vibrational excitation on re-
action rates has been of significant interest in the last 
few years, 1 especially in laser chemistry applications, 
and is now fairly well understood experimentally1 and 
theoretically2 for atom-diatom systems. For reactions 
involving triatomic molecules, the situation is much less 
certain, with only a few experiments reported in which 
the specific mode responsible for an enhancement has 
been studied. 1• 3. 4 Occasionally it has been assumed that 
asymmetric stretch excitation should be most efficient 
in lowering the reaction threshold, 5 although no theo-
retical studies of this point have been reported pre-
viously. 
Consider the collinear atom plus linear triatomic 
molecule reaction A +BCD- AB + CD, where atoms B 
and D are identical. The highest frequency mode of the 
reagents is normally the asymmetric stretch, and if the 
mass of atom C is much less than that of B or D, the 
difference between symmetric and asymmetric stretch 
frequencies can be quite large. At the transition state, 
usually one of the two stable normal modes (here de-
noted v 3) corresponds primarily to CD stretching (the 
"old" bond). If v3 is higher in frequency than the other 
stable mode (v1), then by the noncrossing rule v3 must 
correlate (in a vibrationally adiabatic sense) to the 
highest frequency mode of the reagents, i.e., the asym-
4.5 
4.0 
rz 
J.S 
3.0 
J.5 
.6.2ev 
2.5 
f3 
3.0 
rj rz G o-s-c-s 
r; 
FIG. 1. Two cuts of the potential energy surface for O+CS2, 
one at constant r 1 and one at constant r 3• (See l!!bel.in Figure.) 
All distances are in bohr, and the location of the saddle point is 
is indicated by a cross. Contour energies given are relative to 
a zero of energy at the bottom of the cs2 potential well with 
the 0 atom at infinite separation. A typical reactive trajectory 
for O+CS2(000) at £~=0. 23 eV (total energy=O. 37 eV) is pro-
jected onto these cuts. A "box" indicates caustics of the CS2 
vibrational motion prior to the collision. The directions of the 
symmetric and asymmetric stretch normal coordinates (in r 2 , 
r 3 space} are labelledX8 andXA, respectively, in the figure. 
J. Chern. Phys. 71(1), 1 Jul. 1979 0021·9606/79/010542-02$01.00 © 1979 American Institute of Physics 


Characterization of vibrational overtones and "local" modes

by emission spectroscopy

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Characterization of vibrational overtones and "local" modes by emission spectroscopy

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