Jet-Cooled Laser-Induced Fluorescence Spectroscopy of Isopropoxy

Article pubs.acs.org/JPCA

Jet-Cooled Laser-Induced Fluorescence Spectroscopy of Isopropoxy Radical: Vibronic Analysis of B̃−X̃ and B̃ −Ã Band Systems Rabi Chhantyal-Pun,† Mourad Roudjane,† Dmitry G. Melnik,† Terry A. Miller,*,† and Jinjun Liu‡ †

Laser Spectroscopy Facility, Department of Chemistry and Biochemistry, The Ohio State University, 120 West 18th Avenue, Columbus, Ohio 43210, United States ‡ Department of Chemistry and Conn Center for Renewable Energy Research, University of Louisville, 2320 South Brook Street, Louisville, Kentucky 40292, United States ABSTRACT: Recently we published [Liu et al. J. Chem. Phys. 2013, 139, 154312] an analysis of the rotational structure of the B̃ −X̃ origin band spectrum of isopropoxy, which confirmed that the double methyl substitution of methoxy to yield the isopropoxy radical only slightly lifted the degeneracy of the former’s X̃ 2E state. Additionally the spectral results provided considerable insight into the relativistic and nonrelativistic contributions to the experimental splitting between the components of the 2E state. However, left unexplained was how the Jahn−Teller (JT) vibronic coupling terms within methoxy’s 2E state manifest themselves as pseudo-Jahn−Teller (pJT) vibronic coupling between the Ã 2A″ and X̃ 2A′ levels of isopropoxy. To cast additional light on this subject we have obtained new isopropoxy spectra and assigned a number of weak, “forbidden” vibronic transitions in the B̃ −X̃ spectrum using new electronic structure calculations and rotational contour analyses. The mechanisms that provide the nonzero probability for these transitions shed considerable information on pJT, spin-orbit, and Coriolis coupling between the Ã and X̃ states. We also report a novel mechanism caused by pJT coupling that yields excitation probability to the B̃ state dependent upon the permanent dipole moments in the B̃ and Ã or X̃ states. By combining a new B̃ −Ã and the earlier B̃ −X̃ rotational analyses we determine a much improved value for the experimental Ã −X̃ separation.

1. INTRODUCTION Alkoxy radicals are important intermediates in the oxidation of alkanes in the atmosphere. Large quantities of volatile organic compounds (VOCs) are emitted into the atmosphere each year by biogenic and anthropogenic sources. Methane forms the largest fraction of the VOC emission. Other light alkanes, like ethane and propane, form the largest fraction of the nonmethane saturated hydrocarbon emission.1,2 Methoxy radical (CH3O), the simplest of the alkoxy radicals, is formed as an intermediate in the oxidation of methane. Similarly, ethoxy (C2H5O) and isopropoxy (i-C3H7O) radicals are formed as intermediates in the oxidation of ethane and propane, respectively. Ethoxy is the simplest primary alkoxy radical whereas isopropoxy is the simplest secondary alkoxy radical. Alkoxy radicals are also of significant spectroscopic importance. The ground electronic state of the methoxy radical (X̃ 2E) is subject to both Jahn−Teller effect (JTE) and spinorbit interaction induced by the unpaired electron.3 It is one of the most extensively studied free radicals and has attracted much attention from both experimentalists and theoreticians (see, for example, ref 3 and references therein). Our group reported recently high resolution laser-induced fluorescence (LIF), stimulated emission pumping (SEP), and microwave © XXXX American Chemical Society

experiments on methoxy and fully deuterated methoxy (CD3O) resulting in precise determination of rotational, spin-rotational, and Coriolis constants. Analysis of the results from these isotopologues allowed for benchmarking of ab initio calculations and Jahn−Teller parameters. 4,5 The vibrational degeneracy of the ground state of methoxy can be lifted by asymmetric deuteration (CHD2O and CH2DO) which changes the JTE to the pseudo Jahn−Teller effect (pJTE). Submillimeter-wave, LIF, and SEP studies have shown that the asymmetric deuteration splits the vibrationless level into two levels with A′ and A″ vibronic symmetries.6 The ground vibronic level was determined to be of A′ symmetry, and the magnitude of the splitting was found to be 43 cm−1 for CHD2O. Similarly, the splitting magnitude was determined to be 46 cm−1 in CH2DO, but the symmetries of the split levels were found to be reversed. The reversal of the energy levels was attributed to a zero point energy (ZPE) effect. Global analysis of all four isotopologues provided valuable information about Special Issue: David R. Yarkony Festschrift Received: May 2, 2014 Revised: July 22, 2014

A

dx.doi.org/10.1021/jp504322j | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

Article

therein. The higher resolution afforded by the LIF method compared to the previously used DF method allows for simultaneous rotational contour analysis of the B̃ −X̃ and the B̃ −Ã transitions and a precise determination of the Ã −X̃ separation, as well as rotational and spin-rotational parameters for the Ã state.

isotopic breaking of vibronic symmetry and its ramification for the JTE. Similar to the isotopic substitution study of methoxy radical, study of different methyl derivatives of the methoxy radical is desirable for a global understanding of electronic structure and vibronic interaction in alkoxy radicals. Asymmetric methyl substitution of methoxy radical to give an ethoxy radical, analogous to asymmetric deuteration, lifts the vibronic degeneracy of the ground state by modifying the vibrational kinetic energy operator. In addition, methyl substitution lifts the electronic degeneracy of the ground state. The experimental splitting of the two lowest vibronic levels in ethoxy radical has been reported to be 364 cm−1 and 355(10) cm−1 by dispersed fluorescence7 (DF) and photoelectron studies,8 respectively. Double methyl substitution of methoxy gives the isopropoxy radical. The ground state splitting of isopropoxy has been reported to be much smaller, 68(10) cm−1 by DF studies.9 Rotational analyses for the B̃ −X̃ LIF spectra for ethoxy and isopropoxy radicals have shown that the lowest (hereafter called X̃ ) state in these two radicals to be of A″ and A′ symmetries,10,11 respectively. The reversal of the symmetry of the ground state has been rationalized in terms of interaction of the in-plane π orbital with the methyl group.11,12 The in-plane π orbital is expected to be lowered by stronger interaction with the methyl group in ethoxy compared to the out-of-plane π orbital. The in-plane π a′ orbital is completely filled whereas the out of plane π a″ orbital is half filled, resulting in a ground X̃ 2A″ state and a low-lying Ã A′ state. The interaction of the in-plane π orbital with the hydrogen atom is expected to be small in isopropoxy. The out-of-plane a″ π orbital has better overlap with the methyl group and hence is lower and completely filled, giving rise to a X̃ 2A′ state. However, the interaction is modest as the orbital does not point directly to the methyl groups giving rise to a smaller splitting in isopropoxy than ethoxy. Recently, rotationally resolved LIF spectra of the B̃ −X̃ 000 transition of isopropoxy has been analyzed in detail with a coupled state (2-fold) model which takes into account pJT mixing of the diabatic X̃ and Ã states and spin−vibronic interactions resulting in very accurate rotational, spin-orbit, and Coriolis constants for both the X̃ and B̃ states.13 This work has also resulted in a firm foundation for understanding two previously unanalyzed portions of the isopropoxy LIF spectrum which can provide additional information about the B̃ , Ã , and X̃ state and the pJT vibronic mixing among them. One of the hitherto unexplained spectral features is a series of incompletely analyzed, weak, “forbidden” B̃ −X̃ vibronic transitions. A moderate resolution jet cooled LIF survey spectrum for the B̃ −X̃ transition of isopropoxy reported previously by Carter et al.14 was dominated by a strong progression in the CO stretch mode assigned up to υ = 7. Some of the weak, low frequency vibrations were also tentatively assigned based on the results of contemporary ab initio calculations and a model of a transition between isolated electronic states. The assignments of these transitions as well as other newly identified ones are now revisited in the light of new electronic structure calculations, a new model describing the effects of pJTE coupling among the B̃ , Ã , and X̃ levels and making use of newly recorded rotational contours that reflect the coupling mechanisms. An LIF spectrum for the B̃ −Ã transition of isopropoxy is reported for the first time in this paper. The rotational analysis of these bands complements the previous B̃ −X̃ study and provide a further test for the coupled-state model developed

2. EXPERIMENTAL SECTION The experimental setup is similar to the one described previously.15−18 The precursor, isopropyl nitrite, from a reservoir immersed in a −20 °C bath was expanded through a pinhole nozzle with helium backing pressure to create a supersonic jet into a vacuum chamber which was evacuated by a mechanical booster pump backed by a rotary oil pump. The size of the nozzle orifice and the backing pressure define the temperature of the jet. For a hard, “cold” expansion (≈ 1 K rotational temperature), a 0.5 mm nozzle orifice was used with 80/120 psi pressure of helium, and for a mild, “warm” expansion (≈ 50 K rotational temperature), a 1 mm orifice was used with 5 psi backing pressure of helium. Approximately, 50 mJ/pulse of 351 nm laser beam produced from a XeF excimer laser was focused at the throat of the expansion to photolyze the O−N bond of the precursor molecule. The resulting fragment, isopropoxy radical, was probed by UV radiation ( >⎢ s ⟨χi Γ |qs|KjΓ⟩ + a ⟨χi Γ |qa|KjΓ′⟩⎥ ⎣ ΔU ⎦ ΔU

(A.19a)

μb , c = ⟨Φ Bj (a′)|μb , c |Φ0(a′)⟩ − Yj0′⟨μb , c ⟩XÃ ̃ + X 0j⟨μb , c ⟩B̃

for Γ ≠ Γ′ because ΔU ≫ Ka′ or K′s . Hence it is generally reasonable to drop this term if ⟨Ã A″|μa|X̃ A′⟩ is not much greater than ⟨B̃ A′|μa|X̃ A′⟩. Reference to Table A.3 shows these two matrix elements of μa are comparable, so this term can be neglected. Similar arguments can be made in the case of μb,c for the magnitude of the coefficient of the FC term versus that of the second and third terms representing the PDM contribution. However, as Table A.3 makes clear the change in the PDM is much greater than the B̃ −X̃ transition moment so the PDM term cannot be neglected for μb,c. However, it can be simplified by noting the following. The matrix element involving qa in eq A.22b and qs in eq A.23b connects to a doubly excited level v1s v1a while the qs matrix in eq A.22b connects to q1s q0a, which makes it significantly larger, as is verified by the numerical results in Table A.2. Thus, we neglect the qa terms in eq A.22b and by a similar argument the qs term in eq A.23b. This approximation allows the factoring of the remaining matrix element of a coordinate to combine the second and third terms of eq A.22b and eq A.23b and write it as proportional to the change in the PDM between the B̃ and X̃ states. Applying these approximations to eqs A.22a, A.22b and A.23a, A.23b allows us to obtain considerably simpler expressions for the μα. These simpler expressions are given in eqs 13a, 13b and 14a, 14b of the text.

(A.19b)

and for the transitions to the a″ level in the B̃ state, ̃ ″|μ |XA ̃ ′⟩ μa = ⟨Φ Bj (a″)|μa |Φ0(a′)⟩ − Yj0″⟨AA a

(A.20a)

μb , c = ⟨Φ Bj (a″)|μb , c |Φ0(a″)⟩ − Yj1″⟨μb , c ⟩XÃ ̃ + X1j⟨μb , c ⟩B̃ (A.20b)

where we have made use of relationships, ̃ ′|μ |AA ̃ ″⟩2 = ⟨BA ̃ ′|μ |XA ̃ ′⟩2 + ⟨BA ̃ ′|μ |XA ̃ ′⟩2 ⟨BA c a b

(A.21a)

⟨Φ Bj |μα |ΦmB⟩ = ⟨μα ⟩B δj , m

(A.21b)

⟨μα ⟩A ≈ ⟨μα ⟩X

(A.21c)

⟨χk ′|χi ′⟩ + ⟨χk ″|χi ″⟩ = δi , k

(A.21d)

The numerical values of the X and Y factors depend on the strength of the pJT interaction within the ground manifold defining the form of the |χ⟩ cofactors, the strength of the pJT coupling, Ks′, and the quantum numbers of the upper level j on which the transition terminates. For transitions to the a′ levels, eq A.19a,A.19b expands as ⎡ ⎛ K′ ̃ ′|μ |AA ̃ ″⟩⟨κj′|χ ′⟩ − ⎜ s ⟨χ ′|q |κj′⟩ μa = ⎢⟨BA a 1 ⎝ ΔU 1 s ⎣ ⎤ ⎞ K′ ̃ ″|μ |XA ̃ ′⟩⎥Vj ,00 + a ⟨χ1 ″|qa|κj′⟩⎟⟨AA a ⎠ ⎦ ΔU

Numerical Estimates

Equations A.22a, A.22b and A.23a, A.23b give expressions for the TDM components in terms of parameters of the X̃ , Ã 2-fold Table A.1. Overlap Integrals between the B̃ State Vibrational Eigenfunction and the Vibrational Cofactors of the X̃ and Ã States

(A.22a)

⎡ ⎛ K′ ̃ ′|μ |XA ̃ ′⟩⟨κj′|χ ′⟩ − ⎜ s ⟨χ ′|q |κj′⟩ μb , c = ⎢⟨BA 0 b,c ⎝ ΔU 0 s ⎣ ⎞ K′ + a ⟨χ0 ″|qa|κj′⟩⎟⟨μb , c ⟩XA + ⎠ ΔU ⎤ Ks′ ⟨κj′|qs|χ0 ′⟩⟨μb , c ⟩B ⎥Vj ,00 ⎦ ΔU

⎡ ⎛ K′ ̃ ′|μ |AA ̃ ″⟩⟨κj″|χ ″⟩ − ⎜ s ⟨χ ″|q |κj″⟩ μa = ⎢⟨BA 0 a ⎝ ΔU 0 s ⎣

μb , c

⎤ ⎞ Ka′ ̃ ″|μ |XA ̃ ′⟩⎥Vj ,00 ⟨χ0 ″|qa|κj″⟩⎟⟨AA a ⎠ ⎦ ΔU

|Φ⟩

⟨κ|χ0′⟩

⟨κ|χ0″⟩

⟨κ|χ1′⟩

⟨κ|χ1″⟩

0° 101 261

0.927 0.066 0

0 0 0.216

0.694 −0.164 0

0 0 0.650

Table A.2. Matrix Elements of qk between the B̃ State Vibrational Eigenfunction and the Vibrational Cofactors of the X̃ and Ã States

(A.22b)

Similarly, eq A.20a,A.20b for transitions terminating on a″ levels is expanded as

+

(A.24)

(A.23a)

⟨κ|

⟨κ|q10|χ0′⟩

⟨κ|q10|χ1′⟩

⟨κ|q26|χ0″⟩

⟨κ|q26|χ1″⟩

⟨0°| ⟨101| ⟨κ|

0.047 0.684 ⟨κ|q26|χ0′⟩

−0.116 0.503 ⟨κ|q26|χ1′⟩

0.153 −0.075 ⟨κ|q10|χ0″⟩

0.460 −0.034 ⟨κ|q10|χ1″⟩

⟨261|

0.921

0.585

−0.075

−0.034

vibronic eigenfunctions and the B̃ state product electronicvibrational eigenfunctions. Vibronic interaction within the ground 2-fold is not weak;13 therefore, expressions for |χΓi ⟩ were obtained by direct diagonalization of the X̃ , Ã subblock of the Hamiltonian eq A.1a−A.1d. This is equivalent to performing the transformation, e−iS″, on the primitive basis set, eq A.3. On the other hand, the vibrational cofactors for the upper state levels are simple products of one-dimensional vibrational basis functions corresponding to the normal modes of the B̃ state. The standard vibrational matrix elements of the operator q̂s or q̂a, eqs A.22a, A.22b and A.23a, A.23b, can be obtained using orthogonality relationships and expressions for

⎡ ⎛ K′ ̃ ′|μ |XA ̃ ′⟩⟨κj″|χ ″⟩ − ⎜ s ⟨χ ″|q |κj″⟩ + = ⎢⟨BA 1 b,c ⎝ ΔU 1 s ⎣ ⎤ ⎞ Ka′ K′ ⟨χ1 ′|qa|κj″⟩⎟⟨μb , c ⟩XA + a ⟨κj″|qa|χ1 ′⟩⟨μb , c ⟩B ⎥Vj ,00 ⎦ ⎠ ΔU ΔU (A.23b)

Equations A.22b and A.23b are relatively general but also relatively complicated. Given the imprecision with which some of the parameters are known, it makes sense to neglect some of the smaller terms in the present case. Considering the expression for μa we see that Q



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ACKNOWLEDGMENTS The authors are pleased to acknowledge the support of parts of this research by the National Science Foundation via Grant No. CHE-1012094. J.L. acknowledges financial support from the American Chemical Society Petroleum Research Fund in the form of a Doctoral New Investigator (Grant 53476-DNI6). The authors also acknowledge a grant of computer time from the Ohio Supercomputer Center.

Table A.3. Calculated (UB3LYP with 6-31G+d Basis) Values (in Debye) of the Components of the Electronic TDM X̃

Ã

X̃

Ã

B̃

μa = 0 μb = 1.92 μc = 0.67

μa = 0.434 μb = 0 μc = 0 μa = 0 μb = 1.92 μc = 0.67

μa = 0 μb = 0.066 μc = 0.191 μa = 0.201 μb = 0 μc = 0 μa = 0 μb = 4.13 μc = 0.91

B̃

■

⟨κ| = ⟨v10,v26| ⟨0,0|

⟨1,0|

⟨0,1|

μa μb μc

0.139 0.055 0.174

−0.033 0.062 0.020

0.043 0.090 0.130

the matrix elements32 of the position coordinate for a harmonic oscillator. To obtain numerical values for the TDM components, assumptions need to be made for the vibronic coupling parameters, K, within the 2-fold and between the 2-fold and the B̃ state. We used the 2-fold parameters obtained from fitting the adiabatic potential energy surface in our earlier work13 and the experimental vibrational frequencies of ν10 = 950 cm−1, ν26 = 357 cm−1. However, the assumption that all pJT activity is localized in the pair of modes (ν10,ν26) failed to predict the ratios of the components of TDM for 1010 and 2610 and also resulted in a large overestimation of these band intensities. This inconsistency was resolved by reducing all linear pJT parameters by about factor of 2, to K0s = −150 cm−1, K1s = 218 cm−1, Ka = 154 cm−1 while keeping second order pJT parameters and Kk′ parameters unchanged. The resulting values of ⟨κΓj ′|χΓi ″⟩ and ⟨κΓj ′|qk|χΓi ″⟩ are summarized in Tables A.1 and A.2. Values of the K′ parameters are chosen to give reasonable estimates of both the overall band intensities and the ratio of the components of the TDMs, which resulted in values of Ks′ = Ka′ ≈ 950 cm−1, and corresponding values of K10′/ΔU = K26′/ ΔU ≈ 0.035, assuming ΔU = 27 000 cm−1. In all three cases we note that the second term in parentheses for μa in eqs A.22a and eq A.23a is at least an order of magnitude smaller than the leading FC term and can be neglected. Calculated values of the TDM and PDM are listed in Table A.3 and their method of calculation is detailed in section 3.1. The results of Tables A.1− A.3 are combined according to eqs A.22a, A.22b and A.23a, A.23b to yield the estimated vibronic TDM component values given in Table A.4.

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REFERENCES

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Table A.4. Estimated Relative Values of the Components of the TDM for the Three Categories of the Vibronic Transitions, With Factor Vj,00 Excluded TDM

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Corresponding Author

*E-mail: [email protected]. Phone: 614-292-2569. Fax: 614292-1685. Notes

The authors declare no competing financial interest. R



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Jet-Cooled Laser-Induced Fluorescence Spectroscopy of Isopropoxy

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