Ab initio derived analytical fits of the two lowest triplet potential energy surfaces and theoretical rate constants for the N „ 4 S ... ¿ NO „ X 2 P ... system

This work presents two new analytical fits of the ground potential energy surface ~PES! (A9) and the first excited PES ( A8) involved in the title reaction, considering the N-abstraction ~1! and the O-abstraction~2! reaction channels, and the reverse reaction ~21!. The PESs are derived fromab initio electronic structure calculations by means of second-order perturbation theory on a complete active-space self-consistent-field wave function ~CASPT2 method !. Stationary points and extensive grids ofab initio points~about 5600 points for the A9 PES and 4900 points for the A8 PES! were fitted along with some diatomic spectroscopic data to better account for the experimental exoergicity. Thermal rate constants were calculated ~200–5000 K! for all mentioned reaction processes by means of the variational transition-state theory with the inclusion of a semiclassical tunneling correction. Excellent agreement with the experimental data was observed for reaction ~1! and its reverse, within all the temperature range, substantially improving the results derived from previous analytical PESs. The contribution of the A8 PES to the reaction rate constant ( k1) was small even at high temperatures ~e.g., only 10.8% at 2500 K !. Moreover, the main contribution to reaction rate constant ( k2) was due to the A8 PES, differing from what happens for reaction ~1!. The O-abstraction reaction channel accounts for a 3.0% of the total reaction ( k5k11k2) at 5000 K, consistent with the very limited experimental information available. © 2003 American Institute of Physics. @DOI: 10.1063/1.1586251 #


I. INTRODUCTION
The elementary gas-phase reaction of ground atomic nitrogen with nitric oxide, 1 N͑ 4 S ͒ϩNO͑ X 2 ⌸ ͒→O͑ 3 P ͒ϩN 2 ͑ X 1 ⌺ g ϩ ͒⌬ r H 0K ‫ؠ‬ ϭϪ75.01 kcal/mol, ͑1͒ and its reverse reaction are of interest in atmospheric chemistry. Reaction ͑1͒ is thought to be the dominant removal step for odd nitrogen in the upper stratosphere, the mesosphere, and the thermosphere of the Earth and, possibly, also in Mars and Venus. [2][3][4] The precision of the rate constants for this reaction over a wide range of temperatures ͓e.g., from 185 K in mesopause to approximately 1000 K at 250 km of altitude ͑upper thermosphere͒ ͑Ref. 5͔͒ is of great interest for modeling the concentration of NO x species in these atmospheric regions for different levels of solar activity. Moreover, this reaction has been also proposed as one important step to remove the NO molecules produced in some heterogeneous catalytic processes ͑e.g., in SiO 2 -based materials͒ for airflow cases. 6 The reverse reaction is as well one of the two steps of the Zeldovich mechanism which produces NO, and it is very important for accurate modeling of thermochemical phenomena in rarefied atmospheric flows. A good understanding of the vibrationally and rotationally hot NO molecules pro-duced by the reverse reaction is necessary to establish appropriately the heat flux on the thermal protection systems used in atmospheric reentry vehicles ͑e.g., American space shuttle, Japanese orbital reentry experiment, etc.͒. Reaction ͑1͒ has been the object of abundant kinetic studies over several temperature ranges, but these studies present significant discrepancies, possibly due to its slight temperature dependence. Table I reports a brief summary of some of the main Arrhenius expressions for the experimental rate constants. A small activation energy ͑0.8 -1.6 kcal/mol͒ or even a negative value ͑Ϫ0.2 to Ϫ0.3 kcal/mol͒ were reported in these works. Direct kinetic data for the reverse endothermic reaction have also been obtained mainly at high temperatures (TϾ2000 K), 8 and they are more coincident than in the case of the direct reaction.
There are very few experimental studies dealing with the dynamic properties of reaction ͑1͒ or about its reverse ͑Ϫ1͒. Very early studies showed a product N 2 average vibrational energy fraction of 0.25-0.28. 10,11 However, another past study indicated 75%Ϯ5% of the N 2 molecules appeared with vЈϾ4. 12 To the best of our knowledge, there are no experimental dynamics studies on the reverse reaction. However, theoretical studies are available on both reactions. In earlier studies we presented several theoretical approaches for reaction ͑1͒, and we also gave a wide review of the main experimental and theoretical data that had been published for this reaction. We developed an analytical potential energy surface 13 ͑PES͒ based on limited ab initio information 14 for a͒ Electronic mail: miguel@qf.ub.es b͒ Electronic mail: r.sayos@qf.ub.es the ground 3 AЉ PES. In addition, we also performed dynamical studies on reaction ͑1͒ by means of the quasiclassical trajectory ͑QCT͒ method, 15 reduced quantum mechanical approaches, 16 and simple models. 17 Recently, QCT calculations on a new 3 AЉ PES, 18 which fitted the same aforementioned ab initio data, 14 but adding interpolated semiempirical points, reported good thermal rate constants for the 200-1000 K temperature range. In that work the authors considered the inclusion of a reactant statistical degeneracy factor excluding the NO spin-orbit correction ͑i.e., 3/16͒, missing in previous works. These authors also carried out a QCT study 19 on this reaction, taking into account the first excited PES ( 3 AЈ), previously fitted for the reverse reaction by other authors. 20 It was concluded that the excited PES became important for reaction ͑1͒ only at high energies ͑1-3 eV͒. Several theoretical studies on the reverse reaction, using these analytical PESs ( 3 AЉ and 3 AЈ), produced thermal rate constants and product energy distributions at very high temperatures ͑i.e., 3000-20 000 K͒, for both thermodynamic equilibrium 20 and nonequilibrium conditions. 21 In addition to reaction ͑1͒, a second reaction channel involving the O-abstraction process, can be produced. There is almost no information about it. Some experiments 22,23 at very high energies with 13 N and pure NO have indicated that reaction channel 2 yielding 13 NO could account for up to a 20% of the total reactivity of this system, though with the possible contribution of the first excited states of nitrogen ͓N( 2 D, 2 P)͔. Nevertheless, there are neither kinetic nor dynamic data about this reaction. In a recent study of our own ͑hereafter called paper I͒, 24 we have made an extensive ab initio characterization of the stationary points of the lowest 3 AЉ and 3 AЈ PESs. According to this study, reaction ͑1͒ should be much more important than reaction ͑2͒, which should only contribute to reactivity at high collision energies ͑e.g., over 30 kcal/mol͒. Moreover, we confirmed that the 3 AЉ PES had no energy barrier for reaction ͑1͒ and that the 3 AЈ PES had an energy barrier ͑TS1͒ much lower than the previous ab initio reported value. 14 Both PESs showed the presence of a minimum ͑MIN1͒ and a transition state ͑TS2͒ in the minimum energy path ͑MEP͒ for reaction ͑2͒.
Here we present new analytical PESs for both 3 AЉ and 3 AЈ states, based on the high-level ab initio data published in paper I, along with additional grids of ab initio points now calculated. These new PESs will provide better kinetic and dynamical data, and also will allow a deeper understanding of the two reaction channels involved in the title reaction. Furthermore, these PESs will be useful in the study of the reverse reaction in the nonequilibrium conditions of atmospheric reentry vehicles.
This paper is organized as follows: the ab initio method, the fitting procedure, and the derived analytical PESs are described in Sec. II, several variational transition-state theory calculations on thermal rate constants are presented in Sec. III, and finally Sec. IV contains the main concluding remarks.

A. Ab initio molecular structure and surface fitting methods
We have carried out the calculation of grids of ab initio points for both PESs following the main ab initio method used in paper I. 24 Thus the complete active-space selfconsistent-field ͑CASSCF͒ method 25,26 was used, always including the lowest root in C s symmetry for both triplet PESs ͑i.e., 3 AЈ and 3 AЉ). An active space comprising ten electrons in nine orbitals ͓i.e., CAS͑10,9͔͒ and the standard correlation-consistent cc-pVTZ Dunning's basis set 27 were applied in all calculations. Results obtained in paper I ͑Ref. 24͒ showed that this ab initio level was accurate enough, and the computer time was also reasonable to compute a large number of points for both reaction channels. The dynamical correlation energy was included by performing second-order perturbation theory calculations ͑CASPT2͒ over the CASSCF wave function using the G2 variant. 28 All calculations were carried out by means of the MOLCAS 4.1 program. 29 The analytical representations of the PESs are based on a many-body expansion 30 for the NNЈO system. In both cases this expansion can be written as where V (2) and V (3) are the two-and three-body terms, respectively, and R 1 , R 2 , and R 3 are the NNЈ, NЈO, and NO distances, respectively. The one-body V (1) terms have been omitted here because all the diatomic molecules dissociate into atoms in their ground electronic states ͓N( 4 S) ϩNЈ( 4 S)ϩO( 3 P)͔. The two-body terms ͑diatomic potential energy curves͒ have been fitted using an extended-Rydberg potential up to third or fifth-order,

͑4͒
where D e and R e are the equilibrium dissociation energy and the equilibrium bond distance of each diatomic molecule, respectively, and is defined as being equal to RϪR e .
The three-body term is a product of a sixth-order polynomial P(S 1 ,S 2 ,S 3 ) and a range function T(S 1 ,S 2 ,S 3 ), both expressed in terms of symmetry-adapted coordinates (S 1 ,S 2 ,S 3 ): with i, j, and k being positive integer numbers and

͑7͒
The range function vanishes the three-body term whenever one of the three atoms is separated from the other two. The symmetry-adapted coordinates used were defining a reference C 2v structure. The use of these coordinates guarantees the permutational NNЈ symmetry of the analytical PESs.
The two-body parameters (a i ) were optimized by means of a nonlinear least-squares procedure, 31 while the threebody parameters (c i jk and ␥ i ) were optimized by a weighted nonlinear least-squares method. 32 In both cases we follow a similar strategy as in our previous works ͓e.g., N( 2 D)ϩNO ͑Ref. 33͒. N( 2 D)ϩO 2 ͑Ref. 34͒, or N( 4 S)ϩO 2 ͑Ref. 35͔͒.

B. Analytical representation of the 3 AЉ PES
A total of 30 ab initio points ͓CASPT2͑10,9͒ G2/cc-pVTZ͔ calculated for each diatomic molecule ͑supermolecule calculations for NO and N 2 ) have been fitted by using an extended-Rydberg potential curve ͓Eq. ͑4͔͒ up to third order for the two diatomic curves used in the 3 AЉ PES and up to fifth-order for the 3 AЈ PES. The spectroscopic R e and D e values 36 were used for both curves. The final root-meansquare deviation ͑RMSD͒ of the fit in each diatomic energy curve was below 0.8 kcal/mol ͑with three parameters͒ and 0.4 kcal/mol ͑with five parameters͒ for both molecules. The The dissociation energies and the equilibrium distances used in the fits are given in Table III.   b Extended Rydberg coefficients used for the 3 AЉ PES ͑first row͒ and the 3 optimal parameters are shown in Table II. Although both curves for each molecule are similar ͑Fig. 1͒, it was necessary improve the first diatomic fit ͑with three parameters͒, because the small differences at long distances ͑mainly for N 2 ) were significant to remove spurious minima during the fit of the second PES ( 3 AЈ). The spectroscopic constants of the diatomic molecules derived from the optimal analytical curves are summarized in Table III, which compared very well with the experimental data, only with small differences for both analytical curves. A total of 5630 ab initio points ͓CASPT2͑10,9͒ G2/ cc-pVTZ͔ have been computed in different regions of the 3 AЉ PES to be used in the analytical fit, as summarized below: ͑a͒ 3917 points for the NNЈO region (NЈ-abstraction channel͒ distributed within the following grids: A small modification was introduced in the ab initio data in order to reproduce as accurately as possible the experimental diatomic dissociation energies and, hence, the exoergicity of reaction ͑1͒. As both ab initio values 24 were smaller than their experimental values, a uniform and first energy shift corresponding to the NO difference was introduced in all the points of the entrance valley ͑approximately from the line R NO Ͻ1.8 Å) for reaction ͑1͒ and for all points calculated for reaction ͑2͒. Afterward, an additional energy shift was added to the points of the exit valley ͑approximately from line R NO Ͼ1.8 Å) for reaction ͑1͒. This procedure was made trying to preserve as much as possible the original ab initio shape of the PES. All these ab initio points along with the first-order partial derivatives with respect to both distances and its angle for MIN1 and TS2 were used in a weighted nonlinear least-squares method 32 to obtain the optimal fit. The weights used were equal to 1 for almost all points, with the exception of the grids corresponding to the entrance and exit valleys, and also in the first-order partial derivatives, where we used weights between 50 and 100.
FIG. 1. Ab initio ͓CASPT2͑10,9͒ G2/cc-pVTZ͔ diatomic points for the NO(X 2 ⌸) and the N 2 (X 1 ⌺ g ϩ ) molecules. The lines show the analytical fit which reproduces also the experimental R e and D e , by using a third-order extended-Rydberg potential ͑dotted lines, for the 3 AЉ PES͒ or by using a fifth-order extended-Rydberg potential ͑solid lines, for the 3 AЈ PES͒.  Figure 2͑a͒ shows the energy deviations of the fit ͑i.e., ⌬E fit ϭE analytical ϪE ab initio ), which show a quite narrow distribution supporting the goodness of the fit. On the other hand, the in principle larger RMSD for the NONЈ region is really much lower in relative terms for this quite repulsive PES region related with the O-abstraction channel. Table IV shows the properties of the stationary points fitted in this region of the PES ͑TS2 and MIN1͒, which are located at very high energies over reactants. There is a good agreement between the ab initio properties reported in paper I for these stationary points and the values of the fit shown in Table IV, regardless of the main effort was focused in the fit of the NNЈO region, because reaction ͑1͒ was the principal reaction channel due to the absence of energy barrier along the MEP. Thus the fitted TS2 and MIN1 were located only 0.7 kcal/mol ͑1.7% of error͒ and 2.3 kcal/mol ͑6.2% of error͒ below their ab initio values, 24 respectively. Figure 3 presents some equipotential energy curves corresponding to the 3 AЉ PES, where it becomes evident the absence of an energy barrier for reaction ͑1͒ ͓see Figs. 3͑a͒ and 3͑b͔͒. In Fig. 3͑c͒ we can observe TS2 and MIN, which are energetically and geometrically very close. This proximity produced some difficulties in their characterization, especially for the harmonic vibrational frequency 3 ͑asymmetric stretching of b 2 sym-metry͒. Several intrinsic reaction coordinate ͑IRC͒ calculations were carried out to make sure the MEPs that are schematically shown in Fig. 4͑a͒ for both reaction channels.

C. Analytical representation of the 3 AЈ PES
We have followed for the 3 AЈ PES the same procedure indicated in previous section for the 3 AЉ PES. In this case, as was explained before, the diatomic curves were fitted using a fifth-order extended Rydberg ͑Table II͒. We used as initial reference structure the optimal geometry found for the 3 AЉ PES, which was slightly optimized by trial and error.
A total of 4901 ab initio points ͓CASPT2͑10,9͒ G2/cc-pVTZ͔ have been calculated in different regions of the 3 AЈ PES to be used in the analytical fit, as summarized below: ͑a͒ 2614 points for the NNЈO region (NЈ-abstraction channel͒ distributed within the following grids: Here we used the same correction in the ab initio data as for the 3 AЉ PES. These ab initio points with weight equal to 1 ͑excepting the grid around TS1 that has a weight of 1000͒, together with the first-order partial derivatives with respect to the internal coordinates of TS1, MIN1, and TS2 with weight 100, were used in the weighted nonlinear leastsquares method to obtain the optimal analytical fit. The final RMSD for the 3 AЈ surface was the following: 1.61 kcal/mol for the NNЈO region and 2.85 kcal/mol for the NONЈ region, with a global RMSD of 2.28 kcal/mol. Figure  2͑b͒ shows the distribution of deviations for this fit, which is somewhat poorer than that for the 3 AЉ PES. Figure 5 shows some equipotential curves corresponding to the 3 AЈ PES, where is possible to see the transition state TS1 ͓Figs. 5͑a͒ and 5͑b͔͒ and TS2 and MIN1 ͓Fig. 5͑c͔͒. The properties of the different stationary points are depicted in Table IV. The analytical 3 AЈ PES reproduces very well the ab initio TS1 properties ͓e.g., to be compared with the ab initio geometry R NN Ј ϭ1.9680 Å, R N Ј O ϭ1.1578 Å, ЄNNЈOϭ116.04°, ⌬E ϭ8.38 kcal/mol ͑Ref. 24͔͒ which is the most important stationary point. These results can also be compared with a previous analytical PES ͑Ref. 20͒ based on limited ab initio data, which had a larger energy barrier and a longer NN distance ͑see Table IV͒. The lowering of the energy barrier was discussed in paper I ͑Ref. 24͒ and justified due to the importance of the N and O 2s electron correlation, omitted in early ab initio 14 studies. Furthermore, the strengthening of the NN distance was also observed in similar studies ͓e.g., N( 4 S)ϩO 2 ͑Ref. 37͔͒, when the geometry optimization was carried out directly by including the dynamical correlation energy. 24 The quality of this PES fit is a bit worse for the TS2 and MIN1 structures. Nevertheless, the errors in their fitted ener-gies were lower than a 2% of the corresponding ab initio values. Figure 4͑b͒ presents schematically the MEPs corresponding to both reaction channels. It can be observed by comparison with the MEPs of the 3 AЉ PES that the second reaction channel becomes more accessible than for the 3 AЉ PES, although still at high temperatures.

III. VARIATIONAL TRANSITION-STATE THERMAL RATE CONSTANTS
Thermal rate constants for both reaction channels of N( 4 S)ϩNO(X 2 ⌸) and also for the reverse reaction have been calculated within the 200-5000 K and 600-5000 K temperature intervals, respectively. We have considered different levels of the variational transition-state theory 38 ͑VTST͒, as implemented in the POLYRATE code. 39 The rate constant values finally presented were the improved canonical ͑ICVT͒ ones with a microcanonical optimized multidimensional tunneling correction ͑OMT͒ for reaction ͑1͒ and its reverse and the ICVT ones with a small curvature tunneling correction ͑SCT͒ for the O-abstraction reaction. For this latter reaction this tunnel correction was the only acceptable one, due to the problems generated by the curvature of the MEP, with the presence also of the MIN1 and the two equivalent TS2s.

͑10͒
Primed k i show the rate constants without the inclusion of the electronic partition functions of reactants and the transition state. Due to the presence of a minimum ͑MIN1͒ in the MEP for reaction ͑2͒ ͑Fig. 4͒, we have considered the following microscopic mechanism to determine its rate constant (k 2 ): which is more properly applied to the 3 AЈ PES, which presents a more stable minimum and which as well will produce the most important contribution to the total k 2 . The application of the steady-state assumption to this type of mechanism 40 will give place to the velocity equation Due to k 2b ϭk Ϫ2a , the final rate constant k 2 becomes equal to k 2a /2. Hence VTST calculations determined firstly k 2a for each PES before calculating the total k 2 . The steady-state approximation is valid for k 2a Ӷ(k Ϫ2a ϩk 2b )ϭ2k 2b . 40 We have checked that this condition always fulfills in the present case ͑e.g., for the 3 AЈ PES, k 2b /k 2a Ͼ10 11 for all tempera-tures͒.
For the reverse reaction ͑Ϫ1͒, we have also considered the corresponding oxygen atom spin-orbit states ( 3 P 2 , 3 P 1 , and 3 P 0 ). Thus its electronic partition function is

͑13͒
where g(i) represents the electronic degeneracy of each i spin-orbit state, which are equal to 5, 3, and 1, respectively, and ⌬ i are the energetic differences between the corresponding i excited electronic state and the ground electronic state, ⌬ 1 ( 3 P 1 -3 P 2 ) and ⌬ 2 ( 3 P 0 -3 P 2 ), which are equal to 158.27 and 226.98 cm Ϫ1 , respectively. 1 Therefore, k Ϫ1 can be determined by the equation Table V shows the calculated VTST rate constants for reaction ͑1͒ using the present and previous PESs, comparing also with available experimental data. As was shown in paper I, 24 the estimated complete basis set limit for the energy barrier ͑TS1͒ in 3 AЈ PES is 6.74 kcal/mol. Thus a simple scale factor was introduced in the VTST calculations for this PES to better account for this value, instead of the value reproduced by the analytical PES ͑8. 35.kcal/mol͒. The agreement with the experimental data when considering the new PESs is very good at low and also at very high temperatures. Previous PESs produce poorer rate constants ͑see Table V͒, lower by a 10-15 factor at low temperatures and by a 1.2-2.5 factor at high temperatures (TϾ1500 K). Comparing the rate constants arising from each PES, it is appreciated that the effect of the 3 AЈ is certainly minor. The contribution of this latter PES to the total rate constant is small even at high temperatures ͑e.g., only 10.8% at 2500 K͒. Therefore, the influence of the inclusion of the scaled barrier is very small. For instance, at 2500 K the value of k ( 3 AЈ, with barrier not scaled͒ decreases only until 2.83ϫ10 Ϫ12 cm 3 molecule Ϫ1 s Ϫ1 ͑cf. in Table V͒, which leads to almost the same total rate constant (3.46ϫ10 Ϫ11 cm 3 molecule Ϫ1 s Ϫ1 ). The key improvement in the new theoretical rate constants arises from the new 3 AЉ PES, which gives rate constants higher than the previous PES. 15 In addition, Fig. 6͑a͒ ͑note the enlarged scale in the k axis͒ shows the correct change of slope as compared with the experimental data at low 3,9 and high temperatures, 8 not properly described by using previous PESs.
Nevertheless, there are some differences in comparison to another experimental data 2,7 which do not agree with the recommended experimental data, 8,9 although all of them are actually within a relatively small range of k values. The behavior observed at low temperatures for reaction ͑1͒ due to the 3 AЉ rate constant is not originated by tunnel effect ͑in all cases the transmission coefficient was equal to 1͒, as it should be expected for a barrierless reaction, but to the vibrationally adiabatic effective energy barrier derived from the shape of the MEP at each temperature. A slight contribution to the increase of k 1 when the temperature decreases is also originated by the temperature dependence of Q NO( 2 ⌸) elec (T). This effect was also reported in a previous study, 18 where QCT thermal rate constants were calculated with a different analytical 3 AЉ PES within the 200-1000 K interval. For these calculations, the introduction of this temperature-dependent statistical degeneracy factor was the only way to produce a positive slope in the Arrhenius plot. Moreover, these QCT rate constants were very similar to the present VTST ones, though for a shorter temperature range. For instance, using their QCT values for the 3 AЉ PES and Eq. ͑10͒ ͓assuming that k( 3 AЈ) is negligible for T Ͻ1000 K] we obtain the following QCT values at 200, 300, and 1000 K: 4.24ϫ10 Ϫ11 , 4.02ϫ10 Ϫ11 , and 3.61ϫ10 Ϫ11 cm 3 molecule Ϫ1 s Ϫ1 , respectively ͑cf. Table V͒. The major shortcoming of this earlier 3 AЉ PES is its rather semiempirical character and inability to describe reaction ͑2͒.
Table VI presents the VTST rate constants for reaction ͑2͒, which are also displayed in Fig. 6͑b͒. A three-parameter Kooij expression for k 2 was used according to the following equation: kϭAT n e B/T , ͑15͒ where A, n, and B are parameters to be optimized by means of a least-squares procedure to fit the rate constants, as is given in Fig. 6͑b͒. For this reaction with an important energy barrier, the small effect of the oxygen spin-orbit states is negligible. In this reaction the main contribution to the total rate constant is due to the 3 AЈ PES, following an opposite behavior as for reaction ͑1͒. Although k 2 values are much lower than the k 1 values at low and moderate temperatures (TϽ1000 K), the present results show that the O-abstraction channel accounts for 3.0% of the total reaction ͓the branching ratio k 2 /(k 1 ϩk 2 ) being expressed in percentage͔ at 5000 K. This value is equal to the QCT value calculated for the similar reaction but with N( 2 D) ͑Ref. 33͒ and a much lower temperature ͑1500 K͒. The addition of these values at high temperatures is in good agreement with the qualitative accessible experimental information, which indicates that this branching ratio ranges from 0% to 20% when increasing the nitrogen atom translational energy 22,23 ͓possibly including also N( 2 D) and N( 2 P)]. Although reaction ͑2͒ involves heavy atoms, the transmission coefficients calculated by the SCT method at different temperatures are high even at room temperature ͑e.g., 2.58 for 3 AЉ and 1.79 for the 3 AЈ at 300 K͒ as was also found in similar studies. 35 Table I. Finally, we have also computed the thermal rate constants for the reverse reaction ͑Ϫ1͒ due to the importance of these kinetic data in computational fluid dynamics ͑CFD͒ flow simulations for reentry vehicles in Earth's atmosphere. Thus Fig. 7 and Table VII present the thermal rate constants for each PES and the total rate constant. An excellent agreement with the experimental data 8 ͑Table I͒ is found within the temperature interval 1500-4000 K. The present results with the new PESs also slightly improve the kinetic data derived from previous PESs, as can be seen in Fig. 7. The calculated VTST values are almost independent of the small spin-orbit correction ͑Fig. 7͒. VTST rate constants at higher temperatures can also be compared with published QCT ͑Ref. 20͒ values derived from our earlier 3 AЉ PES ͑Ref. 15͒ and the previous 3 AЈ PES ͑Ref. 20͒, including the corresponding statistical degeneracy factor for each PES ͑i.e., 3/9͒. This QCT study provided a three-parameter expression  , and 6.30ϫ10 Ϫ14 cm 3 molecule Ϫ1 s Ϫ1 for 3000, 4000, and 5000 K, respectively. These QCT results are consistent with the calculated VTST results using these same PESs ͑Table VII͒, which are worse than the present ones, particularly for higher temperatures. At 5000 K the reported QCT k( 3 AЉ)/k( 3 AЈ) ratio 20 was 15 as compared with the VTST value of 5.1 for both previous PESs, which differ from the small value ͑2.9͒ obtained with the new PESs. Therefore, we conclude that the excited PES ( 3 AЈ) must be included in kinetic and dynamic studies of reaction ͑Ϫ1͒ at temperatures lower than those predicted in the QCT study (TϾ8000 K). Whereas the QCT k Ϫ1 ( 3 AЉ)/k Ϫ1 ( 3 AЈ) ratio is 2 at 12 000 K, the same VTST value with the new PESs is obtained at 7800 K. QCT and quantum wave-packet dynamic studies using these new PESs are in progress in our group to provide more detailed information of the kinetics and dynamics of all reaction channels.

IV. CONCLUSIONS AND REMARKS
In this work we have built new analytical fits of the ground PES ( 3 AЉ) and the excited PES ( 3 AЈ) involved in the N( 4 S)ϩNO(X 2 ⌸) reaction ͓N-abstraction ͑1͒ and O-abstraction ͑2͒ channels͔ and also for the reverse, ͑Ϫ1͒, using ab initio data reported in paper I ͑Ref. 24͒ along with new extensive grids of high-level ab initio points ͓CASPT2͑10,9͒ G2/cc-pVTZ calculations͔ computed in the present work. Diatomic D e and R e spectroscopic data were also introduced to better account for the exoergicity of reaction ͑1͒. The final RMSD for the 3 AЉ surface was equal to 1.44 kcal/mol for the NNЈO region and 2.59 kcal/mol for the NONЈ region, with a global RMSD of 1.80 kcal/mol. For the 3 AЈ surface, we obtained a final RMSD equal to 1.61 kcal/mol for the NNЈO region and 2.85 kcal/mol for the NONЈ region, with a global RMSD of 2.28 kcal/mol. These RMSDs were well below the estimated ab initio errors.
Thermal rate constants were calculated for both direct reaction channels and for the reverse reaction by means of the variational transition-state theory with the inclusion of a semiclassical tunneling correction. Theoretical rate constants for reaction ͑1͒ were in excellent agreement with experimental data at low to moderate and also at very high temperatures ͑200-5000 K͒, significantly improving the results obtained by using previous PESs. The contribution of the 3 AЈ PES to the total rate constant was small even at high temperatures ͑e.g., only 10.8% at 2500 K͒. The main enhancement in the rate constants arises from the new 3 AЉ PES, which gives rate constants higher than the previous PES.
The VTST calculation for reaction ͑2͒ showed that the main contribution to the total rate constant was due to the 3 AЈ PES, differing from the behavior in reaction ͑1͒. Despite k 2 values much lower than k 1 values at low and moderate temperatures (TϽ1000 K), the present results have shown that the O-abstraction channel accounts for 3.0% of the total reaction at 5000 K, which is consistent with the limited available experimental information, which indicates that the branching ratio ͓k 2 /(k 1 ϩk 2 )͔ should be between 0% and 20%, depending on the N-atom translational energy.
Calculated VTST rate constants for the reverse reaction ͑Ϫ1͒ were also in very good agreement with the experimental data within the temperature interval 1500-5000 K. The present results with the new PESs also improved slightly the kinetic data derived by using the previous PESs. Hence the 3 AЈ PES should be included in kinetic and dynamic studies of this reverse reaction for temperatures much lower than those predicted in previous QCT studies, although its contribution to the total k Ϫ1 is low ͑e.g., 6.7% at 2000 K͒.
The new analytical PESs accurately describe the NNO C s regions and also the NON C 2v and C s regions, which make them valuable for use in theoretical studies of all three reaction processes. Dynamic and kinetic studies with the new PESs using the QCT method and a quantum wave-packet Using the PES of Ref. 15 and including the electronic statistical degeneracy factor. c ICVT/OMT rate constants calculated on the 3 AЈ PES with a scaled energy barrier ͓for reaction ͑1͔͒ equal to 6.74 kcal/mol ͓the ab initio CBS limit ͑Ref. 24͔͒.  Table I. dynamic approach are in progress in our group to further study the reactions ͑1͒ and ͑2͒, especially regarding the dynamical properties derived from each PES.

ACKNOWLEDGMENTS
This work has been supported by the Spanish Ministry of Education and Culture ͑Project No. PB98-1209-C02-01͒ and the Spanish Ministry of Science and Technology ͑Project Nos. BQU2002-03351 and BQU2002-04269-C02-02͒. Financial support from the European Union ͑INTAS Project No. 99-00701͒ and the ''Generalitat'' ͑Autonomous Govern-ment͒ of Catalonia ͑Project No. 2001SGR 00041͒ is also acknowledged. P.G. thanks the ''Universitat de Barcelona'' for a predoctoral research grant. The authors are grateful to the ''Center de Computació i Comunicacions de Catalunya (C 4 -CESCA/CEPBA͒'' for providing part of the computer time.