Steric Effect in the Energy Transfer Reaction of Oriented CO (a 3Î , v

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Steric Effect in the Energy Transfer Reaction of Oriented CO (a 3Π, v0 = 0, Ω = 1 and 2) + NO (X 2Π) f NO (A 2Σ+, B 2Π) + CO (X 1Σ+) H. Ohoyama* and Y. Matsuura Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan ABSTRACT: The oriented CO (a 3Π, v0 = 0, Ω = 1 and 2) beam has been prepared by using an electric hexapole and applied to the energy transfer reaction of CO (a 3Π, v0 = 0, Ω = 1 and 2) + NO (X 2 Π) f NO (A 2Σ+, B 2Π) + CO (X 1Σ+). The emission spectra of NO (A 2Σ+, B2Π) have been measured at three orientation configurations (C-end, O-end, random). The shape of the emission spectra (and/or the internal excitation of products) turns out to be insensitive to the molecular orientation. The vibrational distributions of NO (A 2Σ+, v0 = 02) and NO (B 2Π, v0 = 02) are determined to be Nv0 =0:Nv0 =1:Nv0 =2 = 1:0.40 ( 0.05:0.10 ( 0.05 and Nv0 =0:Nv0 =1:Nv0 = 2 = 1:0.6 ( 0.1:0.7 ( 0.1, respectively, and the branching ratio γ/β [=NO (A 2Σ+)/NO (B 2Π)] is estimated to be γ/β ∼ 0.3 ( 0.1 by means of spectral simulation. These vibrational distributions of NO (A, B) can be essentially attributed to the product-pair correlations between CO (X, v00 ) and NO (A 2Σ+, v0 = 02), NO (B 2Π, v0 = 02) due to energetic restriction under the vibrational distribution of CO (X, v00 ) produced from the vertical transition of CO (a 3Π, v0 = 0) f CO (X, v00 ) in the course of energy transfer. The steric opacity function has been determined at two wavelength regions: 220 < λ < 290 nm [NO (A f X) is dominant]; 320 < λ < 400 nm [NO (B f X) is dominant]. For both channels NO (A 2Σ+, B2Π), a significant CO (a 3Π) alignment effect is recognized; the largest reactivity at the sideways direction with the small reactivity at the molecular axis direction is observed. These CO (a 3Π) alignment effects can be essentially attributed to the steric asymmetry on two sets of molecular orbital overlap, [CO (2π) + NO (6σ (2π))] and [CO (5σ) + NO (1π (2π))]. All experimental observations support the electron exchange mechanism that is operative through the formation of a weakly bound complex OCNO.

I. INTRODUCTION The energy transfer process is of great importance and relevant to both fundamental and applied studies for chemical reactions such as initial steps in the photosynthetic process.1 The metastable CO (a 3Π) is known as an important energy carrier in the Martian upper atmosphere just like N2 (A 3Σ+) in the Earth’s atmosphere. The reaction of CO (a 3Π) + NO (X 2Π) is one of the important reactions as a benchmark for the collisional energy transfer process in the molecular-molecular systems, and it is also an ideal system for studying the state selectivity in the collisional energy transfer process because there are many emitting excited states: NO (A 2Σ+), NO (B 2Π), and so on. They are easy to be detected in the ultraviolet region through the well-known NO (A f X) γ band and NO (B f X) β band emissions. A large number of studies have been carried out on its collisional quenching and energy transfer.29 Shen et al. studied the energy transfer reaction of CO (a 3Π) + NO (X 2Π) f NO (A 2Σ+, B 2Π) + CO (X 1Σ+) under beambeam condition.10 In their study, the relatively high vibrational distributions of NO (A 2Σ+, v0 ) and NO (B 2Π, v0 ) were observed as compared with the previous results in flow system.26 In addition, they reported that the vibrational distribution of NO (A 2Σ+, v0 ) changes with the vibrational energy of r 2011 American Chemical Society

the CO (a 3Π,v0 ) reactant6 in contrast with the previous result in flow system that the vibrational distribution of NO (A 2Σ+, v0 ) is insensitive to the vibrational distribution of CO (a 3Π, v0 ). It was reported that the branching ratio γ/β = 1.3 ( 0.3 obtained in the beambeam experiment is smaller than those obtained in flow system.3,6 Moreover, it was reported the branching ratio γ0/β0 in flow system significantly decreases as the vibrational energy of the CO (a 3Π, v0 ) reactant increases.11 In addition, the large γ/β [no formation of NO (B)] was reported at high collision energy (1200 eV) under singlecollision condition.12 As shown by the many discrepancies among the experimental results obtained at the different experimental conditions, the greater part of the details of its reaction dynamics is still unsolved. Especially, the steric aspect on the title reaction has not been studied in spite of its important as a benchmark for the collisional energy transfer process in the molecular-molecular systems. So far, the state selection and orientation of CO (a 3Π) has been carried out by Meijer and coworkers using the hexapole Received: March 25, 2011 Revised: May 13, 2011 Published: June 15, 2011 8055

dx.doi.org/10.1021/jp202781g | J. Phys. Chem. A 2011, 115, 8055–8063

The Journal of Physical Chemistry A

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field technique.13,14 They prepared a single rotational state of CO (a 3Π) by an optical pumping using the a 3Π r X 1Σ+ transition, so-called Cameron bands. They applied the state selected CO (a 3Π) to surface reactions.15 Moreover, by the combination of the statistical electric field which split individual M components of a given rotational line of the transition, they also succeeded in the direct preparation of an oriented CO (a 3Π) beam by the optical pumping technique using a pulsed radiation source having Fourier-limited bandwidth which is narrower than the splitting between the individual M components.16 In the present study, a highly intense CO (a 3Π) beam is prepared via the energy transfer scheme from the excited He* to CO (X) by using a dc-discharge source. The steric effect on the energy transfer reaction of CO (a 3Π, v0 = 0, Ω = 1 and 2) + NO (X 2 Π) f NO (A 2Σ+, B 2Π) + CO (X 1Σ+) has been studied under the crossed beam condition by using the oriented CO (a 3Π, v0 = 0, Ω = 1 and 2) beam prepared by an electric hexapole. The emission spectra of NO (A 2Σ+, B 2Π) have been measured at three orientation configurations (C-end, O-end, random). The shape of the emission spectra turns out to be insensitive to the molecular orientation. The vibrational population of NO (A 2Σ+, v0 = 02) and NO (B 2Π, v0 = 02), and the branching ratio γ/β [NO (A 2 + Σ )/NO (B 2Π)] have been determined by means of spectral simulation. Molecular steric opacity functions have been determined for the NO (A 2Σ+) and NO (B 2Π) channels. For both channels, a significant alignment effect of CO (a 3Π, v0 = 0, Ω = 1 and 2) is recognized.

II. ROTATIONAL STATE OF CO (A 3Π) The CO (a 3Π) state is described as an intermediate case between Hund’s case (a) and (b). For low values of J (the total angular momentum quantum number), however, the three different Ω multiplets (Ω = 0, 1, 2) (Ω being the sum of the projection of the electron spin and the electron angular momentum on the molecular axis) are only weakly interacting and can be treated separately. As a result, the CO (a 3Π) state can be approximated as Hund’s case (a). Therefore, the field free rotational wave functions of CO (a 3Π) for low values of J are given by17 1 Φε ðJ;Ω;MÞ ¼ pffiffiffi ½jJ;+Ω; ( Mi + εjJ;Ω; ( Mi ð1Þ 2 where M is the projection of J on the space-fixed axis, ε = (1denotes the parity index quantum number; the states with ε = 1 have e-symmetry and the states with ε = 1 have f-symmetry. In the electric field E, the e-symmetry states and the f-symmetry states are coupled. The coupling matrix elements of μB 3 E B, diagonal in M and Ω, are given by17,18 MΩ ¼ μeff E W Stark ¼ μE JðJ + 1Þ Diagonalizing WStark yields the Stark energy 0 1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2μ E eff A W ( ðEÞ ¼ 1=2W Λ @1 ( 1 + WΛ

ð2Þ

ð3Þ

where W+(E) and W(E) correspond to the upper and lower state of the Λ-doublet, respectively. WΛ denotes the Λ-doubling splitting between the doublet states in zero field,19 μ is the

permanent dipole moment of CO (a 3Π) (μ = 1.37 D), and E is the electric field strength. Because the low field seeking states of CO (a 3Π) molecules are responsible for their focusing by a hexapole field, only metastable CO (a 3Π) molecules with the upper Λ-doublet component with MΩ < 0 (only Ω = 1, 2 states) can be focused. The field dependent eigenfunctions can be expressed as the linear combination of the field free eigenfunctions:20,21 Ψε ðE;J;MÞ ¼ Rε ðEÞΦ1 ðJ;Ω;MÞ + βε ðEÞ Φ+1 ðJ;Ω;MÞ ð4Þ where R-1 2 ðEÞ ¼ β(1 2 ðEÞ ¼

1 1 ( sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2μeff E 2 2 1+ WΛ

To decouple the Λ-doubling splitting (WΛ) of 1150 MHz for the |J = 2, Ω = 1, M = 2æ rotational state,19 an orientation field strength higher than 3 kV cm1 is necessary. Using the field dependent eigenfunction, the orientational distribution function of the molecular axis for each rotational eigenstate is described as22,23 Z Z ε PJ;Ω;M ðE;cos θÞ ¼ Ψε ðE;J;Ω;MÞ Ψε ðE;J;Ω;MÞ dj dψ ¼

2J + 1 2J Cn ðε;E;J;Ω;MÞ Pn ðcos θÞ 2 n¼0

∑

ð5Þ

The expansion coefficients Cn(ε,E,J,Ω,M) of the orientational distribution function PεJ ,Ω,M(E,cos θ) by Legendre polynomials are expressed by Cn ðε;E;J;Ω;MÞ ¼ ðRε ðEÞ + βε ðEÞÞ2 Cn ðJ;Ω;MÞ + ðRε ðEÞ βε ðEÞÞ2 Cn ðJ;Ω;MÞ Cn ðJ;Ω;MÞ ¼ ð2n + 1Þð 1Þ

MΩ

J Ω

J Ω

n 0

!

J M

J M

ð6Þ

n 0

!

III. EXPERIMENTAL SECTION The experiment setup is schematically shown in Figure 1. It is similar to our previous study.24 The CO (a 3Π) is produced by the energy transfer scheme from the excited He* to CO (X): He f He He + COðX1 Σ+ Þ f COða3 ΠÞ + He The CO (a 3Π) beam source consists of two parts. First part is a dc-discharge source for the excited He* formation. This part consists of two electrodes insulated by a 0.5 mm thick ceramic insulator; one is a grounded conical electrode with a hole of 3 mm i.d., another is a 1 mm thick stainless steel ring electrode with a hole of 3 mm i.d. that is biased to negative high voltage (1.8 kV) supplied by a high voltage pulse generator. The He gas was injected from a pulsed valve into this region at a stagnation pressure of 1000 Torr and He* was generated by a pulsed dc discharge with a pulse width of 0.5 ms. Second part is a 20 mm long Teflon channel with a hole of 13 mm i.d. The CO (X) gas 8056

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Figure 1. Experimental setup under crossed beam conditions for the emission spectra measurement. PV1, PV2: pulsed valves. SK1: skimmer 1 mm in diameter. C1, C2, C3: collimators 10, 4, and 2 mm in diameter, respectively. BS: beam stop 3 mm in diameter. HP: 800 mm long hexapole field constructed of 6 mm i.d. rods. Monochro: monochromator. PC-IMD: photon counting-image detector. M: concave mirror. GF: guiding field (1 kV cm1, 380 mm long). OF: orientation field (4 kV cm1, 50 mm long). P.M.: photomultipliers. FL: band-pass filter.

was injected into this channel from a pulsed valve at a stagnation pressure of 350 Torr. In this channel, CO (a 3Π) is produced by the energy transfer from He* to CO (X). Because the most stable Ω = 0 state of CO (a 3Π) is inactive for the electric hexapole field, the CO (a 3Π) beam must be moderately cooled down by the supersonic expansion at the optimized beam condition to efficiently populate CO (a 3Π) to the upper fine structure states with Ω = 1 and 2, which are focusable by an hexapole field. With a conventional time-of-flight method, the velocity distribution of the beam is determined to be the stream velocity of vs = 1400 ms1 and Rs = 350 ms1 (translational temperature of 60 K for He). The rotational distribution of CO (a 3Π) is estimated to be characterized as a Boltzmann distribution with the temperature of 60 K. The emission spectra of the CO (a f X) in the stray light from the CO (a 3Π) source was measured by a photon-counting image detector (PC-IMD) coupled with a monochromator to estimate the vibrational distribution of CO (a 3Π) reactants. The CO (a 3Π) molecules in the Ω = 1 and 2 fine structure states were state-selected and focused by an electrostatic hexapole field into a Teflon collision chamber mounted in a reaction chamber at 150 cm downstream from the CO (a 3Π) nozzle. The electrostatic hexapole is constructed with the 800 mm long cylindrical stainless steel rods (r0 = 6 mm in diameter) mounted with r0 = 0.565R0 (R0 is the distance between the inside surfaces of rods on opposite sides of the hexapole). The Teflon collision chamber in which the effusive NO beam source is mounted was differentially pumped by a turbo pump. NO beam was supplied by a pulsed valve through a 30 mm long Teflon channel with a hole of 2 mm i.d. at a stagnation pressure of 10.0 Torr. The state-selected CO (a 3Π) beam after passing a 38 cm long guiding field (1 kVcm1) collides with the NO beam after the 20 mm long flight path in the Teflon collision chamber where the orientational field (4 kV cm1) was applied to orient the CO (a 3Π, Ω = 1 and 2) molecules to the relative velocity. The electric guiding field was prepared by a pair of electrode plates. The electric orientation field was prepared by four parallel stainless steel rods. The electric orientation field (EOF) is tilted at an angle of 20 [parallel to the relative velocity (vr)] with respect to the direction of CO (a 3Π) beam axis. In the present study, the orientation of CO (a 3Π) molecules in the collision frame was controlled to be three configurations, C-end, O-end, and random (orientation field off and guiding field off), by changing the direction of EOF

with respect to vr at the beam crossing point. The emission from the products NO (A, B f X) was collected by a concave mirror. For the measurement of the emission spectra, the NO (A, B f X) emission was dispersed by a monochromator and detected by a photon-counting image detector (PC-IMD, Hamamatsu C4705-03) mounted on the exit of the monochromator. The spectral sensitivity curve for the whole detection system was calibrated by using a standard tungsten halogen lamp. To avoid the influence from long-time fluctuation of the signal intensity, the experimental condition was switched every 3000 beam pulses at 10 Hz in turn. The emission spectrum was recorded by employing a unit exposure time of 300 s for PC-IMD. To obtain an acceptable signal-to-noise ratio, the data were accumulated up to 3.0 105 beam pulses at each orientation condition. For the subtraction of the background, the spectrum at the hexapole voltage of 0 V was used as the background. For the study to obtain the steric opacity function, a cooled photomultiplier (Hamamatsu R94302) was mounted instead of the spectrometer system. The steric effect has been studied at two wavelength regions: 220 < λ < 290 nm [NO (A f X) is dominant] and 320 < λ < 400 nm [NO (B f X) is dominant]. The emission of NO (A, B f X) was detected by the photomultiplier through the suitable band-pass filters (A, Asahi Spectra (SU0330 & SU0350); B, Asahi Spectra (SU0400 & LU0325)) and counted by a photon counter (Stanford SR400) with the 0.8 ms gate-width. Only the signal enhanced by applying a hexapole field was used as the signal from the CO (a 3Π, Ω = 1 and 2) + NO (X 2Π) reaction. For the subtraction of the background signal, the signal at the hexapole voltage of 0 V was used as the background signal. The experiment has been carried out for three experimental conditions (background, oriented, and random) in turn under two orientation configurations (C-end, O-end) at the hexapole voltage of 5 kV. To avoid the influence from long-time fluctuation of the signal intensity, the experimental condition was switched every 300 beam pulses at 10 Hz in turn. To obtain an acceptable signal-to-noise ratio, the data were accumulated up to 3.0 104 beam pulses at each orientation condition.

IV. RESULTS AND DISCUSSION A. Characterization of the CO (a 3Π) Beam. To estimate the vibrational populations of CO (a 3Π, v0 ), the CO (a f X) 8057



Figure 2. CO (a f X) emission spectrum for the stray light from the CO (a 3Π) source. The vibrational distribution of CO (a 3Π, v0 ) is roughly estimated to be Nv0 =0:Nv0 =1:Nv0 =2 = 1:0.1:0.0 by using the emission Einstein coefficients of CO (a f X) bands.8 The CO (a 3Π) beam is expected to be essentially in the v0 = 0 state due to the collisional vibrational relaxation in the successive supersonic expansion.

emission spectrum for the stray light from the CO (a 3Π) beam source was recorded. Figure 2 shows the CO (a f X) emission spectrum. Although the poor spectral resolution (1.6 nm fwhm) smears out the detail of spectrum shape and prevents to determine the rotational distribution, the CO (a 3Π, v0 ) vibrational distribution can be roughly estimated to be Nv0 =0:Nv0 =1: Nv0 =2 = 1:0.1:0.0 by using the Einstein coefficients of CO (a f X) bands.8 It is expected that the CO (a 3Π, v0 ) molecules are essentially populated into only the v0 = 0 state if we take into account the successive collisional vibrational relaxation in the supersonic expansion. B. Orientational Distribution of the Oriented CO (a 3Π) Beam. For the oriented CO (a 3Π, v0 = 0) molecular beam, the orientational distribution W(cos θ) of the molecular axis with respect to the electric orientation field (E) was estimated by means of the trajectory simulation25 for the state-selection in the electrostatic hexapole field. Here, θ is the angle between the orientation field (E) with the molecular axis. By reproducing the experimental focusing curve that is obtained as the emission intensity from the products NO(A, B) at the random orientation condition as a function of the hexapole voltage (V0), we estimated W(cos θ). Figure 3 shows the experimental focusing curve with the one calculated by the trajectory simulation. Because the degree of orientation (MΩ/J/(J + 1)) becomes small for the large J states, a limited number of states (J e 3 for Ω = 1, J e 6 for Ω = 2) can contribute to the focused beam. Because the lifetime (τ) of CO (a 3Π) strongly depends on the rotational state,26,27 the decay factor of exp(t/τ) is taken into account for the trajectory simulation, here t (∼ 1.07 ms) is the flight time. According to the theoretical calculation,27 the lifetimes for the Ω = 1 (J e 3) states are τ ∼ 3 ms, whereas τ > 20 ms for the Ω = 2 (J e 6) states. The calculated focusing curve (solid line) with the rotational temperature of Trot = 60 K for the CO (a 3Π) beam is in good agreement with the experimental one. It is expected that the reactivity has little dependence on the rotational states. The four rotational states (|J, Ω, Mæ = |1, 1, 1æ, |2, 1, 2æ,

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Figure 3. Focusing curve of CO (a 3Π): experimental (b); calculated one via the trajectory simulation with a rotational temperature of Trot = 60 K (solid line). (Inset) polar coordination representation of the orientational distribution of the molecular axis with respect to the electric orientation field E for the state-selected CO (a 3Π) beam at V0 = 5 kV (solid line) and random orientation (broken line).

|2, 2, 2æ, |3, 2, 3æ) are dominant components in the focused CO (a 3Π) beam at the experimental condition of V0 = 5 kV; |1, 1, 1æ (24%), |2, 1, 2æ (13%), |2, 2, 2æ (19%), |3, 2, 3æ (13%). The calculated orientational distribution W(cos θ) at V0 = 5 kV is shown in the inner panel in Figure 3. The nth Legendre moments, ÆPnæ, for the orientational distribution at EOF = 4 kV cm1 are summarized to be ÆP1æ = 0.467, ÆP2æ = 0.043, ÆP3æ = 0.036, ÆP4æ = 0.004, ÆP5æ = 0.0029, ÆP6æ = 0.0001, ÆP7æ = 0.0003, ÆP8æ = 0.000. The error of the Legendre moments is estimated to be less than 10%. C. Steric Effect on the Emission Spectra. The emission spectra of NO (A, B f X) at three orientation configurations (Cend, O-end, random) are shown in Figure 4 with the vibrational level assignments.28,29 Unfortunately, the emission spectra have been measured only in the wavelength region 220 < λ < 300 nm because of the weak signal in the wavelength region λ > 300 nm, even though the emission in this wavelength region can be identified as the emission dominantly from NO (B f X). The emission intensities at the two oriented conditions (C-end, O-end) are found to be slightly lower than that at the random condition. We cannot recognize the steric effect on the shape of the emission spectra within the experimental error because the poor spectral resolution (1.6 nm fwhm) smears out the detail of spectrum shape. Because we cannot determine the rotational distribution of NO (A, B), we try to determine the vibrational populations of NO (A 2Σ+, v0 = 02) and NO (B 2Π, v0 = 02) and the branching ratio γ/β by means of spectral simulation under the assumption that the rotational distributions of NO (A, B) are the same with those reported in ref 10. The wavelength for each vibrationrotation transition in NO (A, B f X) was calculated by using the standard equation for emission intensity.30 The Einstein coefficients of NO (A, B f X) bands were cited from refs 28 and 29. The slit function for each vibrationrotation transition is experimentally determined to be a Gaussian function having 1.6 nm fwhm. The simulated results are summarized in Table 1. The simulated spectrum at each orientation configuration is shown in Figure 4. The shape of the emission spectra turns out to be insensitive to the molecular 8058



Figure 4. (Solid lines) Simulated emission spectra under the vibrational population of NO (A, v0 = 02) and NO (B, v0 = 02) shown in Table 1 and the branching ratio γ/β (∑20NA,v0 /∑20NB,v0 ) = 0.5 with the vibrational level assignments from refs 20 and 21 NO (A f X) (purple line) and NO (B f X) (blue line). The rotational distribution of NO (A, B) are assumed to be the same in ref 10. The wavelength of each vibrationalrotational transition in NO (A f X) and NO (B f X) was calculated using the standard equation for emission intensity.30 The Einstein coefficients of NO (A f X) and NO (B f X) bands were cited from refs 28 and 29. The slit function for each vibrationalrotational transition is experimentally determined to be a Guassian function having 1.6 nm fwhm. (Symbols) Experimental emission spectra of NO (A, B f X) in the wavelength region 220 nm < λ < 300 nm at three orientation configurations: C-end (green circle), O-end (blue circle), random (red circle). (Dashed lines) The simulated emission spectra.

orientation; the vibrational population of NO (A 2Σ+, v0 = 02) and NO (B 2Π, v0 = 02) is determined to be Nv0 =0:Nv0 =1:Nv0 =2 = 1:0.40 ( 0.05:0.10 ( 0.05 and Nv0 =0:Nv0 =1:Nv0 =2 = 1:0.6 ( 0.1:0.7 ( 0.1, respectively. The branching ratio γ/β (∑20NA,v0 / ∑20NB,v0 ) is estimated to be γ/β ∼ 0.5 ( 0.2 by the spectral simulation. As you can see in the simulated spectrum with γ/β = 0.5 for the NO (A f X) and NO (B f X) emissions, a considerable contribution of β-band is necessary to reproduce

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the experimental spectra. Moreover, because the emission from the reaction volume (sphere with a diameter of 2 mm) is selectively corrected by the concave mirror (collection efficiency is ca. 7%) and focused onto the entrance slit (0.5 mm width, 15 mm long) of the monochromator in the present setup, this simulated branching ratio γ/β should become smaller than 0.3 ( 0.1 if we take into account the correction factor CF (=[1 exp(t/τ)]1, t = d/v)31 due to the difference in the collecting efficiency for NO (A f X) and NO (B f X) emissions; according to the size of observation region d (2 mm) and the relative velocity v (1500 ms1), the collection efficiency of NO (A f X) emission becomes at least 1.7 times higher than that of NO (B f X) emission due to the difference in their lifetimes τ (τ = 200 ns for NO (A), τ = 1.5 μs for NO (B)). D. Comparison with Other Studies. The resultant vibrational populations of NO (A 2Σ+, v0 = 02) and NO (B 2Π, v0 = 02) are different from those in flow system11 but nearly same with those observed in the other studies under beambeam condition.10 However, the ratio γ/β ∼ 0.3 in our beam study is much smaller than the value of γ/β observed in the other studies under the collision free condition; Shen et al. reported the branching ratio of γ/β = 1.3 ( 0.3 with the CO (a, v0 ) vibrational distribution Nv0 =0:Nv0 =1:Nv0 =2:Nv0 =3 = 1:0.51:0.32:0.25 in beam beam experiment.10 On the other hand, Thomas and Katayama reported γ0/β0 ( NA,v0 =0/NB,v0 =0) = 0.679 ( 0.077, 0.204 ( 0.033 and 0.099 ( 0.004 with the each CO (a, v0 ) vibrational distribution Nv0 =0:Nv0 =1:Nv0 =2 = 1:0.17:0.03, Nv0 =0:Nv0 =1:Nv0 =2 = 1:0.25:0.15 and Nv0 =0:Nv0 =1:Nv0 =2 = 1:0.57:0.34 in flow system.11 Shen et al. suggested that the large difference in their γ/β value from those in flow system is due to two corrections that are not performed on the result of Thomas and Katayama: first, vibrational levels v0 = 1 and v0 = 2 of NO (A) are not taken into account according to their populations relative to v0 = 0 level; second, steady-state populations of NO (A) and NO (B) are not converted to formation rates on basis of their lifetimes. Shen et al. suggested that the ratio γ0/β0 = 0.099 becomes approximately γ/β = 0.99 by taking into account these corrections. They also suggested that some discrepancy among their results fundamentally arise from the experimental conditions: the multicollision events in the flow system and the single collision events in beambeam system. However, the ratio γ/β ∼ 0.3 observed in our crossed beam study is much smaller than that with γ/β = 1.3 ( 0.3 in the beambeam experiment by Shen et al.10 This disagreement may arise from the difference in experimental conditions. Vibration of CO (a 3Π, v0 ). Thomas and Katayama reported that γ/β decreases as the CO (a, v0 ) reactants populate in the higher vibrational levels.11 According to this tendency, the smaller ratio γ/β ∼ 0.3 in our beam study cannot be explained by the difference in the vibrational distribution of CO (a 3Π, v0 ) reactants, because our CO (a 3Π) reactants are essentially in only the v0 = 0 state. Collision Energy. Shen et al. carried out their study at thermal collision energy of 0.05 eV,10 while the collision energy in our study is ∼0.3 eV. This difference in collision energy might give some effect on γ/β. However, the large γ/β ratio [no formation of NO (B)] was reported at high collision energy (1200 eV) under the beam condition.12 Therefore, the smaller ratio γ/β ∼ 0.3 in our beam study seems to be not explained by the difference in collision energy. Fine structure Ω of CO (a 3Π, Ω, v0 ). A major difference in the experimental condition between our study and the other studies is the rotational state distribution of CO (a 3Π). Especially, our study has been carried out only for two upper fine structure states 8059



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Table 1. Simulated Vibrational Population and the Branching Ratio γ/β of NO (A, B) NO (A)

NO (B)

vibrational state v0

0

1

2

0

1

2

population Nv0

1.0

0.40 ( 0.05

0.10 ( 0.05

1.0

0.60 ( 0.1

0.70 ( 0.1

rot. temperaturea (K) branching ratio

1500

1200

1000

1400

1200

1600 γ/β = 0.5 ( 0.2b

The rotational temperatures of NO (A, B) are assumed to be those in ref 10. b The branching ratio γ/β becomes smaller than 0.3 ( 0.1, if we take into account the correction factor CF due to the difference in the collecting efficiency for NO (A f X) and NO (B f X) emissions. a

channels despite the low degree of alignment (ÆP2æ = 0.043) for the oriented CO (a 3Π) beam. F. Steric Opacity Function. In general, the observed emission intensity IΘ at each orientation configuration Θ can be expressed in the form of the steric opacity function σ(cos γ) weighted by the orientational distribution of molecular axis WΘ(cos γ) in the collision frame at each orientation configuration as below, Z IΘ ¼

Figure 5. Molecular steric opacity function for the NO (A, B) formations obtained by the EngelLevine function model (expansion up to n = 2) at two wavelength regions: NO (A f X) [220 < λ < 290 nm], NO (B f X) [320 < λ < 400 nm].

(Ω = 1, 2) having small J, whereas the other studies were carried out for every fine structure states (Ω = 0, 1, 2; the most stable Ω = 0 state may be dominant) having large J. The hexapole selected |Ω = 1 and 2æ rotational states have a charge distribution that is noncylindrical symmetric around the CO molecular axis. On the other hand, the |Ω = 0æ rotational states have a charge distribution that is cylindrical symmetric around the CO molecular axis. These differences should have no small effect on the branching ratio γ/β. In other words, it seems likely that the most stable fine structure states (|Ω = 0æ) are favorable for the NO (A 2Σ+) formation as compared with other fine structure states (|Ω = 1 and 2æ). E. Steric Effect. The steric effect has been studied at the two wavelength regions: 220 < λ < 290 nm [NO (A f X) is dominant] and 320 < λ < 400 nm [NO (B f X) is dominant]. The relative cross sections at two orientation configurations (C-end and O-end) to that at random orientation are experimentally determined to be NOðAÞ ½220 < λ < 290 nm : IC-end =IRandom ¼ 0:95 ( 0:01; IO-end =IRandom ¼ 0:94 ( 0:01 NOðBÞ ½320 < λ < 400 nm : IC-end =IRandom ¼ 0:98 ( 0:01; IO-end =IRandom ¼ 0:95 ( 0:01 A negligible molecular orientation dependence is observed in spite of the significant degree of orientation (ÆP1æ = 0.467) for the oriented CO (a 3Π) beam. In contrast, a notable molecular alignment effect on CO (a 3Π) is observed for both NO (A, B)

1 1

W Θ ðcos γÞ σðcos γÞ d cos γ

ð7Þ

Here, γ is the molecular orientation angle in the collision frame (γ = 0 is defined as the C-end) and the steric opacity function σ(cos γ) is defined as the reactive cross section as a function of γ. To quantitatively evaluate the observed steric effects, it is suitable to represent them in the form of the steric opacity function. Using the EngelLevin function model described below,32 here, we convolute the steric opacity function by reproducing the experimental steric asymmetry (IC-end/IRandom, IO-end/IRandom) using eq 7. σðcos γÞ ¼ expðλ0 +

2

∑ λnPnðcos γÞÞ n¼1

ð8Þ

where Pn(cos γ) is the nth Legendre function, λn are the fitting parameters, and λ0 is the normalization factor. In this model calculation, only the parameters λn up to n = 2 were sufficient for reproducing the experimental results. When the experimental steric asymmetry (IC-end/IRandom, IO-end/IRandom) are reproduced, the fitting parameters (λ1, λ2, and λ0) are determined to be (λ1 = 0.02, λ2 = 1.66, λ0 = 0.222) for NO (A) and (λ1 = 0.05, λ2 = 1.01, λ0 = 0.088) for NO (B). The steric opacity functions σ(cos γ) are summarized in Figure 5. A large molecular alignment effect (i.e., the largest reactivity at the sideways direction with the poor reactivity at the molecular axis direction) is recognized for both the NO (A, B) channels. Because the emission at the wavelength region 220 < λ < 290 nm contains some contribution of the β-band, the molecular alignment effect for the real NO (A) channel is expected to be somewhat larger than that for the NO (B) channel. G. Effect of Product-Pair Correlations on the Vibrational Distribution of NO (A 2Σ+, v0 ) and NO (B 2Π, v0 ). Figure 6 shows the energy level for each vibrational state of the products, NO (A, v0 = 02), NO (B, v0 = 02), and the available energy for the formation of each vibrational state of CO (X, v00 = 03). If the CO (X, v00 = 1) is produced, the formation of NO (A, v0 = 2) is energetically impossible; besides, the formation of CO (X, v00 = 2) prevents the formations of NO (A, v0 = 12) and NO (B, v0 = 12). Therefore, the following product-pair correlations due to energetic restriction are recognized between CO (X, v00 ) and NO 8060



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(A, v0 ), NO (B, v0 ). COðX; v00 ¼ 0Þ T NOðA; v 0 ¼ 02Þ; NOðB; v 0 ¼ 02Þ COðX; v00 ¼ 1Þ T NOðA; v 0 ¼ 01Þ; NOðB; v 0 ¼ 02Þ COðX; v00 ¼ 2Þ T NOðA; v 0 ¼ 0Þ; NOðB; v 0 ¼ 0Þ COðX; v 00 ¼ 3Þ T NOðA; v 0 ¼ 0Þ These product-pair correlations can explain the stepwise characteristics on the vibrational distribution of NO (A, B). If we assume the vertical transition of CO (a 3Π, v0 = 0) f CO (X, v00 ) in the course of energy transfer, the vibrational distribution of CO (X, v00 ) can be estimated to be (Nv00 =0:Nv00 =1:Nv00 =2:Nv00 =3 = 1:1:0.46:0.12) from the FranckCondon factor for the CO (a 3Π, v0 = 0) f CO (X, v00 ) transition.8 It was shown in Figure 7A. From the product-pair correlations, the population of each CO (X, v00 ) equals the sum of the correlated population of NNO (A,v0 )-CO(X,v00 ) and NNO(B,v0 )-CO(X,v00 ) over v0 as below,

Figure 6. Energy level for each vibrational state of the products. (Solid lines) NO (A 2Σ+, v0 = 02) and NO (B 2Π, v0 = 12). (Dashed lines) Available energy for the formation of each vibrational state of CO (X, v00 ). The product-pair correlations due to energetic restriction are recognized between NO (A, v0 ) [NO (B, v0 )] and CO (X, v00 ).

N COðX;v00 ¼ 0Þ ¼

2

2

∑ N NOðA v Þ-COðX;v ¼ 0Þ; v∑¼ 0 N NOðB v ÞCOðX;v ¼ 0Þ v ¼0 0 0

00

0

0 0

00

0

N COðX;v00 ¼ 1Þ ¼

1

2

∑ N NOðA v Þ-COðX;v ¼ 1Þ ; v∑¼ 0 N NOðB v ÞCOðX;v ¼ 1Þ v ¼0 0 0

0

00

0 0

00

0

N COðX;v00 ¼ 2Þ ¼ N NOðA;v0 ¼ 0Þ-COðX;v00 ¼ 2Þ ; N NOðB;v0 ¼ 0ÞCOðX;v00 ¼ 2Þ N COðX;v00 ¼ 3Þ ¼ N NOðA;v0 ¼ 0Þ-COðX;v00 ¼ 3Þ According to these product-pair correlations without any dynamical effects, we can calculate the vibrational distributions of NO (A, B) by using NCO(X,v00 ) in Figure7A as follows: NOðA 2 Σ+ ; v0 Þ; ðN v0 ¼ 0 :N v0 ¼ 1 :N v0 ¼ 2 ¼ 1 : 0:59 : 0:23Þ NOðB 2 Π; v 0 Þ; ðN v0 ¼ 0 :N v0 ¼ 1 :N v0 ¼ 2 ¼ 1 : 0:59 : 59Þ They are shown in Figure7B,C. These calculated vibrational distributions of NO (A, B) turn out to fairly reproduce the experimental ones. It seems reasonable to suggest that the vibrational distributions of the products, NO (A, B), are essentially attributed to the product-pair correlations under the vibrational distribution of CO (X, v00 ) produced from the vertical transition of CO (a 3Π, v0 = 0) f CO (X, v00 ) in the course of energy transfer. H. Molecular Alignment Effect of CO (a 3Π) on Electron Exchange. The dependence of the cross section on the CO (a 3Π) alignment indicates that the dynamics is significantly controlled by the alignment of CO (a 3Π) in the collision frame. The electron configurations related to the title reaction are summarized as below. COðX 1 Σ+ Þ: ½ð1σÞ2 ð2σÞ2 ð3σÞ2 ð4σÞ2 ð5σÞ2 ð1πÞ4 COða 3 ΠÞ: ½ð1σÞ2 ð2σÞ2 ð3σÞ2 ð4σÞ2 ð5σÞ1 ð1πÞ4 ð2πÞ1

Figure 7. (A) Vibrational distribution of CO (X, v00 ) estimated from the FranckCondon factor for the transition CO (a 3Π, v0 = 0) f CO (X, v00 ). (B) Vibrational distributions of NO (A, v0 ) estimated from the product-pair correlations between NO (A, v0 ) and CO (X, v00 ) without any dynamical effects. (Color bars) Contribution of each population correlated with CO (X, v00 ), NNO(A,v0 )-CO(X,v00 ). (Gray bar) Experimental. (C) Vibrational distributions of NO (B, v0 ) estimated from the productpair correlations between NO (B, v0 ) and CO (X, v00 ) without any dynamical effects. (Color bars) Contribution of each population correlated with CO (X, v00 ), NNO(B,v0 )-CO(X,v00 ). (Gray bar) Experimental.

NOðX 2 ΠÞ: ½ð1σÞ2 ð2σÞ2 ð3σÞ2 ð4σÞ2 ð5σÞ2 ð1πÞ4 ð2πÞ1 NOðA 2 Σ+ Þ: ½ð1σÞ2 ð2σÞ2 ð3σÞ2 ð4σÞ2 ð5σÞ2 ð1πÞ4 ð6σÞ1 NOðB 2 ΠÞ: ½ð1σÞ2 ð2σÞ2 ð3σÞ2 ð4σÞ2 ð5σÞ2 ð1πÞ3 ð2πÞ2 If the title reaction proceeds via the electron exchange process, the reaction is controlled by the following two electron-transfer processes. 1. Electron transfer (ET) NO (A 2Σ+): from the 2π orbital of CO (a 3Π) to the empty 6σ orbital of NO (X 2Π) NO (B 2Π): from the 2π orbital of CO (a 3Π) to the unpaired 2π orbital of NO (X 2Π) 2. Back electron transfer (BET) 8061



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orbital overlap [CO (2π) + NO (6σ)] and [CO (5σ) + NO (2π)] are allowed only at the sideways configuration of CO (a 3Π). NO (B 2Π). As shown in Figure 8B, the orbital overlap [CO (2π) + NO (2π)] in ET is favorable at both the sideways and the axial configurations of CO (a 3Π). However, the axial configuration of CO (a 3Π) is unfavorable for the orbital overlap [CO (5σ) + NO (1π)] in BET because the 1π orbital has a nodal plane along the NO molecular axis. As a result, two sets of orbital overlap [CO (2π) + NO (2π)] and [CO (5σ) + NO (1π)] are allowed only at the sideways configuration of CO (a 3Π). In summary, only the sideways configuration of CO (a 3Π) turns out to be favorable for the electron exchange for both the NO (A 2Σ+) and NO (B 2Π) formations. In addition, the favorable mutual orientational configuration between CO (a 3 Π) and NO (X 2Π) is almost the same for the NO (A 2Σ+) and NO (B 2Π) formations. In other words, the electron exchange mechanism that is operative through the formation of a weakly bound complex OCNO can explain the experimental results; no steric effect on the internal excitation for NO (A 2Σ+) and NO (B 2Π); significant CO (a 3Π) alignment effect on the reactivity for the NO (A 2Σ+) and NO (B 2Π) formations.

Figure 8. Electron exchange process for the NO (A) and NO (B) formations via the orbital overlap at the two representative alignments of CO (a 3Π) (axial, sideways). (A) NO (A 2Σ+): Electron transfer from the 2π orbital of CO (a 3Π) to the empty 6σ orbital of NO (X 2Π) and back electron transfer from the unpaired 2π orbital of NO (X 2Π) to the unpaired 5σ orbital of CO (a 3Π). (B) NO (B 2Π): Electron transfer from the unpaired 2π orbital of CO (a 3Π) to the unpaired 2π orbital of NO (X 2Π) and back electron transfer from the 1π orbital of NO (X 2Π) to the unpaired 5σ orbital of CO (a 3Π).

NO (A 2Σ+): from the 2π orbital of NO (X 2Π) to the unpaired 5σ orbital of CO (a 3Π) NO (B 2Π): from the 1π orbital of NO (X 2Π) to the unpaired 5σ orbital of CO (a 3Π) For the energy transfer, two sets of molecular orbital overlap, [CO (2π) + NO (6σ (2π))] and [CO (5σ) + NO (1π (2π))], must be allowed. A clear molecular alignment dependence observed in the title reaction indicates that the alignment of CO (a 3Π) gives a significant effect on the electron and/or the back electron transfer processes. We have to consider the steric effect on the electron exchange probability in the electron transfer processes 1 and 2. For this purpose, we calculate the electron density distribution of the CO molecular orbitals (2π, 5σ) and the NO molecular orbitals (1π, 2π, 6σ) by ab initio calculation using MP4 with the UHF/6-311++G(3df,3pd) basis set. They are summarized in Figure 6. The efficiency of molecular orbital overlap for the NO (A) and NO (B) formations are summarized as below, NO (A 2Σ+): As shown in Figure 8A, the sideways configuration of CO (a 3Π) is favorable for the orbital overlap [CO (2π) + NO (6σ)] in ET, whereas the axial configuration is unfavorable for the orbital overlap in ET because the 2π orbital has a nodal plane along the CO molecular axis. At the sideways configuration of CO (a 3Π), the efficient orbital overlap [CO (5σ) + NO (2π)] in BET also should be possible. As a result, two sets of

V. CONCLUSIONS The oriented CO (a 3Π, v0 = 0, Ω = 1 and 2) beam has been prepared by using an electric hexapole and applied to the energy transfer reaction of CO (a 3Π, v0 = 0, Ω = 1 and 2) + NO (X 2Π) f NO (A 2Σ+, B 2Π) + CO (X 1Σ+). The emission spectra have been measured at three orientation configurations (C-end, O-end, random). The shape of the emission spectra turns out to be insensitive to the molecular orientation; the vibrational population of NO (A 2Σ+, v0 = 02) and NO (B 2Π, v0 = 02) are roughly determined to be Nv0 =0:Nv0 =1:Nv0 =2 = 1:0.40 ( 0.05:0.10 ( 0.05 and Nv0 =0:Nv0 =1:Nv0 =2 = 1:0.6 ( 0.1:0.7 ( 0.1, respectively, and the branching ratio of NO (A) and NO (B) is estimated to be γ/β ∼ 0.3 ( 0.1 by means of spectral simulation. The effect of product-pair correlations between CO (X, v00 ) and NO (A 2Σ+, v0 = 02), NO (B 2Π, v0 = 02) on the vibrational distribution of NO (A 2Σ+, v0 ) and NO (B 2Π, v0 ) is discussed. Steric opacity function has been determined for the NO (A 2Σ+) and NO (B 2Π) channels. For both channels, the largest reactivity at the sideways with the small reactivity at the molecular axis direction is observed. These CO (a 3Π) alignment effects are discussed in terms of the steric asymmetry on two sets of molecular orbital overlap, [CO (2π) + NO (6σ (2π))] and [CO (5σ) + NO (1π (2π))]. ’ ACKNOWLEDGMENT We acknowledge Professor T. Munakata for lending us the PC-IMD detector. ’ REFERENCES (1) (2) (3) (4) (5) (6) (7) 8062

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Steric Effect in the Energy Transfer Reaction of Oriented CO (a 3Î , v

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