Collision-Induced Harpooning Observed in the Excimer Formation in

ARTICLE pubs.acs.org/JPCA

Collision-Induced Harpooning Observed in the Excimer Formation in the Oriented NF3 þ Oriented Kr*(3P2, MJ = 2) Reaction Y. Matsuura and H. Ohoyama* Department of Chemistry, Graduate School of Science, Osaka University Toyonaka, Osaka 560-0043, Japan ABSTRACT: We have studied how the KrF* formation in the NF3 þ Kr*(3P2) reaction depends on the mutual configuration between the orientation of the NF3 molecule and the alignment of the Kr*(3P2, MJ = 2) atom in the collision frame. The molecular steric opacity function has been determined as a function of the atomic orbital alignment (ML0 ) in the collision frame. The molecular steric opacity function turns out to depend remarkably on ML0 ; the |ML0 | = 1 alignment is favorable at the molecular axis direction, whereas the ML0 = 0 alignment is favorable at the sideways direction with a very poor reactivity at the molecular axis direction. The influence of deformation of the NF3 geometry on the electron affinity has been evaluated by ab initio calculation, and the ML0 dependent intermolecular potential has been estimated from the interaction potential for the brominerare gas system. We propose the “collision-induced harpooning mechanism” as a novel process for the harpooning in which collisional deformation of the NF3 geometry with Cs symmetry plays an important role as an initiating factor on electron transfer for the formation of NF3 due to increasing the electron affinity of NF3 and due to localizing the negative charge on the closest F-atom of NF3 anion. All experimental observations can support the collision-induced harpooning mechanism.

I. INTRODUCTION The harpoon mechanism is known as a fundamental process for the metal halide MX formation in the M þ RX reaction;1 the harpoon mechanism is based on a model of the reaction that pictures the M atom as approaching the RX molecules, and when the two are close enough an electron (the harpoon) flips across to the RX molecule. In place of two neutral particles there are now two ions, and so there is a Coulombic attraction between them. Under its influence the ions move together, the reaction takes place, and MX and X emerge. Similarly, the RgX* formation in the Rg*(3P) þ RX reaction is also known to proceed via the harpoon mechanism.27 If the RgX* formation is initiated by the harpoon mechanism, the cross section can be approximated as πrc2 by using rc in eq 11 e2 =r c ¼ IE  EA

ð1Þ

where IE is the ionization potential of Rg*(3P2), EA is the electron affinity of RX, and rc is the crossing distance between the covalent potential surface [Rg*(3P2) þ RX] and the ionic surface [Rgþ(2P3/2) þ RX]. The cross section is essentially determined by the distance (rc) at which the outermost s-electron jump takes place because Coulomb force between the ions [Rgþ(2P3/2)  X(1S0)] essentially ensures RgX* formation. σ ¼ πr 2c

ð2Þ

However, it is not obvious that this estimation is of general relevance because rc is not well-defined for the polyatomic r 2011 American Chemical Society

systems. At least, the reaction systems can be classified into two groups. One (group 1) is the reaction systems in which the experimental cross section is comparable to the estimated one. For example, in the CF3I þ Xe*(3P2) f XeI* þCF3 reaction, the estimated cross-section of 103 Å2 from eq 2 (IE(Xe*(3P2)) = 3.82 eV8 and EA(CF3I) = 1.57 eV9) is roughly in accordance with the experimental quenching cross section (116.1 Å2).10 Another (group 2) is the reaction systems in which the experimental cross section is far from the estimated one. For example, the experimental quenching cross section of 29 Å211 for the reaction of NF3 þ Kr*(3P2) f KrF* þ NF2 is extremely smaller than the cross section of 116 Å2 estimated from eq 2. In order to make clear the relationship between theory and practice, we have to thrash out problems with the electron affinity of reactant molecules in the harpooning process. In general, it is a very difficult problem to define the electron affinity in the reaction systems, because polyatomic reactant molecules can change their geometry along the reaction path, and besides, the electron affinity remarkably depends on the geometry. For example, Oster et al.12 reported that the dissociative attachment (DA) reaction (e þ CF3I f CF3 þ I) has no activation energy. This result means that the curve crossing between CF3I and CF3I takes place within the FranckCondon region of CF3I. In other words, the geometry of the CF3I anion is similar Received: January 29, 2011 Revised: March 24, 2011 Published: April 14, 2011 4583

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II. EXPERIMENT The experimental apparatus is similar to the one in our previous study.22,23 In brief, the Kr*(3P2, MJ = 2) atomic state was selected by using a 35 cm long magnetic hexapole, and the

)

)

)

Figure 1. Geometrical relationship between the molecular orientation configuration (parallel (Φ : N-end), antiparallel (Φa: F3-end), and orientation field off (Φoff: random orientation)) and the atomic orientation configuration (parallel (Θ ), perpendicular (Θ^), and antiparallel (Θa)) with respect to the direction of relative velocity vR with a Newton diagram for the title reaction. )

to that of the neutral CF3I. This similarity in geometry leads to the fact that the experimental adiabatic electron affinity of CF3I is suitable to consider the reaction dynamics. On the other hand, it was reported that the DA reaction (e þ NF3 f NF2 þ F) has the activation energy of Ea = 0.1 ( 0.05 eV.13 This result means that the curve crossing between NF3 and NF3 takes place out of the FranckCondon region. Since the geometry of NF3 must be far from that of the neutral NF3, in this case, an adiabatic electron affinity of NF3 is apparently unsuitable to consider the reaction dynamics. The steric asymmetry is an important index to study the detail of reaction dynamics.1417 Recently, we studied the multidimensional steric effects for the excimer (XeX*) formations in the reactions of the oriented Xe*(3P2, MJ = 2) with the oriented molecules (RX: CF3I, CH3I, CF3Br; X3R: CCl3F)1821 which commonly have the relatively large quenching cross sections (σQ ∼ a few hundred Å2);27 they belong to group 1. The X (or X3) end is commonly most reactive as expected from the chemical intuition like “steric hindrance” due to the nonreactive bulky group R. Every system exhibits a wide range of molecular orientation (and alignment) dependence affected by the atomic orbital alignment which does not correlate well with the chemical intuition. Especially, every system commonly shows the poor reactivity at the sideways direction in the molecular steric opacity function. We proposed the indirect mechanism for the dark channels (Xe þ X þ R) via the back electron transfer from the R segment (or dissociating R 3 3 3 X) to Xeþ as the origin of the poor reactivity at the sideways direction in the molecular steric opacity function. Except for this point, however, the simple consideration from the molecular geometry of RX and from the harpoon mechanism with the M0L conservation turns out to fairly explain the characteristics in the M0L dependent molecular steric opacity functions. Most recently, we studied the multidimensional steric effects for the XeF*(B, C) formations in the oriented Xe*(3P2, MJ = 2) þ oriented NF3 reaction22 that has the small quenching cross 2 11 3 section (σNF Q = 23 Å ); it belongs to group 2. In contrast with the other molecules belonging to group 1, the largest reactivity is observed at the sideways direction with poor reactivity at the molecular axis direction. A good correlation between the direction of the reactive lobe and the F-atoms direction from the center-of-mass of NF3 is recognized. We proposed the “collisioninduced harpooning mechanism” for the XeF*(B, C) formations. In order to verify the proposed mechanism, and to make clear the problem of the electron affinity of reactant molecule in the harpooning process, further studies on the other reaction systems belonging to group 2 are important and interesting to get additional evidence. In the present study, we have studied the multidimensional steric effect in the analogous reaction of NF3 þ Kr*(3P2) f KrF* þ NF2. Since the IE of Kr*(3P2) is larger than that of Xe*(3P2), the harpooning is expected to take place at the shorter intermolecular distance. In addition, some theoretical consideration of electron affinity and of the intermolecular potential has been carried out for better understanding of the multidimensional steric effect in the harpooning process.

ARTICLE

oriented NF3 was prepared by using a 40 cm long electrostatic hexapole. In the present study, the oriented Kr*(3P2, MJ = 2) atomic beam is oriented to the homogeneous magnetic orientation field B, and the oriented NF3 molecular beam is oriented to the homogeneous electric orientation field E. For the collision processes, however, the relative velocity vector (vR) serves as the other relevant quantization axis (i.e., collision frame). The cross section is then a function of the angle between those quantization axes. We have accomplished the double-orientation control by using both the oriented NF3 molecular beam and the oriented Kr*(3P2, MJ = 2) atomic beam whose configurations in the collision frame are independently controlled. The NF3 molecular beam is the same as the one used in our recent study for the XeF* formation in the NF3 þ Xe*(3P2) reaction;22 the velocity distribution of the NF3 molecular beam is characterized by the stream velocity of vs = 400 ms1 and the translational temperature of Ttrans = 200 K. The orientational distribution W(cos γE) of the molecular axis with respect to the electric orientation field direction (E) was determined by the trajectory simulation for the state selection in the hexapole field. Here, γE is the orientation angle of the NF3 molecular axis with respect to E. The nth Legendre moments, ÆPnæ, for the orientational distribution W(cos γE) calculated for the experimental condition at V0 = 12 kV are summarized to be ÆP1æ = 0.60, ÆP2æ = 0.22, ÆP3æ = 0.022, ÆP4æ = 0.021, ÆP5æ = 0.007, ÆP6æ = 0.003, and ÆP7æ = 0.002. The errors for the Legendre moments are estimated to be less than 10%. An oriented metastable Kr*(3P2, MJ = 2) beam was generated by a pulsed glow discharge with a pulse width of 100 μs, and then state-selected by the magnetic hexapole. The MJ state distribution of the state-selected Kr*(3P2) beam at the beam crossing point (1000 mm downstream from the Kr*(3P2) beam source) was directly determined by separating each MJ state using a SternGerlach type inhomogeneous magnetic state-selector (SGIM) as a function of arrival time, t0.24 The state-selected metastable Kr*(3P2) beam within the arrival time region (I) (1.90 e t0 e 2.15 ms) (corresponds to vs = 495 ( 30 ms1) is composed of almost pure Kr*(3P2, MJ = 2) (more than 95%). The emission signal produced from the collision with Kr*(3P2, MJ = 2) within this time region (I) was used for the present study. Figure 1 shows a schematic drawing of the configurations for the oriented NF3 molecule (i.e., the direction of the uniform electric orientation field E) and for the oriented Kr*(3P2, MJ = 2) atom (i.e., the direction of the magnetic orientation field B) with 4584

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pffiffiffiffiffiffiffiffiffiffiffi 0:125  jjM 0J j ¼ 2æ

pffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi 0:5  jjM 0J j ¼ 1æ þ 0:375  jM 0J ¼ 0æ ð3Þ

Under the doubly orientation controlled conditions, the oriented Kr*(3P2, MJ = 2) atomic beam collides with the oriented NF3 molecular beam at the beam crossing point. Unfortunately, in the present study, we have studied the KrF*(B, C) formations without separation because the small chemiluminescence intensity of KrF*(B, C) after separation prevents to obtain the signal intensity enough to analyze the steric effect with the good signalto-noise ratio. The chemiluminescence signal from the product KrF*(B, C) (λ = 190390 nm) was detected by a cooled and magnetic shielded photomultiplier. Only the signal enhanced by applying the electric hexapole field (V0 = 12 kV) was used as the chemiluminescence signal from the oriented NF3 þ oriented Kr*(3P2, MJ = 2) reaction. For the subtraction of the background signal, the signal at V0 = 0 kV was used as the background signal.

)

)

)

)

)

)

AðΘÞ ¼

)

IðΘ, F3 -endÞ þ IðΘ, N-endÞ 1 2 3 IðΘ, randomÞ

ð4Þ

IðΘ, F3 -endÞ  IðΘ, N-endÞ 2 3 IðΘ, randomÞ

ð5Þ

OðΘÞ ¼

Here, I(Θ, N-end), I(Θ, F3-end), I(Θ, random) is the emission intensity at the N-end (Φ ), F3-end (Φa), and random (Φoff) configurations, respectively. The orientation (O(Θ)) and alignment (A(Θ)) terms are shown in Figure 3 as a function of the atomic orientation configuration (Θ). Figure 3 shows that O(Θ ) (and O(Θa)) and A(Θ ) (and A(Θa)) are positive, while O(Θ^) and A(Θ^) are negative. B. Correlation between the Molecular Orientation and the Atomic Orbital Alignment. The observed emission intensity 4585

)

þ

0 J

 2æ

)

0 J

0 J

)

d2M 2 ð90ÞjM 0J æ ¼ ∑ M

0 J

)

jΘ^ æ ¼

)

d2M 2 ð180ÞjM 0J æ ¼ jM 0J ¼ ∑ M

)

0 J

jΘa æ ¼

A. Multidimensional Steric Effect. Figure 2 shows the emission intensities I(Θ, Φ) of KrF* under the nine mutual configurations between the molecular orientation configuration (Φ , Φa, and Φoff) and the atomic orientation configuration (Θ , Θ^, and Θa). The dependence on molecular orientation configuration is found to be opposite at two atomic alignment configurations; the F3-end configuration is most reactive at Θ (and Θa) but least reactive at Θ^, and besides, the random configuration is least reactive at Θ (and Θa) but most reactive at Θ^. The Θ dependence is different at each molecular orientation configuration; the random configuration shows a poor Θ dependence, whereas the F3-end configuration shows the significant Θ dependence. In order to accentuate the steric effects, we define the orientation term (O(Θ)) and the alignment term (A(Θ)) by22,23 )

d2M 2 ð0ÞjM 0J æ ¼ jM 0J ¼ 2æ ∑ M 0 J

III. RESULT

)

)

jΘ æ ¼

The emission intensities (I(Θ,Φ)) from the products KrF* (B, C) were measured at the nine mutual configurations between the atomic orientation Θ and molecular orientation Φ. The molecular orientation configuration Φ was changed every 500 beam pulses in turn at each atomic orientation configuration Θ. The atomic orientation configuration was changed every 1500 beam pulses in turn. To obtain an acceptable signal-to-noise ratio, the data were accumulated up to 1.0  105 beam pulses at each mutual configuration condition.

)

)

)

)

)

)

)

respect to vR. The molecular orientation in the collision frame was controlled by changing the direction of a uniform electric orientation field E at the beam crossing point. The electric orientation field (E = 600 V cm1) was prepared by a pair of electrode plates tilted at an angle of 39 (i.e., the direction of the relative velocity, vR) with respect to the direction of the Kr*(3P2) beam axis. The atomic orientation in the collision frame was controlled by rotating the direction of the magnetic orientation field B that was prepared by four pieces of ferrite magnets mounted on a motor-driven rotatable stage. Three representative configurations were selected for the molecular orientation, i.e., parallel (Φ : N-end), antiparallel (Φa: F3-end), and orientation field off (Φoff: random orientation). Similarly, for the atomic orientation of Kr*(3P2, MJ = 2), three configurations were representatively selected, i.e., parallel (Θ ), perpendicular (Θ^), and antiparallel (Θa). The Kr*(3P2, MJ = 2) states |Θæ at three atomic orientation configurations can be simply ex2 0 (Θ  Θ ), as pressed by using the Wigner’s d function,25 dM J2 2 0 |Θæ = ∑M0J dM0J 2(Θ  Θ )|MJæ in terms of the magnetic M0J substates |M0Jæ in the collision frame.

Figure 3. Molecular orientation O(Θ) and alignment A(Θ) terms for the KrF* formation under three atomic orientation configurations (parallel (Θ ), perpendicular (Θ^), and antiparallel (Θa)): O(Θ) (green b), A(Θ) (red b). The error bar shows the confidence interval for 95% confidence coefficient.

)

Figure 2. Θ dependence of the chemiluminescence intensity of KrF* under the three molecular orientation configurations: N-end collision (blue b), F3- end collision (red b), and random (green b). The error bar shows the confidence interval for 95% confidence coefficient.

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I(Θ, Φ) can be expressed in terms of the molecular steric opacity function as below23,24 Z 1 ð6Þ IðΘ, ΦÞ ¼ W Φ ðcos γÞ σ Θ ðcos γÞ dcos γ 1

σ Θ ðcos γÞ ¼ IðΘ, Φoff Þ  expðλ0 ðΘÞ þ

)

)

where γ is the orientation angle of the NF3 molecular axis in the collision frame (i.e., with respect to vR), σΘ(cos γ) is the molecular steric opacity function at each atomic orientation configuration (Θ), and WΦ(cos γ) is the orientational distribution of the molecular axis for the NF3 molecular beam in the collision frame at each molecular orientation configuration (Φ). Since the observed stereoanisotropies depend on the orientational distribution WΦ(cos γ), it is suitable to represent them in the form of the molecular steric opacity function σΘ(cos γ) in order to quantitatively evaluate the observed steric effects. Here, we obtain the molecular steric opacity functions σΘ(cos γ) at three atomic orientation configurations (Θ , Θ^, and Θa) by applying the EngelLevine function model described below26 n

∑1 λnðΘÞ Pnðcos γÞÞ ð7Þ

where Pn(cos γ) is the nth Legendre function and λn(Θ) are the fitting parameters. λ0(Θ) is the normalization factor. In this model calculation, only two parameters λ1(Θ) and λ2(Θ) are sufficient for reproducing the present experimental results. By reproducing the experimental emission intensities I(Θ, Φ), the fitting parameters (λ1, λ2) and λ0 can be determined as below

in the collision frame can be expressed as below by using eq 9 1 1 ðRÞj2  σM0L ¼ 0 ðcos γÞ þ jdj1j0 ðRÞj2 σðcos γ, RÞ ¼ jd00

)

)

σ Θ , ðΘa Þ ðcos γÞ : ðλ1 ¼ 0:10 ( 0:02,

Figure 4. Steric opacity function based on a EngelLevine function model as a function of the molecular orientation angle (γ) and the atomic orbital alignment angle (R) in the collision frame; γ = 0 corresponds to the F3-end and γ = 180 to the N-end, R = 0 corresponds to the M0L = 0 and R = 180 to the |M0L| = 1 atomic orbital alignment. (Boxed panel) Relationship between the molecular orientation angle (γ) and the atomic orbital alignment angle (R) in the collision frame (with respect to vR).

λ2 ¼ 0:7 ( 0:1, λ0 ¼  0:059

σ jM0L j ¼ 1 ðcos γÞ ¼ 2cos2 R  σ Θ^ ðcos γÞ

σΘ^ ðcos γÞ : ðλ1 ¼  0:19 ( 0:02,

þ ð1  2cos2 RÞ  σ Θjj ðcos γÞ

λ2 ¼  0:94 ( 0:1, λ0 ¼  0:081Þ Since the atomic alignment effects on the KrF*(B, C) formations are known to be controlled by the alignment of the unpaired 4p electron of Kr*(3P2, MJ = 2) in the collision frame, the cross section (σM0J ) for each M0J state can be alternatively expressed by the cross sections (σM0L) based on the |L, S, ML0 , MS0 æ basis using the standard recoupling procedure through the Clebsch Gordan coefficients.25 Since the MS0 and the sign of M0L give no effect for the reactivity in the excimer formation, the cross section σ|M0J | can be directly related to σ|M0L| as below σ jM0J j ¼ 2 ¼ σjM0L j ¼ 1 1 1 σ jM0J j ¼ 1 ¼  σ jML 0 j ¼ 1 þ  σ M0L ¼ 0 2 2 1 2 σ M0J ¼ 0 ¼  σ jM0L j ¼ 1 þ  σM0L ¼ 0 3 3

ð8Þ

)

)

)

)

The steric opacity functions σ(cos γ, R) are shown in Figure 4. The relationship between the molecular orientation angle (γ) and the atomic orbital alignment angle (R) in the collision frame is schematically shown in the boxed panel in Figure 4. The alignment (R) of the unpaired 4p electron in the collision frame gives a significant effect on both the shape of molecular steric opacity function σ|M0L|(cos γ) and the cross section; M0L = 0 (R = 0) is most reactive at the sideways direction with the poor reactivity at the molecular axis direction whereas |M0L| = 1 (R = 90) is favorable at the molecular axis direction.

IV. DISCUSSION

From eq 8, the cross sections (σΘ) at three atomic orientation configurations (Θ , Θ^, and Θa) can be expressed by using the cross section (σ|M0L|) at each atomic orbital alignment (|M0L|) in the collision frame as follows σΘ , ðΘa Þ ¼ σ jM0L j ¼ 1 σΘ^ ¼ 0:5  σ M0L ¼ 0 þ 0:5  σ jM0L j ¼ 1

ð10Þ

ð9Þ

The cross section σ(cos γ, R) as a function of the molecular orientation angle (γ) and the atomic orbital alignment angle (R)

A. M0L Dependent Intermolecular Potential. On the basis of the small total quenching cross section,11 the excimer formation should take place at a rather close intermolecular distance. The remarkable atomic orbital alignment (M0L) dependence observed in the opacity function also supports this expectation. At such close intermolecular distance, the open shell nature of the Krþ(2Pj) ion core should give an important role to the effective adiabatic potentials. In other words, the electrostatic induction terms should contribute in the entrance potentials. In order to correctly understand the M0J dependent process, it should be necessary to take into account the M0J dependence of the entrance potentials due to the open shell nature of the Krþ(2Pj) ion core. The effective adiabatic potentials can be considered as the sum of three terms: Vso, spinorbit; Vrot, centrifugal term; 4586

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Figure 5. Geometric arrangements of each constituent atom in the interaction potential. The N-atom and the F1-atom and the Kr*(Rb)atom are located on the yz plane. The center-of-mass of the NF3 molecule is defined as the origin of coordinate. The z axis is defined along the C3V symmetry axis of the NF3 molecule. θ is the angle between the F1Kr*(3P2, MJ = 2) axis and the z axis. M00L is the configuration of the 4p orbital of Kr(3P2) in the molecular frame (with respect to the Kr(3P2)F1 axis). Three atomic orbital configurations in the xyz frame are designated by pz, px, py, whereas three atomic orbital configurations in the collision frame are designated by pz0 , px0 , py0 . θ0 is the angle between the F1Kr*(3P2, MJ = 2) axis and the relative velocity vR.

and Vel; electrostatic interaction, when only the fine structure states are introduced in the close coupling equations. For Hund’s cases (a) and (c), the explicit expressions of the effective adiabatic potential-energy curves following LS coupling with the small impact parameters were formulated by Aquilanti et al.27,28 The interaction potential consists of two components: spherical (V0) and anisotropic component (V2). According to this formulation, the intermolecular potential of the NF3Kr*(3P2, MJ = 2) system at each atomic orbital alignment M00L with respect to intermolecular axis, we designate the configuration of the 4p orbital along the Kr(3P2)F axis as M00L , which can be expressed by27,28 1 M 00L ¼ 1 ðV 22 Þ : V 22 ¼ V 0  V 2 5

ð11Þ

M 00L ¼ 0 ðV 20 Þ : V 20

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 1 9 2 2 V þ ε20  ε0 V 2 ð12Þ ¼ V 0 þ V 2 þ ε0  10 2 2 25 2 5

Here ε0 is the energy of the Kr(3P0) above the Kr(3P2) level. According to eqs 9 and 10, the V2 component is described as below ΔV 2  ε0 ΔV 2 3 ΔV þ ε0 5 5 ΔV  V 22  V 20 V2 ¼

ð13Þ

In the present study, interaction potential between NF3 molecule and a ground-state rubidium atom was calculated as a spherical component (V0) of the approximate potential of NF3 þ Kr(3P2) based on the similarity due to the analogous outer valence electron configuration between Kr*(4p55s1) and Rb (4p65s1). This approximation enables us to circumvent calculation of highly excited states, which involve much greater difficulties. The spherical component (V0) was calculated by using the MP3

Figure 6. Calculated intermolecular potential of the Kr*(3P2, MJ = 2) NF3 system at three atomic orbital configurations in the xyz frame: (A) pz, (B) px, (C) py.

method with 6-31G basis set for nitrogen atom and fluorine atoms and with LanL2DZ basis set for rubidium atom.29 Figure 5 shows the geometric arrangements of each constituent atom in the intermolecular potential. The N-atom and the F1-atom and the Rb-atom are located on the yz plane. The geometry of NF3 is fixed to the experimental one. The center-of-mass of NF3 molecule is defined as the origin of coordinate. The z axis is defined along the C3V symmetry axis of the NF3 molecule. In order to take into account the angle dependence of the interaction potential around the C3V axis (z axis), we calculated the potential energy at the different dihedral angle of Rb-atom with respect to the yz plane at intervals of 20. The averaged interaction potential over the dihedral angle was used as the V0 component having axial symmetry around the C3V axis. By scanning y and z coordinates, the V0 component of the interaction potential of the rubidiumNF3 system was obtained. On the other hands, the anisotropic component (V2) of the intermolecular potential due to the open shell nature of the Krþ(2Pj) ion core has been estimated from the interaction potential for the BrNe system in the same manner as reported in refs 27 and 28. The V2 component was estimated by using eq 11 from the intermolecular potential experimentally derived from the scattering experiment for the BrNe system.30 In the present study, the V2 term was approximated as the interaction of Kr(3P2) with only the closest F1-atom of NF3 because the V2 term plays an important role only at close distance. According to this approximation, the configuration of the 4p orbital of Kr(3P2) (M00L ) should be defined along the Kr(3P2)F1 axis. In this manner, we can calculate the V22 and V20 intermolecular potentials from eqs 11 and 12 by using the spherical component 4587

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(V0) and the anisotropic component (V2). In addition, we assumed that the configuration of the 4p orbital in the collision frame (M0L) is conserved in the course of ion pair (KrþNF3) formation5,31 because the remarkable M0L dependence is observed in the opacity function. According to this assumption, the relationship between M0L and M00L can be simply expressed by using Wigner’s d-function as follows25 0

jM L æ ¼

∑ jdM1

M

00

00

00

0 LM L

ðθ0 Þj 3 jM L æ

ð14Þ

Figure 7. Geometric parameters for the NF3 molecule and NF3 anion. R1 and R2 are the length for the NF3 and FF1 bonds, respectively. R and β are the angles between the perpendicular from the vertex N of a triangle NF2F3 and the NF3 and NF1 bonds, respectively.

L

Here, θ0 is the angle between the F1Kr*(3P2, MJ = 2) axis and the direction of relative velocity vR. Since the relationship between M0L and M00 L depends on the reflection symmetry with respect to the collision plane, another notation (px0 , py0 , pz0 ) is used for the alignment of the 4p orbital to supplement the M0L labeling because it is the relevant quantity in any mechanistic interpretation of a reaction process. These alignments, px0 , py0 , pz0 , are simply expressed in terms of M0L by i 0 ð15Þ px ¼ pffiffiffiðjM 0L ¼ 1æ þ jM 0L ¼  1æÞ 2 1 0 py ¼ pffiffiffiðjM 0L ¼ 1æ  jM 0L ¼  1æÞ 2 0

pz ¼ jM 0L ¼ 0æ

ð16Þ ð17Þ

Similarly, the alignment of 4p orbital (px0 , py0 , pz0 ) in the collision frame can be expressed by using another notation (px, py, pz) in the xyz frame. By using eq 14, the alignment of the 4p orbital in the xyz frame can be expressed in terms of M00L by i ð18Þ px ¼ pffiffiffiðjM 00L ¼ 1æ þ jM 00L ¼  1æÞ 2 1 py ¼ pffiffifficos θjM 00L ¼ 1æ 2 1  sin θjM 00L ¼ 0æ  pffiffifficos θjM 00L ¼  1æ 2

ð19Þ

1 pz ¼ pffiffiffisin θjM 00L ¼ 1æ 2 1 þ cos θjM 00L ¼ 0æ þ pffiffiffisin θjM 00L ¼  1æ 2

ð20Þ

In this case, θ is defined as the angle between the F1Kr*(3P2, MJ = 2) axis and the z axis. Since the sign of M00L gives no effect for the interaction potential, the intermolecular potential at each atomic orbital configuration can be expressed by V ðpx Þ ¼ V ðM 00L ¼ 1Þ

ð21Þ

V ðpy Þ ¼ cos2 θ 3 V ðM 00L ¼ 1Þ þ sin2 θ 3 V ðM 00L ¼ 0Þ

ð22Þ

V ðpz Þ ¼ sin2 θ 3 V ðM 00L ¼ 1Þ þ cos2 θ 3 V ðM 00L ¼ 0Þ

ð23Þ

The calculated intermolecular potential at each atomic orbital configuration is shown in Figure 6. It is found that the intermolecular potentials are commonly more attractive at the F3-end. The effect of the atomic orbital configuration on the entrance potentials comes up prominently near the closest F-atom of NF3;

Table 1 R/deg

β/deg

R1/Å

R2/Å 1.3700000

A

51.2

110.0412831

1.3700000

B

57.275

140.2254065

1.633858

1.633858

C

50.62

108.7600000

1.411200

2.213000

the attractive force due to V(M00L ) = 0 component is derived from the py-configuration, whereas the other configurations induce the repulsive force due to V(M00L ) = 1 component near the closest F1atom of NF3. The interaction potential at the px-configuration is almost the same with that at the pz-configuration. The intermolecular distance of closest approach (and/or the repulsive wall) turns out to be about 4 Å. B. Electron Affinity of NF3. We have to thrash out problems with the electron affinity of NF3 in the harpooning process. At the beginning, we have determined the geometry of neutral NF3 and of the NF3 anion by ab initio calculation using the B3LYP method with the aug-cc-pVTZ basis set.29 The geometric parameters for calculation are summarized in Figure 7. The optimized geometry for the neutral NF3 (geometry A) and for the NF3 anion with both Cs symmetry (geometry C) and C3V symmetry (geometry B) are summarized in Table 1. Since the geometry optimization from the geometry B with no symmetry condition converges to the geometry C, the NF3 anion with C3V symmetry (geometry B) turns out to be an unstable hypothetical geometry. Theoretical calculation revealed that the geometry of the anion (geometry C) is far from the geometry of the neutral one (geometry A). The neutral NF3 has C3V symmetry whereas anion has Cs symmetry. It is found that the experimental electron affinity of NF3(or adiabatic electron affinity, EA(ad)) is not suitable for the harpooning process, but the vertical electron affinity, EA(ver) has to be taken into account. The vertical electron affinity is calculated to be -0.06 hartree (1.63 eV) at the geometry of neutral NF3 (geometry A). According to the intermolecular distance of closest approach of 4 Å (see Figure 6), it is unlikely that the 5s electron jump (harpooning) takes place via the vertical transition at the shorter intermolecular distance because the estimated rcver = 3.4 Å from eq 2 is located medial to the repulsive wall on the intermolecular potential. Therefore, in order for the harpooning for the NF3 formation to take place, the collisional deformation of NF3 geometry must be necessary to reach the curve crossing point between NF3 and NF3 located out of the FranckCondon region. Here, we use the term “collision-induced harpoon mechanism” to such specific harpooning process induced by collisional deformation of the molecular geometry. The influence of deformation of NF3 geometry on the electron affinity has been evaluated by ab initio calculation with DFT using the B3LYP function and augcc-pVTZ basis set. Geometry change of NF3 from the geometry 4588

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Figure 8. Influence of deformation of NF3 geometry on the electron affinity calculated by ab initio calculation. The optimized geometry (see Table 1) for the neutral NF3, NF3 anion with both Cs symmetry and NF3 with C3V symmetry are designated by A, C, B, respectively. Deformation of NF3 from the geometry A to the geometry C (and geometry B) is representatively used as the reaction coordinate. (Symbols) Energy change of neutral NF3 and NF3 anion along the reaction coordinate. NF3: (O) A to C; (0) A to B. NF3: (red 9) A to C; (blue b) A to B. (Inner panel) Calculated vertical electron affinity EA (ver) within the energetically accessible region along the reaction coordinate which was estimated from the sum of the zero-point energy of every vibrational mode of NF3 (0.191 eV) and the collision energy (0.05 eV).

A to the geometry C (and geometry B) is representatively used as the reaction coordinate. The energies of neutral NF3 and NF3 anion along the reaction coordinate were calculated by scanning the geometric parameters at uniform intervals of 1/10 of the displacement of the geometric parameters from the geometry A to the geometry C (and geometry B). The calculated results are shown in Figure 8. The inner panel shows the vertical electron affinity EA(ver) within the energetically accessible region along the reaction coordinate, which was estimated from the sum of the zero-point energy of every vibrational mode of NF3 (0.191 eV)32 and the collision energy (0.05 eV). It is found that deformation of NF3 geometry with Cs symmetry drastically increases the vertical electron affinity of NF3; EA(ver) is increases to be 0.15 eV for deformation with Cs symmetry while 0.65 eV for C3V symmetry. In addition, negative charge of anion with Cs symmetry is efficiently localized on one F-atom (F1) of NF3 unlike in the case with C3V symmetry where every F-atom equivalently has less negative charge. Theoretical calculation suggests that collisional deformation of NF3 geometry with Cs symmetry plays an important role as an initiating factor for the formation of NF3 due to increasing the vertical electron affinity and due to localizing the negative charge on the F1-atom of NF3 anion. C. Comparison with the Experimental Result. First, we consider the linear trajectory along the z = 0 line (i.e., the sideways collision (vR//y)). Figure 9 A shows the cross-sectional view of the intermolecular potential for V(py) and V(pz) at z = 0 (see Figure 6). The ionic surface of [Krþ(2P3/2) þ NF3] was approximated by the point charge model as follows1  e2 =r þ IE  EA

ð24Þ

Figure 9. (A) Cross-sectional view of the intermolecular potentials of the Kr*(3P2, MJ = 2)NF3 system at two atomic orbital configurations (pz, py) at z = 0: (blue 9) V(py), (O) V(pz). The ionic surface of [Krþ(2P3/2) þ NF3] for three representative cases: (1) NF3 with C3V symmetry (EA = 0.65 eV), (2) NF3 with Cs symmetry (EA = 0.15 eV), (3) NF3 with Cs symmetry (EA = 0.15 eV) besides the localized negative charge on F1-atom of NF3. (Short dashed line) Collision energy of 0.05 eV. (B) (Solid line) Cross-sectional view of the effective intermolecular potentials (including a centrifugal barrier) of the Kr*(3P2, MJ = 2)NF3 system at two atomic orbital configurations (pz, py) at y = 4.2: (blue 9) V(py), (O) V (pz). As a reference, spherical component (V0) is shown as a dashed line. (Short dashed line) Collision energy of 0.05 eV.

For comparison, the ionic surfaces for three representative cases were presented: (1) NF3 with C3V symmetry (EA = 0.65 eV), (2) NF3 with Cs symmetry (EA = 0.15 eV), (3) NF3 with Cs symmetry (EA = 0.15 eV) besides the localized negative charge on the F1-atom of NF3. It is found that collisional deformation of NF3 geometry with Cs symmetry plays an important role as an initial step for the formation of NF3 due to increasing the electron affinity of NF3 and due to localizing the negative charge on the F1-atom of NF3 anion. In other words, it is unlikely that the harpooning takes place from the NF3 with C3V symmetry. This result can well explain the large cross section at the sideways direction because deformation of NF3 geometry with Cs symmetry is expected to be favorable for the collision from the sideways direction. The effect of the atomic orbital configuration on the entrance potentials comes up prominently near the F1atom of NF3. The attractive force is derived from the py0 configuration, whereas the other configurations induce the repulsive force. The crossing distance between the covalent potential surface [Kr*(3P2) þ NF3] and the ionic surface [Krþ(2P3/2) þ NF3] is found to significantly depend on the atomic orbital configuration. It is expected that the py4589

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The Journal of Physical Chemistry A configuration (and/or M0L = 0) becomes more reactive at the sideways direction due to the attractive force from the anisotropic component (V2) of the intermolecular potential. This result can well explain both the large cross section and the superiority of the M0L = 0 alignment at the sideways direction. Since the molecular steric opacity function at |M0L| = 1 is favorable at the molecular axis direction with the comparable reactivity between the F3-end and the N-end, the |M0L| = 1alignment is expected to be favorable at the relatively large impact parameter collision. Figure 9 B shows the cross- sectional view of the effective intermolecular potential (including a centrifugal barrier)1 for V(py) and V(pz) at a representative impact parameter of y = 4.2 Å (see Figure 6). It is found that the attractive force due to the V2 term at the pz configuration reduces the potential barrier; in contrast, the repulsive force induced by the V2 term at the py configuration increases the potential barrier. If we assume the linear trajectory along the y = 4.2 Å line (i.e., the molecular axis collision (vR//z)), it is found that only the py-configuration (and/or |M0L| = 1) can reach the crossing point between the covalent potential surface [Kr*(3P2) þ NF3] and the ionic surface [Krþ(2P3/2) þ NF3]. In addition, the F3-end is expected to be more reactive than the N-end because the potential barrier at the pz-configuration is lower at the F3-end as compared with that at the N-end. This result can well explain the reactivity at the molecular axis direction in the molecular opacity function at the |M0L| = 1 alignment. On the other hand, it is unlikely that the harpooning at the molecular axis direction takes place at the M0L = 0 alignment (the pz-configuration) because the repulsive potential barrier inhibits access to the crossing point. This result can well explain the poor reactivity at the molecular axis direction in the molecular opacity function at the M0L = 0 alignment. In contrast with the NF3 þ Kr*(3P2) system, the NF3 þ Xe*(3P2) system has no reactivity at the molecular axis direction regardless of the atomic orbital alignment M0L.22 This difference can be explained by the difference in the interaction potential between two reaction systems; a theoretical calculation on the V0 term for the NF3 þ Xe*(3P2) system reveals that the NF3 þ Xe*(3P2) system has the larger V0 (repulsive) term as compared with that of the NF3 þ Kr*(3P2) system from the longer intermolecular distance. Because the repulsive energy due to larger V0 term supersedes the attractive energy due to the V2 term, the enhanced potential barrier inhibits access to the crossing point even at the py-configuration (and/or |M0L| = 1). This difference in the interaction potential leads to the poor reactivity along the molecular axis direction for NF3 þ Xe*(3P2) reaction even at the atomic orbital configuration of |M0L| = 1. As a result, all experimental observations turn out to support the “collisioninduced harpooning mechanism”.

’ CONCLUSIONS Molecular steric opacity function has been determined for the KrF* formation in the NF3 þ Kr*(3P2) reaction as a function of the atomic orbital alignment (M0L) in the collision frame. The molecular steric opacity functions are found to depend remarkably onto M0L; the |M0L| = 1 alignment is favorable at the molecular axis direction, whereas the M0L = 0 alignment is favorable at the sideways direction with a very poor reactivity at the molecular axis direction. The influence of the deformation of NF3 geometry on the electron affinity has been evaluated by ab initio calculation, and the M0L dependent intermolecular potential

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has been estimated from the interaction potential for the brominerare gas system. We propose the “collision-induced harpooning mechanism” as a novel process for the harpooning in which the collisional deformation of NF3 geometry with Cs symmetry plays an important role as an initiating factor on electron transfer for the formation of NF3 due to reducing the electron affinity of NF3 and due to localizing the electron on one F-atom of NF3 anion. All experimental observations can support the collision-induced harpooning mechanism.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

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