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Infrared spectrum of tbutyl hydroperoxide excited to the 4νOH vibrational overtonelevelP. R. Fleming and T. R. Rizzo Citation: The Journal of Chemical Physics 95, 1461 (1991); doi: 10.1063/1.461060 View online: http://dx.doi.org/10.1063/1.461060 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/95/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Vibrational overtone spectroscopy of the 4νOH+νOH’ combination level of HOOH v i a sequential localmode–local mode excitation J. Chem. Phys. 96, 5659 (1992); 10.1063/1.462665 Vibrationally mediated photodissociation of tbutyl hydroperoxide: Vibrational overtone spectroscopy andphotodissociation dynamics J. Chem. Phys. 90, 6266 (1989); 10.1063/1.456343 Unimolecular reactions near threshold: The overtone vibration initiated decomposition of HOOH (5νOH) J. Chem. Phys. 84, 1508 (1986); 10.1063/1.450496 A theoretical analysis of photoactivated unimolecular dissociation: The overtone dissociation of tbutylhydroperoxide J. Chem. Phys. 81, 455 (1984); 10.1063/1.447325 A search for modeselective chemistry: The unimolecular dissociation of tbutyl hydroperoxide induced byvibrational overtone excitation J. Chem. Phys. 77, 4447 (1982); 10.1063/1.444447
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Infrared spectrum of t-butyl hydroperoxide excited to the 4VOH vibrational overtone level
P. R. Fleming and T. R. Rizzo Department a/Chemistry, University 0/ Rochester, Rochester, New York 14627
(Received 2S February 1991; accepted 19 April 1991)
The infrared predissociation spectrum of t-butyl hydroperoxide excited to the 4VOH level reveals extensive mixing between the zeroth-order OH stretch state and nearly isoenergetic zeroth-order dark states. Because most of these dark states have an OH stretch quantum number of zero, the predissociation spectrum strongly resembles the infrared spectrum of an unexcited molecule. The observed intensity distribution in the predissociation spectrum is what one would expect if the eigenstates prepared by 4VOH vibrational overtone excitation were statistical mixtures of all the nearly isoenergetic zeroth-order states.
I. INTRODUCTION
Over the last decade, intense effort has been directed toward understanding the intramolecular processes that occur upon excitation of light atom stretch overtone transitions. ' -
25 In the time domain, intramolecular vibrational energy redistribution (lVR) from these highly excited levels can be viewed as a dynamical process in which energy flows out of the light atom stretch into other vibrational modes. In the frequency domain, IVR manifests itself as an interaction between zeroth-order vibrational states that results in spectral splittings and mixed wave functions. To fully characterize the IVR process, one needs to know the identity of the zeroth-order dark states that mix with the X-H stretch state (i.e., the zeroth-order bright state) and the matrix elements responsible for the mixing. Highly resolved absorption spectra can determine the number of coupled states and the coupling matrix elements by directly resolving the spectral splittings of the zeroth-order states. 2
6--28 Infrared absorption or emission spectra subsequent to vibrational excitation can determine the extent of state mixing and the identity of the coupled zeroth-order states. 29
-32 Although very powerful,
this latter technique has been applied almost exclusively to molecules excited via vibrational fundamentals inasmuch as the small oscillator strength of vibrational overtone transitions makes direct infrared absorption or emission studies subsequent to overtone excitation extremely difficult. 32
We have recently developed an optical-infrared double resonance method in which we monitor the infrared absorption of a molecule subsequent to overtone excitation by spectroscopically detecting predissociation products. 25
,33 The resulting infrared predissociation spectrum provides information about the extent of vibrational state mixing and the identity of the zeroth-order dark states that mix at the excited overtone level. For example, if the zeroth-order bright state for a 41'XH stretch overtone transition in a polyatomic molecule is unmixed, the infrared predissociation spectrum in the X-H stretch region will contain a single band at the 5 ..... 4 X-H stretch frequency. If the zeroth-order 4~'XH stretch couples to nearly isoenergetic dark states, the resulting mixed eigenstates can contain zeroth-order components with X-H stretch quantum number n ranging from
o to 4. Because each zeroth-order component of an eigenstate can provide oscillator strength for an infrared transition in the X-H stretch mode, the infrared predissociation spectrum may contain vibrational bands at the 4 ..... 3,3 ..... 2, 2 <-1, and 1 ..... 0 X-H stretch frequencies in addition to the S ..... 4 X-H stretch transition. The members of this vibrational progression will be separated by approximately twice the X-H anharmonicity, or ~ 100-200 cm- I
. An infrared predissociation spectrum subsequent to excitation of a vibrational overtone level can therefore classify the coupled zeroth-order states by the their X-H stretch quantum number and determine how much they contribute to the mixed eigenstate. If vibrational mixing of an overtone level is extensive, the eigenstates prepared by overtone excitation will contain many zeroth-order components, some of which will have the same value of n. While infrared transitions that derive oscillator strength from zeroth-order components with different n will be well separated, transitions that arise from zeroth-order states with the same n will be clumped together. In this case, the integrated clump intensity reflects the total contribution to the eigenstate from zeroth-order states with a particular value of n.
Application of this optical-infrared double resonance method to HOOH-H and HON02
25 has revealed radically different state mixing behavior for these two molecules. The zeroth-order 4VOH level of HOOH is nearly a single vibrational eigenstate (i.e" shows very little state mixing). 33 Consequently, the predominant feature in the infrared predissociation spectrum subsequent to 4VOH excitation in this molecule is the transition that derives oscillator strength from the zeroth-order state with n = 4. In contrast, the zeroth-order 4VOH bright state in HON02 is distributed among at least 30 eigenstates, with no one eigenstate containing more than 3% bright state character. 25 The infrared spectrum subsequent to 4VOH excitation in this molecule reveals a progression of vibrational bands separately by ~ 150 cm - I (twice the OH stretch anharmonicity) which correspond to transitions from zeroth-order states with a range of n values. The relative intensities of these bands are close to what one would expect if the eigenstates prepared by 4VOH
excitation were statistical mixtures of all the zeroth-order states nearly isoenergetic with the 4VOH bright state.
J. Chem. Phys. 95 (3), 1 August 1991 0021-9606/91/151461-05$03.00 @ 1991 American Institute of PhYSics 1461 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
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1462 P. R. Fleming and T. R. Rizzo: t-butyl hydroperoxide
This report describes results from applying our opticalinfrared double resonance technique to investigate vibrational state mixing at the 4VOH level of t-butyl hydroperoxide. If the difference in state mixing characteristics between HOOR and RON02 is determined primarily by their relative vibrational state densities at the 4VOH energy (4 vs 150, respectively), then t-butyl hydroperoxide, with a state density of _10 10
, should represent an extreme case. Moreover, if the relative band intensities in the infrared predissociation spectrum of t-butyl hydroperoxide reflect a statistical mixture of all the nearly isoenergetic zeroth-order states (as they seem to in HON02 ), then the spectrum will resemble an ordinary infrared spectrum of the ground state molecule, since greater than 99% ofthe zeroth-order states at the 4VOH energy have OH quantum number n = O.
II. EXPERIMENTAL APPROACH
A previous publication describes the experimental approach in detai1.25 A Nd:YAG pumped dye laser, operating on LOS 751 laser dye, generates 25 mJ pulses in a 0.2 cm - I
bandwidth to excite t-butyl hydroperoxide molecules via the 4 ..... 0 OH stretch vibrational overtone transition at 13 303 cm- I
. Thirty nanoseconds later, 1-3 mJ pulses from a 1 cm- I bandwidth Nd:YAG pumped optical parametric oscillator (OPO) induce infrared transitions from the mixed 4VOH level to quasibound eigenstates above the 44 kcal/mol dissociation threshold. 34 After an 800 ns delay from the infrared pulse, the frequency doubled output of a second Nd:Y AG pumped dye laser probes the OH dissociation products via laser-induced fluorescence (LIF) in the A-X band. This long delay is needed to accommodate the relatively slow unimolecular dissociation of t-butyl hydroperoxide. At the sample pressures of 10-60 mTorr employed here, there are no collisions in the 30 ns between the overtone pump pulse and infrared predissociation pulse. An infrared predissociation spectrum of the vibration ally excited molecules results from collecting the total LIF signal of the OH products as a function of the OPO frequency. For comparison with this infrared predissociation spectrum, we use our OPO to record a photoacoustic spectrum of ground state tbutyl hydroperoxide over the same spectral region. Commercially available 90% t-buty I hydroperoxide (Aldrich), which contains 5% t-butyl alcohol and 5% water, was used without purification.
Because the overtone excitation laser has a 0.2 cm - I
bandwidth, we initially prepare vibrationally excited molecules in a distribution of rotational states. Moreover, vibrational state mixing, if present, may distribute each zerothorder rovibrational state among several vibrational eigenstates, and our overtone excitation laser may overlap transitions to more than one of these eigenstates. The conclusions we draw from the infrared predissociation spectrum therefore pertain to a weighted average over all the eigenstates excited. However, as we have discusssed previously,25.33 the infrared predissociation spectrum provides an upper limit for the amount of bright state character contained in any of the eigenstates that fall within the laser bandwidth.
III. RESULTS AND DISCUSSION
Figure 1 (a) shows an infrared predissociation spectrum of vibrationally excited t-butyl hydroperoxide generated by first exciting the molecules to the 4VOH level and then scanning the OPO frequency while detecting the OH dissociation products via LIF. There are three major features in this spectrum. The highest energy feature occurs at 3590 cm - I, and we assign this band to a collection of 1 ..... 0 OR stretch transitions from the mixed eigenstates prepared by vibrational overtone excitation. The other two major features in Fig. 1 (a) appear at 2979 and 2935 cm - I, and we attribute them to 1 ..... 0 CH stretch transitions. Figure 1 (b) shows a photoacoustic spectrum of ground state t-butyl hydroperoxide in the same spectral region. All three major features in the infrared predissociation spectrum of the vibrationally excited molecule [Fig. 1 (a)] occur at essentially the same frequency as the corresponding features of the unexcited molecule [Fig. 1 (b) ] , verifying our spectral assignments. The similarity of the doublet structure in the C-H stretch region of the two spectra indicates that the splitting in Fig. 1 (a) is not a consequence of the initial vibrational excitation, but rather a spectral signature ofthe t-butyl moiety. 35.36 There appears to be a small feature in the infrared predissociation spectrum -100cm -I to the red of the l ..... OOH stretch transition, and this may result from An = 1 transitions from zeroth-order states with n = 0, but with one or more quanta of low frequency vibration. It could also be a low frequency combination band built upon the CH stretch transition. Notably absent from this spectrum is a clear progression ofOH stretch bands spaced by twice the OH stretch anharmonicity ( - 180 cm - I) originating from zeroth-order states with different OH stretch quantum numbers.25
The lack of transition intensity in the region of the 5 ..... 4 OH stretch transition (2887 cm- I
) indicates that the zeroth-order bright state (i.e., the zeroth-order state with n = 4) makes no more than - 2 % contribution to the mixed molecular eigenstates prepared by 4VOH excitation. Moreover, the absence of an OH stretch progression and the similarity of the infrared predissociation spectrum of the vibrationally excited molecule and the photoacoustic spectrum of the ground state molecule indicate that on the average, the largest collective contribution of zeroth-order states to the mixed molecular eigenstates prepared by 4VOH vibrational overtone excitation are those with zero quanta of OH stretch. It is enlightening to compare the observed intensity pattern to that which would result if all the zeroth-order states near the 4VOH energy contributed equally to the eigenstates prepared by vibrational overtone excitation. To make this comparison, we first estimate the total density of states at the4vQH energy, and then, by a procedure described in the Appendix, we determine the fraction of zeroth-order states with each value of the OH stretch quantum number n. Of the 1. 6 X 10 10 vibrational states per cm - I at the 4VOH energy, only 1.2 X 10K have n = 1, and even fewer have n> 1. Because greater than 99% of the zeroth-order dark states nearly isoenergetic with the 4VOH level have n = 0, if each state in a small range about the 4VOH energy contributes equally to the eigenstates prepared by vibrational overtone excitation, the infrared predissociation spectrum will strongly resemble
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P. R. Fleming and T. R. Rizzo: t-butyl hydroperoxide 1463
(a) infrared spectrum subsequent to 4VOH excitation If-OCR
If-O OR
(b) photoacoustic spectrum
_. ___ ..... _ ....... _____ . __ =-~.£~~~_=...f:::._==_~~=__=_""""'''__o:::_== __ ~_'''' __ ==_~_.=--____ ""' .. ~. __________ ... __ :.. _ _:, __
3600 3400 3200 3000 2800
OPO Wavenumber (em-I)
FIG. I. (a) Infrared predissociation spectrum of t-butyl hydroperoxide subsequent to 4VOH excitation. The overtone excitation frequency was 13 303 cm - I
and the cell pressure was 60 mTorr. The apparent structure on the 1-0 OH band results from dips in the OPO power resulting from atmospheric water absorption. (b) Photoacoustic spectrum of ground state t-butyl hydroperxide. The pressure in the photoacoustic cell was ~ 10 Torr. The small sharp features in the spectrum arise from well-known photoacoustic transitions of water which is a 5% impurity in the t-butyl hydroperoxide sample.
the infrared absorption spectrum of the ground state molecule.
The infrared predissociation spectrum of Fig. 1 (a) is therefore precisely what one expects if the eigenstates prepared by vibrational overtone excitation were statistical mixtures of all zeroth-order states at the 4VOH energy. The observation of such a pattern does not imply that all zeroth-order states contribute equally to the mixed molecular eigenstate, but rather it indicates that the vibrational mixing does not discriminate on the basis of the OH stretch quantum number. Since we only observe spectra in the OH stretch region of the infrared, our results provide no information on the distribution of other vibrational quantum numbers in the mixed 4VOH eigenstates. However, because of the large frequency mismatch between the OH stretch and and other vibrational modes, one expects that this high frequency motion would be the most poorly coupled to the rest of the molecule. If the vibrational mixing does not discriminate on the basis of the OH stretch quantum number, it is not
likely to discriminate with respect to the number of quanta in lower frequency vibrational modes. If this is indeed the case, the chemistry of a large molecule excited via a vibrational overtone transition will differ little from one excited thermally.
An intriguing aspect of the infrared predissociation spectrum of Fig. 1 (a) is the relatively narrow linewidth of the 1 ..... 0 CH stretch transition at 2979 cm - I. Although this transition (together with the initial overtone excitation) prepares molecules with approximaty 16 280 cm - 1 of vi brational energy, its ~ 17 cm - 1 linewidth is several times smaller than that of most direct C-H stretch vibrational overtone transitions at equivalent energies.4
•3
6-41 The double resonance nature of our excitation scheme will simplify the rotational contour of the transition somewhat, even though the 0.2 cm - 1 overtone excitation laser bandwidth is not sufficiently narrow to select individual rotational states. Thus, even though the states accessed via our 4 ..... 0 OH, 1 ..... 0 CH double resonance excitation are different in vibrational char-
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1464 P. R. Fleming and T. R. Rizzo: t-butyl hydroperoxide
acter from those reached by direct overtone excitation from the ground state, the observation of 17 cm - I wide resonances at this energy suggests that much of the broadening observed in vibrational overtone spectra oflarge molecules is inhomogeneous in nature and could in principle be eliminated.
ACKNOWLEDGMENTS
We gratefully acknowledge the support of this work by the Office of Basic Energy Sciences of the Department of Energy and the Donors of the Petroleum Research Fund, administered by the American Chemical Society
APPENDIX: DENSITY OF STATES CALCULATION
We use the Whitten-Rabinovitch approximation42•43 to
estimate the total density of zeroth-order vibrational states I
at the 4VOH energy and then break this total state density down according to the OR stretch quantum number n. The density of states at the 4VOH energy with n = 3, which we will call Pn = 3 (En = 4)' is simply the total state density at 3053 cm - I, the difference between the energies of the 4VOH and 3vOH levels (calculated using the Birge-Sponer parameters44 A = 3690, B = 91). Thus
The density of states with n = 2 at the 4VOH energy Pn = 2 (En = 4) is the total state density at an energy corresponding to the difference between the 4VOH and 2VOH levels minus Pn = 3 (En = 4):
Pn=2(En=4) =P(En=4 -En=2) -Pn=3(En=4)
= p(6288 cm- I) - p(3053 cm- I
).
We apply a similar approach to determine the density of states with n = 1 and 0:
Pn=I(En=4) =P(En=4 -En=I) -Pn=3(En=4) -Pn=2(En=4)
= p(9705 cm- I) - p(3053 cm- I
) - [p(6288 cm- I) - p(3053 cm- I
) 1
= p(9705 cm- I ) - p(6288 cm- I )
and
Pn=O (En =4) =P(En=4 - Ell =0 ) - Pn = 3 (Ell =4) - Pn=2 (En=4) - Pn = I (En=4)
= p(13 304 cm- I) - p(3053 cm- I
)
- [p(6288cm- I) -p(3053cm- I)] - [(p(9705cm- I) -p(6288cm- I)]
=p(13 304cm- I) -p(9705 cm- I
).
This breakdown scheme for the density of zeroth-order states neglects only off-diagonal anharmonicities (as is done by most state counting routines), although in using the Whitten-Rabinovitch procedure, we neglect diagonal anharmonicities as well. We obtain vibrational frequencies of the t-butyl group from Snyder and Schachtschneider45 and estimate those of the hydroperoxyl moiety by analogy to similar compounds.46 We make no attempt to treat explicitly the hindered methyl rotations, but rather consider them as harmonic low frequency modes.
While the total vibrational density of states calculated in this way is likely to be substantially in error, the relative number of zeroth-order states with each value of n will be insensitive to the details of the state counting method. The large ratio of the number of zeroth-order states with n = 1 depends on the slope of P (E) in the region of the 4VOH energy. For any large polyatomic molecule, peE) will have a sufficiently steep slope that the zeroth-order states with n = 0 will far outnumber those with n > O.
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