- Email: [email protected]
N2+O2 product branching in the O(1D)+N2O reaction: a classical trajectory study on a new global potential energy surface for the lowest 1A′ state
9 September 2002
Chemical Physics Letters 363 (2002) 298–306 www.elsevier.com/locate/cplett
Translational energy dependence of NO þ NO=N2 þ O2 product branching in the Oð1DÞ þ N2O reaction: a classical trajectory study on a new global potential energy surface for the lowest 1A0 state Toshiyuki Takayanagi a
a,b,*
, Hiroshi Akagi
c
Advanced Science Research Center, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan b Department of Theoretical Studies, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan c Department of Materials Science, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan Received 29 April 2002; in final form 16 July 2002
Abstract An analytical potential energy surface of the lowest singlet 1 A0 state for the Oð1 DÞ þ N2 O ! NO þ NO=N2 þ O2 reaction has been developed on the basis of extensive ab initio electronic structure calculations at the CASPT2/cc-pVDZ level of theory within Cs constraint. A many-body expansion type function was employed to fit the calculated ab initio points. Classical trajectory calculations have been carried out using the newly developed potential energy surface. We found that the initial orientation angle significantly affects the NO þ NO=N2 þ O2 product branching and the branching ratio decreases as the relative translational energy increases. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction The reaction of singlet oxygen atoms Oð1 DÞ with N2 O is one of the important reactions in the stratosphere and is known to be a major source of the stratospheric NO, which plays a relevant role in the natural degradation of ozone [1]. The Oð1 DÞ þ N2 O reaction proceeds with a nearly single collision efficiency [2] and has two major production 1 channels, 2NOðX2 PÞ and N2 ðX1 Rþ g Þ þ O2 ða Dg Þ.
*
Corresponding author. Fax: +81-29-282-5927. E-mail address: [email protected] (T. Takayanagi).
The exothermicities of both the two channels are very large: 81.9 kcal/mol for the former channel and 102.3 kcal/mol for the latter channel [3]. The branching ratio for the two production channels is a very important parameter for understanding the mechanism of the degradation of ozone and has been measured by many research groups in the past [4–7]. Although the branching ratio at room temperature is known to be about 1.6, the determination of the collision energy (or temperature) dependence of the branching ratio is somewhat controversial. Wiebe and Paraskevoulos [4] and Marx et al. [5] have concluded that the branching ratio is not affected by the collision energy of the Oð1 DÞ atom. On the other hand, Davidson et al. [6]
0009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 1 1 7 9 - X
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have found that the branching ratio increases slowly with increasing temperature over the range 170–434 K. However, note that all these experimental studies were carried out in static gas cells and the branching ratio were determined using indirect methods including a product analysis technique. As far as we are aware, no direct spectroscopic detection 1 1 of N2 ðX1 Rþ g Þ or O2 ða Dg Þ produced in the Oð DÞ þ N2 O has not been applied. In this Letter, we address the collision energy dependence of the branching ratio for the two production channels from a viewpoint of theory. It is quite well-known that Oð1 DÞ atoms are primarily produced from the photodissociation of ozone in the 200–300 nm wavelength region [1]. Recently, Matsumi et al. [8,9] have found that the translational relaxation rate of hot Oð1 DÞ atoms by collisions with N2 is not fast enough compared with the electronic quenching by N2 . This indicates that the translation energy distribution of Oð1 DÞ in the upper stratosphere is superthermal. Therefore, it is quite probable that the reaction of Oð1 DÞ with N2 O takes place under nonequilibrium conditions in the upper stratosphere. Thus, it is very important to know the collision energy dependence of the branching ratio for further understanding the mechanism of the ozone degradation. There have been many experimental studies [10– 14] for understanding the reaction dynamics of Oð1 DÞ þ N2 O; however, most of these studies focused on the product energy distributions for the NO + NO product channel. This is simply because laser spectroscopic techniques can easily be applied to the detection of NO. As far as we are aware, no such dynamics study has been reported for the N2 þ O2 channel. There have also been reported several ab initio and dynamical theoretical studies [10,15–22]. However, due to lack of a global potential energy surface that can describe the two production channels, dynamical information including the collision energy dependence of the branching ratio is still insufficient. We have previously developed an analytical potential energy surface and carried out reduced-dimensionality quantum reactive scattering calculations [19,21]; however, only the NO + NO production channel was considered. Gonz alez et al. [20,22] have recently carried out stationary point calculations on the
299
potential energy surfaces of the lowest two singlet states using the CASPT2//CASSCF (complete active space second-order perturbation//complete active space self-consistent field) level of theory and performed transition state theory calculations of thermal rate constants. Thus, only kinetic information is available from the theoretical side. The main goal of the present contribution, which follows and extends our previous work [19,21], is to study theoretically the dynamics of the Oð1 DÞ þ N2 O ! NO þ NO=N2 þ O2 reaction with particular emphasis on the collision energy dependence of the branching ratio of the two production channels. First, we develop an analytical potential energy function for the lowest singlet state using ab initio electronic structure theory and then calculate the branching ratio as a function of the collision energy using the classical trajectory method.
2. Construction of a global analytical potential energy surface Since the Oð1 DÞ atom has an open-shell singlet electronic structure, the selection of the appropriate ab initio level is a very important step for describing the global feature of the potential energy surface for the Oð1 DÞ þ N2 O ! NO þ NO=N2 þ O2 reaction. As in our previous work [19], we employed the CASPT2 method, where an optimized CASSCF wavefunction was employed. The effects of different levels of theory as well as basis sets on the calculated potential surface have been previously studied in detail [19]. The most important conclusion of our previous work is that the ab initio calculations which do not include dynamical electron do not give even qualitative features of the potential energy surface at least for the N2 O2 system. In fact, the potential energy curves obtained from the CASSCF calculations were very different from those obtained from the CASPT2 calculations. This was also confirmed in the ab initio calculations by Gonzalez et al. [20]. The active space used in CASSCF calculations generally plays an important role in accurate determination of the potential energy surface. In our previous Letter [19], however, we have demonstrated that the CASPT2 ð10e ; 8o Þ level calculations, for which 10 electrons are
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distributed in eight active orbitals (4a0 þ 4a00 in Cs symmetry), yield comparable results at a more accurate CASPT2 ð14e ; 12o Þ level of theory ð8a0 þ 4a00 orbitals) at least for the Oð1 DÞ + N2 O ! NO þ NO reaction channel. Thus, we have done the CASPT2(10e ; 8o ) level calculations over 7000 geometries in [21]. In our previous work, both the correlation-consistent polarized valence doublezeta (cc-pVDZ) and triple-zeta (cc-pVTZ) basis sets of Dunning [23] were employed and we found that the effect of the difference in basis sets were relatively small (with a few kcal/mol). Thus, we employed the cc-pVDZ basis set though out this study. Two sets of ab initio data have been employed in a fitting procedure. The first one is our previous ab initio result at the CASPT2(10e ; 8o )/cc-pVDZ level over 7000 geometries [21]. Note that these ab initio calculations were carried out only in the region of the Oð1 DÞ þ N2 O ! NO þ NO channel. In contrast to this NO production channel, we have found that the CASPT2(14e ; 12o ) level of theory is necessary to describe the potential energy surface for the Oð1 DÞ þ N2 O ! N2 þ O2 reaction channel. Then, we have additionally carried out the CASPT2(14e ; 12o )/cc-pVDZ level calculation over 3000 geometries, which was used as the second data set. As mentioned above, these two data sets give a very small energy difference in the Oð1 DÞ þ N2 O ! NO þ NO channel region (typically smaller than 1 kcal/mol). All these ab initio calculations were carried out using the MO L C A S 4 quantum chemistry program package [24]. In this work we used an analytical function expressed in the many-body expansion. The explicit form used for the ONNO system can be written as follows: V ðR1 ; R2 ; R3 ; R4 ; R5 ; R6 Þ ¼ VNN ðR1 Þ þ VNO ðR2 Þ þ VNO ðR3 Þ þ VNO ðR4 Þ þ VNO ðR5 Þ þ VOO ðR6 Þ þ VNNO ðR1 ; R2 ; R3 Þ þ VNNO ðR1 ; R4 ; R5 Þ þ VNOO ðR2 ; R3 ; R6 Þ þ VNOO ðR4 ; R5 ; R6 Þ þ V4 ðR1 ; R2 ; R3 ; R4 ; R5 ; R6 Þ; ð1Þ
where Ri is the diatomic internuclear distance. The first six terms are the two-body terms for the six diatomic fragments, the next four terms are the three-body terms, and the last term is the fourbody term. The diatomic potential energy curves and the N2 O three-body term are taken from our previous study [21]. In our previous work, the three-body term corresponding to the NO2 molecule was not included since the N2 þ O2 production channel was ignored. In this work, the NO2 three-body term of Say os et al. [25] was employed, which has been constructed to calculate rate con2 stants for the Nð4 SÞ þ O2 ðX3 R g Þ ! NOðX PÞ þ 3 Oð PÞ reaction. The four-body term V4 of Eq. (1) was expressed as a polynomial of order M, V4 ðR1 ; R2 ; R3 ; R4 ; R5 ; R6 Þ ¼
M X
ci;j;k;l;m;n qi1 qj2 qk3 ql4 qm5 qn6
ð2Þ
i;j;k;l;m;n
with the constraints i þ j þ k þ l þ m þ n 6 M: The variables 0
qi ¼ Ri eaðRi Ri Þ
ð3Þ
vanish for Ri ¼ 0 and Ri ! 1: This functional form was proposed by Aguado and Paniagua [26]. The parameters of the four-body term were determined with the nonlinear least-square method using the ab initio grid points ( 10 000 points). The order of the polynomial was taken as M ¼ 7. It should be emphasized that the analytical potential energy function thus determined in this work is valid only for planer Cs configurations although the potential surface is a function of the six internuclear distances. This is simply because the ab initio calculations have been carried out by assuming the Cs symmetry constraint. Since the parameters are too extensive to present here, we will make a FORTRAN version of the potential energy surface available to readers upon request. Table 1 compares the properties for the reactants and products obtained from the new potential energy surface with ab initio results and experimental data [27,28]. Although our analytical surface gives somewhat large harmonic vibrational
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Table 1 Comparison of properties of the reactants and products for the Oð1 DÞ þ N2 O ! NO þ NO=N2 þ O2 reaction
N2 O ) RNN (A ) RNO (A Frequency (cm1 )
NO ) RNO (A Frequency (cm1 ) O2 ) ROO (A Frequency (cm1 ) N2 ) RNN (A Frequency (cm1 ) Exothermicity DH 0 (kcal/mol) (NO + NO) DH 0 (kcal/mol) (N2 + O2 )
Ab initio
Analytical surface
Experimental
1.151 1.192 2280 1312 602
1.142 1.176 2256 1383 746
1.13a 1.18a 2224a 1285a 589a
1.166 1902
1.151 1904
1.15b 1904b
1.230 1450
1.2157 1509
1.216b 1509b
1.100 2380
1.0977 2359
1.098b 2359b
81.8
83.3
81.9c
103.0
103.2
102.3c
a
Ref. [27]. Ref. [28]. c Ref. [3]. b
frequencies for N2 O, overall agreement with experimental data is seen to be good. Fig. 1 compares the analytical function developed as mentioned above with the ab initio points in the entrance region of the Oð1 DÞ þ N2 O potential energy surface. The potential energy is measured from the Oð1 DÞ þ N2 O reactants with the N2 O geometry being fixed at its equilibrium value. Both the N- and O-attack regions are presented in Fig. 1. It is found that the analytical function reproduces the ab initio points at a fairly good level. As found in our previous work [19], it is seen that the interaction of Oð1 DÞ and N2 O is attractive in a wide range of Oð1 DÞ–N–N angle for the N-attack region. On the other hand, for the Oattack region, the potential energy curve is essentially repulsive except for the potential curve for \Oð1 DÞ–O–N ¼ 100°, for which a very shallow attractive well is seen. Fig. 2 shows a contour plot of the potential energy surface as a function of the Cartesian coordinates of Oð1 DÞ with N2 O being fixed in a
Fig. 1. Potential energy curves for entrance regions of the Oð1 DÞ þ N2 O reaction. Panels (a)–(d) show the N-attack case at different Oð1 DÞ–N–N angles of approach, while panels (e)– (h) the O-attack case at different Oð1 DÞ–O–N angles. Solid curves correspond to the analytical function and solid circles to the ab initio results at the CASPT2(14e ; 12o )/cc-pVDZ level of theory. The N2 O geometry is kept fixed at its equilibrium one.
linear optimized geometry. An attractive region is clearly seen in a wide range of the Oð1 DÞ–N–N angle from collinear to nearly perpendicular configurations. It is found that the approach of the Oð1 DÞ atom to the O atom side of N2 O reveals a repulsive character; however, the energetically favorable approach is seen at the Oð1 DÞ–O–N angle 100°. Fig. 3 presents two-dimensional contour plots of the potential energy surface; panels (a)–(e) are for Oð1 DÞ þ N2 O ! NO þ NO while panels (f)–(j) for Oð1 DÞ þ N2 O ! N2 þ O2 . The main feature of the potential surface for the NO production
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Fig. 2. Contour plot of the potential energy surface as a function of the position of the Oð1 DÞ atom, with the N2 O being fixed to Y ¼ 0 axis. The N–N and N–O distances are fixed at its equilibrium values. Contours are spaced by 10 kcal/mol; solid curves are used for energies that are positive relative to Oð1 DÞ þ N2 O, dashed lines are used for negative energies, and a bold line denotes the zero contour.
channel is essentially the same as our previous work [19]. As the Oð1 DÞ–N–N angle decreases, it is seen that the potential well of the local minimum becomes shallow and that the exit barrier height decreases. The behavior of the N2 þ O2 production channel is very different from the NO production case. There exists a large entrance barrier for the Oð1 DÞ þ N2 O ! N2 þ O2 reaction in the Oð1 DÞ– O–N angle range of 140–180°. This barrier significantly decreases at \Oð1 DÞ–O–N ¼ 100–120°. This result is qualitatively consistent with the Cartesian contour plot presented in Fig. 2. It can be predicted that the initial orientation angle, i.e., N- or O-attack angle, plays an important role in determining the branching ratio of the NO þ NO=N2 þ O2 production channels.
Fig. 3. Two-dimensional contour plots of the potential energy surface for Oð1 DÞ þ N2 O. Left panels (a)–(e) correspond to the NO + NO production channel at different Oð1 DÞ–N–N angles. . Right panels (f)–(j) corThe N–O distance is fixed to 1.18 A respond to the N2 þ O2 production channel at Oð1 DÞ–O–N . The N–N–O angles. The N–N distance is fixed to 1.13 A bending configurations are linear in both cases. Contours are spaced by 10 kcal/mol; solid curves are used for energies that are positive relative to Oð1 DÞ þ N2 O, dashed lines are used for negative energies, and a bold line denotes the zero contour.
3. Classical trajectory calculations In order to obtain deeper insight into the Oð DÞ þ N2 O reaction dynamics, we have carried out classical trajectory calculations using the analytical potential energy surface developed in the previous section. The classical equations of motion 1
for the Oð1 DÞ þ N2 O collision were integrated using space-fixed Cartesian coordinates. The standard predictor–corrector method was employed for numerical integration. A standard normal mode sampling scheme [29] was used for selecting the
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initial coordinates and momenta of the N2 O molecule. The actual trajectory calculations were performed within Cs symmetry; i.e., the Oð1 DÞ þ N2 O collision system is confined to a single plane. This is simply because the potential energy surface developed above is valid only for the Cs geometries as mentioned in the previous section. However, since the N2 O molecule is linear, we believe that this limitation does not largely alter the essential feature of the Oð1 DÞ þ N2 O reaction dynamics. In order to further confirm the validity of the present planar trajectory, we have estimated the out-of-plane bending frequencies in some points in the entrance region of the potential energy surface. The calculated frequencies were in the range 500–600 cm1 . Interestingly, these values are in qualitative agreement with the CASSCF results of Gonz alez [20]. Since we are mainly interested in product branching, these large frequencies value suggests the validity of planar trajectories. All classical trajectory calculations presented in this Letter were performed with zero impact parameter conditions and with the vibrational ground state conditions, N2 Oðm1 ¼ 0; m2 ¼ 0; m3 ¼ 0Þ, where mi is the vibrational quantum number. We have calculated 10 000–15 000 trajectories for each translational energy. Numerical integrations were carried out using the standard predictor–corrector method with a sufficiently small time step (typically 1–5 atomic time unit) so as that the total energy is conserved within 106 kcal/mol. We have also confirmed that the fluctuation of the angular momentum conservation is typically smaller than 0.01%. The initial and final distances between fragments . The gradients of the potential were set to 18–20 A energy surfaces were computed by a numerical finite difference scheme. Fig. 4 shows the reaction probabilities for the Oð1 DÞ þ N2 O ! NO þ NO and Oð1 DÞ þ N2 O ! N2 þ O2 reactions as a function of the initial orientation angle (c) at different translational energies, where the orientation angle is defined as a usual Jacobi angle between the Oð1 DÞ atom and N2 O molecule. Note that c ¼ 0° corresponds to collinear attack of Oð1 DÞ from the O side of N2 O while c ¼ 180° to collinear attack from the N side. At the energy of 6.9 kcal/mol, it is seen that the N2 þ O2 production probability is large only in the
303
Fig. 4. Oð1 DÞ þ N2 O reaction probabilities as a function of the initial orientation (Jacobi) angle at different translational energies. Solid lines correspond to probabilities for the Oð1 DÞ þ N2 O ! NO þ NO reaction, while dashed lines for Oð1 DÞ þ N2 O ! N2 þ O2 . Dotted lines correspond to the O þ NN0 O0 ! NO0 þ N0 O process (see text for details).
range c ¼ 30–80°, while that the NO + NO production probability is large in the wider range c ¼ 80–180°. This behavior is quite reasonable and consistent with the feature of the potential energy surface plotted in Figs. 2 and 3. It is interesting to note that, for the N2 þ O2 production, the reaction range increases as the collision energy increases. For example, at the energy of 34.6 kcal/mol,
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collinear collisions can produce N2 + O2 with 100% probability. This result is simply due to the fact that high energy collisions can overcome the entrance barrier for the Oð1 DÞ þ N2 O ! N2 þ O2 process. Thus, the total N2 þ O2 production probability increases as the collision energy increases. On the other hand, the total NO + NO production probability is seen to gradually decrease as the collision energy increases. We found that this comes from the increase in the number of rebound trajectories. The dotted lines also plotted in Fig. 3 correspond to the NO + NO production probability but produced from the O þ NN0 O0 ! NO0 þ N0 O process. Although the contribution of this scrambling process is always smaller than that of the normal O þ NN0 O0 ! NO þ N0 O0 scheme, it should be emphasized that we cannot ignore it. Although the existence of this scrambling process has not been identified from the experimental side, previous ab initio calculations of Vincent et al. [18] suggest that the scrambling process is energetically possible. They have characterized numerous stationary points (local minima and transition states) on the lowest singlet surface of the N2 O2 system at both the Brueckner doubles theory and density functional theory levels. They have shown that the several isomerization transition states lie in energy below the Oð1 DÞ þ N2 O reactant energy level. In the near future, we will report stationary point properties on our analytical potential energy surface and systematically compare to results of previous ab initio studies. Fig. 5 shows the reaction probabilities for the two production channels and the branching ratio as a function of the translational energy. It can be seen that the NO + NO production probability begins to decrease at the translational energy of about 15 kcal/mol, while the N2 þ O2 production probability increases as the energy increases. Hence, the NO þ NO=N2 þ O2 branching ratio decreases as the energy increases, except for very low energy threshold region (2–4 kcal/mol), where the validity of the classical treatment is uncertain. Note that, since we ignored the contribution of nonzero impact parameters and did not calculate reaction cross-sections, the branching ratio presented in Fig. 5 is only semiquantitative. If we include the contribution of nonzero impact
Fig. 5. Reaction probabilities (a) and NO þ NO=N2 þ O2 branching ratio (b) as a function of the translational energy for the Oð1 DÞ þ N2 O reaction. Dashed lines with open circle and dotted line with open squares correspond to probabilities for the NO + NO and N2 þ O2 production channels, respectively. Solid lines with solid circles correspond to total reaction probabilities.
parameters, the calculated branching ratio may probably increases since a larger impact parameter can contribute to the NO + NO production than to the N2 þ O2 production due to attractive vs. repulsive interaction in the entrance region. We will report full accounts of such a study as well as more detailed results including product vibrational, rotational and translational energy distributions, that can be obtained from the extensive classical trajectory calculations, in the near future. Although the purpose of the present study is to develop the potential energy surface of the lowest singlet 1 A0 state for the Oð1 DÞ þ N2 O reaction, it should finally be mentioned that the second lowest potential energy surface can also contribute to both
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the NO + NO and N2 þ O2 production. Very recently, Gonz alez et al. [22] have addressed this issue using the ab initio calculations at the CASPT2// CASSCF level of theory. They have characterized some stationary points on the second lowest 1 A00 surface. According to their calculations, the entrance barrier height for Oð1 DÞ þ N2 O ! NO þ NO is only 2.4 kcal/mol and the barrier height for the Oð1 DÞ þ N2 O ! N2 þ O2 process is somewhat larger (11.5 kcal/mol). This suggests that the contribution of the 1 A00 surface becomes more important for the NO + NO production. Thus, it is important to develop the 1 A00 potential energy surface in order to understand all aspects of the Oð1 DÞ þ N2 O reaction dynamics from a theoretical point of view. Theoretical work along this line is currently progress in our research group. In addition, we hope that our work stimulates further experimental studies including direct spectroscopic 1 detection of N2 ðX1 Rþ g Þ or O2 ða Dg Þ produced in 1 the Oð DÞ þ N2 O reaction.
4. Summary An analytical 11 A0 potential energy surface for the Oð1 DÞ þ N2 O reaction has been developed, that can describe both the NO + NO and N2 þ O2 production channels, on the basis of extensive ab initio calculations at the CASPT2/ cc-pVDZ level of theory. A many-body expansion type analytical function has been employed to fit ab initio results. Classical trajectory calculations assuming planer configurations have been performed on the new potential energy surface. It is found that the initial orientation angle significantly affects the NO þ NO=N2 þ O2 product branching and that the branching ratio is strongly dependent on the translational energy. Although the present computational results are still preliminary, we believe that this study may contribute to further understanding the natural degradation of ozone in the stratosphere, where nonthermal processes are suggested to play an important role. We have also found that the scrambling process, O þ NN0 O0 ! NO0 þ N0 O, can occur for the NO production on our new potential energy surface.
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Acknowledgements The authors are grateful to Professor T. Suzuki, Professor S. Nanbu, and Professor M. Aoyagi for their valuable comments and discussions.
References [1] P. Warneck, Chemistry of the Natural Atmosphere, Academic Press, San Diego, CA, 1988. [2] R. Atkinson, D.L. Baulch, R.A. Cox, R.F. Hampson Jr., J.A. Kerr, M.J. Rossi, J. Troe, J. Phys. Chem. Ref. Data 26 (1997) 1329 (and references therein). [3] M.W. Chase Jr., C.A. Davies, J.R. Downey Jr., D.J. Frurip, R.A. McDonald, A.N. Syverud, JANAF Thermochemical Tables (3rd Edn.), J. Phys. Chem. Ref. Data 14 (Suppl. 1) (1985) 1. [4] H.A. Wiebe, G. Paraskevopoukos, Can. J. Chem. 52 (1974) 2165. [5] W. Marx, F. Bahe, U. Schurath, Ber. Bunsenges. Phys. Chem. 83 (1979) 225. [6] J.A. Davidson, C.J. Howard, H.I. Schiff, F.C. Fehsenfeld, J. Chem. Phys. 70 (1974) 1697. [7] C.A. Cantrell, R.E. Shetter, J.G. Calvert, J. Geophys. Res. 99 (1994) 3739 (and references therein). [8] Y. Matsumi, S.M. Shamsuddin, Y. Sato, M. Kawasaki, J. Chem. Phys. 101 (1994) 9610. [9] Y. Matsumi, A.M.S. Chowdhury, J. Chem. Phys. 104 (1996) 7036. [10] K. Honma, Y. Fujimura, O. Kajimoto, J. Chem. Phys. 88 (1988) 4739. [11] M. Brouard, S.P. Duxon, P.A. Enriquez, J.P. Simons, J. Chem. Phys. 97 (1992) 7414. [12] P.J. Pisano, M.S. Westley, P.L. Houston, Chem. Phys. Lett. 318 (2000) 385. [13] H. Akagi, H. Tsurumaki, Y. Fujimura, O. Kajimoto, Z. Phys. Chem. 215 (2001) 1137 (and references therein). [14] R. Li, R.E. Continetti, J. Phys. Chem. A 106 (2002) 1183. [15] X. Wang, H. Li, Q. Zhu, F. Kong, H. Yu, J. Chin. Chem. Soc. 42 (1995) 399. [16] I. Last, A. Aguilar, R. Say os, M. Gonzalez, M. Gilibert, J. Phys. Chem. A 101 (1997) 1206. [17] M. Gonzalez, D. Troya, M.P. Puyuelo, R. Say os, P.A. Enriquez, Chem. Phys. Lett. 300 (1999) 603. [18] M.A. Vincent, I.H. Hiller, L. Salsi, Phys. Chem. Chem. Phys. 2 (2000) 707 (and references therein). [19] H. Akagi, A. Yokoyama, Y. Fujimura, T. Takayanagi, Chem. Phys. Lett. 324 (2000) 420. [20] M. Gonzalez, R. Valero, J.M. Anglada, R. Say os, J. Chem. Phys. 115 (2001) 7015. [21] T. Takayanagi, A. Wada, Chem. Phys. 269 (2001) 37. [22] M. Gonzalez, R. Say os, R. Valero, Chem. Phys. Lett. 355 (2002) 123. [23] T.H. Dunning Jr., J. Chem. Phys. 90 (1989) 1007.
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[24] K. Andersson et al., MO L C A S , version 4, Lund University, Sweden, 1997. [25] R. Say os, J. Hijazo, M. Gilbert, M. Gonzalez, Chem. Phys. Lett. 284 (1998) 101. [26] A. Aguado, M. Paniagua, J. Chem. Phys. 96 (1992) 1265. [27] J.T. Teffo, A. Chedin, J. Mol. Spectrosc. 135 (1989) 389.
[28] K.P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure IV, Constants of Diatomic Molecules, Van Nostrand Reinhold, New York, 1979. [29] G.C. Schatz, M. ter Horst, T. Takayanagi, in: D.L. Thompson (Ed.), Modern Methods for Multidimensional Dynamics Computations in Chemistry, World Scientific, Singapore, 1998, p. 1.
Chemical Physics Letters 363 (2002) 298–306 www.elsevier.com/locate/cplett
Translational energy dependence of NO þ NO=N2 þ O2 product branching in the Oð1DÞ þ N2O reaction: a classical trajectory study on a new global potential energy surface for the lowest 1A0 state Toshiyuki Takayanagi a
a,b,*
, Hiroshi Akagi
c
Advanced Science Research Center, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan b Department of Theoretical Studies, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan c Department of Materials Science, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan Received 29 April 2002; in final form 16 July 2002
Abstract An analytical potential energy surface of the lowest singlet 1 A0 state for the Oð1 DÞ þ N2 O ! NO þ NO=N2 þ O2 reaction has been developed on the basis of extensive ab initio electronic structure calculations at the CASPT2/cc-pVDZ level of theory within Cs constraint. A many-body expansion type function was employed to fit the calculated ab initio points. Classical trajectory calculations have been carried out using the newly developed potential energy surface. We found that the initial orientation angle significantly affects the NO þ NO=N2 þ O2 product branching and the branching ratio decreases as the relative translational energy increases. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction The reaction of singlet oxygen atoms Oð1 DÞ with N2 O is one of the important reactions in the stratosphere and is known to be a major source of the stratospheric NO, which plays a relevant role in the natural degradation of ozone [1]. The Oð1 DÞ þ N2 O reaction proceeds with a nearly single collision efficiency [2] and has two major production 1 channels, 2NOðX2 PÞ and N2 ðX1 Rþ g Þ þ O2 ða Dg Þ.
*
Corresponding author. Fax: +81-29-282-5927. E-mail address: [email protected] (T. Takayanagi).
The exothermicities of both the two channels are very large: 81.9 kcal/mol for the former channel and 102.3 kcal/mol for the latter channel [3]. The branching ratio for the two production channels is a very important parameter for understanding the mechanism of the degradation of ozone and has been measured by many research groups in the past [4–7]. Although the branching ratio at room temperature is known to be about 1.6, the determination of the collision energy (or temperature) dependence of the branching ratio is somewhat controversial. Wiebe and Paraskevoulos [4] and Marx et al. [5] have concluded that the branching ratio is not affected by the collision energy of the Oð1 DÞ atom. On the other hand, Davidson et al. [6]
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have found that the branching ratio increases slowly with increasing temperature over the range 170–434 K. However, note that all these experimental studies were carried out in static gas cells and the branching ratio were determined using indirect methods including a product analysis technique. As far as we are aware, no direct spectroscopic detection 1 1 of N2 ðX1 Rþ g Þ or O2 ða Dg Þ produced in the Oð DÞ þ N2 O has not been applied. In this Letter, we address the collision energy dependence of the branching ratio for the two production channels from a viewpoint of theory. It is quite well-known that Oð1 DÞ atoms are primarily produced from the photodissociation of ozone in the 200–300 nm wavelength region [1]. Recently, Matsumi et al. [8,9] have found that the translational relaxation rate of hot Oð1 DÞ atoms by collisions with N2 is not fast enough compared with the electronic quenching by N2 . This indicates that the translation energy distribution of Oð1 DÞ in the upper stratosphere is superthermal. Therefore, it is quite probable that the reaction of Oð1 DÞ with N2 O takes place under nonequilibrium conditions in the upper stratosphere. Thus, it is very important to know the collision energy dependence of the branching ratio for further understanding the mechanism of the ozone degradation. There have been many experimental studies [10– 14] for understanding the reaction dynamics of Oð1 DÞ þ N2 O; however, most of these studies focused on the product energy distributions for the NO + NO product channel. This is simply because laser spectroscopic techniques can easily be applied to the detection of NO. As far as we are aware, no such dynamics study has been reported for the N2 þ O2 channel. There have also been reported several ab initio and dynamical theoretical studies [10,15–22]. However, due to lack of a global potential energy surface that can describe the two production channels, dynamical information including the collision energy dependence of the branching ratio is still insufficient. We have previously developed an analytical potential energy surface and carried out reduced-dimensionality quantum reactive scattering calculations [19,21]; however, only the NO + NO production channel was considered. Gonz alez et al. [20,22] have recently carried out stationary point calculations on the
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potential energy surfaces of the lowest two singlet states using the CASPT2//CASSCF (complete active space second-order perturbation//complete active space self-consistent field) level of theory and performed transition state theory calculations of thermal rate constants. Thus, only kinetic information is available from the theoretical side. The main goal of the present contribution, which follows and extends our previous work [19,21], is to study theoretically the dynamics of the Oð1 DÞ þ N2 O ! NO þ NO=N2 þ O2 reaction with particular emphasis on the collision energy dependence of the branching ratio of the two production channels. First, we develop an analytical potential energy function for the lowest singlet state using ab initio electronic structure theory and then calculate the branching ratio as a function of the collision energy using the classical trajectory method.
2. Construction of a global analytical potential energy surface Since the Oð1 DÞ atom has an open-shell singlet electronic structure, the selection of the appropriate ab initio level is a very important step for describing the global feature of the potential energy surface for the Oð1 DÞ þ N2 O ! NO þ NO=N2 þ O2 reaction. As in our previous work [19], we employed the CASPT2 method, where an optimized CASSCF wavefunction was employed. The effects of different levels of theory as well as basis sets on the calculated potential surface have been previously studied in detail [19]. The most important conclusion of our previous work is that the ab initio calculations which do not include dynamical electron do not give even qualitative features of the potential energy surface at least for the N2 O2 system. In fact, the potential energy curves obtained from the CASSCF calculations were very different from those obtained from the CASPT2 calculations. This was also confirmed in the ab initio calculations by Gonzalez et al. [20]. The active space used in CASSCF calculations generally plays an important role in accurate determination of the potential energy surface. In our previous Letter [19], however, we have demonstrated that the CASPT2 ð10e ; 8o Þ level calculations, for which 10 electrons are
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distributed in eight active orbitals (4a0 þ 4a00 in Cs symmetry), yield comparable results at a more accurate CASPT2 ð14e ; 12o Þ level of theory ð8a0 þ 4a00 orbitals) at least for the Oð1 DÞ + N2 O ! NO þ NO reaction channel. Thus, we have done the CASPT2(10e ; 8o ) level calculations over 7000 geometries in [21]. In our previous work, both the correlation-consistent polarized valence doublezeta (cc-pVDZ) and triple-zeta (cc-pVTZ) basis sets of Dunning [23] were employed and we found that the effect of the difference in basis sets were relatively small (with a few kcal/mol). Thus, we employed the cc-pVDZ basis set though out this study. Two sets of ab initio data have been employed in a fitting procedure. The first one is our previous ab initio result at the CASPT2(10e ; 8o )/cc-pVDZ level over 7000 geometries [21]. Note that these ab initio calculations were carried out only in the region of the Oð1 DÞ þ N2 O ! NO þ NO channel. In contrast to this NO production channel, we have found that the CASPT2(14e ; 12o ) level of theory is necessary to describe the potential energy surface for the Oð1 DÞ þ N2 O ! N2 þ O2 reaction channel. Then, we have additionally carried out the CASPT2(14e ; 12o )/cc-pVDZ level calculation over 3000 geometries, which was used as the second data set. As mentioned above, these two data sets give a very small energy difference in the Oð1 DÞ þ N2 O ! NO þ NO channel region (typically smaller than 1 kcal/mol). All these ab initio calculations were carried out using the MO L C A S 4 quantum chemistry program package [24]. In this work we used an analytical function expressed in the many-body expansion. The explicit form used for the ONNO system can be written as follows: V ðR1 ; R2 ; R3 ; R4 ; R5 ; R6 Þ ¼ VNN ðR1 Þ þ VNO ðR2 Þ þ VNO ðR3 Þ þ VNO ðR4 Þ þ VNO ðR5 Þ þ VOO ðR6 Þ þ VNNO ðR1 ; R2 ; R3 Þ þ VNNO ðR1 ; R4 ; R5 Þ þ VNOO ðR2 ; R3 ; R6 Þ þ VNOO ðR4 ; R5 ; R6 Þ þ V4 ðR1 ; R2 ; R3 ; R4 ; R5 ; R6 Þ; ð1Þ
where Ri is the diatomic internuclear distance. The first six terms are the two-body terms for the six diatomic fragments, the next four terms are the three-body terms, and the last term is the fourbody term. The diatomic potential energy curves and the N2 O three-body term are taken from our previous study [21]. In our previous work, the three-body term corresponding to the NO2 molecule was not included since the N2 þ O2 production channel was ignored. In this work, the NO2 three-body term of Say os et al. [25] was employed, which has been constructed to calculate rate con2 stants for the Nð4 SÞ þ O2 ðX3 R g Þ ! NOðX PÞ þ 3 Oð PÞ reaction. The four-body term V4 of Eq. (1) was expressed as a polynomial of order M, V4 ðR1 ; R2 ; R3 ; R4 ; R5 ; R6 Þ ¼
M X
ci;j;k;l;m;n qi1 qj2 qk3 ql4 qm5 qn6
ð2Þ
i;j;k;l;m;n
with the constraints i þ j þ k þ l þ m þ n 6 M: The variables 0
qi ¼ Ri eaðRi Ri Þ
ð3Þ
vanish for Ri ¼ 0 and Ri ! 1: This functional form was proposed by Aguado and Paniagua [26]. The parameters of the four-body term were determined with the nonlinear least-square method using the ab initio grid points ( 10 000 points). The order of the polynomial was taken as M ¼ 7. It should be emphasized that the analytical potential energy function thus determined in this work is valid only for planer Cs configurations although the potential surface is a function of the six internuclear distances. This is simply because the ab initio calculations have been carried out by assuming the Cs symmetry constraint. Since the parameters are too extensive to present here, we will make a FORTRAN version of the potential energy surface available to readers upon request. Table 1 compares the properties for the reactants and products obtained from the new potential energy surface with ab initio results and experimental data [27,28]. Although our analytical surface gives somewhat large harmonic vibrational
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Table 1 Comparison of properties of the reactants and products for the Oð1 DÞ þ N2 O ! NO þ NO=N2 þ O2 reaction
N2 O ) RNN (A ) RNO (A Frequency (cm1 )
NO ) RNO (A Frequency (cm1 ) O2 ) ROO (A Frequency (cm1 ) N2 ) RNN (A Frequency (cm1 ) Exothermicity DH 0 (kcal/mol) (NO + NO) DH 0 (kcal/mol) (N2 + O2 )
Ab initio
Analytical surface
Experimental
1.151 1.192 2280 1312 602
1.142 1.176 2256 1383 746
1.13a 1.18a 2224a 1285a 589a
1.166 1902
1.151 1904
1.15b 1904b
1.230 1450
1.2157 1509
1.216b 1509b
1.100 2380
1.0977 2359
1.098b 2359b
81.8
83.3
81.9c
103.0
103.2
102.3c
a
Ref. [27]. Ref. [28]. c Ref. [3]. b
frequencies for N2 O, overall agreement with experimental data is seen to be good. Fig. 1 compares the analytical function developed as mentioned above with the ab initio points in the entrance region of the Oð1 DÞ þ N2 O potential energy surface. The potential energy is measured from the Oð1 DÞ þ N2 O reactants with the N2 O geometry being fixed at its equilibrium value. Both the N- and O-attack regions are presented in Fig. 1. It is found that the analytical function reproduces the ab initio points at a fairly good level. As found in our previous work [19], it is seen that the interaction of Oð1 DÞ and N2 O is attractive in a wide range of Oð1 DÞ–N–N angle for the N-attack region. On the other hand, for the Oattack region, the potential energy curve is essentially repulsive except for the potential curve for \Oð1 DÞ–O–N ¼ 100°, for which a very shallow attractive well is seen. Fig. 2 shows a contour plot of the potential energy surface as a function of the Cartesian coordinates of Oð1 DÞ with N2 O being fixed in a
Fig. 1. Potential energy curves for entrance regions of the Oð1 DÞ þ N2 O reaction. Panels (a)–(d) show the N-attack case at different Oð1 DÞ–N–N angles of approach, while panels (e)– (h) the O-attack case at different Oð1 DÞ–O–N angles. Solid curves correspond to the analytical function and solid circles to the ab initio results at the CASPT2(14e ; 12o )/cc-pVDZ level of theory. The N2 O geometry is kept fixed at its equilibrium one.
linear optimized geometry. An attractive region is clearly seen in a wide range of the Oð1 DÞ–N–N angle from collinear to nearly perpendicular configurations. It is found that the approach of the Oð1 DÞ atom to the O atom side of N2 O reveals a repulsive character; however, the energetically favorable approach is seen at the Oð1 DÞ–O–N angle 100°. Fig. 3 presents two-dimensional contour plots of the potential energy surface; panels (a)–(e) are for Oð1 DÞ þ N2 O ! NO þ NO while panels (f)–(j) for Oð1 DÞ þ N2 O ! N2 þ O2 . The main feature of the potential surface for the NO production
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Fig. 2. Contour plot of the potential energy surface as a function of the position of the Oð1 DÞ atom, with the N2 O being fixed to Y ¼ 0 axis. The N–N and N–O distances are fixed at its equilibrium values. Contours are spaced by 10 kcal/mol; solid curves are used for energies that are positive relative to Oð1 DÞ þ N2 O, dashed lines are used for negative energies, and a bold line denotes the zero contour.
channel is essentially the same as our previous work [19]. As the Oð1 DÞ–N–N angle decreases, it is seen that the potential well of the local minimum becomes shallow and that the exit barrier height decreases. The behavior of the N2 þ O2 production channel is very different from the NO production case. There exists a large entrance barrier for the Oð1 DÞ þ N2 O ! N2 þ O2 reaction in the Oð1 DÞ– O–N angle range of 140–180°. This barrier significantly decreases at \Oð1 DÞ–O–N ¼ 100–120°. This result is qualitatively consistent with the Cartesian contour plot presented in Fig. 2. It can be predicted that the initial orientation angle, i.e., N- or O-attack angle, plays an important role in determining the branching ratio of the NO þ NO=N2 þ O2 production channels.
Fig. 3. Two-dimensional contour plots of the potential energy surface for Oð1 DÞ þ N2 O. Left panels (a)–(e) correspond to the NO + NO production channel at different Oð1 DÞ–N–N angles. . Right panels (f)–(j) corThe N–O distance is fixed to 1.18 A respond to the N2 þ O2 production channel at Oð1 DÞ–O–N . The N–N–O angles. The N–N distance is fixed to 1.13 A bending configurations are linear in both cases. Contours are spaced by 10 kcal/mol; solid curves are used for energies that are positive relative to Oð1 DÞ þ N2 O, dashed lines are used for negative energies, and a bold line denotes the zero contour.
3. Classical trajectory calculations In order to obtain deeper insight into the Oð DÞ þ N2 O reaction dynamics, we have carried out classical trajectory calculations using the analytical potential energy surface developed in the previous section. The classical equations of motion 1
for the Oð1 DÞ þ N2 O collision were integrated using space-fixed Cartesian coordinates. The standard predictor–corrector method was employed for numerical integration. A standard normal mode sampling scheme [29] was used for selecting the
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initial coordinates and momenta of the N2 O molecule. The actual trajectory calculations were performed within Cs symmetry; i.e., the Oð1 DÞ þ N2 O collision system is confined to a single plane. This is simply because the potential energy surface developed above is valid only for the Cs geometries as mentioned in the previous section. However, since the N2 O molecule is linear, we believe that this limitation does not largely alter the essential feature of the Oð1 DÞ þ N2 O reaction dynamics. In order to further confirm the validity of the present planar trajectory, we have estimated the out-of-plane bending frequencies in some points in the entrance region of the potential energy surface. The calculated frequencies were in the range 500–600 cm1 . Interestingly, these values are in qualitative agreement with the CASSCF results of Gonz alez [20]. Since we are mainly interested in product branching, these large frequencies value suggests the validity of planar trajectories. All classical trajectory calculations presented in this Letter were performed with zero impact parameter conditions and with the vibrational ground state conditions, N2 Oðm1 ¼ 0; m2 ¼ 0; m3 ¼ 0Þ, where mi is the vibrational quantum number. We have calculated 10 000–15 000 trajectories for each translational energy. Numerical integrations were carried out using the standard predictor–corrector method with a sufficiently small time step (typically 1–5 atomic time unit) so as that the total energy is conserved within 106 kcal/mol. We have also confirmed that the fluctuation of the angular momentum conservation is typically smaller than 0.01%. The initial and final distances between fragments . The gradients of the potential were set to 18–20 A energy surfaces were computed by a numerical finite difference scheme. Fig. 4 shows the reaction probabilities for the Oð1 DÞ þ N2 O ! NO þ NO and Oð1 DÞ þ N2 O ! N2 þ O2 reactions as a function of the initial orientation angle (c) at different translational energies, where the orientation angle is defined as a usual Jacobi angle between the Oð1 DÞ atom and N2 O molecule. Note that c ¼ 0° corresponds to collinear attack of Oð1 DÞ from the O side of N2 O while c ¼ 180° to collinear attack from the N side. At the energy of 6.9 kcal/mol, it is seen that the N2 þ O2 production probability is large only in the
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Fig. 4. Oð1 DÞ þ N2 O reaction probabilities as a function of the initial orientation (Jacobi) angle at different translational energies. Solid lines correspond to probabilities for the Oð1 DÞ þ N2 O ! NO þ NO reaction, while dashed lines for Oð1 DÞ þ N2 O ! N2 þ O2 . Dotted lines correspond to the O þ NN0 O0 ! NO0 þ N0 O process (see text for details).
range c ¼ 30–80°, while that the NO + NO production probability is large in the wider range c ¼ 80–180°. This behavior is quite reasonable and consistent with the feature of the potential energy surface plotted in Figs. 2 and 3. It is interesting to note that, for the N2 þ O2 production, the reaction range increases as the collision energy increases. For example, at the energy of 34.6 kcal/mol,
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collinear collisions can produce N2 + O2 with 100% probability. This result is simply due to the fact that high energy collisions can overcome the entrance barrier for the Oð1 DÞ þ N2 O ! N2 þ O2 process. Thus, the total N2 þ O2 production probability increases as the collision energy increases. On the other hand, the total NO + NO production probability is seen to gradually decrease as the collision energy increases. We found that this comes from the increase in the number of rebound trajectories. The dotted lines also plotted in Fig. 3 correspond to the NO + NO production probability but produced from the O þ NN0 O0 ! NO0 þ N0 O process. Although the contribution of this scrambling process is always smaller than that of the normal O þ NN0 O0 ! NO þ N0 O0 scheme, it should be emphasized that we cannot ignore it. Although the existence of this scrambling process has not been identified from the experimental side, previous ab initio calculations of Vincent et al. [18] suggest that the scrambling process is energetically possible. They have characterized numerous stationary points (local minima and transition states) on the lowest singlet surface of the N2 O2 system at both the Brueckner doubles theory and density functional theory levels. They have shown that the several isomerization transition states lie in energy below the Oð1 DÞ þ N2 O reactant energy level. In the near future, we will report stationary point properties on our analytical potential energy surface and systematically compare to results of previous ab initio studies. Fig. 5 shows the reaction probabilities for the two production channels and the branching ratio as a function of the translational energy. It can be seen that the NO + NO production probability begins to decrease at the translational energy of about 15 kcal/mol, while the N2 þ O2 production probability increases as the energy increases. Hence, the NO þ NO=N2 þ O2 branching ratio decreases as the energy increases, except for very low energy threshold region (2–4 kcal/mol), where the validity of the classical treatment is uncertain. Note that, since we ignored the contribution of nonzero impact parameters and did not calculate reaction cross-sections, the branching ratio presented in Fig. 5 is only semiquantitative. If we include the contribution of nonzero impact
Fig. 5. Reaction probabilities (a) and NO þ NO=N2 þ O2 branching ratio (b) as a function of the translational energy for the Oð1 DÞ þ N2 O reaction. Dashed lines with open circle and dotted line with open squares correspond to probabilities for the NO + NO and N2 þ O2 production channels, respectively. Solid lines with solid circles correspond to total reaction probabilities.
parameters, the calculated branching ratio may probably increases since a larger impact parameter can contribute to the NO + NO production than to the N2 þ O2 production due to attractive vs. repulsive interaction in the entrance region. We will report full accounts of such a study as well as more detailed results including product vibrational, rotational and translational energy distributions, that can be obtained from the extensive classical trajectory calculations, in the near future. Although the purpose of the present study is to develop the potential energy surface of the lowest singlet 1 A0 state for the Oð1 DÞ þ N2 O reaction, it should finally be mentioned that the second lowest potential energy surface can also contribute to both
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the NO + NO and N2 þ O2 production. Very recently, Gonz alez et al. [22] have addressed this issue using the ab initio calculations at the CASPT2// CASSCF level of theory. They have characterized some stationary points on the second lowest 1 A00 surface. According to their calculations, the entrance barrier height for Oð1 DÞ þ N2 O ! NO þ NO is only 2.4 kcal/mol and the barrier height for the Oð1 DÞ þ N2 O ! N2 þ O2 process is somewhat larger (11.5 kcal/mol). This suggests that the contribution of the 1 A00 surface becomes more important for the NO + NO production. Thus, it is important to develop the 1 A00 potential energy surface in order to understand all aspects of the Oð1 DÞ þ N2 O reaction dynamics from a theoretical point of view. Theoretical work along this line is currently progress in our research group. In addition, we hope that our work stimulates further experimental studies including direct spectroscopic 1 detection of N2 ðX1 Rþ g Þ or O2 ða Dg Þ produced in 1 the Oð DÞ þ N2 O reaction.
4. Summary An analytical 11 A0 potential energy surface for the Oð1 DÞ þ N2 O reaction has been developed, that can describe both the NO + NO and N2 þ O2 production channels, on the basis of extensive ab initio calculations at the CASPT2/ cc-pVDZ level of theory. A many-body expansion type analytical function has been employed to fit ab initio results. Classical trajectory calculations assuming planer configurations have been performed on the new potential energy surface. It is found that the initial orientation angle significantly affects the NO þ NO=N2 þ O2 product branching and that the branching ratio is strongly dependent on the translational energy. Although the present computational results are still preliminary, we believe that this study may contribute to further understanding the natural degradation of ozone in the stratosphere, where nonthermal processes are suggested to play an important role. We have also found that the scrambling process, O þ NN0 O0 ! NO0 þ N0 O, can occur for the NO production on our new potential energy surface.
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Acknowledgements The authors are grateful to Professor T. Suzuki, Professor S. Nanbu, and Professor M. Aoyagi for their valuable comments and discussions.
References [1] P. Warneck, Chemistry of the Natural Atmosphere, Academic Press, San Diego, CA, 1988. [2] R. Atkinson, D.L. Baulch, R.A. Cox, R.F. Hampson Jr., J.A. Kerr, M.J. Rossi, J. Troe, J. Phys. Chem. Ref. Data 26 (1997) 1329 (and references therein). [3] M.W. Chase Jr., C.A. Davies, J.R. Downey Jr., D.J. Frurip, R.A. McDonald, A.N. Syverud, JANAF Thermochemical Tables (3rd Edn.), J. Phys. Chem. Ref. Data 14 (Suppl. 1) (1985) 1. [4] H.A. Wiebe, G. Paraskevopoukos, Can. J. Chem. 52 (1974) 2165. [5] W. Marx, F. Bahe, U. Schurath, Ber. Bunsenges. Phys. Chem. 83 (1979) 225. [6] J.A. Davidson, C.J. Howard, H.I. Schiff, F.C. Fehsenfeld, J. Chem. Phys. 70 (1974) 1697. [7] C.A. Cantrell, R.E. Shetter, J.G. Calvert, J. Geophys. Res. 99 (1994) 3739 (and references therein). [8] Y. Matsumi, S.M. Shamsuddin, Y. Sato, M. Kawasaki, J. Chem. Phys. 101 (1994) 9610. [9] Y. Matsumi, A.M.S. Chowdhury, J. Chem. Phys. 104 (1996) 7036. [10] K. Honma, Y. Fujimura, O. Kajimoto, J. Chem. Phys. 88 (1988) 4739. [11] M. Brouard, S.P. Duxon, P.A. Enriquez, J.P. Simons, J. Chem. Phys. 97 (1992) 7414. [12] P.J. Pisano, M.S. Westley, P.L. Houston, Chem. Phys. Lett. 318 (2000) 385. [13] H. Akagi, H. Tsurumaki, Y. Fujimura, O. Kajimoto, Z. Phys. Chem. 215 (2001) 1137 (and references therein). [14] R. Li, R.E. Continetti, J. Phys. Chem. A 106 (2002) 1183. [15] X. Wang, H. Li, Q. Zhu, F. Kong, H. Yu, J. Chin. Chem. Soc. 42 (1995) 399. [16] I. Last, A. Aguilar, R. Say os, M. Gonzalez, M. Gilibert, J. Phys. Chem. A 101 (1997) 1206. [17] M. Gonzalez, D. Troya, M.P. Puyuelo, R. Say os, P.A. Enriquez, Chem. Phys. Lett. 300 (1999) 603. [18] M.A. Vincent, I.H. Hiller, L. Salsi, Phys. Chem. Chem. Phys. 2 (2000) 707 (and references therein). [19] H. Akagi, A. Yokoyama, Y. Fujimura, T. Takayanagi, Chem. Phys. Lett. 324 (2000) 420. [20] M. Gonzalez, R. Valero, J.M. Anglada, R. Say os, J. Chem. Phys. 115 (2001) 7015. [21] T. Takayanagi, A. Wada, Chem. Phys. 269 (2001) 37. [22] M. Gonzalez, R. Say os, R. Valero, Chem. Phys. Lett. 355 (2002) 123. [23] T.H. Dunning Jr., J. Chem. Phys. 90 (1989) 1007.
306
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[24] K. Andersson et al., MO L C A S , version 4, Lund University, Sweden, 1997. [25] R. Say os, J. Hijazo, M. Gilbert, M. Gonzalez, Chem. Phys. Lett. 284 (1998) 101. [26] A. Aguado, M. Paniagua, J. Chem. Phys. 96 (1992) 1265. [27] J.T. Teffo, A. Chedin, J. Mol. Spectrosc. 135 (1989) 389.
[28] K.P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure IV, Constants of Diatomic Molecules, Van Nostrand Reinhold, New York, 1979. [29] G.C. Schatz, M. ter Horst, T. Takayanagi, in: D.L. Thompson (Ed.), Modern Methods for Multidimensional Dynamics Computations in Chemistry, World Scientific, Singapore, 1998, p. 1.