Characterization of ν3 Vibrational Levels in S0 Formyl Fluoride Using Dispersed Fluorescence Spectroscopy

Journal of Molecular Spectroscopy 210, 98–109 (2001) doi:10.1006/jmsp.2001.8435, available online at http://www.idealibrary.com on

Characterization of ν3 Vibrational Levels in S0 Formyl Fluoride Using Dispersed Fluorescence Spectroscopy Karen E. Hahn, Katie M. Horsman, and William F. Polik1 Department of Chemistry, Hope College, Holland, Michigan 49423 Received June 19, 2001; in revised form August 6, 2001

The harmonic frequency and anharmonic constants of the CH bend (ν3 ) of formyl fluoride (HFCO) have been determined using the technique of dispersed fluorescence spectroscopy. Sample molecules were cooled in a supersonic expansion and excited to low J0 , Ka0 = 0 rotational states in the 31 vibrational level of S1 HFCO. The resulting fluorescence to the ground electronic state was dispersed and a 23 000 cm−1 pure vibrational spectrum was recorded. A total of 142 new vibrational assignments were made, which extends the total number of vibrational assignments for S0 HFCO to 382. Of these assignments, 109 involve ν3 with v3 = 1–2. The data were analyzed using a multiresonant Hamiltonian model, which accounts for resonant interactions among C 2001 Elsevier Science nearly degenerate states, with a standard deviation of 4.5 cm−1 . ° Key Words: HFCO; formyl fluoride; dispersed fluorescence spectroscopy; highly excited vibrational states; pure vibrational spectroscopy; multiresonant Hamiltonian; vibrational constants.

shorter progressions were seen in the CF stretch (v4 = 0–2) and FCO bend (v5 = 0–2). The DF spectrum filled the gap between 5000 and 13 000 cm−1 , and its analysis resulted in the assignment of 240 vibrational states. This large increase in the number of assignments is due to the high signal-to-noise ratio, wide spectral coverage, and rapid wavelength scanning of dispersed fluorescence spectroscopy. While knowledge of the excited vibrational state structure of S0 HFCO has increased, progressions in the CH stretch (ν1 ) and CH bend (ν3 ) have not yet been observed. These states can be accessed by DF spectroscopy, shown in Fig. 1, if HFCO is initially excited to S1 vibrational levels with Franck–Condon overlap. In this study, HFCO is excited to the 31 vibrational level, and a 23 000 cm−1 DF spectrum of S0 HFCO was recorded to characterize ν3 and its combination with other vibrational modes. The anharmonic model previously used by Horsman et al. (9) is extended here to explicitly include vibrational resonances. The total number of vibrational assignments of HFCO is increased to 382. Of these assignments, 109 involve the CH bend (ν3 ) with v3 = 1–2. From this information, harmonic and anharmonic constants involving ν3 were determined, leading to a more complete characterization of the HFCO potential energy surface. In addition to expanding the knowledge of HFCO, this information will help to develop and improve theories for calculating the potential energy surfaces of molecules, determining the couplings among vibrational modes, and describing unimolecular dissociation.

1. INTRODUCTION

The excited vibrational level structure of S0 formyl fluoride (HFCO) is of particular interest as formyl fluoride is a prototypical four-atom molecule able to undergo unimolecular dissociation at relatively low energy. The dissociation barrier (1) of 17 000 cm−1 and wide emission spectrum allow access to vibrational levels both above and below the dissociation threshold through various spectroscopic techniques. Highly excited vibrational levels involve nuclear motion that sample the molecular potential energy surface far from equilibrium. Assignment of highly excited vibrational quantum states will permit the testing of recently calculated HFCO potential energy surfaces (2–4), and assist in the development of theories describing the potential energy surfaces of more complex polyatomic molecules. The vibrational spectrum of HFCO has been studied by several groups. Stratton and Nielson (5), Wong et al. (6), and Kattenberg et al. (7) studied the spectrum from 500 to 5000 cm−1 using infrared spectroscopy and assigned 10 vibrational states. Choi and Moore (8) extended the knowledge of the vibrational structure by employing the technique of stimulated emission pumping (SEP) to access levels between 13 000 and 22 550 cm−1 , resulting in 48 new vibrational assignments. Horsman et al. (9) used dispersed fluorescence (DF) spectroscopy to record a spectrum of S0 HFCO from 0 to 22 500 cm−1 . In that study, HFCO was excited to the 62 vibrational level of S1 HFCO, and the resulting fluorescence to the ground electronic state was dispersed. Long Franck–Condon progressions were observed in the CO stretch (v2 = 0–6) and out-of-plane bend (v6 = 0–23), while 1

2. EXPERIMENTAL DETAILS

Formyl fluoride was prepared from formic acid and cyanuric fluoride in acetonitrile according to the method first developed

To whom correspondence should be addressed. E-mail: [email protected].

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FIG. 1. Dispersed fluorescence (DF) technique for HFCO. A laser excites a narrow range of rotational states in 31 S1 HFCO. The resulting fluorescence to vibrational levels below and above the dissociation threshold is dispersed with a monochromator.

by Olah and Kuhn (11). The preparation and purification proceeded in the same manner as described in Horsman et al. (9). The HFCO was stored as a solid at −196◦ C in liquid nitrogen or as a liquid in a −78◦ C freezer until use. Horsman et al. (9) have described the experimental set-up in detail. A summary is given here, noting the details of any changes. A Nd:YAG laser provided 10-Hz 140-mJ pulses at 355 nm which pumped a dye laser with Coumarin 500 dye, giving a 10-mJ pulsed output at 516 nm as measured by an energy detector (Molectron PM101V1). The pulsed output from the dye laser was frequency doubled with a BBO crystal to produce 258-nm light. This ultraviolet light was separated from the undoubled light with prisms and directed into the supersonic jet expansion chamber, where its energy was measured to be 0.9 mJ. The HFCO was vacuum distilled from a storage finger to a Pyrex U-tube, where it was maintained with a constant temperature controller (Neslab Agitainer) at −29◦ C, corresponding to a vapor pressure of 760 Torr. The neat HFCO flowed at its natural 1.0-atm backing pressure into a pulsed nozzle mounted 1 cm above the laser beam in a diffusion pumped vacuum chamber. The HFCO was cooled by supersonic expansion to approximately 40 ± 10 K, as determined by the rotational structure in the fluorescence excitation (FE) spectrum. The laser was tuned to the pQ 1 (J 00 )o branch at 38 769.20 cm−1 to excite the overlapping 101 ← 111 , 201 ← 212, 301 ← 313 rotational transitions in the 31 S1 ← S0 vibronic band (12, 13). The fluorescence excitation intensity was monitored with a photomultiplier tube (PMT) positioned perpendicular to the laser beam and free jet axes, and the signal was integrated, averaged, and sent to a computer for analysis. Filters were placed in front of the PMT to reduce intensity and decrease scattered light. Fluorescence was directed with mirrors and baffles onto an entrance slit 300 µm wide × 1 cm high on a 1.25-m monochromator with a 600 groove/mm holographic diffraction grating. The slit width of 300 µm was chosen to maximize the signalto-noise ratio while still permitting the resolution of adjacent vibrational transitions in spectroscopic progressions. An ordersorting filter was in place for measurements greater than 500 nm.

The fluorescence was measured with an intensified charge coupled device (ICCD) array detector cooled to −40◦ C, which ˚ interval of the spectrum in recorded an approximately 280 A first order. The dispersed fluorescence signal was summed for 2000 accumulations. The fwhm line width was observed to be ˚ which is consistent with the specifications of 3.9 A ˚ for the 4.0 A, monochromator with a 300-µm slit width and 600 groove/mm grating. The DF spectrum was calibrated using an iron hollow cath˚ an ode tube and mercury lamp for wavelengths less than 3200 A and neon–thorium hollow cathode lamp for wavelengths greater ˚ Immediately after each interval of the spectrum than 2800 A. was recorded, a calibration spectrum was taken by reducing the slit width to 50 µm. After both the DF and calibration spectra were taken, the grating was moved to the next interval. The iron, neon, thorium, and mercury peaks were assigned using the MIT Fe wavelength tables (14), the LANL Atlas of the Thorium Spectrum (15), and the CRC Handbook of Chemistry and Physics (16). The standard deviation between the fitted calibra˚ indicating tion lines and their literature positions was 0.060 A, the accuracy of the measurement and calibration procedure. 3. RESULTS AND ANALYSIS

A. Excitation of Ka = 0 31 S1 Formyl Fluoride A fluorescence excitation spectrum was recorded from the ground vibrational state of S0 to the 31 vibrational state in S1 . The C-type FE spectrum, shown in Fig. 2, was assigned using the XASYROT program (17) with ground state spectroscopic parameters from Wong et al. (6) and excited state parameters of A0 = 2.126 cm−1 , B 0 = 0.4011 cm−1 , and C 0 = 0.3389 cm−1 . To record the least congested DF spectrum, the optimal S1 rotational state to excite is 000 , which minimizes the number of possible fluorescing transitions (18). However, as in the case with 62 , the transition to 000 in 31 is weak and partially overlapped by the strong neighboring pQ 1 (J 00 )o branch. The pQ 1 (J 00 )o branch

FIG. 2. Fluorescence excitation (FE) spectrum of 31 S1 HFCO. The 000 rotational level is relatively weak and not well resolved. The intense pQ 1 (J 00 )o branch is used to prepare the 101 , 202 , and 303 states in 31 S1 HFCO.

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much because higher energy excited states fluoresce to higher energy lower states. For A/B-hybrids, there are more transitions, but a similar analysis shows that the fluorescence wavelengths again do not vary much. A quantitative model of the peak-broadening due to excitation of overlapping K a00 = 0 transitions is presented in Horsman et al. (9). At the monochromator resolution used in this experiment, each vibrational state in S0 is associated with a single peak in the dispersed fluorescence spectrum. These DF spectra are called pure vibrational spectra because there is no rotational congestion outside the observed linewidth. The energy of each S0 vibrational level is determined by 00 0 0 00 = E vibronic + E rotational − E fluorescence − E rotational , [1] E vibrational

FIG. 3. Dispersed fluorescence (DF) spectrum recorded from the pQ 1 (J 00 )o branch of the 31 vibrational state of S1 HFCO. The abscissa scale is adjusted to read in S0 rovibrational energy.

was therefore excited, which prepares the 101 , 202 , and 303 states. As discussed in Horsman et al. (9), the DF spectrum from the K a00 = 0 states remains uncongested because higher energy S1 states fluoresce to higher energy S0 states, resulting in a narrow spread of transition frequencies. B. Dispersed Fluorescence Spectroscopy of S0 Formyl Fluoride A 23 000 cm−1 DF spectrum of S0 HFCO was recorded from the pQ 1 (J 00 )o branch of the 31 vibrational state in S1 HFCO and is shown in Fig. 3. The maximum signal-to-noise ratio was calculated to be 100 : 1. This is less than the signal-to-noise ratio of 250 : 1 in previous work (9) due to a combination of a slight decrease in laser energy and substantially weaker fluorescence from the 31 state. However, the 100 : 1 ratio is still high enough to give confidence in the identification of vibronic transitions. Electric dipole selection rules allow only a limited number of transitions from the 101 , 202 , and 303 rotational levels of S1 HFCO down to S0 HFCO. For a near-prolate top like HFCO, the rotational selection rules are 1J = 0, ±1, 1K a = 0, and 1K c = ±1 for an A-type transition; 1J = 0, ±1, 1K a = ±1, and 1K c = ±1 for a B-type transition; and 1J = 0, ±1, 1K a = ±1, and 1K c = 0 for a C-type transition (19). In the S0 –S1 electronic transition of HFCO, A/B-hybrid transitions occur between vibrational states where 1v6 is odd, and Ctype transitions occur between vibrational states were 1v6 is even. For C-type transitions, there are two possible transitions from each of the populated rotational levels of 31 S1 HFCO. The 101 rotational level can fluoresce to only the 212 and 111 rotational levels of S0 HFCO, the 201 level fluoresces to the 312 and 211 , and the 303 level to the 414 and 311 . Although the energies of the excited levels are very different, fluorescence wavelengths do not vary

where the single and double primes represent the upper and lower states, respectively. Using the model developed by Horsman et al. (9), the rotational energy difference for C-type transitions with an even 1v6 is 0 00 − E rotational = −3.24 cm−1 + 0.049v600 cm−1 [2a] E rotational

and with an odd 1v6 is 0 00 E rotational − E rotational = −1.46 cm−1 + 0.023v600 cm−1 . [2b] 0 = Equations [1] and [2], together with the value E vibronic −1 38 769.2 cm , allow the energies of highly excited vibrational 00 , to be determined from observed fluorescence states, E vibrational energies, E fluorescence . The contribution of overlapping rotational transitions to the observed linewidth is substantially less than the instrumental resolution, which is determined by the entrance slit width to be 24.5 cm−1 at 14 000 cm−1 of S0 energy, where the most intense peaks of the spectrum are located. In summary, the narrow rotational structure line width and the selected monochromator bandwidth result in every peak in the DF spectrum corresponding to a different S0 level.

C. Vibrational Assignments HFCO has six normal vibrational modes, which are shown in Fig. 4. S0 vibrational assignments are shown on the DF spectrum in Figs. 5 and 6. These assignments were made by considering energies of the observed states, smoothness of intensity variation within a series, and relative intensities among series. Comparison of peak intensities between this 31 DF spectrum and the previously recorded 62 DF spectrum was useful in identifying states involving ν3 due to differences in Franck–Condon overlap. A combined data set of the peaks assigned previously by Horsman et al. (9) and the peaks assigned in this work is compiled in Table 1. When a peak is observed in both data sets, a straight average is used as the value for the peak position. The standard deviation of the peak position difference is 4.3 cm−1 for the 53 assignments common to both data sets.

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TABLE 1 Vibrational State Assignments and Positions (cm−1 ) for S0 HFCO and Comparison to Multiresonant Hamiltonian Calculated Frequencies Assignment

Frequency

Calculated Frequency

Difference

Assignment

Frequency

Calculated Frequency

Difference

00 61 41 51 21 21 51 21 61 21 41 11 21 52 21 51 61 21 41 51 22 21 62 21 41 61 64 21 52 61 22 51 21 51 62 22 61 22 41 11 21 21 63 22 52 65 22 51 61 22 41 51 23 21 51 63 22 62 22 41 61 22 42 11 21 61 21 64 22 52 61 66 41 65 23 51 21 31 63 22 51 62 22 41 51 61 31 65 23 61 23 41 22 63 22 41 62 22 42 61 23 52 21 65 21 41 64 67 22 31 62 23 51 61 24

0.2 1007.0 1724.7 1836.1 2498.9 2844.1 2895.2 2976.4a 3153.2 3501.7 3547.0 3656.5 3843.0 3899.9 4012.3 4166.7 4307.3 4499.8 4651.9 4706.3 4801.8 4831.2 4959.2 4999.1 5298.7 5353.1 5449.7 5492.6 5645.9 5691.7 5742.1 5796.8 5813.9 5955.3 5979.9 6039.6 6095.4 6186.6 6292.1 6346.4 6346.8 6435.9 6496.0 6627.5 6688.5 6736.1 6748.0 6797.6 6855.1 6958.4 7012.4 7082.9 7224.9

0.0 1010.8 1719.8 1838.3 2498.8 2841.2 2896.5 2981.0b 3161.3 3501.2 3546.0 3654.6 3838.5 3895.8 4010.2 4163.2 4307.8 4498.0 4649.9 4708.1 4818.1b 4830.1 4962.9 4998.7 5302.6 5350.2 5449.6 5489.1 5639.4 5699.7 5744.8 5821.0b 5815.9 5957.2 5981.6 6043.6 6095.4 6192.0 6291.6 6341.4 6345.9 6437.6 6498.4 6623.1 6685.6 6732.8 6743.2 6796.0 6859.7 6958.8 7011.0 7082.9 7224.2

−0.2 3.8 −4.9 2.2 −0.1 −2.9 1.3 4.6c 8.1 −0.5 −1.0 −1.9 −4.5 −4.1 −2.1 −3.5 0.5 −1.8 −2.0 1.8 16.3c −1.1 3.7 −0.4 3.9 −2.9 −0.1 −3.5 −6.5 8.0 2.7 24.2c 2.0 1.9 1.7 4.0 0.0 5.4 −0.5 −5.0 −0.9 1.7 2.4 −4.4 −2.9 −3.3 −4.8 −1.6 4.6 0.4 −1.4 0.0 −0.7

22 51 63 22 41 51 62 23 62 21 51 65 23 41 61 23 42 22 64 22 41 63 23 52 61 21 66 23 31 61 24 51 68 22 31 63 23 51 62 23 41 51 61 21 31 65 24 61 22 51 64 24 41 31 67 23 63 21 51 66 23 41 62 21 41 51 65 24 52 22 65 24 31 41 51 67 23 52 62 21 67 23 31 62 24 51 61 69 22 31 64 25 23 51 63 21 31 66 24 62 22 51 65 24 41 61 22 41 51 64 24 42 23 64 21 51 67 21 41 51 66 24 52 61 22 66 22 41 65 25 51 23 52 63 21 68 23 31 63

7277.9 7326.3 7423.9 7453.6 7483.6 7529.6 7599.7 7663.3 7728.4 7768.9 7821.0 7862.3 7930.4 7986.3 8064.6 8121.3 8139.0 8202.7 8253.2 8266.3 8300.4 8404.6 8420.4 8464.2 8478.7 8505.4 8572.4 8612.2 8653.1 8709.9 8737.7 8795.4 8845.0 8896.2 8953.6 8973.7 9042.7 9113.2 9180.1 9220.5 9245.5 9278.4 9294.1 9364.8 9388.8 9454.3 9484.1 9539.4 9605.9 9610.9 9686.5 9699.6 9768.0

7274.8 7326.8 7419.7 7454.0 7482.7 7530.3 7600.9 7665.7 7730.2 7770.3 7818.9 7862.6 7930.2 7989.3 8064.6 8117.0 8147.2 8205.2 8252.1 8268.2 8295.4 8395.9 8427.8 8461.2 8483.1 8503.1 8572.9 8615.3 8649.6 8711.4 8738.7 8795.6 8843.2 8895.7 8961.7 8979.1 9040.2 9116.2 9180.2 9223.6 9245.6 9280.1 9295.4 9366.0 9395.7 9453.3 9483.2 9538.9 9608.3 9610.2 9686.6 9701.2 9766.2

−3.1 0.5 −4.2 0.4 −0.9 0.7 1.2 2.4 1.8 1.4 −2.1 0.3 −0.2 3.0 0.0 −4.3 8.2 2.5 −1.1 1.9 −5.0 −8.7 7.4 −3.0 4.4 −2.3 0.5 3.1 −3.5 1.5 1.0 0.2 −1.8 −0.5 8.1 5.4 −2.5 3.0 0.1 3.1 0.1 1.7 1.3 1.2 6.9 −1.0 −0.9 −0.5 2.4 −0.7 0.1 1.6 −1.8

a

Not observed in spectrum; value from Ref. (24). States involving ν1 were calculated using ω10 = 3041.6 cm−1 and x11 = −60.61 cm−1 from Ref. (24). c Not included in fit. b

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TABLE 1—Continued Assignment

Frequency

Calculated Frequency

Difference

Assignment

Frequency

Calculated Frequency

Difference

21 31 41 51 65 24 51 62 610 24 41 51 61 22 31 65 25 61 31 41 51 67 25 41 21 31 67 24 63 22 51 66 22 41 51 65 24 42 61 23 65 21 41 51 67 24 52 62 22 67 24 31 62 25 51 61 21 69 26 23 31 64 24 51 63 611 22 31 66 25 62 31 41 51 68 25 41 61 21 31 68 21 31 41 67 22 51 67 22 41 51 66 23 66 26 51 23 41 65 22 68 24 31 63 22 41 67 25 51 62 21 610 26 61 23 31 65 612 22 31 67 25 63 31 41 51 69 23 51 66 25 41 62 21 31 69 21 31 41 68 24 65 22 51 68 22 51 68 24 41 64 31 41 610 23 67 26 51 61 25 31 62

9820.0 9818.2 9853.1 9877.3 9925.4 9948.6 9978.4 10024.5 10077.4 10149.1 10183.1 10243.4 10269.9 10337.3 10416.2 10456.4 10498.6 10562.6 10583.5 10654.1 10710.8 10726.6 10785.6 10804.3 10879.6 10914.7 10941.8 10988.2 11036.8 11102.9 11147.5 11203.2 11296.0 11339.2 11362.2 11455.4 11528.8 11530.2 11550.1 11604.5 11676.2 11677.8 11753.1 11839.9 11882.5 11904.5 11932.6 11947.0 11995.9 12056.6 12068.5 12100.0 12109.0 12145.4 12181.5 12244.1 12307.8 12313.7

9827.1 9817.8 9855.5 9872.6 9928.2 9953.6 9979.0 10018.4 10079.3 10149.2 10189.1 10248.0 10269.2 10330.1 10417.6 10457.2 10498.9 10560.4 10584.2 10657.8 10715.3 10730.9 10786.2 10809.3 10888.8 10921.8 10941.0 10989.2 11036.5 11101.4 11148.6 11209.8 11288.1 11339.0 11360.7 11452.8 11523.8 11527.0 11552.0 11608.5 11683.4 11689.6 11757.2 11843.4 11883.8 11897.2 11931.1 11953.8 11987.9 12055.0 12068.6 12102.1 12102.1 12141.4 12192.7 12240.0 12306.7 12306.2

7.1 −0.4 2.4 −4.7 2.8 5.0 0.6 −6.1 1.9 0.1 6.0 4.6 −0.7 −7.2 1.4 0.8 0.3 −2.2 0.7 3.7 4.5 4.3 0.6 5.0 9.2 7.1 −0.8 1.0 −0.3 −1.5 1.1 6.6 −7.9 −0.2 −1.5 −2.6 −5.0 −3.2 1.9 4.0 7.2 11.8 4.1 3.5 1.3 −7.3 −1.5 6.8 −8.0 −1.6 0.1 2.1 −6.9 −4.0 11.2 −4.1 −1.1 −7.5

22 69 22 41 68 24 31 64 21 611 21 41 610 23 31 66 613 22 31 68 31 41 51 610 23 51 67 25 41 63 26 52 61 21 31 610 24 66 22 51 69 24 41 65 31 41 611 23 68 26 51 62 25 31 63 21 32 69 22 610 24 31 65 21 612 23 52 67 21 41 611 23 31 67 614 24 51 66 21 31 41 51 69 22 31 69 25 65 23 51 68 21 31 611 26 52 62 21 31 41 610 23 32 66 24 67 52 613 22 41 51 69 22 32 68 23 69 25 31 64 26 51 63 22 611 22 41 610 24 31 66 21 613 23 52 68 21 41 612 23 31 68 615 21 31 41 51 610 24 51 67 22 52 610 22 31 610 25 66 22 31 41 69

12402.1 12479.9 12481.3 12548.6 12632.5 12633.9 12695.5 12790.1 12854.2 12883.3 12906.2 12936.8 12943.4 13019.3 13049.3 13091.8 13138.2 13190.1 13264.4 13275.4 13285.4 13342.5 13422.2 13491.6 13524.7 13574.1 13579.1 13631.5 13656.1 13656.4 13735.8 13782.5 13829.2 13880.9 13897.3 13940.4 13971.0 13964.9 14011.6 14054.7 14108.5 14130.2 14220.3 14220.5 14280.4 14359.4 14371.5 14423.5 14470.5 14508.1 14524.5 14561.2 14596.5 14600.6 14647.5 14672.9 14726.6 14751.9

12400.8 12477.4 12481.1 12553.1 12630.6 12642.1 12699.2 12792.0 12847.6 12882.5 12912.2 12931.9 12933.3 13018.9 13049.4 13094.4 13137.9 13185.8 13268.1 13262.7 13289.1 13342.6 13432.1 13491.7 13527.0 13571.7 13588.6 13635.2 13654.6 13651.2 13734.6 13789.0 13827.8 13872.7 13892.9 13944.6 13967.1 13963.0 14022.3 14059.4 14102.2 14125.3 14212.9 14223.1 14278.2 14359.9 14377.0 14424.2 14471.7 14506.7 14528.8 14565.1 14592.4 14598.3 14640.9 14671.0 14732.0 14744.6

−1.3 −2.5 −0.2 4.5 −1.9 8.2 3.7 1.9 −6.6 −0.8 6.0 −4.9 −10.1 −0.4 0.1 2.6 −0.3 −4.3 3.7 −12.7 3.7 0.1 9.9 0.1 2.3 −2.4 9.5 3.7 −1.5 −5.2 −1.2 6.5 −1.4 −8.2 −4.4 4.2 −3.9 −1.9 10.7 4.7 −6.3 −4.9 −7.4 2.6 −2.2 0.5 5.5 0.7 1.2 −1.4 4.3 3.9 −4.1 −2.3 −6.6 −1.9 5.4 −7.3

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TABLE 1—Continued Assignment

Frequency

Calculated Frequency

Difference

Assignment

Frequency

Calculated Frequency

Difference

23 51 69 21 31 612 26 52 63 24 68 22 51 611 52 614 22 32 69 23 610 23 41 69 25 31 65 22 612 22 41 611 24 31 67 21 614 22 31 41 51 69 23 52 69 21 41 613 23 31 69 616 24 51 68 23 31 41 68 22 52 611 22 31 611 25 67 23 51 610 21 31 613 24 69 22 51 612 23 32 68 52 615 26 31 64 22 32 610 23 611 21 51 614 23 41 610 25 31 66 22 613 23 31 41 51 68 24 52 68 22 41 612 24 31 68 21 615 25 51 67 22 31 41 51 610 21 41 614 23 31 610 617 24 51 69 23 31 41 69 22 52 612 22 31 612 25 68 23 51 611 21 31 614 24 610 22 51 613 24 41 69 26 31 65

14769.2 14811.0 14844.3 14896.1 14924.0 14959.1 15041.0 15066.5 15145.7 15165.7 15214.7 15292.4 15304.2 15347.4 15381.3 15408.2 15437.4 15460.8 15486.4 15533.7 15536.8 15581.3 15604.3 15667.2 15716.7 15741.9 15836.8 15852.6 15852.6 15882.7 15937.1 15968.7 15992.6 16004.8 16073.7 16098.0 16129.2 16168.6 16170.4 16219.3 16242.5 16267.2 16294.9 16311.9 16357.6 16388.2 16404.7 16467.0 16475.5 16502.4 16523.9 16596.4 16637.6 16662.6 16759.6 16783.7 16844.5 16878.1

14766.8 14806.1 14847.5 14900.8 14925.9 14957.0 15039.4 15058.5 15141.4 15156.7 15207.7 15292.0 15315.5 15350.6 15385.9 15410.3 15435.6 15462.9 15489.0 15535.6 15537.7 15575.4 15601.4 15668.6 15699.6 15733.5 15832.2 15854.8 15842.8 15885.5 15927.2 15970.5 15985.5 16003.5 16071.0 16094.2 16131.0 16172.3 16172.3 16217.9 16247.7 16270.9 16296.6 16318.3 16358.5 16390.7 16406.8 16466.5 16468.1 16503.9 16525.6 16598.7 16626.0 16654.9 16757.1 16777.5 16843.5 16864.1

−2.4 −4.9 3.2 4.7 1.9 −2.2 −1.6 −8.0 −4.3 −9.0 −7.0 −0.4 11.3 3.2 4.6 2.1 −1.8 2.1 2.6 1.9 0.9 −5.9 −2.9 1.4 −17.1c −8.4 −4.6 2.2 −9.8 2.8 −9.9 1.8 −7.1 −1.3 −2.7 −3.8 1.8 3.7 1.9 −1.4 5.2 3.7 1.7 6.4 0.9 2.5 2.1 −0.5 −7.4 1.5 1.7 2.3 −11.6c −7.7 −2.5 −6.2 −1.0 −14.0

22 32 611 23 612 21 51 615 23 41 611 21 41 51 614 21 41 51 614 25 31 67 22 614 24 52 69 23 31 41 51 69 22 41 613 24 31 69 21 616 25 51 68 22 31 41 51 611 21 41 615 23 31 611 618 23 31 41 610 22 31 613 22 31 41 612 25 69 23 51 612 21 31 615 21 52 615 27 31 64 24 611 23 32 610 52 617 26 31 66 23 613 23 41 612 25 31 68 22 615 23 31 41 51 610 22 41 614 24 31 610 21 617 25 51 69 22 31 41 51 612 21 41 616 619 23 31 612 23 31 41 611 24 51 611 22 31 614 25 610 23 51 613 24 32 69 21 52 616 24 612 23 32 611 23 614 23 41 613 25 31 69 22 616 22 41 615 23 31 41 51 611

16894.7 16909.0 16932.1 16997.5 16998.6 16998.6 17032.3 17046.9 17099.2 17101.2 17139.9 17163.3 17181.3 17221.5 17246.7 17275.3 17311.7 17318.1 17397.9 17446.4 17519.4 17520.2 17553.6 17574.2 17582.0 17625.3 17677.2 17704.3 17719.7 17793.6 17824.4 17915.7 17954.5 17958.2 18027.2 18051.2 18085.4 18089.1 18147.9 18166.8 18184.0 18224.0 18226.7 18314.6 18326.7 18356.1 18434.0 18463.2 18475.0 18492.8 18594.2 18606.2 18726.6 18825.9 18857.1 18860.9 18953.4 18944.2

16895.6 16906.1 16923.2 16994.4 17000.4 17000.4 17025.1 17048.1 17102.8 17102.3 17137.6 17173.5 17185.1 17226.3 17244.5 17275.2 17312.2 17318.6 17392.3 17443.7 17524.9 17522.2 17546.2 17570.2 17577.4 17624.9 17675.6 17693.7 17724.4 17794.5 17820.4 17911.4 17949.5 17958.9 18026.0 18051.1 18092.9 18093.0 18149.5 18164.6 18185.8 18224.2 18227.4 18310.2 18309.1 18355.6 18439.2 18460.0 18485.7 18490.3 18587.7 18609.8 18728.4 18822.1 18867.4 18863.5 18958.3 18943.4

0.9 −2.9 −8.9 −3.1 1.8 1.8 −7.2 1.2 3.6 1.1 −2.3 10.2 3.8 4.8 −2.2 −0.1 0.5 0.5 −5.6 −2.7 5.5 2.0 −7.4 −4.0 −4.6 −0.4 −1.6 −10.6 4.7 0.9 −4.0 −4.3 −5.0 0.7 −1.2 −0.1 7.5 3.9 1.6 −2.2 1.8 0.2 0.7 −4.4 −17.6c −0.5 5.2 −3.2 10.7 −2.6 −6.5 3.6 1.8 −3.8 10.3 2.6 4.9 −0.8

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TABLE 1—Continued Assignment

Frequency

Calculated Frequency

Difference

Assignment

Frequency

Calculated Frequency

Difference

21 618 24 31 611 21 41 617 620 23 31 613 23 31 41 612 24 51 612 22 31 615 22 31 41 614 23 51 614 24 32 610 21 52 617 27 31 66 24 613 23 32 612 26 31 68 23 615 22 617 25 31 610 23 31 41 51 612 21 619 24 31 612

18990.8 19004.4 19087.1 19127.1 19136.6 19215.3 19232.6 19265.2 19347.7 19368.6 19394.0 19398.1 19483.7 19497.6 19513.9 19627.2 19632.3 19758.4 19773.7 19847.6 19887.0 19916.3

18994.9 19005.9 19090.3 19123.7 19136.4 19221.8 19220.7 19261.3 19347.7 19367.4 19399.4 19396.9 19478.7 19493.2 19519.6 19635.1 19629.9 19761.8 19778.6 19854.6 19890.5 19912.3

4.1 1.5 3.2 −3.4 −0.2 6.5 −11.9c −3.9 0.0 −1.2 5.4 −1.2 −5.0 −4.4 5.7 7.9 −2.4 3.4 4.9 7.0 3.5 −4.0

621 24 51 613 23 51 615 24 614 23 616 22 618 21 620 622 24 51 614 23 51 616 21 52 619 24 615 23 617 22 619 21 621 623 24 51 615 23 51 617 24 616 23 618 22 620 21 622

20024.2 20138.1 20265.6 20394.3 20525.3 20647.2 20778.2 20907.7 21033.0 21155.5 21187.8 21289.6 21412.2 21532.3 21664.5 21788.3 21917.0 22047.0 22171.5 22296.7 22413.9 22540.1

20017.0 20125.8 20268.4 20392.1 20525.1 20653.9 20779.9 20904.2 21024.3 21163.0 21191.3 21284.6 21413.8 21539.6 21663.2 21785.3 21916.2 22051.2 22170.4 22296.2 22419.1 22540.3

−7.2 −12.3c 2.8 −2.2 −0.2 6.7 1.7 −3.5 −8.7 7.5 3.5 −5.0 1.6 7.3 −1.3 −3.0 −0.8 4.2 −1.1 −0.5 5.2 0.2

Long progressions are seen in series involving 2m 6n due to the Franck–Condon principle, which states that transitions involving a large geometry change will be the most prominent in the spectrum. For HFCO, the C=O stretch (ν2 ) and the outof-plane bend (ν6 ) involve the largest geometry changes due to the excitation of a nonbonding electron to a π* antibonding or-

FIG. 4. Six normal vibrational modes of formyl fluoride (HFCO).

bital in the S0 → S1 transition. This increases the length of the C=O bond and causes the molecule to become pyramidal, resulting in long progressions in the 2m 6n series. The strongest transitions are assigned to the 2m 31 6n series because the HFCO molecules were excited to the 31 vibrational level in S1 , and they are therefore most likely to fluoresce to S0 levels involving ν3 , the most intense being 31 . The molecules will also fluoresce at slightly lower intensity to series involving 30 and 32 , and therefore the series 2m 6n and 2m 32 6n were also assigned to longer progressions. Shorter progressions are seen in the C–F stretch (ν4 ) and the FCO bend (ν5 ) because of the involvement of the fluorine p orbital with the molecular π system. Therefore, weaker intensity peaks were assigned to the 2m 41 51 6n , 2m 41 6n , 2m 51 6n , 2m 31 41 6n , and 2m 31 41 51 6n series. Some peak positions were predicted to be overlapped at high energy between the 2m 32 6n , 2m 31 41 6n , and the 2m 31 41 51 6n series. The assignments were made to the series involving 2m 31 41 51 6n rather than to the others because peaks involving both 41 51 are observed to be more intense than peaks involving only 41 or 51 and because peaks involving 31 were the most intense peaks in the spectrum. Peaks in the 2m 31 51 6n series could not be assigned because of the near-degeneracy between 2ω2 and ω5 + 3ω6 . For example, 22 at 3700 cm−1 and 51 63 at 3707 cm−1 have a difference of only 7 cm−1 , resulting in overlap between the 2m 31 51 6n series and the 2m+2 31 6n−3 series. The 2m+2 31 6n−3 series is predicted to be the most intense in the spectrum, as discussed above, and

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FIG. 5. Dispersed fluorescence (DF) spectrum and vibrational assignments of S0 HFCO. The spectrum was recorded from the pQ 1 (J 00 )o branch of the 31 vibrational state of S1 HFCO. The abscissa scale is adjusted to read in S0 rovibrational energy.

therefore the overlapping peaks are assigned to the 2m+2 31 6n−3 series instead of the 2m 31 51 6n series. In fact, the peaks assigned to the 2m+2 31 6n−3 series were the largest in the spectrum. However, the overlap leads to a slight broadening of these peaks in the assigned 2m+2 31 6n−3 series and a slightly larger error for these lines. A total of 142 new assignments were made, resulting in 382 total vibrational assignments for HFCO. Of these assignments, 109 involve ν3 , which have previously not been made. Of the 260 total peaks seen in the 31 DF spectrum, 192 (75%) were able to be assigned, with the others being overlapped and preventing unambiguous assignment.

4. DISCUSSION

A. Multiresonant Hamiltonian Model In the previous spectroscopic analyses of highly excited vibrational levels of S0 HFCO (8, 9), the anharmonic oscillator model was used to fit the data, which is described by the equation

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E vib (v1 , v2 , . . . , vn ) X X X = ωi0 vi + xi j vi v j + yi jk vi v j vk , i

i≤ j

i≤ j≤k

[3]

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HAHN, HORSMAN, AND POLIK

FIG. 6. Dispersed fluorescence spectrum and vibrational assignments of S0 HFCO. See Fig. 5 caption.

where ωi0 are normal mode harmonic vibrational frequencies, xi j are first-order anharmonicity vibrational constants, yi jk are second-order anharmonicity constants, n is the total number of normal modes, vi is the number of quanta in the ith normal mode, and the zero of energy is defined at the vibrationless level. Second-order anharmonicity corrections were used to fit levels involving ν2 and ν6 because each of these modes is involved in long progressions. This model is based on second-order perturbation theory and is applicable when there are no strong interactions among vibrational states. The anharmonic terms serve to compress or expand the progressions of harmonically spaced energy levels. If strong

interactions are present, they will destroy the smooth variation of energy level spacing observed in the spectrum. In the present work, a better model is used that accounts for state mixing. When two vibrational states are nearly degenerate in energy, they can resonantly interact which results in state mixing and peak shifting. For example, if ωi + ω j is approximately equal to ωk , then the resonance denoted by ki j,k couples states in which one quantum of mode k can be exchanged for one quantum of mode i and one quantum of mode j. The anharmonic oscillator model fails to account for resonantly interacting states. The current approach uses a multiresonant Hamiltonian model (10) in which the nonresonant interactions are treated by

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and for a resonance of the form ki, j j are

perturbation theory and the resonant interactions are treated explicitly by matrix diagonalization. The multiresonant Hamiltonian model is implemented by forming a matrix using harmonic oscillator products as basis states. The diagonal elements are hv1 , . . . , vn |Hvib |v1 , . . . , vn i X X X = ωi0 vi + xi j vi v j + yi jk vi v j vk . i

i≤ j

h. . . , vi , v j , . . . |Hvib | . . . , vi + 1, v j − 2, . . .i = ki, j j hvi |qi |vi + 1ihv j |q j |v j − 2i ¶1 µ ¶1 µ vi + 1 2 v j (v j − 1) 2 = ki, j j , 2 4

[4]

i≤ j≤k

Off-diagonal matrix elements for a resonance of the form ki j,k are h. . . , vi , v j , vk , . . . |Hvib | . . . , vi + 1, v j + 1, vk − 1, . . .i = ki j,k hvi |qi |vi + 1ihv j |q j |v j + 1ihvk |qk |vk − 1i ¶1 µ ¶1 µ ¶1 µ vi + 1 2 v j + 1 2 vk 2 = ki j,k 2 2 2

[5]

[6]

which are two commonly experienced resonances (20, 21). Diagonalization of this matrix yields the energies and wavefunctions of the excited vibrational states. The scaling of harmonic oscillator elements with vibrational quantum numbers allow the multiresonant Hamiltonian to account for extensive state mixing throughout the spectrum with a minimum number of parameters, each of which has a straightforward physical interpretation (22). The multiresonant Hamiltonian model was applied with the POLYAD computer program (23). Transitions observed in the

TABLE 2 Spectroscopic Vibrational Constants for S0 HFCO (in cm−1 ) Experiment Parameter

Horsman et al. (9)

This Work

ω10 ω20 ω30 ω40 ω50 ω60 x11 x12 x13 x14 x15 x16 x22 x23 x24 x25 x26 x33 x34 x35 x36 x44 x45 x46 x55 x56 x66 y222 y226 y266 y666 k2,66

3041.6a 1849.27(130)

3041.6a 1849.84 (125) 1388.26 (232) 1071.31 (280) 665.87 (191) 1013.66 (41) −60.61a −1.20a

a

1071.46(271) 665.16(156) 1014.29(35) −60.61a

−11.19(54) −4.38(50) −6.56(23) −7.95(14)

−8.90(119) −8.66(176) −3.58(13) 0.84(60) −0.51(6) −2.84(4) 0.071(57) 0.152(21) −0.068(6) −0.0033(13)

−11.45 (47) 4.33 (47) −4.73 (46) −7.36 (29) −7.71 (19) −14.43 (95) −10.87 (170) 3.59 (219) −5.37 (16) −8.39 (147) −11.01 (162) −3.61 (14) 0.98 (80) −0.51 (8) −2.81 (6) 0.136 (5) 0.158 (3) −0.048 (2) −0.0095 (0.3) 11.07 (274)

Not determined by fit; values from Ref. (24).

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Theory Ref. (24) 3160 1845 1377 1043 651 1027 −60.61 −1.20 −21.19 0.79 0.64 −15.62 −10.81 −4.59 −6.75 −4.79 −7.34 −8.90 −8.79 −1.34 2.63 −6.77 −8.10 −3.93 −0.59 −1.10 −2.86

States contributing to constant 0 369 109 94 119 370 0 0

369 109 93 118 364 109 29 16 109 94 33 93 119 118 370 369 364 364 370 369

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HAHN, HORSMAN, AND POLIK

spectrum and the corresponding resonance constant could not be determined. Higher resolution would be required to use more resonances in the model and obtain a better fit of the data. Some vibrational states in the 2m 32 6n , 2m 31 41 6n and the 2m 31 41 51 6n series are predicted to be at the same location at high energy. The actual assignments were made on relative intensities and quanta as discussed previously in the Results section. However, because these series overlap, it makes it difficult to unambiguously determine the assignment of these states. In addition, there is no previous knowledge of the anharmonic constants involved. Hence the standard deviations of the first-order anharmonic constants x33 , x34 , and x35 are slightly larger than those of the other constants. C. Comparison to Previous Assignments FIG. 7.

Polyad created from S0 HFCO vibrational states linked by k2,66 .

spectrum are assigned to ground state levels labeled by their predominant harmonic oscillator product state quantum numbers, and the energies of these levels are determined from Eqs. [1] and [2]. A resonant model is defined, and the energy levels are calculated by matrix diagonalization. The resonant model parameters are adjusted to minimize the least squares difference between observed and calculated energy levels. In addition to outputting model parameters and calculated energy levels, the POLYAD program predicts all vibrational energy levels to assist in further assignments. B. Spectroscopic Vibrational Constants The combined data set involving vibrational state assignments from this DF spectrum and the assignments from Horsman et al. (9) was used to obtain the most complete set of spectroscopic constants for HFCO currently available. Using the multiresonant Hamiltonian model and POLYAD program, a set of vibrational constants was obtained, which are shown in Table 2. There is a standard deviation of 4.51 cm−1 for the combined set of vibrational state assignments. This standard deviation is consistent with the knowledge of the peak position based on the standard deviation of 4.3 cm−1 between the data sets. The only way to improve the fit of the data through the inclusion of more resonances in the model would be to determine the peak positions with greater precision. In this study, k2,66 was the only resonance fit, which could be determined from the long, intense progressions observed in both ν2 and ν6 . An example of vibrational states interacting through this resonance is shown in Fig. 7. Observation of this resonant interaction suggests that the CO bond length (ν2 ) varies along the out-of-plane bending coordinate (ν6 ), which will hopefully stimulate future theoretical calculations to confirm the magnitude of this coupling. Other near-degeneracies among states arose, for example between the 2m 31 51 6n series and the 2m+2 31 6n−3 series. However, the overlapping series were not resolved in the

The present assignments agree with the previous work done by Horsman et al. (9). Since a combined data set was used, it was possible to obtain constants for HFCO using the largest possible set of vibrational state locations. Additionally, some unassigned peaks in Horsman et al. can now be assigned to the 31 series. This combined data collection allows the most complete set of vibrational constants to be determined for HFCO. 5. CONCLUSION

This work presents the determination of several new constants, including those harmonic and anharmonic terms involving ν3 , and provides a more complete understanding of the vibrational structure of HFCO. The number of assigned vibrational transitions was increased to 382, with 109 of these involving ν3 . Overall, the larger set of vibrational states allows for a more complete characterization of the potential energy surface of formyl fluoride as well as for the development of better theoretical models for more complex molecules. In addition, a resonance constant, k2,66 , was determined for HFCO. Peaks involving ν1 were not observed, and future work will focus on determining vibrational constants involving this mode. ACKNOWLEDGMENTS K.E.H. and K.M.H. acknowledge the Beckman Foundation for the receipt of Beckman Scholar Awards. K.E.H. also acknowledges the Cupery Research Fund for a summer research stipend. This research was supported by National Science Foundation Grant CHE-9157713.

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