The lowest doublet and quartet potential energy surfaces involved in the N(4S)+O2 reaction. II. Ab initio study of the C2v-symmetry insertion mechanism

In the present work we have carried out ab initio complete active space self-consistent field (CASSCF) and second-order perturbation theory on CASSCF wave function (CASPT2) calculations and also some density functional theory calculations with the aug-cc-pVTZ Dunning’s basis set on the lowest A1, B1, A2, and B2 doublet and quartet potential energy surfaces (PES) that could be involved in the title reaction. Thus, several minima, transition states, and surface crossings have been found for the C2v-insertion reaction mechanism. The results agree very well with available experimental data [i.e., for NO2 (2A1), MIN2 (2B2), NO2 (2Πu)] and with other previous ab initio calculations. Six A′/A′- and four A′/A″-type surface crossings were located and classified for these PES’, whose only one (i.e., 2B2/2A1) has been previously reported in theoretical and experimental studies. High-energy barriers were found for the direct C2v-insertion mechanism (3.11 and 2.54 eV for the lowest doublet and quartet PES’ at the CASPT2/aug-cc-pVTZ level, respectively), clearly showing that this competitive mechanism is much less favorable than the direct Cs-abstraction or the indirect Cs-insertion reaction mechanisms reported in Paper I.In the present work we have carried out ab initio complete active space self-consistent field (CASSCF) and second-order perturbation theory on CASSCF wave function (CASPT2) calculations and also some density functional theory calculations with the aug-cc-pVTZ Dunning’s basis set on the lowest A1, B1, A2, and B2 doublet and quartet potential energy surfaces (PES) that could be involved in the title reaction. Thus, several minima, transition states, and surface crossings have been found for the C2v-insertion reaction mechanism. The results agree very well with available experimental data [i.e., for NO2 (2A1), MIN2 (2B2), NO2 (2Πu)] and with other previous ab initio calculations. Six A′/A′- and four A′/A″-type surface crossings were located and classified for these PES’, whose only one (i.e., 2B2/2A1) has been previously reported in theoretical and experimental studies. High-energy barriers were found for the direct C2v-insertion mechanism (3.11 and 2.54 eV for the lowest doublet and quartet PES’ at the CASP...


I. INTRODUCTION
In a previous paper 1 ͑hereafter referred to as Paper I͒ we have described the C s -symmetry direct abstraction and indirect insertion mechanisms for the following reaction: ⌬ r H 0K 0 ϭϪ32.09 kcal/mol. ͑1͒ In the present work we have studied the insertion of a nitrogen atom into the O 2 molecule preserving the C 2v symmetry. We have taken into account the lowest doublet and quartet AЈ ͑C s -symmetry͒ potential energy surfaces ͑PES͒ involved in the title reaction. From these surfaces only one crossing between the C 2v PES' corresponding to the NO 2 (X 2 A 1 ) and the NO 2 (A 2 B 2 ) minima 3-8 has been previously described.
All the previous theoretical studies [3][4][5] try to explain the extremely complex spectrum of NO 2 . From multireference configuration interaction ͑MR-CI͒ 3 calculations coupling elements have been obtained, and with this information potential energy functions for the two lowest 2 AЈ NO 2 states, in both the diabatic and adiabatic representations, have been derived. 4,5 Experimental studies of electron impact energy loss spectra of the NO 2 A 2 B 2 ←X 2 A 1 transition 8 agree with the theoretical results for the transition vertical energy. 4 The geometrical parameters obtained theoretically agree with those estimated from extrapolations of observed spectroscopic bands. 6,7 In the above-mentioned theoretical studies, both minima involved in the crossing ͓i.e., NO 2 (X 2 A 1 ) and NO 2 (A 2 B 2 )͔, and the NO 2 ( 2 ⌸ u ) linear minimum have also been described. Some papers deal with the characterization of a great number of different NO 2 minima for the doublet surface 9,10 and for the quartet one. 9 In those papers, some intersections between different surfaces and the electronic configurations implicated were described. More recent calculations for the NO 2 (X 2 A 1 ) minimum have been done at the CASSCF and CISD ab initio levels, where the energetic difference between the bend (X 2 A 1 ) and linear ( 2 ⌸ u ) minima was studied. 11 Some symmetry breaking studies for the NO 2 radical have also been done at the CASSCF 12 and MR-CCSD 13 levels, where geometries and frequencies for the NO 2 (X 2 A 1 ) and NO 2 (A 2 B 2 ) minima were obtained. Ab initio studies of the peroxy and cyclic isomers of NO 2 and NO 2 Ϫ have been done, being the NO 2 ( 2 B 1 ) cyclic minimum described. 14 In all previous theoretical works about the 2 A 1 and 2 B 2 surfaces, the nuclear regions explored correspond to ONO angles in the range 80°-90°; consequently, they are not able to describe the C 2v -symmetry insertion reaction mechanism coming from N( 4 S)ϩO 2 (X 3 ⌺ g Ϫ ). Crossings between surfaces of different electronic states can be important in different molecular processes. When there is a conical intersection between both PES', the excited state is funneled into the intersection region favoring its radiationless decay to the ground state. 15 This is a direct effect 16 because nuclear motion takes place on both surfaces, the ground one and the excited one, and is due to the PES topology of the excited state near the intersection. Another direct effect is the nonadiabatic recrossing, 17 where the potential motion takes place on both surfaces but the overall a͒ Authors for correspondence. Electronic mail: miguel@qf.ub.es, r.sayos@qf.ub.es process begins and ends on the same surface. In this case, due to derivative couplings, the nuclear motion cannot follow the adiabatic reactive path and follows a nonadiabatic nonreactive one, the intersection region being recrossed several times. This effect will be more important if the intersection point and the true saddle point connecting the two intersection regions are so close. 18 An indirect effect, in which the nuclear motion only takes place on one potential energy surface, is produced by the geometric phase effect. 19 Due to this effect the nuclear wave function transported around a conical intersection acquires a nondynamical or geometric phase, which is necessary to compensate the phase changes of the adiabatic electronic wave function. This effect could have important consequences in reaction dynamics because it can affect reaction probabilities ͑e.g., the H 3 system 20 ͒. The main point is that the conical intersection has not to be energetically accessible; only a closed loop around the conical intersection is necessary to be accessible itself. As a consequence, the effect of a conical intersection on reaction dynamics cannot be anticipated, taking into account only its energy. For all these reasons, conical intersections [21][22][23] have to be thought as normal features on potential energy surfaces whose effects have to be taken into account.
We are particularly interested in the effects that these intersections could produce in the dynamics of the title reaction for electronically ground or excited reactants. Moreover, the characterization of these intersections can also help in the elucidation of the rather complicated spectra of the NO 2 molecule, and also in the construction of new analytical PES' ͑e.g., 2 AЈ and 4 AЈ͒, essential for accurate theoretical studies of the title reaction.
This work is organized as follows: the method of calculation is described in Sec. II, our results are presented in Sec. III, and in Sec. IV the concluding remarks are given.

II. THEORETICAL METHODS
The CASSCF method 24,25 was used throughout this study, always choosing the lowest two roots in C s symmetry for both the doublet and the quartet PES' ͑i.e., AЈ and AЉ͒, which were obtained using the two-state-averaged methodology. 26 Calculations in C 2v symmetry were also performed to locate the different intersections of the diabatic PES', in this case obtaining the first root of each symmetry ͑A 1 , B 1 , A 2 , and B 2 ͒, with the exception of the I2 intersection, where we made calculations with the first and second roots due to the fact that this intersection implied two states of the same symmetry.
The full-valence active space comprising 17 electrons in 12 orbitals ͓i.e., CAS͑17,12͔͒ was applied in all calculations as in Paper I. The standard correlation-consistent aug-cc-pVTZ Dunning's basis set 27 was also used in the present study; this implies a total of 138 basis functions, 46 on each atom. The dynamical correlation was included by performing CASPT2 calculations using the G2 variant. 28 All the CASSCF and CASPT2 G2 calculations were done with the MOLCAS 4.1 program. 29 The location of stationary points ͓i.e., minima ͑MIN͒ and transition states ͑TS͔͒ was achieved by employing ana-lytic CASSCF gradients. The full characterization of them was effected by calculating the numerical Hessian matrix at the optimized geometries. Intrinsic reaction coordinate ͑IRC͒ and approximate minimum energy paths ͑MEP͒ calculations were also carried out to verify connections between the stationary points. In some cases, we have used the SURVIBTM program 30 to locate some stationary points using a grid of points previously calculated at the CASSCF or CASPT2 levels, following the same method described in Paper I.
In order to locate the intersections ͑I͒ we have fitted different regions of each diabatic surface using bicubic splines. 31 Using these fittings we have calculated more points around the intersection regions and we have done the difference between both surfaces that were likely to intersect. Doing that, we were able to extract the seam of the conical intersection and to locate the minimum of this seam. We have studied the topology of the located intersections, which allows us to classify them. To do this, we have used the GAUSSIAN 98 program 32 with a reduced active space CAS͑7,6͒ and the 6-31G͑d͒ Pople's basis set in order to identify the two coordinates that define a conical intersection.
In spite of a rigorous check of whether or not the intersection is of a conical type was not carried out, we will use through the paper this name indistinctly. An intersection is conical if the electronic wave function changes its sign when is transported around a closed loop that encircles the intersection. For this to occur it is necessary that the two conditions that have to be accomplished to find an intersection ͓⌬H(q)ϭH AA (q)ϪH BB (q)ϭ0 and H AB (q)ϭ0͔ were satisfied for all N values of the internal coordinates (q ϭq 1 ,q 2 ,...,q N ) that describe the geometry of the nuclear arrangement. Sometimes the second condition is accomplished by symmetry ͑e.g., both states belong to different irreducible representations in C 2v ͒ but not all C 2v geometries give rise to conical intersections. 18 Apart from ab initio calculations we have also performed some density functional theory ͑DFT͒ calculations ͑i.e., UB3LYP/aug-cc-pVTZ͒ with a GAUSSIAN 98 code too, such as in Paper I, where we found a very similar and accurate description in comparison to the largest ab initio calculations.
Supermolecule calculations were considered in the determination of all energies in both the ab initio and the DFT calculations.
The present methodology has previously provided good results concerning the location of all stationary points on the 2 AЈ and 4 AЈ PES' ͑C s geometries͒ involved in the N( 4 S) ϩO 2 (X 3 ⌺ g Ϫ ) reaction, 1 in comparison with experimental data or larger calculations, and also in the study of similar reactions ͓e.g., N( 2 D)ϩNO 33 and N( 2 D)ϩO 2 34 ͔.

A. Stationary points
The first step in our study was the search of the main C 2v stationary points belonging to 2 B 2 , 4 B 2 , 2 A 1 and 4 A 1 PES' to compare with available previous published data. We found several minima and transition states on these surfaces ͑i.e., 2 AЈ and 4 AЈ PES' in C s symmetry͒, whose geometry, harmonic frequencies and energy are shown in Table I. The most energetic ones correspond to TS in 2 A 1 and 4 A 1 PES', ͑i.e., TS3 and TS1, respectively͒. Neither these stationary points nor TS2 in 4 A 1 and MIN1 in 4 B 2 PES' have been described previously.
For NO 2 ( 2 A 1 ) molecule and MIN2, there are preceding theoretical and experimental data to compare with. The results presented in Table I at the highest ab initio level ͑i.e., CASPT2͒ are very close to the experimental ones and much better than the earlier theoretical studies. The exception is mainly the MIN2 asymmetric stretching harmonic frequency, which is difficult to calculate due to the closeness of a conical intersection. As there will be show later ͑Sec. III C͒, all TS are close to the crossings between PES' of AЈ or AЉ symmetry.
TS1 connects two equivalent NOO( 4 AЈ) peroxy minima ͑R e(NO) ϭ1.3779 Å, R e(OO) ϭ1.3546 Å,ϽNOOϭ102.73°⌬E ϭ4.90 eV at the same ab initio level͒ described in Paper I. TS3 probably connects also with two equivalent NOO( 2 AЈ) peroxy minima described also in Paper I ͑R e(NO) ϭ1.2170 Å, R e(OO) ϭ1.3491 Å, ϽNOOϭ123.81°⌬Eϭ3.73 eV at the same ab initio level͒. TS2 is the transition state for the oxygen exchange reaction: O( 3 P)ϩNOЈ→NOϩOЈ( 3 P), with an energy barrier of 0.85 eV respect this surface asymptote. The connectivity of these transition states was also confirmed by doing IRCs at the UB3LYP/aug-cc-pVTZ level, although for TS3 we were not able to do the IRC at this level due to the convergence problems originated by the spin contamination ͑i.e., ͗S 2 ͘ was 1.78 to be compared with the correct expectation value of 0.75͒, which arises from the proximity of the quartet TS1.
MIN1 presents an imaginary frequency at the CASSCF level, but that disappears at CASPT2 G2 and UB3LYP lev- The CASPT2 G2 energies, geometries, and harmonic vibrational frequencies reported were derived from a grid of points by using the SURVIBTM program ͑Ref. 30͒. In some cases only the CASPT2 energy at the CASSCF geometry is given. b Harmonic vibrational frequencies: s ͑sym. str., a 1 ͒, b ͑bend., a 1 ͒, and a ͑asym. str., b 2 ͒, respectively ͑YZ taken as the molecular plane͒. Masses of the most abundant isotopes were used: 14  els. The imaginary frequency found at the CASSCF level corresponds to the asymmetric stretching mode. This fact means that this stationary point is a saddle point and that the surface bifurcates at this point, thus MIN1 showing symmetry breaking only at the CASSCF level. Table II presents the different minima found for the 2 A 2 , 4 A 2 and 2 B 1 PES' ͑i.e., 2 AЉ and 4 AЉ PES' in C s symmetry͒. Minima 4 and 5 have a rather cyclical structure. The calculated properties of the cyclic 2 B 1 isomer ͑MIN5͒ are reasonably consistent at both levels of theory and also with theoretical earlier predictions. Another open minimum in the 2 A 2 PES was also located ͓R e(NO) ϭ1.2855 Å, ϽONO ϭ110.00°⌬Eϭ1.86 ͑2.31͒ eV at the same ab initio level as shown in Table II͔, although more details and a comparison with experimental and other theoretical studies will be reported in a paper in progress about the excited AЉ PES. The most stable angular minima found are the MIN2( 2 B 2 ) and the MIN3( 4 A 2 ) for the doublet and quartet cases apart from the NO 2 ( 2 A 1 ) molecule.
We have also studied the linear NO 2 ( 2 ⌸ u ) stationary point ͑Table III͒. At this geometrical configuration the 2 A 1 and the 2 B 1 states become degenerated, as has been previously shown. [3][4][5]11 Upon bending the 2 ⌸ u state splits into the 2 A 1 -2 B 1 pair via a Renner-Teller mechanism. 40 Its strong interaction produces an upper state with a linear conformation and a lower state with a bent one. 10 The calculated energies and geometries ͑Table III͒ agree very well with the experimental values and with another published ab initio data. This structure is characterized as a minimum in the 2 B 1 surface and as a transition state in the lower 2 A 1 surface at its equilibrium geometry, as it is shown in Table III.
In order to understand how these stationary points could affect the reactivity we have approximately derived MEPs ͑Figs. 1 and 2͒ from grids of ab initio points, by using as the reaction coordinate a combination of the distance from the N atom to the center of mass of the diatomic OO molecule ͑R͒ and the diatomic OO distance ͑r͒. At the beginning of the C 2v insertion approach the reaction coordinate is practically equal to the R distance and at the end it coincides approximately with the r distance, but for middle configurations both coordinates become important ͑r and R͒. In C 2v symmetry the N( 4 S)ϩO 2 (X 3 ⌺ g Ϫ ) reactants correlate with 2,4 B 2 PES' and the O( 3 P)ϩNO (X 2 ⌸) products with 2 ( 2,4 A 1 ), 2 ( 2,4 B 1 ), 2,4 B 2 and 2,4 A 2 PES'. This means that reactants and products can be connected through a B 2 PES in the doublet case and also in the quartet one. In the doublet case We can see that this C 2v insertion reaction path ͑or with a C s -symmetry approach close to C 2v symmetry͒ shows very high-energy barriers on both surfaces ͓2.54 and 2.13 eV for the 2 AЈ ͑TS5͒ and 4 AЈ ͑TS4͒ PES' at the CASPT2 G2/augcc-pVTZ level, respectively͔, but lower for the quartet surface. This behavior is just contrary to the one observed in the direct C s -abstraction reaction mechanism studied in Paper I, where, in addition, much lower-energy barriers were reported for both PES' ͑0.20 and 0.55 eV, respectively, at the same ab initio level͒. Table IV summarizes the properties of both transition states. C 2v structures ͑TS4Ј and TS5Ј͒ are secondorder saddle points that connect with the true transition states ͑TS4 and TS5͒. These latter results confirm that the direct C 2v insertion reaction pathway is much less favorable than the other competitive reaction pathways ͑e.g., C s -symmetry abstraction and insertion mechanisms through the 2 AЈ PES͒ presented in Paper I.

B. Location and nature of several surface crossings
At the beginning we considered only the AЈ/AЈ intersections because we were mainly interested in the study of the N( 4 S)ϩO 2 (X 3 ⌺ g Ϫ ) reaction. Finally, we took also into account some AЈ/AЉ intersections because they help us to explain some imaginary frequencies appearing in several C 2v stationary points, and also for its importance in the study of the N( 2 D)ϩO 2 (X 3 ⌺ g Ϫ ) reaction. 34 The several crossings found among the doublet and quartet A 1 , A 2 , B 1 , and B 2 PES' that could become important for the C 2v insertion N( 4 S)ϩO 2 (X 3 ⌺ g Ϫ ) reaction mechanism are summarized in Table V. Figures 1 and 2 show approximately the energy of these crossings. Three crossings between 2 B 2 and 2 A 1 PES' ͑I4, I5, and I6͒ have been located, although the ground 2 B 2 PES crosses before with the 2 B 1 PES ͑I9͒ and latter with the 2 A 2 PES. These results agree with previous studies, where information about 2 A 1 / 2 B 2 crossings in the C 2v region 41 were reported. Another 2 B 1 / 2 B 2 crossing was also studied ͑I10͒. Two crossings between 4 B 2 and 4 A 1 PES' ͑I1 and I3͒ were found, and one more that seems to be of the 4 A 1 / 4 A 1 type ͑I2͒. The most stable minimum ͑MIN3͒ on surface 4 A 2 crosses twice, one with the 4 A 1 surface ͑I7͒ and another with a 4 B 2 one ͑I8͒.
Regarding to the role of point group symmetry 18 conical intersections can be qualitatively classified as ͑a͒ symmetry required, when both states are the components of a degenerate irreducible representation ͑i.e., Jahn-Teller type 22 ͒, ͑b͒ symmetry-allowed accidental intersection, when we have an Harmonic vibrational frequencies: ͑a͒ C 2v : s ͑sym. str., a 1 ͒, b ͑bend., a 1 ͒, and a ͑asym. str., b 2 ͒, respectively ͑YZ taken as the molecular plane͒ and ͑b͒ C s : 1 ͑NO str., aЈ͒, 2 ͑NOO bend., aЈ͒, and 3 ͑OO str., aЈ͒, respectively. Masses of the most abundant isotopes were used: 14 N and 16 O. e Energy respect to NO 2 (X 2 A 1 ). intersection of two states of different spatial symmetry, and ͑c͒ same-symmetry accidental intersections between states of the same symmetry. All the intersections we have found are symmetry-allowed accidental intersections, with the exception of I2, which is a same-symmetry accidental intersection. In the present work, this approximate classification has been applied by using the C 2v highest molecule group symmetry, due to the fact that this classification could depend whether C 2v or C s symmetry are considered. 42 To locate the intersections we have computed a grid of points for each surface using the Jacobi coordinates shown in Fig. 1 ͑r and R͒ at the CASSCF and CASPT2 G2 levels. The range of R goes from 0.0 to 4.5 Å and for r it goes from 1.0 to 2.5 Å. We have used an increment of 0.1 Å except for the reactants asymptotic region (RϾ2.5 Å) where it is longer and increases as R increases. Doing the energy difference between different diabatic surfaces we were able to extract, approximately, the intersection seam for each case. To have an intersection between two adiabatic states two conditions have to be satisfied. If we express the two adiabatic states ͑1 and 2͒ as a combination of two diabatic states ͑A and B͒ and we solve the 2ϫ2 Hamiltonian problem between these diabatic states, we will see that to have a crossing ͑i.e., E 1 ϭE 2 , E 1 , and E 2 being the energies of the two adiabatic states͒ the two conditions to be fulfilled are H AA (q) ϭH BB (q) and H AB (q)ϭ0. Therefore, the dimension of the intersection space will be (N-2) when both states are of the same spatial symmetry and (N-1) when both are of different spatial symmetry, because the H AB (q)ϭ0 condition will be satisfied by symmetry in this last case ͑N being the number of internal degrees of freedom of the system͒. Hence, the symmetry of the system has to be taken into account too. If we are working in a higher symmetry group ͑i.e., C 2v instead of C s ͒ we have less internal degrees of freedom to satisfy both conditions ͑M instead of N, with M ϽN͒. For the first type of intersections ͑i.e., AЈ/AЈ͒ the dimension of the intersection space corresponds to a line for C 2v (M -1ϭ1) and C s (N-2ϭ1) geometries when both surfaces belong to a different irreducible representation in C 2v , but to the same one in C s ; the dimension of this space is a point for C 2v (M -2ϭ0) geometries and a line for C s (N-2ϭ1) geometries if both surfaces are of the same symmetry in C 2v and in C s symmetries. In surface intersections, where the dimension of the intersection space be lower at C 2v geometries than at C s ones, the intersection space will be probably part of a C s symmetry intersection that passes through C 2v .
Intersections I1, I3, I4, I5, and I6 correspond to the first case and I2 to the second one ͑Table V͒. On the other hand, if the crossing implies two surfaces of different symmetry in C 2v and in C s ͑i.e., the AЈ/AЉ type͒, the dimension of the intersection space is a line in C 2v (M -1ϭ1) but a plane in C s (N-1ϭ2), as occurs in I7, I8, I9, and I10.
Once we had found the C 2v seams, we have chosen a local grid around these intersection seams between the diabatic surfaces and we have fit these points for each surface involved in the crossing by means of bicubic splines, obtaining a root mean square deviation less than 1 kcal/mol in all cases. With the local fit we have interpolated more points for each surface and doing the energy difference we have ob-tained the intersection seam again in a more accurate way. The minimum energy point on each seam corresponds to the given geometries reported in Table V. Intersection I2 has been located in a different way because it takes place between two states of the same spatial symmetry ( 4 A 1 ). It corresponds to a point in C 2v instead of a line as in the other cases. Both 4 A 1 PES' ͑i.e., the ground one and the first excited one͒ were calculated using the twostate-averaged methodology. 26 The intersection point has been located as the minimum point in the energetic difference hypersurface ⌬EϭE(2 4 A 1 )ϪE (1 4 A 1 ). I2 was located at R NO ϭ2.0703 Å and ЄONOϭ54.56°, with ⌬E ϭ0.07 kcal/mol at the CASSCF level. We had not located I2 at the CASPT2 level due to problems with some points near the intersection because both roots were interchanged, which means that the ground state was more unstable than the excited one in those points. Because of that we were not able to see a minimum point in the ⌬E hypersurface at the CASPT2 level. This problem could be solved using the multistate CASPT2 method, 43 but this intersection is so far from the MEP for the N( 4 S)ϩO 2 (X 3 ⌺ g ) reaction and therefore we were not interested in its location in so extensive a way.
To verify much more our results about the intersections we have tried to locate as well some of those with GAUSSIAN 98 program, 32,44 by using the CASSCF method with a reduced active space ͑7,6͒ and a Pople basis set ͓6-31G͑d͔͒ to decrease the effort of the calculation. We were able to find two intersections, I6 and I10, which agree with our results. For I6 and I10 we have found CASSCF C s geometries with R NO ϭ1.1982 and 1.3868 Å and ЄONOϭ109.85°, and R NO ϭ1.3342 and 1.3563 Å and ЄONOϭ78.90°, respectively, to be compared with the similar but C 2v structures indicated in Table V. At this ab initio level the energy differences between the two states involved in the crossing were the following: 0.04 kcal/mol for I6 and 0.06 kcal/mol for I10. The slightly difference for I6 in R NO distance can be explained in terms of the different active space and basis set used, but as it is shown in Table V the C 2v structure agrees with previous theoretical 3,4,12 and experimental 6-8 results found in the literature. For I6 we have also computed the energy difference between both states implicated in the crossing and we have obtained a value of 8 ϫ10 Ϫ3 kcal/mol at CASSCF͑17,12͒/aug-cc-pVTZ level, which confirms that we have found the true geometry to describe the intersection.
The bending of NO 2 structures has been previously studied, 9,10 where intersections between doublet and quartet states have been predicted, but not located. The approximate angles at what intersections take place in those papers are close to our results. The possible connections between the NO 2 minima and the NϩO 2 reactants has not been studied up to now. Previous studies only explored the bending region between 70°-180°, but did not study smaller angles that would correspond to I1, I2, I4, I5, and I9 intersections.
We have studied the orbitals responsible for the electronic configuration exchange in each crossing ͑Table VI͒. For I1 the configurations for the lower state before and after the crossing change one electron between 7a 1 and 5b 2 orbitals, both are NO antibonding, but the former is OO bond-ing and the later OO antibonding. The inclusion of one electron in an antibonding OO orbital (5b 2 ) favors the breaking of the OO distance that is necessary to insert the N atom. For I2, one electron initially in the 5b 2 orbital goes to the 4b 2 one without changing the electronic state symmetry ( 4 A 1 ). Both orbitals are OO antibonding but the 4b 2 is NO bonding and its occupation favors the NO bond formation in the insertion path. In I3, the 6a 1 orbital loses an electron that goes to the 4b 2 orbital, the former is OO bonding and the latter OO antibonding, becoming more stable as the insertion reaction goes forward.
Intersections of 4 AЈ/ 4 AЉ type show the same behavior ͑Table VI͒. In I7 we have an electron that goes from the 6a 1 orbital ͑OO bonding͒ to the 1a 2 one ͑OO antibonding͒ favoring the OO breaking. In I8 one of the 1a 2 electrons goes to the 4b 2 orbital, both are OO antibonding orbitals, but in the 4b 2 appears a bonding NO interaction that makes possible the NO bond formation. For the doublet case we have the same type of explanation for the electronic configuration exchange. In I4 an electron in the 7a 1 orbital goes to the 4b 2 orbital, both are NO antibonding, but only the latter is OO antibonding. In I5, the 2b 1 electron jumps to the 1a 2 orbital, the former does not favor the NO bond formation, and the OO bond breaking because it is NO antibonding and OO bonding, but the a 2 is NO no bonding and OO antibonding and favors the insertion mechanism with the necessary OO breaking and NO formation. For I6, the occupation changes between the 6a 1 orbital and the 4b 2 one, where the OO interaction becomes antibonding and the NO no bonding favoring the insertion of a N atom as in the I5 case above. For the second type of intersections ( 2 AЈ/ 2 AЉ) the change is as follows: for I9 one 7a 1 electron jumps to the 1a 2 orbital more stable after intersection due to an antibonding OO in-teraction, which becomes less repulsive as the OO distance increases in the insertion path. In I10, the 2b 1 electron goes to the 4b 2 orbital; the latter becomes more stable after intersection for the same reason that the 1a 2 orbital above in the I9 case.
To sum up, different interactions are important in the C 2v -insertion mechanism depending on the surface region we are exploring. At the beginning of the insertion path the main ones are the NO antibonding interaction and the OO bonding one ͑i.e., a N atom and an O 2 molecule separately͒. In the barrier region the OO antibonding interaction becomes important and sometimes the NO no bonding one too ͑i.e., breaking the OO bond to insert the N atom͒. At the insertion end the main interaction is the NO bonding one ͑i.e., the OO bond is broken and the NO bond is formed͒.

C. Topological analysis of the surface crossings
To study the topology of the potential energy surfaces around the intersections, two vectors can be defined, the gradient difference (x 1 ) and the gradient of the interstate coupling (x 2 ) vectors: 44,45

͑3͒
where C 1 and C 2 are the configuration interaction eigenvectors and H is the corresponding CI or MC-SCF Hamiltonian.
c The weight of the most important CSF in the CASSCF͑17,12͒ wave function for this region of the PES.
will form the intersection space, where both adiabatic states are degenerated, and the other two coordinates ͑x 1 and x 2 ͒ will form the branching space, where both adiabatic states lose their degeneracy. We have studied the topology of the intersections between states of the same symmetry in C s ͑i.e., AЈ/AЈ͒ but not those of different symmetry in C s ͑i.e., AЈ/AЉ͒. This fact was essentially motivated because the second type of intersections cannot be conical nor were involved in the title reaction. This only occurs in triatomic molecules that have all vibrational modes symmetric (aЈ) because they do not have a no totally symmetric mode ͑as b 2 in C 2v ͒ that can couple the degenerate states. 18 The topology of intersection I2 has not been studied either because, as we previously see, it is located so far from the minimum energy path.
In our case we have represented the energies in front of the ЄONO angle and respect to a coordinate, which breaks the C 2v symmetry of the system ͑i.e., x͒. This latter coordinate is defined as xϭ(R (NO) ϩn⌬R)Ϫ(R (NO) Ϫn ⌬R) ϭ2n ⌬R, where nϭ1, 2,3,4,..., is the point number, ⌬R ϭ0.01 Å and R (NO) is the NO distance given in Table V for each intersection. We have used the above-mentioned coordinates after identifying the vectors of the branching space by using the GAUSSIAN 98 code, 32 the x 1 vector corresponds basically to the bending motion ͑a 1 symmetry͒, and the x 2 vector to the asymmetric NO stretching ͑b 2 symmetry͒ of the C 2v structure, with minor participation of the bending motion. In order to compute the bending motion for I1, I3, I4, I5, and I6 at the CASSCF level, the NO distances were kept fixed at their corresponding intersection values ͑Table VI͒ and the ONO angle was varied in the appropriate range for each case ͑Fig. 3͒. Intersections I1 and I4 take place at small angles ͑around 46°͒, which correspond to the beginning of the insertion path. I5 is located at about 64°, and I3 and I6 appear at the end of the insertion path, when the C 2v minima have been formed, at around 105°.
Intersections can be classified regarding their local topology, 23 Table V for each intersection. Zero of energy in the NO 2 (X 2 A 1 ) molecule. one side of the intersection and E 2 has zero slope on the other side of the intersection. We have found these three types of topologies: ͑a͒ peaked intersections: I3 and I6; ͑b͒ sloped intersections: I5; and ͑c͒ intermediate intersections: I1 and I4. The last case implies intersections that almost coincide with stationary points ͑null slope by definition͒. Thus, I1 is very close to TS1 and I4 to TS3.
In Fig. 4 the ground adiabatic surface and the first excited one are shown for three representative intersections: I1 ͑intermediate͒, I5 ͑sloped͒, and I6 ͑peaked͒ using Jacobi coordinates ͑i.e., r and R͒ at the CASSCF ͑17,12͒/aug-cc-pVTZ level; the same topological results were found at the CASPT2 level too. For the intermediate case ͑I1͒, apart from the change in the slope, TS1 appears very close to the intersection seam. In I5 only, is possible to see the change of slope in both adiabatic surfaces. In the I6 plot, the lower surface shows a saddle point and a minimum ͑MIN2͒ very close to the intersection point. The excited surface presents another minimum. In the approximate plot shown in Fig. 2 for this crossing at the CASPT2 G2/aug-cc-pVTZ level, the MIN2 seems to be in the excited PES but really it is in the lower surface as in the CASSCF results.
We have drawn in Fig. 5 an estimated asymmetric stretch around the I1-I6 intersections at the CASSCF ͑17,12͒/aug-cc-pVTZ level. To do this, we have increased one NO distance 0.01 Å and have decreased another one of the same quantity. The ONO angle has been frozen to its intersection value reported in Table V. In all cases we see how both surfaces separate each other from xϭ0. For I6 we can see a pseudo-Jahn-Teller distortion with an asymmetric minimum ͑NO distances equal 1.2117 and 1.3117 Å͒ around 1.3 kcal/mol below the conical intersection. For I5 and I4 an opposite behavior is found, and two asymmetric maxima for the excited surfaces are observed ͑NO distances equal to 1.6951 and 1.8351 Å, and 1.6918 and 1.7518 Å for I4 and I5, respectively͒. In all cases the excited surface is funneled into the intersection region (xϭ0), where there is a minimum. On the other hand, the ground surface has a maximum at the intersection and thereby the minimum energy path in the ground surface has the tendency to avoid the intersection point and to take place through asymmetric geometries ͑i.e., C s symmetries͒. This explains the problems to locate the transition states for the C 2v -insertion mechanism through the doublet and quartet PES', where the strictly C 2v stationary points found are second-order saddle points ͑TS5Ј and TS4Ј, as given in Table IV͒, being preferred a direct C s -insertion mechanism for both PES' ͑TS5 and TS4 for the 2 AЈ and 4 AЈ PES', respectively, as shown in Table IV͒.
We have also calculated the splitting between both adiabatic surfaces at the crossing point of the two diabatic surfaces ͑geometries given in Table V͒ by means of ab initio C s calculations. The following values have been obtained at the CASSCF ͑17,12͒/aug-cc-pVTZ level: 1.76 kcal/mol ͑I1͒, 0.45 kcal/mol ͑I3͒, 3.60 kcal/mol ͑I4͒, 0.45 kcal/mol ͑I5͒, and 8ϫ10 Ϫ3 kcal/mol ͑I6͒. As can be seen, the energy values obtained for the intermediate intersections ͑I1͒ and ͑I4͒ are very high, possibly because the search method was not accurate enough for these intersections. The other intersections showed much lower values ͑under 0.5 kcal/mol͒. We have also observed that the point of closest approach between both adiabatic surfaces is not exactly at the same position as that of the crossing between both diabatic surfaces, the former being slightly shifted from the MEP. Figure 6 shows contours diagrams around I6 for its approximate branching space ͑i.e., x, ЄONO͒, which allows now ͑not seen in Fig. 4 due to the C 2v symmetry͒ to see directly the mentioned transition state ͑TS6͒ that connects MIN2 with the NO 2 (X 2 A 1 ) molecule through C s symmetry. Due the symmetry of the system there are two equivalent transition states. The problem mentioned in Sec. III A that respects the dispersion of the theoretical asymmetric frequencies of MIN2 ͑Table I͒, which are quite different from the experimental value, can be now better rationalized. The proximity of I6 implies an asymmetric NO 2 distortion along the minimum energy path that affects the MIN2 asymmetric stretching frequency. The low value obtained for this frequency can be understood, considering the bifurcation nature of the surface between MIN2 and I6. The nature of this reaction path from the MIN2 ( 2 B 2 ) to the NO 2 (X 2 A 1 ) molecule on the lowest 2 AЈ surface has been previously discussed. 46 In that paper an asymmetric path was also de- FIG. 4. Contour diagrams around I1 ͑intermediate͒, I5 ͑sloped͒, and I6 ͑peaked͒ in the Jacobi space ͑r and R͒ at the CASSCF͑17,12͒/aug-cc-pVTZ level. The lower adiabatic PES for each intersection is depicted on the left, and the upper adiabatic one on the right. The contour interval is 0.05 eV. Zero of energy in the NO 2 (X 2 A 1 ) molecule. Crosses show the location of the lowest point in each intersection and also other stationary points. scribed, and MIN2 was characterized as a saddle point because its asymmetric stretching initialized the through down to the NO 2 (X 2 A 1 ) minimum. We think this bifurcation point due to the asymmetric motion begins in a region between MIN2 and I6 ͑i.e., TS6͒, but not exactly in MIN2, because we have obtained a real frequency for the asymmetric stretching at this point. In Fig. 6 we can see that the intersection I6 ͑Table V͒ and TS6 ͓R (NO) ϭ1.2117, 1.3117 Å, ЄONOϭ107.5°⌬Eϭ1.23 eV at the CASSCF ͑17,12͒/augcc-pVTZ level, or 1.30 eV at the CASPT2 level͔ are so close that also a nonadiabatic recrossing could be important between both surfaces. 18 FIG. 5. Asymmetric distortion ͑x͒ at the CASSCF͑17,12͒/aug-cc-pVTZ level for different A 1 /B 2 intersections. The x coordinate is defined as xϭ(R (NO) ϩn ⌬R)Ϫ(R (NO) Ϫn ⌬R)ϭ2n ⌬R, where nϭ1,2,3,4,..., is the point number, ⌬Rϭ0.01 Å and R (NO) is the NO distance given in Table V for each intersection. Negative values are obtained by NO interchange symmetry. The ЄONO angle was kept frozen at the value corresponding at each intersection ͑Table V͒. ͑छ͒ represents the ground AЈ adiabatic curve and ͑ࡗ͒ the first excited AЈ adiabatic one. Zero of energy in the NO 2 (X 2 A 1 ) molecule.
FIG. 6. Contour diagrams around I6 with respect to the x and ЄONO coordinates at the CASSCF͑17,12͒/aug-cc-pVTZ level. The lower adiabatic PES of this intersection is depicted on the left, and the upper adiabatic one on the right. The contour interval is 0.025 eV. Zero of energy in the NO 2 (X 2 A 1 ) molecule. Crosses show the location of the intersection I6 and the TS6.

IV. CONCLUSIONS AND REMARKS
This work presents a theoretical study of the lowest doublet and quartet potential energy surfaces involved in the C 2v -insertion mechanism of the N( 4 S)ϩO 2 (X 3 ⌺ g Ϫ ) →NO(X 2 ⌸)ϩO( 3 P) reaction. Ab initio molecular electronic structure CASSCF and CASPT2 methods with a standard correlation-consistent Dunning's basis sets ͑aug-cc-pVTZ͒ and a full-valence active space were used to characterize the stationary points and the different conical intersections for the A 1 , B 1 , A 2 , and B 2 doublet and quartet PES'. The UB3LYP DFT method was also used to facilitate the search of the stationary points and to make IRCs for the transition states, producing similar results to the ab initio ones. Thus, several minima, transition states, and surface crossings have been found along the different C 2v -MEPs connecting reactants and products on these surfaces. The results agree very well with available experimental data ͓i.e., for NO 2 ( 2 A 1 ), MIN2( 2 B 2 ), NO 2 ( 2 ⌸ u )͔ and with other previous ab initio calculations.
Six AЈ/AЈ and four AЈ/AЉ-type surface crossings were located and classified by their topology on the mentioned doublet and quartet PES'. Among these, only one ͑i.e., 2 B 2 / 2 A 1 ͒ had been reported previously in theoretical and experimental studies. The results presented here are almost coincident with them and can be taken as a validation of the theoretical method used. Although these surface crossings produce important changes ͑i.e., changes of slope, maxima, cusps,...͒ in the shape of the adiabatic surfaces ͑ 2 AЈ and 4 AЈ͒ in its C 2v geometrical region, their influence on the N( 4 S) ϩO 2 (X 3 ⌺ g Ϫ ) reaction should be small at low collision energies apart from possible geometric phase effects. Major importance could be expected for the reaction with electronically excited reactants ͓i.e., N( 4 S)ϩO 2 (a 1 ⌬ g ) or N( 2 D) ϩO 2 (X 3 ⌺ g Ϫ )͔, where this region of the PES is much more energetically accessible and possible nonadiabatic decays to the ground PES' could be likely throughout the reaction.
There was demonstrated that the direct C 2v -insertion mechanism studied here presented very high-energy barriers ͑3.11 and 2.54 eV for the lowest doublet and quartet PES' at the CASPT2 G2/aug-cc-pVTZ level, respectively͒, clearly being more unfavorable than the direct C s -abstraction or indirect C s -insertion mechanisms reported in Paper I for the same reaction, which showed 0.20 and 0.55 eV energy barriers ͑C s -abstraction mechanism͒, respectively, at the same ab initio level. Moreover, the corresponding C 2v -symmetry transition states ͓TS4Ј( 4 AЈ) and TS5Ј( 2 AЈ)͔ were located as second-order saddle points, giving place under an asymmetric distortion to true C s transition states ͓TS4( 4 AЈ) and TS5( 2 AЈ)͔ with lower-although still high-energy barriers ͑2.13 and 2.54 eV values, respectively͒, in comparison to the other competitive microscopic mechanisms.
The present results complete the ab initio study initiated in Paper I aiming to describe the full topology ͑i.e., C s and C 2v geometries͒ of the lowest adiabatic doublet and quartet PES' involved in the title reaction. All the theoretical information obtained about the stationary points and the different surface crossings along with new grids of ab initio points has been used in the construction of two analytical PES' ͑ 2 AЈ and 4 AЈ͒ 47 that will improve the quality of previous analytical ones. A dynamics and kinetics study on both PES' is in progress at present in our research group to see the importance of the several microscopic mechanisms found for this reaction and to reveal the influence of some of the conical intersections found for this system.