Collision Energy Dependent Cross Section and Rotational Alignment

Collision Energy Dependent Cross Section and Rotational Alignment of NO (A 2Σ+) in the Energy-Transfer Reaction of N2 (A3Σu+) + NO (X 2Π) → N2 (X...
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Collision Energy Dependent Cross Section and Rotational Alignment of NO (A 2Σ+) in the Energy-Transfer Reaction of N2 (A3Σu+) + NO (X 2 Π) → N2 (X 1Σg+) + NO (A 2Σ+) H. Ohoyama* Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan ABSTRACT: We have studied the collision energy dependent cross section and alignment of NO (A 2Σ+) rotation in the energy-transfer reaction of N2 (A 3Σu+) + NO (X 2Π) → N2 (X 1Σg+) + NO (A 2Σ+) at the collision energy (E) region of 0.03−0.2 eV. NO (A 2Σ+) emission in two linear polarization directions in the collision frame (parallel (∥) and perpendicular (⊥) with respect to the relative velocity vector (vR)) has been measured as a function of collision energy. NO (A 2Σ+) rotation (J-vector) turns out to be aligned perpendicular to vR. In addition, collision energy is found to enhance the degree of alignment of NO (A 2Σ+) rotation. The collision energy dependent cross sections σ∥,(⊥)(E) (excitation functions) show a rapid fall-off following an initial rise with a threshold less than 0.02 eV. The excitation function at the parallel alignment of NO (A 2Σ+) rotation, σ(J∥vR, (E), is slightly shifted to the low collision energy region as compared with σ(J ⊥ vR, E). We propose that the rapid fall-off feature in the excitation function is attributed to the multidimensional nonadiabatic transitions.

1. INTRODUCTION In the past decade, studies on reaction dynamics have progressed rapidly, especially for the atom−molecular reactions. Molecular beam experiments have made it possible to examine the chemical processes on a molecular level through differential cross section,1−3 steric effect,4−10 and so on. However, the reaction dynamics in the molecular−molecular reactions has been rarely studied experimentally.11−14 In contrast to the extensive studies on the reaction dynamics for the electronically excited atoms,15−18 the studies on the reaction dynamics for the electronically excited molecules have been extremely limited. The molecular−molecular reactions involving an electronically excited molecule are fundamental processes in the chemistry such as of the upper atmosphere, combustion, photonic synthesis, and so on.19 These reactions oftentimes involve excitation energy (E−E) transfer,

system like AB + CD, whose potential energy surface must be at least six dimensions on entrance and on exit, respectively. From this point of view, it is imperative to identify the important degree of freedom among the multidegree of freedom on the potential energy surfaces. The vector correlation related to mutual orientation configuration (here, we call such a vector correlation stereo− vector correlation) is expected to be an important index for the screening of the important degree of freedom in the multidegree of freedom reaction system. Recently, we succeeded to study the aligned N2 (A 3Σu+) + oriented NO (X 2Π, Ω = 1/2) reaction as a function of the mutual orientational configuration between the two reactants in the collision frame by employing the state-selecting hexapole techniques on both reactants.31 This led to the determination of a multidimensional steric opacity function (stereo−vector correlation). Moreover, we studied another stereo−vector correlation between the alignment of NO (A 2Σ+) rotation and the reactant N2 (A 3Σu+) alignment in the collision frame.32 From a series of studies on the stereo−vector correlations,31−33 we suggested that the title reaction is related to the multidimensional nonadiabatic transitions with the energy resonance to the product-pair states (N2 (X, v″ = 0−2) + NO (A, v′ = 0−2)), which are selectively favorable at the short N−N distance within the attractive region on the entrance potential surface. We proposed the multidimensional non-

AB* + CD → AB + CD*

wherein electronic energy is transferred from the excited molecule AB* to the collision partner CD.20−22 The collisional deactivation reactions of the lowest excited states of N2, N2 (A 3Σu+), are of particular interest because N2 (A 3Σu+) is known as an important energy carrier in the Earth’s atmosphere. In particular, the title reaction is significant as a benchmark for the collision dynamics in the open-shell molecular−molecular systems. Despite numerous studies on the kinetics of N2 (A 3Σu+),22−30 the details of its reaction dynamics still remain unsolved. This is because it is impossibly difficult to get the full dimensional information on the potential energy surface even for a simple molecule−molecule reaction © 2014 American Chemical Society

Received: July 31, 2014 Revised: September 24, 2014 Published: September 25, 2014 9646

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The discharge was ignited by applying a pulsed grid voltage, which also serves as the time origin for the time-of-flight measurement with a flight length of 970 mm. Because the discharge is restricted within the narrow space region in the discharge source (a few millimeters in length along the beam axis), the generation of N2 (A 3Σu+) almost exactly follows the pulsed grid voltage with a pulse width of 40 μs, which can be confirmed by measuring the time variation of the vacuum ultraviolet (VUV) stray light from the discharge source. Although the velocity distribution in the pulsed N2 (A 3Σu+) beam might not be uniform depending on the beam part, even if this is the case, we can obtain the sufficiently accurate TOF spectrum without any correction due to the nonuniform velocity distribution within the pulsed N2 (A 3Σu+) beam because the pulse width of N2 (A 3Σu+) beam is sufficiently short as compared with the flight time. In our TOF method, the time variation for the generation of the pulsed N2 (A 3Σu+) beam corresponds to the gate function for the commonly used TOF method using a mechanical chopper. The N2 (A 3Σu+) beam is detected by a microchannel plate (MCP) detector (Hamamatsu, F4655−10). The NO (X 2Π) beam with a pulse width of 10 ms is injected from a pulsed valve with a stagnation pressure of 10 Torr that is placed at a distance of 8 cm from the beam crossing point. The mean velocity of NO (X 2Π) beam is determined to be 406 ms−1. The N2 (A 3Σu+) beam collides with the uniform part in NO (X 2Π) beam at the beam crossing point (970 mm downstream from the N2 (A 3Σu+) beam source). NO (A 2Σ+) emission (190−300 nm) from the beam crossing point (ca. 2 mm sphere in diameter) is detected by a solar blind photomultiplier (Hamamatsu R6836) through a polarizer (Opto−line PUV−D25.4). The polarizer is set at two polarization directions (parallel (∥) and perpendicular (⊥) to vR). Needless to say, for the rigorous procedure, the polarizer should be rotated to make sure that it measures parallel or perpendicular to the relative velocity for each velocity of N2 (A 3 + Σu ) beam because the relative velocity vector changes as the velocity of N2 (A 3Σu+) changes. Fortunately, however, the misalignment angle (θvr) of the relative velocity (vr) for each velocity to vR is restricted within the range of less than 10° over the velocity range of N2 (A 3Σu+) beam. This misalignment gives a minor correction of less than 5% for the second Legendre moment of the angular distribution of J-vector of NO (A 2Σ+) rotation, P2(cos(θvr)), which means the minor effect on the degree of polarization within the experimental error range (see eq 5). Therefore, as a good approximation, we can measure the polarization over the velocity range of N2 (A 3Σu+) beam at the fixed two polarization directions to vR (parallel (∥) and perpendicular (⊥) to vR). The signal from the photomultiplier was counted by a multichannel scaler (Stanford SR430) as a function of flight time of N2 (A 3Σu+) beam.

adiabatic transitions like tunneling type along the N−N (and N−O) distance (and NO rotation) as well as a nonadiabatic transition like Landau−Zener type along the intermolecular distance between N2 (A 3Σu+) and NO (X 2Π).32 To ascertain the proposed mechanism and to verify the effectiveness of the stereo−vector correlation as an index for screening of the important degree of freedom, it is of great importance to explore the collision energy dependent cross section (excitation function) because such experiments give particularly detailed information on the interaction potential in the course of energy-transfer processes (or the height of any barrier on the entrance surface leading to the surface crossing). Ottinger et al. studied the collision energy dependence of NO(A) formation, and they found that the cross sections for excitation of NO(A) by N2(A) drop by about 2 orders of magnitude between 1 and 200 eV.34 However, no study has been carried out at the collision energy region less than 1 eV. In the present study, we have studied the collision energy dependence of the cross section and of the alignment of NO (A 2 + Σ ) rotation in the collision frame. Collision energy is found to give a significant effect on the alignment of NO (A 2Σ+) rotation as well as on the energy-transfer probability. The excitation functions show a rapid fall-off following an initial rise with a threshold estimated to be less than 0.02 eV. These characteristics of the excitation function confirm the criterion for the reaction path favorability proposed from the stereo− vector correlations that the energy transfer takes place via the multidimensional nonadiabatic transitions which facilitate on the attractive entrance surface.32

2. EXPERIMENT Figure 1 shows the Newton diagram for the title reaction with the geometric relationship between the angle of J-vector of NO

Figure 1. Newton diagram for the title reaction with the geometric relationship between the angle of J-vector of NO (A 2Σ+) rotation (JvR) and the two polarization directions (parallel (∥) and perpendicular (⊥)) in the collision frame (with respect to the mean relative velocity vector, vR)).

(A 2Σ+) rotation (JvR) and the two polarization directions (parallel (∥) and perpendicular (⊥)) in the collision frame (with respect to the mean relative velocity vector (vR) which is tilted at 25° degrees to the N2 (A3Σu+) beam axis). Collision energy dependence of the cross section and of the degree of polarization of NO (A 2Σ+) emission were determined by using a time-of-flight (TOF) technique with a pulsed N2 (A 3Σu+) beam. The experimental apparatus and procedures were almost the same with the previous one.33 A N2 (X 1Σg+) beam with a pulse width of 1 ms was generated by a supersonic expansion from a pulsed valve. A metastable N2 (A 3Σu+) beam was generated via the excitation of the uniform part in N2 (X 1Σg+) beam by a pulsed glow discharge with a pulse width of 40 μs.

3. RESULTS AND DISCUSSION 3.1. Collision Energy Dependent Cross Section and Rotational Alignment of NO (A 2Σ+). The collision energy (E) dependent cross section, σ∥,(⊥)(E), is measured by using a time-of-flight (TOF) method with a pulsed N2 (A 3Σu+) beam (pulse width of 40 μs). Figure 2 shows the TOF spectrum of N2 (A 3Σu+) beam measured by the MCP detector, IN2(A)(t), and those for the product NO (A 2Σ+) emission under the two polarization directions, I∥,(⊥)(t). We can observe a notable 9647

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Figure 2. Time-of-flight spectrum of N2 (A 3Σu+) beam measured by an MCP detector, IN2(t), black, and those for the product NO (A 2Σ+) emission under the two polarization conditions: I∥(t), red; I⊥(t), blue.

difference between IN2(A)(t) and I∥,(⊥)(t). The cross sections, σ∥,(⊥)(E), are determined from the TOF spectra as35 σ , ⊥(E) ∝

I

,(⊥)(t )vN2(A)

IN2(A)(t )vrel

(1) 2

Figure 4. (A) Degree of polarization of NO (A 2Σ+) emission as a function of collision energy (E), P(E). Experimental, open circle; smoothed, solid line. (B) The second Legendre moment of the angular distribution of J-vector of NO (A 2Σ+) rotation as a function of the collision energy (E), ⟨P2(cos JvR)⟩E, determined from eq 5 by substitution of P(E): experimental, open circle; smoothed, solid line.

2 0.5

vN2(A) = L /t , vrel = [(vN2(A)) + ( vNO) ] , m N2mNO (vrel)2 E= 2(m N2 + mNO)

(2)

where L is the flight length (970 mm), t is the flight time, vN2(A) is the velocity of N2 (A 3Σu+), vNO is the mean velocity of NO beam (406 ms−1), and vrel is the relative velocity. As can be seen in Figure 3, σ∥,(⊥)(E) shows a rapid fall-off following an initial

F(Jv , E) = R

∑ n

2n + 1 × ⟨Pn(cos Jv )⟩E × Pn(cos Jv ) R R 2 (4)

where JvR is the angle of J-vector of NO (A Σ ) rotation in the collision frame and where ⟨Pn(cos JvR)⟩E is the nth Legendre moment of the angular distribution of J averaged over the relative velocity distribution at the collision energy (E). Pn(cos JvR) is the nth Legendre polynomial. The relationship between ⟨P2(cos JvR)⟩E and P(E) can be approximated by32 2 +

⟨Pn(cos Jv )⟩E = R

(5)

Figure 4B shows ⟨P2(cos JvR)⟩E estimated from eq 5 by substitution of P(E). As mentioned in the Experiment section, the misalignment (angle θvr) between the relative velocity (vr) for each velocity and vR gives the minor correction of less than 5% for the second Legendre moment of the angular distribution of J-vector of NO (A 2Σ+) rotation because of the correction term of P2(cos(θvr)) > 0.95). This correction is ignorable because it is less than the experimental error of ⟨P2(cos JvR)⟩E. We can find a pronounced change of ⟨P2(cos JvR)⟩E on E: the magnitude of ⟨P2(cos JvR)⟩E turns out to increase as the collision energy increases. The cross section at each (JvR, E) can be approximated by using P2(cos JvR)E as follows36

Figure 3. Collision energy dependence of the cross sections under the two polarization conditions, which are determined from the TOF spectra using eq 1: σ∥(E), red; σ⊥(E), blue.

rise with a threshold less than 0.02 eV. In addition, we can recognize that NO (A 2Σ+) emission is polarized perpendicular to vR. Figure 4A shows the degree of polarization of NO (A 2 + Σ ) emission, P(E), as a function of collision energy, which is defined as P(E) ≡ [σ (E) − σ⊥(E)]/[σ (E) − σ⊥(E)]

8 × P(E) 3 − P(E)

(3)

It is found that the magnitude of negative P(E) increases as the collision energy (E) increases. This means that the rotational alignment of NO (A 2Σ+) is enhanced by the collision energy. The angular distribution of J-vector of NO (A 2Σ+) rotation in the collision frame, F(JvR, E), can be expressed by

σ(Jv , E) = [σ (E) + 2σ ⊥(E)] R

× [1 + 5/2 × ⟨P2(cos Jv )⟩E × P2(cos Jv )] R

R

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The resultant σ(JvR, E) is plotted in Figure 5 as a 3D representation. It is revealed that the collision energy gives a significant effect on the alignment of NO (A 2Σ+) rotation as well as the energy-transfer probability.

Figure 5. 3D representation of the angular distribution of J-vector of NO (A 2Σ+) rotation in the collision frame at each E, σ(JvR, E), calculated from eq 6 by substitution of ⟨P2(cos JvR)⟩E.

According to our recent studies on the stereocorrelated reactivity and on the stereocorrelated alignment of NO (A 2Σ+) rotation, the following stereo−vector correlations (designated by a double-headed arrow) are recognized.31,32 (i) NO (A 2Σ+) (J ⊥ vR) ↔ [N2 (A 2Σ+) (axial and sideways) ↔ NO (X 2Π) (axial)] (ii) NO (A 2Σ+) (J ∥ vR) ↔ [N2 (A 2Σ+) (oblique) ↔ NO (X 2Π) (sideways)] As a reference, these favorable mutual configurations are summarized in Figure 6A. Therefore, the cross section of σ(J ⊥ vR, E) corresponds to the excitation function at the mutual configuration of (i) [N2 (A 2Σ+) (axial and sideways) ↔ NO (X 2 Π) (axial)], while the cross section of σ(J ∥ vR, E) corresponds to that at the mutual configuration of (ii) [N2 (A 2Σ+) (oblique) ↔ NO (X 2Π) (sideways)]. Figure 6B shows the cross-sectional views of σ(JvR, E) in Figure 5 at the two alignment conditions σ(J ⊥ vR, E) and σ(J ∥ vR, E). In both cases, the excitation function shows a rapid fall-off following an initial rise with a threshold less than 0.02 eV. It is found that σ(J ∥ vR, E) is slightly shifted to the low collision energy region as compared with σ(J ⊥ vR, E). This difference might reflect the difference in the intermolecular potential between these two favorable mutual configurations (i, ii). The enhancement of the negative rotational alignment of NO (A 2Σ+) by collision energy means that the fraction of configuration (i) becomes large as the collision energy increases. The rapid fall-off feature observed in the excitation function is consistent with the one reported by Ottinger et al. at the higher energy region (1−200 eV).34 3.2. Comparison with Stereo−Vector Correlations. Although the intermolecular potential was studied for the ground state of NO−N2 and (NO−N2)+ system,37 unfortunately, no calculation is there for the [N2 (A 3Σu+) − NO (X 2 Π)] and [N2 (X 1Σg+) − NO (A 2Σ+)] system. Figure 7 schematically shows the mechanism proposed from the stereo− vector correlations.32 We suggested that the title reaction is related to the multidimensional nonadiabatic transitions from

Figure 6. (A) Stereocorrelated reactivity and the alignment of NO (A 2 + Σ ) rotation cited from the references.31,32 (i) NO (A 2Σ+) (J ⊥ vR) ↔ [N2 (A 2Σ+) (axial and sideways) ↔ NO (X 2Π) (axial)] and (ii) NO (A 2Σ+) (J ∥ vR) ↔ [N2 (A 2Σ+) (oblique) ↔ NO (X 2Π) (sideways)]. (B) The cross-sectional view of σ(JvR, E) in Figure 4 at the two alignment conditions σ(J ⊥ vR, E), σ(J ∥ vR, E). The cross section of σ(J ⊥ vR, E) corresponds to the excitation function at the mutual configuration (i) [N2 (A 2Σ+) (axial and sideways) ↔ NO (X 2Π) (axial)], while the cross section of σ(J ∥ vR, E) corresponds to that at the mutual configuration (ii) [N2 (A 2Σ+) (oblique) ↔ NO (X 2Π) (sideways)].

the entrance surface (I) [ N2 (A 3Σu+) + NO (X 2Π)] to the exit surface (II) [N2 (X 1Σg+) + NO (A 2Σ+)] with the energy resonance to the product-pair states (1∼3: N2 (X, v″ = 0−2) + NO (A, v′ = 0−2)), which is selectively favorable at the short N−N distance (R(N−N)) within the attractive region on the multidimensional entrance potential surface. The multidimensional nonadiabatic transitions like tunneling type are expected along R(N−N) (and N−O distance (R(N−O)), NO rotation) as well as a nonadiabatic transition like Landau−Zener type along the intermolecular distance between N2 (A 3Σu+) and NO (X 2Π), R(N2−NO). The criterion for the reaction path favorability should be based on comparing either the height of any barrier on the entrance surface (I) (or the energy at the surface crossing point) with the available energy. Therefore, the entrance surface (I) might be attractive (or at least less repulsive), while the exit surface (II) should be repulsive as shown in Figure 7. The observed initial rise in the excitation function with a threshold less than 0.02 eV should confirm this expectation that the title reaction is favorable at the attractive (or less repulsive) region on the entrance surface (I). As can be seen in Figure 6, the excitation functions show a rapid fall-off feature. We propose that this rapid fall-off feature in the excitation function is attributed to the multidimensional nonadiabatic transitions with the energy resonance to the 9649

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Figure 7. (A) A schematic drawing for the effect of intermolecular interaction on the energy transfer via the surface crossing (Rx) between entrance surface (I, red line) and exit surface (II, blue line) along the N2 (A 3Σu+) − NO (X 2Π) distance, R(N2−NO). The two potential curves designated by a and b correspond to the potential curves at the different R(N−N) distance: (a) (solid line) potential minimum of N2 (A 3Σu+), (b) (dashed line) end of Franck−Condon region of N2 (A 3Σu+, v = 0), see Figure 7B. The double arrows indicate the energy difference between a and b. The surface crossing along R(N2−NO) should lead to a Landau−Zener type transition combined with the multidimensional nonadiabatic transitions along other reaction coordinates. The surface crossing between the entrance surface (I) and the exit surface (II) should be possible only at the short R(N−N) distance near the end of Franck−Condon region designated by b in Figure 7B. (B) A schematic drawing of the mechanism proposed from the stereo−vector correlations with the schematic cross sectional views of the potential energy surfaces (I and II) along R(N−N) distance in arbitrary mutual orientational configuration at long R(N2−NO) and at the crossing point R(N2−NO) = Rx. Three groups of product-pair states on the surface (II) because of energetic restriction between N2 (X, v″ = 0−2) and NO (A, v′ = 0−2) are designated by 1−3. The efficient energy transfer via the surface crossing needs the energy resonance with the product-pair states (1∼3) at the surface crossing point. According to the significant change of the bond length by energy transfer, [N2 (A) (1.286 Å) → N2 (X) (1.097 Å) and NO (X) (1.150 Å) → NO (A) (1.063 Å)], the R(N−N) distance (and R(N−O)) must be an important reaction coordinate for the energy transfer. The surface crossings along R(N−N), R(N− O), and NO rotation might induce the multidimensional nonadiabatic transitions of tunneling type. The attractive entrance surface (I) is favorable to arrive at the crossing point within the available energy and to improve the energy resonance with the product-pair states.

to the potential curves depending on the mutual configuration of reactants: (2πV2)/(ℏ|ΔF|). In this case, the overall transition probability (QLZ) for the Landau−Zener type via the surface crossing along R(N2−NO) is expressed by38,39

product-pair states at the surface crossing points. Generally speaking, the surface crossing along the intermolecular distance between N2 (A 3Σu+) and NO (X 2Π), R(N2−NO), should lead to a Landau−Zener type transition. The transition probability for the Landau−Zener type (PLZ) is expressed by ⎡ 2πV 2 ⎤ PLZ = exp⎢ − ⎥ ∝ exp( −C / |E − Ex| ) ⎣ ℏvx|ΔF | ⎦

Q LZ ≡ 2PLZ(1 − PLZ) (7)

∝ exp( −C / |E − Ex| )

where V is the strength of nonadiabatic coupling, vx is the relative velocity at the potential crossing point (Rx), |ΔF| is the absolute vale of the difference in slopes at Rx, E is the collision energy, Ex is the potential energy at Rx, (E − Ex)1/2 corresponds to the relative velocity vx at Rx, and C is the parameter related

× [1 − exp( −C / |E − Ex| )]

(8)

The results fitted by using eq 8 with Ex = 0.02 eV are summarized in Figure 8 (designated by s = 0). It is found that the experimental excitation function has an extremely rapid fall9650

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where s is the number of reaction coordinates for the multidimensional nonadiabatic transitions except for R(N2− NO). The fitted results by using eq 9 with Ex = 0.02 eV are summarized in Figure 8 as a function of s. In spite of a simple model, the fitting with s = 3−4 turns out to fairly reproduce the experimental result. Therefore, it seems to be reasonable to consider that the rapid fall-off feature reflects the multidimensional nonadiabatic transitions via the multidimensional surface crossings between the entrance surface (I) and the exit surface (II) along the reaction coordinates like R(N2−NO), R(N−N), R(N−O), NO rotation, and so on with the energy resonance to the product-pair states.

4. CONCLUDING REMARKS As a whole, the characteristics of the excitation function can confirm the criterion for the reaction path favorability proposed from the stereo−vector correlations.32 In other words, the present result strongly indicates that the stereo−vector correlation is an important index for the screening of the important degree of freedom in the multidegree of freedom reaction system. Specifically, the results and the proposed Landau−Zener model combined with the multidimensional nonadiabatic transitions via the multidimensional surface crossings along other reaction coordinates may be a starting point for a deeper understanding of the involved multidimensional nonadiabatic transitions. In particular, in the present study, we proposed the direct coupling between the entrance surface (I) [ N2 (A 3Σu+) + NO (X 2Π)] and the exit surface (II) [N2 (X 1Σg+) + NO (A 2 + Σ )] with the energy resonance to the product-pair states (1∼3: N2 (X, v″ = 0−2) + NO (A, v′ = 0−2)) because the vibrational distribution of product NO (A 2Σ+, v′ = 0, 1, 2) can be well explained by the Franck−Condon factor for the N2 (A, v′ = 0) → N2 (X, v″) transition.28,32 However, we cannot rule out a crucial “harpooning” type of mechanism for the mediating coupling between the entrance and exit vibrational manifolds through a charge−exchange N2−−NO+ ion-pair curve. A quantitative guideline can be given following the treatment for an analogous system, Xe* + N2 → Xe* + N2* in refs 40and 41; applied to the present case, an ion−covalent interaction region can be estimated at an intermolecular distance of about 3 Å or larger.

Figure 8. Excitation functions at the two alignment conditions fitted by using eq 8 as a simple Landau−Zener type transition (QLZ, blue line) and by using eq 9 as a Landau−Zener type transition combined with the multidimensional nonadiabatic transitions along other reaction coordinates (Q): (A) σ(J ⊥ vR, E), (B) σ(J ∥ vR, E). Closed circle, experimental; lines, fitted ones. The numbers (s) in the figure indicate the number of reaction coordinates for the multidimensional nonadiabatic transitions except for R(N2−NO). The degree of fitting is fairly improved by taking into account the multidimensional nonadiabatic transitions with s = 3−4.

off feature as compared with the one expected from the Landau−Zener type transition. In other words, a simple Landau−Zener type transition cannot explain the experimental results. As shown in Figure 7A, the surface crossing between the entrance surface (I) and the exit surface (II) should be possible only at the short R(N−N) near the end of Franck− Condon region designated by b. According to the stereo− vector correlations, the stretching of N−N (and N−O) and NO rotation must be one of the important reaction coordinates for the multidimensional nonadiabatic transitions as well as R(N2−NO). The surface crossings along each reaction coordinate, R(N−N) (and R(N−O), NO rotation), might induce the nonadiabatic transition of tunneling type.39 These probabilities should be roughly proportional to the frequency to reach the short R(N−N) because of the N−N stretch motion (and similarly for R(N−O), NO rotation), which should increase in proportion to the residence time at the crossing point (or decreases in inverse proportion to the velocity (vx) at the crossing point). According to this simple model, the overall multidimensional nonadiabatic transition (Q) via the Landau− Zener type transition combined with the multidimensional nonadiabatic transitions along other reaction coordinates is expressed by

■

Corresponding Author

*E-mail: [email protected]−u.ac.jp. Notes

The authors declare no competing financial interest.

■

∝

C |E − Ex|

⎛ ⎞ ⎡ ⎟ × 1 − exp⎜ − ⎝ ⎠ ⎢⎣ [ |E − Ex| ]s

C |E − Ex|

REFERENCES

(1) Casavecchia, P. Chemical Reaction Dynamics with Molecular Beams. Rep. Prog. Phys. 2000, 63, 355−414. (2) Yang, X.; Liu, K. Advanced Series in Physical Chemistry 14, Modern Trends in Chemical Reaction Dynamics; World Scientific: Singapore, 2004. (3) Wang, F.; Liu, K.; Rakitzis, T. P. Revealing the Stereospecific Chemistry of the Reaction of Cl with Aligned CHD3 (ν1 = 1). Nat. Chem. 2012, 4, 636−641. (4) Orr-Ewing, A. J.; Zare, R. N. Orientation and Alignment of Reaction Products. Annu. Rev. Phys. Chem. 1994, 45, 315−366. (5) Loesch, H. J. Orientation and Alignment in Reactive Beam Collisions: Recent Progress. Annu. Rev. Phys. Chem. 1995, 46, 555− 594.

Q ≡ 2PLZ(1 − PLZ)/vx s ⎛ exp⎜ − ⎝

AUTHOR INFORMATION

⎞⎤ ⎠⎥⎦

⎟

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(29) Golde, M. F.; Moyle, A. M. Study of the Products of the Reactions of N2(A3Σu+): The Effect of Vibrational Energy in N2(A). Chem. Phys. Lett. 1985, 117, 375−380. (30) Thomas, J. M.; Katayama, D. H. Branching Fractions of the Product NO(A 2Σ+, ν=0, 1) and NO (B2Πr, ν=0) Emissions Observed as a Function of ν′ in the Energy Transfer Reaction N2(A3Σ+u, ν′) + NO (X2Πr, ν″=0). Chem. Phys. Lett. 1993, 214, 250−256. (31) Ohoyama, H.; Maruyama, S. Stereo Correlated Dynamics in the Energy Transfer Process of Aligned N2 (A 3Σu +) + Oriented NO (X 2 Π, Ω = 1/2) → NO (A 2Σ+) + N2 (X 1Σg +). J. Chem. Phys. 2012, 137, 064311. (32) Ohoyama, H. Vector Correlation Between the Alignment of Reactant N2 (A 3Σu +) and the Alignment of Product NO (A 2Σ+) Rotation in the Energy Transfer Reaction of Aligned N2 (A 3Σu +) + NO (X 2Π) → NO (A 2Σ+) + N2 (X 1Σg +). J. Chem. Phys. 2013, 139, 234308. (33) Ohoyama, H.; Maruyama, S. Alignment Effect of N2(A3Σu+) in the Energy Transfer Reaction of Aligned N2(A3Σu+) + NO(X2Π) → NO(A2Σ+) + N2(X1Σg+). J. Phys. Chem. A 2012, 116, 6685−6692. (34) Ottinger, Ch.; Simons, J.; Setser, D. W. Spectroscopic Study of Electronic Energy Transfer from N2(A) and CO(a) to NO in a Beam Experiment. Ber. Bunsenges, Phys. Chem. 1978, 82, 655−660. (35) Scoles, G. Atomic and Molecular Beam Methods; Oxford: New York, 1988. (36) Zare, R. N. Angular Momentum; Wiley: New York, 1998. (37) Bartolomei, M.; Cappelletti, D.; de Petris, G.; Teixidor, M. M.; Pirani, F.; Rosi, M.; Vecchiocattivi, F. The Intermolecular Potential in NO−N2 and (NO−N2)+ Systems: Implications for the Neutralization of Ionic Molecular Aggregates. Phys. Chem. Chem. Phys. 2008, 10, 5993−6001. (38) Levine, R. D. Molecular Reaction Dynamics; Cambridge University Press: Cambridge, U.K., 2005. (39) Zhu, C.; Nakamura, H. Improvement of the Adiabatic Phase Integral for the Landau−Zener-type Curve Crossing. J. Chem. Phys. 1998, 109, 4689−4690. (40) Aquilanti, V.; Candori, R.; Pirani, F.; Krümpelmann, T. Ottinger, Ch. On the Interaction Potentials for the Electronic Energy Transfer Reactions Xe(3P0,2) + N2(X) → Xe(1S0) + N2(B 3Πg). Chem. Phys. 1990, 142, 47−57. (41) Aquilanti, V.; Candori, R.; Pirani, F. Ottinger, Ch. On the Dynamics of the Vibrationally Selective Electronic Energy Transfer from Metastable Xenon Atoms to Nitrogen Molecules. Chem. Phys. 1994, 187, 171−183.

(6) Bernstein, R. B.; Herschbach, D. H.; Levine, R. D. Dynamical Stereochemistry Issue. J. Phys. Chem. 1987, 91, 5365−5515. (7) Soep, B.; Vetter, R. Stereodynamics and Active Control in Chemical Reactions. J. Phys. Chem. 1995, 99, 13569−13754. (8) Loesch, H. J. Stereodynamics of Chemical Reactions. J. Phys. Chem. A 1997, 101, 7461−7690. (9) Stolte, S.; Suits, A.; Linnartz, H. Stereodynamics of Molecular Reactions. Chem. Phys. 2004, 301, 159−334. (10) Herschbach, D. Stereodynamics of Chemical Reactions. Eur. Phys. J. D 2006, 38, 3−236. (11) Alagia, M.; Balucani, N.; Casavecchia, P.; Stranges, D.; Volpi, G. G. Crossed Beam Studies of Four-Atom Reactions: The Dynamics of OH + D2. J. Chem. Phys. 1993, 98, 2459−2462. (12) Wang, J. H.; Liu, K.; Schatz, G. C.; ter Horst, M. Experimental and Theoretical Angular and Translational Energy Distributions for the Reaction CN + D2 → DCN + D. J. Chem. Phys. 1997, 107, 7869− 7875. (13) Hung, L. C.; Lee, Y. T.; Kaiser, R. I. Crossed Beam Reaction of the Cyanogen Radical, CN (X2Σ+), with Acetylene, C2H2 (X1Σ+g): Observation of Cyanoacetylene, HCCCN (X1Σ+). J. Chem. Phys. 1999, 110, 7119−7122. (14) Ohoyama, H.; Yamakawa, K.; Oda, R.; Nagamachi, Y.; Kasai, T. Rotationally Correlated Reactivity in the CH (v = 0, J, Fi) + O2 → OH (A) + CO Reaction. J. Chem. Phys. 2011, 134, 114306. (15) Watanabe, D.; Ohoyama, H.; Matsumura, T.; Kasai, T. Steric Effect in the Energy Transfer Reaction of Ar(3P2) + N2. J. Chem. Phys. 2006, 125, 084316. (16) Watanabe, D.; Ohoyama, H.; Matsumura, T.; Kasai, T. Effect of Mutual Configuration between Molecular Orientation and Atomic Orientation in the Oriented Ar(3P2) + Oriented CF3H Reaction. Phys. Rev. Lett. 2007, 99, 043201. (17) Ansersen, N.; Gallagher, J. W.; Hertel, I. V. Collisional Alignment and Orientation of Atomic Outer Shells I. Direct Excitation by Electron and Atom Impact. Phys. Rep. 1988, 165, 1−188. (18) Kishimoto, N.; Ohno, K. Observation of Anisotropic Interactions between Metastable Atoms and Target Molecules by Two-Dimensional Collisional Ionization Electron Spectroscopy. Int. Rev. Phys. Chem. 2007, 26, 93−138. (19) Marcus, R. A. Electron Transfer Reactions in Chemistry: Theory and Experiment (Nobel Lecture). Angew. Chem., Int. Ed. Engl. 1993, 32, 1111−1121. (20) Ohoyama, H.; Matsuura, Y. Steric Effect in the Energy Transfer Reaction of Oriented CO (a 3Π, v′ = 0, Ω = 1 and 2) + NO (X 2Π) → NO (A 2Σ+, B 2Π) + CO (X 1Σ+). J. Phys. Chem. A 2011, 115, 8055− 8063. (21) Shen, G.; Chen, H.; Xu, D.; Li, X.; Lou, N.; Liu, C.; Guo, J. The Study of E-E Energy Transfer between CO(a3Π, ν′) and NO(X2Π, ν″ = 0) in Beams. Chem. Phys. Lett. 1996, 257, 439−446. (22) Wategaonkar, S. J.; Setser, D. W. Excitation-Transfer Reactions from Nitrogen N2(A3Σu+) and Carbon Monoxide (a3Π) to Hydroxyl. J. Phys. Chem. 1990, 94, 7200−7205. (23) Ho, G. H.; Golde, M. F. Experimental Study of the Reactions of N2(A 3Σ+ u) with H Atoms and OH Radicals. J. Chem. Phys. 1991, 95, 8866−8870. (24) Golde, M. F. Reactions of N2(A3Σu+). Int. J. Chem. Kinet. 1988, 20, 75−92. (25) Herron, J. T. Evaluated Chemical Kinetics Data for Reactions of N(2D), N(2P), and N2(A3Σ+u) in the Gas Phase. J. Phys. Chem. Ref. Data 1999, 28, 1453−1484. (26) Stolarski, R. S.; Green, A. E. S. Calculations of Auroral Intensities from Electron Impact. J. Geophys. Res. 1967, 72, 3967− 3974. (27) Clark, W. G.; Setser, D. W. Energy Transfer Reactions of N2(A3Σu+). 5. Quenching by Hydrogen Halides, Methyl Halides, and Other Molecules. J. Phys. Chem. 1980, 84, 2225−2233. (28) Piper, L. G.; Coeles, L. M.; Rawlinks, W. T. State-to-State Excitation of NO(A 2Σ+, v′=0,1,2) by N2(A 3Σ+ u, v′=0,1,2). J. Chem. Phys. 1986, 85, 3369−3378. 9652

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