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.

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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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