The lowest doublet and quartet potential energy surfaces involved in the N (cid:132) 4 S (cid:133) ¿ O 2 reaction. I. Ab initio study of the C s -symmetry (cid:132) 2 A 8 , 4 A 8 (cid:133) abstraction and insertion mechanisms

In this work we have carried out ab initio complete active space self-consistent-ﬁeld ~ CASSCF ! calculations, second-order perturbation calculations based on CASSCF wave functions ~ CASPT2 ! , uncontracted multireference conﬁguration interaction calculations, and some density functional calculations with standard correlation-consistent Dunning basis sets and atomic natural orbital basis sets on the lowest 2 A 8 and 4 A 8 potential energy surfaces involved in the title reaction. The ground 2 A 8 surface has an average energy barrier of 5.3 kcal/mol in the CASPT2 complete basis set limit. A peroxy NOO minimum is found in agreement with preceding ab initio works, which seems to play an important role in the opening of a double microscopic mechanism: direct C s abstraction and indirect C s insertion through the NO 2 ( X 2 A 1 ) molecule. The ground 4 A 8 surface shows an average energy barrier of 13.5 kcal/mol in the CASPT2 complete basis set limit. Despite this excited surface displays another peroxy minimum, in this case only a direct C s -abstraction mechanism can be expected. The present results improve previous high quality ab initio studies and provide lower energy barriers in both potential energy surfaces, which would produce larger total thermal rate constants in better agreement with experimental data. Finally, it is demonstrated that the N and O 2 s electron correlation cannot be neglected as it produces a signiﬁcant decrease in both energy barriers. © 2001


I. INTRODUCTION
The elementary gas-phase reaction of N( 4 S) with molecular oxygen, N͑ 4 S ͒ϩO 2 ͑ X 3 ⌺ g Ϫ ͒→O͑ 3 P ͒ϩNO͑ X 2 ⌸ ͒, ͑1͒ ⌬ r H 0 K 0 ϭϪ32.09 kcal/mol ͑Ref. 1͒ and its reverse reaction play an important role in atmospheric chemistry. This reaction is a source of infrared chemiluminescence in the upper atmosphere. 2 High temperature studies of the kinetics and dynamics of the N( 4 S)ϩO 2 and N( 4 S)ϩNO reactions and their reverse ones are very important for the understanding of the chemical and physical phenomena taking place during the re-entry of spacecrafts into the Earth's atmosphere, 3 where nonthermal equilibrium conditions between the different degrees of freedom may play an essential role. Reaction ͑1͒ with hot N atoms provides an additional mechanism for the production of nitric oxide in the earth thermosphere. 4 This reaction is also of interest in the context of combustion of hydrocarbon-air mixtures. 5 In several preceding papers [6][7][8][9][10] we have presented different theoretical approaches to this reaction and we have also given a detailed review of the main experimental and theoretical data that have been published for this reaction. Thus, in the current introduction we will summarize only the principal information and we will update that with the latest and the most significant contributions to this reaction.
Experimental kinetics studies are available dealing with resembling thermal rate constants in a wide interval of temperatures: kϭ1.5ϫ10 Ϫ11 e Ϫ3600/T cm 3 molecule Ϫ1 s Ϫ1 at 280-910 K ͑Ref. 11͒ or 1.5ϫ10 Ϫ14 T e Ϫ3270/T cm 3 molecule Ϫ1 s Ϫ1 at 298 -5000 K. 12 Measurements of NO vibrational distributions, populated between vЈϭ0 -7, show some important differences on their shapes for reactants at room temperature. [13][14][15][16][17] Several ab initio studies have been reported on the ground ( 2 AЈ) and the first excited ( 4 AЈ) potential energy surfaces ͑PES͒ involved in this reaction. Thus, CASSCF and multireference contracted CI calculations with large Gaussian basis sets 18 have been carried out for both PESs aimed at characterizing the transition states and minimum energy reaction paths. The same ab initio method but with large ANO basis sets were also used in a more recent theoretical study of the ground 2 AЈ PES. 19 Several studies have dealt with the controversy about the existence of a NOO peroxy isomer on the ground doublet PES [20][21][22] that could have some influence in the studied reaction.
In order to study the kinetics and the dynamics of this reaction, several analytical fits of the lowest doublet PES have been reported in previous works based mainly in the before mentioned ab initio data. 18,19 Most of them 23,10 are based on the analytical form ͑many-body expansion͒ and parameters ͑diatomic terms and reference structure of the threebody term͒ employed in our first study, 6 and made use of the a͒ Authors to whom correspondence should be addressed. Electronic mail: r.sayos@qf.ub.es and miguel@qf.ub.es ab initio data of Ref. 18 with some kind of correction in the energy and including experimental diatomic data. Two earlier analytical 2 AЈ PESs, one of bond-order-type based on ab initio data, 19 and another of double many-body form based on diatomics-in-molecules ͑DIM͒ and ab initio data, 24 are available in the literature, although they do not reproduce properly neither the ab initio information nor the experimental data. In Ref. 10 we reported a detailed comparison on the transition states for most of these PESs. Regarding to the first excited PES, only one analytical PES is available, which was constructed using a similar procedure than for the ground 2 AЈ PES. 23 Several quasiclassical trajectory ͑QCT͒ studies, 3,6 -8,23,25,26 variational transition state theory ͑VTST͒ studies 10,19 and quantum approaches 9,27 have been performed to study the kinetics and dynamics of the reaction ͑1͒ by using the mentioned PESs.
In the present work we will present a new contribution to the study of the N( 4 S)ϩO 2 reaction based on highly accurate and extensive ab initio calculations. We initiate a series of papers that will try to study this reaction by using new global analytical PESs ͑ 2 AЈ and 4 AЈ͒ based in the current ab initio data. Up to now, the published PESs do not reproduce properly the properties of the NO 2 (X 2 A 1 ) molecule and its isomers, nor the C 2v -insertion mechanism, which involves several surface crossings ͑i.e., between the 2 A 1 , 2 A 2 , 2 B 1 and 2 B 2 PESs͒. QCT, VTST and wave packet time-dependent quantum dynamics studies will follow the current paper and will try to elucidate the importance of several microscopic mechanisms ͑i.e., abstraction versus C s or C 2v insertion͒ that can compete in this reaction as it will be shown in the present work.
Section II will offer a summary of the ab initio and density functional theory ͑DFT͒ procedures used in this work. Section III will provide the ab initio and DFT results on the stationary points of both PESs ͑ 2 AЈ and 4 AЈ͒, and the corresponding minimum energy reaction paths ͑MERP͒ connecting minima ͑MIN͒ and transition states ͑TS͒. Finally, Sec. IV will summarize the concluding remarks.

II. THEORETICAL METHODS
The ab initio calculations presented in this work have been performed with the MOLCAS 4.1 ͑Ref. 28͒ package of programs. The complete active space self-consistent-field method ͑CASSCF͒ 29,30 was employed throughout this study, always choosing the lowest root in C s symmetry for both the doublet and the quartet PESs ͑i.e., 2 AЈ and 4 AЈ͒, which correlate reactants and products of reaction ͑1͒. The location of each stationary point geometry on the PESs was achieved by optimization searches of both minima and transition states employing analytic CASSCF gradients. Full characterization of them was effected by calculating the numerical Hessian matrix at the optimized geometries. Calculations at secondorder perturbation theory based on a zeroth-order CASSCF wave function ͑CASPT2 method͒ using the standard correction ͑i.e., std͒ or some G i (iϭ1,2,3) variants 31 as implemented in MOLCAS 4.1 were applied to refine the stationary points obtained at the CASSCF level. In some cases a grid of CASPT2 points was generated to search directly the station-ary point. Thus, local fits were performed by means of bicubic splines 32 or Taylor expansions in the bond angle together with symmetry adapted internal coordinates expansion in the bond lengths to obtain the optimal geometry and the harmonic frequencies at CASPT2 level by using the SURVIBTM code of molecular rovibrational analysis. 33 More details of the procedure used can be found in a recent paper of our group. 34 Two different active spaces of the NO 2 system were used in the present study: ͑a͒ the full-valence active space, i.e., all the atomic 2s and 2p electrons are distributed among the corresponding derived bonding and antibonding molecular orbitals ͑MO͒ ͓i.e., CAS ͑17,12͔͒ and ͑b͒ a smaller active space with only the 2p electrons ͓i.e., CAS ͑11,9͔͒. This latter active space has been assumed to be accurate enough for this system in some preceding papers; 18,19,22 in both cases the natural MO occupation has been checked for all stationary points. The CAS ͑17,12͒ comprising 17 electrons in 12 orbitals generates 28 503 and 20 376 configuration state functions ͑CSF͒ for the 2 AЈ and 4 AЈ PESs, respectively, while the CAS ͑11,9͒ produces only 3048 and 1878, respectively.
CASPT2 and CASSCF calculations have been performed checking the effect of the correlation energy of the three atomic 1s or 2s electrons; previously, the 1s and 2s orbitals were optimized at the CASSCF level. The results were very similar to those obtained previously without the 1s frozen core option. In all cases the barrier energies were around 10% higher if the 1s orbitals were kept frozen. 2s valence orbitals were only kept frozen in some CASPT2 calculations to compare with earlier CASSCF followed by multireference contracted CI ͑CCI͒ calculations. 18 The standard correlation-consistent ͑cc-pVnZ and augcc-pVnZ, nϭD,T,Q,5͒ Dunning's basis sets 35 and small and large atomic natural orbital ͑ANO͒ basis sets 36 were used in the present study. The basis sets were obtained from the Extensible Computational Chemistry Environment Basis Set Database, version 1.0, as developed and distributed by the Molecular Science Computing Facility. 37 Some density functional theory ͑DFT͒ studies by using the unrestricted B3LYP method as implemented in the GAUSSIAN 98 ͑Ref. 38͒ code were adopted to facilitate the search of the stationary points.
Supermolecule calculations were considered in the determination of all energies in both the ab initio and the DFT methods.
Recent studies on similar reactions ͓e.g., N( 2 D)ϩNO ͑Ref. 34͒ and N( 2 D)ϩO 2 , 39 systems͔ using the present methods have shown that they are accurate enough to provide a good description of them in comparison with experimental data or larger calculations.

A. Stable molecules and reaction exoergicity
A first verification of the degree of accuracy of the theoretical approach has been carried out by calculating the properties of the diatomic and NO 2 (X 2 A 1 ) molecules, and the exoergicity of reaction ͑1͒. Thus, Table I summarizes the bond length, the harmonic vibrational frequency and the dissociation energy of both diatomic molecules at different ab initio levels. The comparison of the calculated geometries with the experimental data shows a small effect of the size and quality of the basis set on the optimized bond length, although the most remarkable enhancement is produced when the geometry is optimized directly at the CASPT2 G2 level. The results are comparable for both types of basis sets ͑i.e., ANO and cc-pVnZ/aug-cc-pVnZ͒ for a similar number of basis functions ͑e.g., compare the ANO-A basis set with the cc-pVTZ one both with a total number of 90 basis func-tions͒. An excellent agreement was also obtained for the harmonic frequencies. However, the description of both O 2 and NO dissociation energies was somewhat worse. First, the introduction of the dynamical correlation energy by means of the CASPT2 method was essential for a reasonable description. Second, the G i variants gave similar results although much better than the standard Fock matrix one, as it should be expected. 31 The O 2 dissociation energy presented a significant error ͑4.5% with respect to the experimental value͒ even at the highest ab initio calculation level ͓i.e., CASPT2 G2͑17,12͒/aug-cc-pVTZ method͔, that originated mainly the G2 optimum geometries and harmonic vibrational frequencies obtained by using the VIBROT module of the MOLCAS 4.1 program ͑Ref. 28͒. Masses of the most abundant isotopes were used: 14 N and 16 O. e The lowest spin-orbit states ͓i.e., NO(X 2 ⌸ 1/2 ) and O( 3 P 2 )͔ were used for the experimental data ͑Ref. 40͒. discrepancy in the exoergicity with respect to the experimental value. The differences arised from the use of two different active spaces were very small as should be expected owing to the high occupation number ͓over 1.99 in CAS͑17,12͔͒ of two of the natural MOs in this asymptotic region of the PES.
The difficulty in the O 2 theoretical treatment is well known and can only be amended with very refined and computationally expensive ab initio calculations with inclusion of complete basis set ͑CBS͒ limits. 41,42 However, we believe that is not crucial in the context of the present study, which tries to account for all the stationary points of the lowest doublet and quartet PESs at the same level, with a foremost importance concerning the energy barriers.
On the other hand, DFT calculations at the UB3LYP/ aug-cc-pVTZ level offered good results and improved substantially the reaction exoergicity. Table II presents the results for the NO 2 (X 2 A 1 ) molecule. In spite of the calculated geometry and harmonic frequencies were very similar for both actives spaces ͓i.e., ͑11,9͒ and ͑17,12͔͒ and match very well the experimental values, important differences were observed in the dissociation energies. The increase of the active space size improved significantly the calculated dissociation energies, although was necessary the introduction of the dynamical correlation energy by means of the CASPT2 method to accurately reproduce the experimental values. The reference weight into the CASPT2 wave function was high enough to describe properly the molecule ͓i.e., approximately 90% at CAS͑17,12͔͒. The importance of the higher active space was confirmed by the occupation of the 12 natural MOs: a 1 :1.998, 1.984, 1.980, 1.039, 0.0424, b 1 :1.965, 0.115, a 2 :1.923, and b 2 :1.998, 1.966, 1.960, 0.0284. The nitrogen 2s contribution in several active MOs was important in the description of the NO 2 molecule, especially for bent geometries as it has been also observed in previous works. 49 On the other hand, the multireference character of the wave function of the NO 2 molecule can be clearly illustrated taking into account the three most important CSFs and their coefficients: The present study improves the previous ab initio results for NO 2 molecule as it can be observed in Table II.

B. Characterization of the lowest 2 AЈ potential energy surface
The geometries, frequencies, and energies relative to reactants, N( 4 S)ϩO 2 , for all the stationary points characterized at the ab initio ͑i.e., CASSCF and CASPT2͒ and DFT ͑i.e., UB3LYP͒ levels for the ground doublet PES are given in Tables III, IV, and V. Figure 1 shows the MERPs connecting reactants and products. The attack of the N( 4 S) atom to the O 2 molecule produces a bent transition state ͑TS1͒ with the highest energy barrier along the MERP, which leads to a shallow NOO peroxy minimum ͑MIN1͒ previously reported in the literature. 21,22 The system can directly produce O( 3 P)ϩNO after surmounting another transition state ͑TS2͒ or can evolve through another shallow NOO minimum ͑MIN2͒ and through the much deeper ground state NO 2 (X 2 A 1 ) molecule after surmounting two transition states ͑TS3 and TS4͒. No barrier seems to exist between NO 2 molecule and products. Table III presents a comparative study about the properties of TS1. First of all, CASSCF calculations with different basis sets and the lower active space ͑11,9͒ yield similar geometries, frequencies and a very small decrease in the energy barrier. Nevertheless, the increase in the active space to ͑17,12͒ produces a significant enlargement of the NO distance ͑ca., 0.025 Å͒ and also an additional energy barrier reduction. The introduction of the dynamical correlation energy through the CASPT2 method ͑std or G2͒ originates a dramatic decrease in the energy barrier. In some cases the obtained value ͓e.g., 4.14 kcal/mol at CASPT2͑17,12͒ G2/ aug-cc-pVTZ͔ is too small in comparison with a value compatible with the experimental activation energy ͓i.e., 7.2 kcal/ mol within 280-910 K ͑Ref. 11͔͒. Due to this fact, and also taking into account previous published results ͑see Table III͒ that evidence the important effect of the dynamical correlation energy into the NO distance optimization of this TS ͓e.g., 1.821 Å at MR-CCIϩQ/CASSCF (11,9)/͓11s6p/ 5s3 p2d1 f ͔ 18 or 1.825 Å at MR-ICCIϩQ/CASSCF(9,8)/ cc-pVTZ 22 ͔, we carried out a numerical optimization at the CASPT2͑17,12͒ G2 level. An optimum NO distance of 1.825 Å was obtained for TS1, which produced an energy barrier of 4.70 kcal/mol ͓5.00 kcal/mol including zero point energy ͑ZPE͒ differences͔.
A detailed study of the energy barrier of TS1 has been made by increasing the quality of the basis set at the optimum CASPT2͑17,12͒ G2 geometry. The basis set dependence is usually well described by a simple exponential-like function 50 of the form where n is the cardinal number of the basis set ͑2, 3, 4, and 5 for DZ, TZ, QZ, and 5Z, respectively͒ and ⌬E ϱ corresponds to the estimated complete basis set ͑CBS͒ limit as n→ϱ. The estimated CASPT2͑17,12͒ CBS limits for this energy barrier were ͑a͒ 4.90 and 4.73 kcal/mol at the G2 level, and ͑b͒ 5.99 and 5.69 kcal/mol at the std level for the cc-pVnZ and aug-cc-pVnZ series, respectively, with a maximum error of Ϯ 0.3 kcal/mol, estimated by using other ex-ponential functions. Therefore, similar CBS energy barriers were found for both series of basis sets. The main difference ͑ca., 1 kcal/mol͒ arises from the use of the G2 or the standard CASPT2 variants. However, these values are very close to the energy barrier finally fitted in our previous analytical PES ͑i.e., 6.2 kcal/mol 10 ͒, which was derived from ab initio data 18 and variational transition state rate constants which reproduced the experimental rate constants in a wide interval of temperatures ͑300-5000 K͒, with the inclusion of the k( 4 AЈ) contribution.
We have also calculated the TS1 energy barrier using the uncontracted multireference SD-CI ͑MR-CI͒ method with the inclusion of the Davidson correction ͑Q͒, based on the same CASSCF͑11,9͒ MOs; 11 e have been correlated ͑1s and 2s electrons were frozen͒. We have done these calcula-tions to verify the previous results of Walch and Jaffe 18 ͑Table III͒ and to show how those MR-CIϩQ calculations overestimate energy barriers, specially when the 2s electrons are not correlated. We have obtained an energy barrier of 8.16 kcal/mol by using a MR-CI with 24 CSFs of reference ͑3.709.673 CSF in all for C s symmetry͒. If the 2s electrons are neither correlated in the CASPT2͑11,9͒ G2 calculations, the barrier increases to 8.07 kcal/mol, which is very similar to the mentioned MR-CIϩQ value. Therefore, it is very important to correlate the 2s electrons in both the CASPT2 and MR-CI calculations, which produces lower energy barriers,  20 from an early ab initio study, proposed the existence of a NOO (AЈ) peroxy isomer as a stable species that could play an important role in atmospheric chemistry. The same authors confirmed later this point by using much more accurate ab initio calculations. 21 They found a very shallowly bound isomer, 85.3 kcal/mol over the NO 2 molecule at the CISDϩQ/QZϩ2P level ͑Table IV͒, al-though no TSs were reported for its dissociation. In a latter paper Walch 22 checked the low stability of this minimum, separated from O( 3 P)ϩNO by an energy barrier of only 0.25 kcal/mol ͓at the MR-ICCIϩQ/CASSCF (9,8) level without the inclusion of ZPE differences͔. This energy barrier corresponds approximately to that of TS3 ͑Table V͒. Here we have found this peroxy minimum ͑MIN1͒ at the CASSCF, CASPT2, and UB3LYP levels as is shown in Table  IV. Geometry and frequencies are very similar to those previously obtained by the above-mentioned authors. We have obtained an energy with respect to the NO 2 molecule of 81.01, 86.14, and 84.99 kcal/mol at the CASSCF͑17,12͒, CASPT2͑17,12͒ G2, and UB3LYP with the aug-cc-pVTZ basis set, respectively, also very close to the previous results. 21 The most important CSFs for this minimum are   16 O. c Energy respect to O( 3 P)ϩNO and N( 4 S)ϩO 2 , respectively. In Ref. 21 relative energies to NO 2 (X 2 A 1 ) were given, here ⌬E has been obtained by using the NO 2 (X 2 A 1 ) experimental dissociation energies ͑Ref. 46͒. d CASPT2͑17,12͒ energies, geometries, and harmonic vibrational frequencies derived from a grid of points by using the SURVIBTM program ͑Ref. 33͒. e Reference 22. f Reference 21. The energy referred to NO 2 (X 2 A 1 ) was 75.3 and 85.3 kcal mol Ϫ1 at CASSCF͑17,12͒/DZϩP and CISDϩQ/QZϩ2P levels, respectively. We obtained 81.01, 86.14, and 84.99 kcal mol Ϫ1 at CASSCF͑17,12͒/aug-cc-pVTZ, CASPT2͑17,12͒ G2/aug-cc-pVTZ, and UB3LYP/aug-cc-pVTZ levels, respectively. g Obtained by summing up the experimental exoergicity ͑Ref. 40͒ ͑see Table I͒. 0.917 ... ͑ 4aЈ͒ 2 ͑ 5aЈ͒ 2 ͑ 6aЈ͒ 2 ͑ 7aЈ͒ 2 ͑ 8aЈ͒ 2 ͑ 9aЈ͒ 2 ͑ 10aЈ͒ 1 ͑ 11aЈ͒ 0 ͑ 12aЈ͒ 0 ͑ 1aЉ͒ 2 ͑ 2aЉ͒ 2 ͑ 3aЉ͒ 0 , where their coefficients are also reported. For this minimum we have also performed calculations using the full valence active space ͑17,12͒, and we have seen that increasing the size of the basis set slightly decreases the bond lengths. The geometry optimized at the CASPT2 level is very close to the CASSCF one, with the main difference being observed in the OO distance, which is shorter at the CASPT2 level. As a consequence of this OO shortening the OO stretching frequency is higher at the CASPT2 level compared to the CASSCF one. From this peroxy minimum two TSs ͑i.e., TS2 and TS3͒ with almost no energy barrier over MIN1 lead directly to products O( 3 P)ϩNO ͑direct mechanism͒ or to another shallow minimum ͑MIN2͒, respectively. In spite of the good fit obtained for the ab initio points grids around MIN1 and TS2 ͑i.e., a root-mean-square deviation below 5ϫ10 Ϫ3 kcal/mol͒, as their energies at the CASPT2 level are very close ͑Fig. 1͒, a somewhat lower energy for TS2 ͑0.45 kcal/mol͒ has been achieved, due to the uncertainty in the use of numerical derivatives. Nevertheless, the UB3LYP method, which uses analytical derivatives, gives the correct location.
The minimum MIN2 is a previous step in the indirect insertion mechanism through the NO 2 molecule to produce also O( 3 P)ϩNO. TS4 connects MIN2 and the NO 2 molecule. MIN2 and TS4 correspond to C s stationary points with a lengthened OO bond to allow for the N atom insertion. The absence of energy barriers above reactants apart from the one corresponding to TS1 opens a competition between both kinds of microscopic reaction mechanisms: direct C s -abstraction and indirect C s -insertion. The alternative C 2v -insertion mechanism, which involves different PESs and their crossings and conical intersections, is under study in our group. The importance of the indirect C s -insertion mechanism has been observed in a recent wave packet timedependent quantum dynamics study 51 by using our previous 2 AЈ PES. 10 Although this analytical PES does not properly reproduce the NO 2 geometry ͓a linear D ϱh minimum is present at Ϫ151.3 kcal/mol respect to O( 3 P)ϩNO͔ and fits and estimated energy barrier for the C 2v approach ͓i.e., 47.46 kcal/mol respect to N( 4 S)ϩO 2 ͔, it presents similar stationary points to the present MIN2 and TS4, which allow the access to the deep linear minimum. This produces a particularly high contribution of the C s -insertion mechanism and a decrease in the overall reactivity. The importance of the C s -insertion mechanism has also been observed by us in a preliminary QCT study using a new analytical PES based in the present ab initio data.
The NO 2 molecule does not present a potential energy barrier for the ground state dissociation ͓i.e., O( 3 P)ϩNO͔ in agreement with preceding ab initio studies of its photodissociation 52 or unimolecular dissociation. 45

C. Characterization of the lowest 4 AЈ potential energy surface
The geometries, harmonic vibrational frequencies, and energies relative to reactants, N( 4 S)ϩO 2 , for all the stationary points characterized at the ab initio ͑i.e., CASSCF and CASPT2͒ and DFT ͑i.e., UB3LYP͒ levels for the lowest quartet PES are shown in Tables VI and VII. Figure 2 depicts the MERP connecting reactants and products, which is much simpler than for the doublet PES. All stationary points display C s symmetry. The highest energy barrier corresponds to TS1Ј, whose values are compared in Table VI. CASSCF calculations with different basis sets and the lower active space ͑11,9͒ provide resembling geometries, frequencies, and energy barriers.
The increase in the active space to ͑17,12͒ produces a significant enlargement of the NO distance ͑ca., 0.020 Å͒ and a little energy barrier decrease. The introduction of the dynamical correlation energy through the CASPT2 method ͑std or G2͒ originates a large decrease in the energy barrier. The numerical optimization at the CASPT2͑17,12͒ G2 level gives a geometry ͑Table VI͒ for TS1Ј with a much longer NO distance ͑i.e., 1.7803 Å͒ and a shorter OO distance ͑i.e., 1.2559 Å͒. An energy barrier of 12.74 kcal/mol ͑12.79 kcal/ mol including ZPE differences͒ is obtained at the CASPT2͑17,12͒ G2/aug-cc-pVTZ level. The estimated CASPT2͑17,12͒ CBS limits for this energy barrier were ͑a͒ 13.06 and 12.82 kcal/mol at the G2 level and ͑b͒ 14.38 and 13.80 kcal/mol at the std. level, for cc-pVnZ and aug-cc-pVnZ series, with a maximum error of Ϯ 0.3 kcal/mol, estimated by using other exponential functions. The main difference in both CBS limits ͑ca. 1.6 kcal/mol͒ arises again from FIG. 1. The lowest 2 AЈ PES MERP at the CASPT2͑17,12͒ G2 ͑regular numbers͒ and UB3LYP ͑italic numbers͒ levels with the aug-cc-pVTZ basis set. Energies are given relative to reactants, N( 4 S)ϩO 2 , in kcal/mol. the use of the G2 or standard CASPT2 variants, as it happens for the TS1 in the doublet PES. The present energy barriers are somewhat lower than the energy barrier fitted in a previous analytical quartet PES 23 ͑i.e., 15.0 kcal/mol͒ based on MR-CCIϩQ/CASSCF (11,9)/͓11s6 p/5s3 p2d1 f ͔ calculations, 18 which presented a original value of 18.0 kcal/mol but with a very similar geometry to the CASPT2͑17,12͒ G2 one ͑Table VI͒. We have also calculated the TS1Ј energy barrier using the MR-CIϩQ/aug-cc-pVTZ method with 11 electrons correlated ͑N and O 1s and 2s electrons were kept frozen͒, as for the doublet PES to compare with previous ab initio data. 18 An energy barrier of 15.51 kcal/mol was determined by using a MR-CI calculation with 12 CSFs of reference, which is very close to the mentioned published data. CASPT2͑11,9͒ G2 calculations without 2s electron cor-relation increases the barrier to 16.07 kcal/mol, which is very similar to the aforementioned MR-CIϩQ value. Therefore, the 2s electron correlation becomes very important in both the CASPT2 and MR-CI calculations to calculate the energy barrier for both doublet and quartet PESs. The lower energy barrier found for the TS1Ј in the quartet PES respect previous published data will produce larger thermal rate constants at high temperatures, where this excited PES becomes quite important ͓e.g., at 1500 K the k( 4 AЈ) contributes around a 10% of the total rate constant͔.
DFT calculations at the UB3LYP/aug-cc-pVTZ level provide too long NO distances ͑i.e., 1.9206 Å͒ although a similar energy barrier of 14.18 kcal/mol ͑14.38 kcal/mol including ZPE differences͒. Some spin contamination was also TS1Ј leads to a very shallow minimum (MIN1Ј) with a structure comparable to the peroxy minimum in the doublet PES. This minimum dissociates to O( 3 P)ϩNO products through TS3Ј, which has an energy barrier ͑7.81 kcal/mol͒ below that of TS1Ј. Hence, only a direct microscopic mechanism is expected for this PES differing from the double mechanism proposed for the doublet PES. DFT calculations at the UB3LYP/aug-cc-pVTZ level exactly corroborate the ab initio MERP.

IV. CONCLUSIONS AND REMARKS
This work presents a detailed theoretical study of the N( 4 S)ϩO 2 (X 3 ⌺ g Ϫ )→NO(X 2 ⌸)ϩO( 3 P) exothermic reaction on its lowest 2 AЈ and 4 AЈ potential energy surfaces. Ab initio CASSCF, CASPT2, and MR-CI methods with standard correlation-consistent ͑cc-pVnZ and aug-cc-pVnZ, nϭD, T, Q, 5͒ Dunning's basis sets and small and large atomic natural orbital basis sets were used; CBS limits were also reported for the main energy barriers ͑TS1 and TS1Ј͒. DFT methods were also used to facilitate the search of the stationary points, producing similar results too. Thus, several minima and transition states have been found along the different MERPs connecting reactants and products on both surfaces.
The ground 2 AЈ PES presents an average energy barrier ͑TS1͒ of 4.8 kcal/mol and 5.8 kcal/mol in the CBS limits for the G2 and std CASPT2 levels, respectively. The second value is almost coincident with the energy barrier ͑6.2 kcal/mol͒ derived from thermal rate constants in our previous paper. A peroxy NOO minimum is found in agreement with preceding ab initio works, which seems to play an important role in the opening of a double microscopic reaction mechanism: direct C s -abstraction and indirect C s -insertion. The importance of this second mechanism through the NO 2 molecule has been recently anticipated in a wave packet time-dependent quantum dynamics study on our previous analytical doublet PES and also in our preliminary QCT study.
The alternative C 2v -insertion mechanism with the different PESs and their crossings and conical intersections is currently under study in our group.
The ground 4 AЈ PES presents an average energy barrier (TS1Ј) of 12.9 kcal/mol and 14.1 kcal/mol in the CBS limits for the G2 and std CASPT2 levels, respectively. In this surface another peroxy minimum is found, although in this case only a direct C s -abstraction mechanism should be expected.
The present results improve previous high quality ab initio studies and provide lower energy barriers for both PESs, which would produce larger values of both thermal rate constants, and therefore a larger total rate constant, with an expected better agreement with the available experimental data.
The good results obtained for reactants and products as well as for the peroxy NOO( 2 AЈ) minimum and for the NO 2 (X 2 A 1 ) molecule point towards the suitability of describing both PESs at the CASPT2͑17,12͒ level of theory. Thus, two analytical PESs ͑ 2 AЈ and 4 AЈ͒ based on several grids of ab initio points have been almost fitted and dynamics and kinetics studies are currently in progress.
Finally, the study of the N and O 2s electron correlation in the MR-CI and CASPT2 methods shows that it is very important to correlate the 2s electrons, in both CASPT2 and MR-CI calculations, which produces lower energy barriers, much closer to the value estimated from experimental data. This point was not taken into account in previous ab initio studies.  2000SGR 00016͒ is also acknowledged. One of the authors ͑C.O.͒ thanks the Spanish Ministry of Education and Culture for a predoctoral research grant. The authors are grateful to the ''Centre de Computació i Comunicacions de Catalunya ͑C 4 -CESCA/CEPBA͒'' for providing a part of the computer time. Thanks are also given to Professor Carlo Petrongolo ͑Università di Siena͒ for providing us a copy of his recent paper about the time-dependent wave packet study of the N( 4 S)ϩO 2 reaction.