A theoretical approach to the O „ 1 D ... ¿ H 2 O „ X 1 A 1 ... reaction : Ab initio potential energy surface and quasiclassical trajectory dynamics study

An ab initio study of the ground potential energy surface ~PES! of the O(D)1H2O system has been performed, employing Møller–Plesset methods. From the stationary and additional points calculated, the ground PES has been modeled as a triatomic system, with an OH group of the H 2O molecule treated as a single atom of 17.0 amu. The rate constant of reaction ~1!, O(D) 1H2O→2OH ~main reaction channel !, estimated from the quasiclassical trajectory ~QCT! calculations is reasonably close to the recommended experimental value. For the relative translational energies explored ( ET50.234, 0.303, and 0.443 eV ! and H2O at T5300 K, the QCT OH vibrational populations are in good agreement with the experimental values reported for the new OH fragment, but the QCT OH average rotational energies are in general quite larger than the experimental ones. Regarding the stereodynamics, for ET50.234 eV there is not a clear tendency to a particular rotational alignment of the OH product with respect to the initial relative velocity vector, in agreement with experiments. The QCT results also show that nearly all reactive trajectories leading to reaction~1! take place through an insertion microscopic mechanism, which, even at the highestET value considered~0.443 eV!, is mainly~70%! a nondirect one. The collision complex has an average lifetime of about three rotational periods and a geometry around that of the HO ~OH! hydrogen peroxide molecule. The QCT results concerning the microscopic mechanism of reaction ~1! are in agreement with the suggested ones by the experimentalists to interpret their results. The present study should be considered as a starting point in the study of reaction ~1! from which different aspects on the dynamics may be learned. © 2000 American Institute of Physics. @S0021-9606 ~00!30840-6#

An ab initio study of the ground potential energy surface ͑PES͒ of the O( 1 D)ϩH 2 O system has been performed, employing Møller-Plesset methods. From the stationary and additional points calculated, the ground PES has been modeled as a triatomic system, with an OH group of the H 2 O molecule treated as a single atom of 17.0 amu. The rate constant of reaction ͑1͒, O( 1 D) ϩH 2 O→2OH ͑main reaction channel͒, estimated from the quasiclassical trajectory ͑QCT͒ calculations is reasonably close to the recommended experimental value. For the relative translational energies explored (E T ϭ0.234, 0.303, and 0.443 eV͒ and H 2 O at Tϭ300 K, the QCT OH vibrational populations are in good agreement with the experimental values reported for the new OH fragment, but the QCT OH average rotational energies are in general quite larger than the experimental ones. Regarding the stereodynamics, for E T ϭ0.234 eV there is not a clear tendency to a particular rotational alignment of the OH product with respect to the initial relative velocity vector, in agreement with experiments. The QCT results also show that nearly all reactive trajectories leading to reaction ͑1͒ take place through an insertion microscopic mechanism, which, even at the highest E T value considered ͑0.443 eV͒, is mainly ͑70%͒ a nondirect one. The collision complex has an average lifetime of about three rotational periods and a geometry around that of the HO͑OH͒ hydrogen peroxide molecule. The QCT results concerning the microscopic mechanism of reaction ͑1͒ are in agreement with the suggested ones by the experimentalists to interpret their results. The present study should be considered as a starting point in the study of reaction ͑1͒ from which different aspects on the dynamics may be learned. © 2000 American Institute of Physics. ͓S0021-9606͑00͒30840-6͔

I. INTRODUCTION
The reactivity of the oxygen atom in the first excited electronic state, O( 1 D), is important in various fields of chemistry, and its reaction with water is relevant in stratospheric chemistry in the context of ozone degradation processes through the OH/HO 2 catalytic cycle. 1,2 The highly different reactive behavior of O( 1 D) with respect to the ground-state oxygen atom, O( 3 P), also makes the study of this kind of systems very interesting from a more fundamental point of view, to understand the origin of the different reactivities observed. Thus, the O( 1 D) atom is claimed to react very efficiently with compounds containing X-H bonds ͑such as H-H, C-H, O-H, and N-H͒, mainly through an insertion mechanism, while the analogous reactions with O( 3 P) present activation energy and occur by an abstraction mechanism.
The aim of this work is to study theoretically the gas phase reactions involved in the O( 1 D)ϩH 2 O system, considering the ground potential energy surface ͑PES͒ O͑ 1 D ͒ϩH 2 O͑X 1 A 1 ͒→2 OH͑X 2 ⌸ ͒ ⌬H 0K 0 ϭϪ28.9 kcal mol Ϫ1 , 3 ͑1͒ Reaction ͑1͒ is known to be very fast, the thermal rate constant value approaching the gas kinetics value. The recommended rate constant value for reaction ͑1͒, k(1), is 2.2(Ϫ0. 45,ϩ0.57)ϫ10 Ϫ10 cm 3 molecule Ϫ1 s Ϫ1 over the temperature range 200-350 K. 4 This result suggests that reaction ͑1͒ does not have activation energy, in contrast to what happens for the analogous reaction with O( 3 P), which has activation energy. At 298 K the k(2)/k (1) ratio was found to be 0.01 ͑ϩ0.005, Ϫ0.01͒, 5 and there is no information available on reaction ͑3͒. Hence, reaction ͑1͒ clearly corresponds to the main reaction of the O( 1 D)ϩH 2 O system, accounting for around 99% of the reactivity at 298 K.
The nascent internal energy distribution of the OH radical has been measured in several experiments, [6][7][8][9][10][11][12][13][14][15][16][17] mainly involving the 16 O( 1 D)ϩH 2 using the laser induced fluorescence ͑LIF͒ technique. The reaction with D 2 O has also been studied in some cases. 9,17 The O( 1 D) atom has been generated by photodissociation of either N 2 O (ϭ193 or 212.8 nm͒ or O 3 (ϭ248 or 266 nm͒. Therefore, OH(X 2 ⌸) rovibrational, spin-orbit, and lambdadoublet populations considering different O( 1 D)ϩH 2 O collision energy distributions have been determined experimentally. For the 16 OH molecule ͑new OH bond͒, vibrational populated levels up to vЈϭ2 have been observed. 7,10 The vibrational and rotational distributions of the 18 OH molecule ͑old OH bond͒ have also been measured. 6,7,10,11,14 The 18 OH molecules are vibrationally and rotationally much colder than the 16 OH ones, nearly all of them being produced in vЈϭ0. The OH spin-orbit population ratio (X 2 ⌸ 3/2 / X 2 ⌸ 1/2 ) slightly deviates from the statistical expectation, and the lambda-doublet population ratio ͓⌸(AЈ)/⌸(AЉ)͔ exhibits some preference for the ⌸(AЈ) state. 10,11,14,17  The stereodynamics of reaction ͑1͒ for the state-specific reaction channel leading to OH ͑vЈϭ2, NЈϭ5͒ has also been examined 16 using polarized Doppler-resolved LIF spectroscopy. The differential cross section ͑DCS͒ is nearly isotropic and the OH rotational angular momentum vector is predominantly perpendicular to both the initial and final relative velocity vectors. In addition, in a previous experiment 11 it has been shown that the 16 OH(vЈϭ0,1) molecule shows a negligible rotational alignment with respect to the initial relative velocity vector.
The above-mentioned experimental results regarding the internal energy distributions of 16 OH and 18 OH and the information about the stereodynamics are better explained considering that reaction ͑1͒ mainly takes place according to a microscopic mechanism which involves an HOOH collision complex formed by insertion of the O( 1 D) atom into the H 2 O molecule. The average lifetime of the collision complex should be of the order of the HOOH rotational period, and would not allow for a complete energy redistribution in the complex between the two resulting OH fragments.
Although there is a relatively large number of experimental studies reported on reaction ͑1͒, the corresponding theoretical information available is very limited. Thus, the theoretical studies are mainly devoted to the characterization of the PES around the hydrogen peroxide molecule [18][19][20] and OHϩOH long-range 21 regions.
Because of the relevance of this system, and taking into account the very scarce theoretical information available on it, an ab initio characterization of the O( 1 D)ϩH 2 O ground PES has been performed in this work. Moreover, as a first approximation, a triatomic analytical representation of this PES has been derived, and a quasiclassical trajectory ͑QCT͒ dynamics study of reaction ͑1͒ has been performed. To the best of our knowledge, this contribution represents the first ab initio study carried out on the ground PES of the O( 1 D) ϩH 2 O system, taking into account all possible reactions, and also the first theoretical study on the dynamics of reaction ͑1͒.
This work is organized as follows. Section II deals with the ab initio calculations and triatomic analytical fitting of the ground PES, and Sec. III shows the QCT dynamics study. In Sec. IV the summary and concluding remarks are given.
We have carried out an ab initio study of the ground PES ( 1 A) using the GAUSSIAN 94 package of programs. 22 The wave function associated with this system is mostly multireferent for the ground PES. Thus, in most of the PES regions the system behaves as an open-shell singlet, and only for arrangements close to the geometry of the closed-shell minima min 1 and H 2 O 2 ͑hydrogen peroxide͒ and for the saddle point that connects both minima the wave function is single referent. Hence, the most suitable ab initio methods to study this PES are those which are multireferent, such as the second-order multiconfigurational perturbation theory ͑CASPT2͒ and multireference configuration interaction ͑MRCI͒ methods. But, although these ab initio methods are nowadays accessible for the characterization of PES stationary points, recent benchmark calculations with molecular correlated wave functions on simple triatomic reactions, such as FϩH 2 , 23,24 OϩH 2 , 24 and HϩHCl, 24 have shown that only using very large wave functions and basis sets it is possible to achieve energy values close to the experimental data. This kind of high-level calculations are very expensive, especially when the characterization of a global PES involving a large number of electrons and atoms is desired. On the other hand, it has been shown that, under certain conditions, ab initio methods, such as the Møller-Plesset perturbational method, can reproduce quite satisfactorily the energetics of this kind of systems when the ''broken symmetry'' approach is considered. 25,26 In this context, the elimination of the spin contamination of the wave function becomes a critical aspect, as the use of the broken symmetry approach leads to energy values which lie between the triplet and singlet ones. An efficient projection algorithm 25 for the elimination of the spin contamination when Møller-Plesset perturbational methods are used is included in the GAUSSIAN 94 package. 22 However, although the single-point energy obtained using the broken symmetry approach can be corrected using this projection technique, the optimal geometries determined in this context are probably located between the singlet and the triplet ones.
Hence, we have selected as a suitable method of calculation the unrestricted second-order Møller-Plesset perturbation theory ͑UMP2͒ method using a large basis set ͓6-311G͑3d2 f ,3p2d) standard, 128 basis functions͔, and considering the frozen core ͑FC͒ approach ͑only valence electrons are correlated͒, UMP2͑FC͒/6-311G͑3d2 f ,3p2d) ab initio level hereafter, to characterize ͑geometry optimization and harmonic vibrational frequencies calculation͒ the stationary points of the ground PES. The energies of the stationary points and of the set of ab initio points required to obtain, as a first approximation, a triatomic analytical representation of the PES ͑Sec. II B͒ have been calculated at the spin-projected unrestricted fourth-order Møller-Plesset perturbation theory ͑PUMP4͒ method, using the same basis set as before but considering in this case the full electron ͑FU͒ approach ͑all electrons are correlated͒, PUMP4͑FU͒/ 6-311G͑3d2 f ,3p2d) ab initio level hereafter. The standard GAUSSIAN 94 option ͓MP4͑SDTQ͔͒ has been employed. The spin-projected method has been employed to eliminate large spin contaminations on the PES (0.00Ͻ͗S 2 ͘/ប 2 Ͻ1.10). In summary, the strategy used in the calculation of the PES has been the following: ͑a͒ first, the stationary points of the PES ͑reactants, products, saddle points, H 2 O 2 , and other mini-mum͒ have been optimized at the UMP2͑FC͒/ 6-311G͑3d2 f ,3p2d) level; ͑b͒ second, the connections ͓minimum energy paths ͑MEP͒ and mostly intrinsic reaction coordinate ͑IRC͒ calculations͔ between these stationary points have been calculated at the UMP2͑FC͒/ 6-311G͑2d f ,2pd); ͑c͒ finally, the energy of each point previously calculated at the UMP2͑FC͒ level has been computed using the PUMP4͑FU͒/6-311G͑3d2 f ,3p2d) ab initio method. In the next paragraphs the present ab initio results will be compared with experimental data and previous ab initio calculations.
The energetics of the system using different methods and basis sets is shown in Table I, considering the H 2 O 2 hydro-gen peroxide minimum and the three different product asymptotes. No significant differences appear when the 6-311G͑2d f ,2pd) basis set is used instead of the larger 6-311G͑3d2 f ,3p2d) one. In fact, the methods selected here are the ones which best reproduce the exothermicity of the main reaction ͓reaction ͑1͔͒ and predict the depth of the H 2 O 2 minimum with 1% of deviation with respect to the experimental value. The results obtained for the geometries and harmonic frequencies of the H 2 O, OH, H 2 , O 2 (a 1 ⌬ g ), and HO 2 reactant and product molecules using these methods also show a good agreement with experimental information.
splittings have only been described adequately at the PUMP4 level.
In what follows, the reported data correspond to the highest level calculation ͓PUMP4͑FU͒//UMP2͑FC͒/ 6-311G͑3d2 f ,3p2d)], and the energies are given, including the zero-point energy ͑ZPE͒, with respect to reactants, unless otherwise indicated. The geometries ͓UMP2͑FC͔͒ of the stationary points placed between reactants and products are plotted in Fig. 1, and the energies ͓PUMP4͑FU͒// UMP2͑FC͔͒, including the UMP2͑FC͒ zero-point energies ͑ZPE͒, are indicated in Fig. 2. In this figure the different reaction pathways for reactions ͑1͒-͑3͒ are also shown schematically, where ''ts'' and ''min'' refer to the saddle points and minima, respectively. In Table II the harmonic vibrational frequencies ͓UMP2͑FC͔͒ of the stationary points are reported.
Reaction ͑1͒ can take place along two possible reaction pathways. The first one ͓insertion microscopic mechanism ͑via H atom migration͔͒ involves the formation of products when the system evolves from reactants through the H 2 O 2 hydrogen peroxide minimum, according to the following way: O( 1 D)ϩH 2 O→ts8→min1→ts9→H 2 O 2 →ts2→OH ϩOH. The saddle point ts8 explains the formation of min1 from reactants, and the second one ͑ts9͒ the formation of H 2 O 2 from min1. The saddle point ts2 allows one to connect the hydrogen peroxide with the hydroxyl products. The saddle points ts8 and ts2, however, have only been obtained using the UMP2͑FC͒ method and for all basis sets considered, i.e., 6-311G(d, p), 6-311G͑2d f ,2pd), and 6-311G͑3d2 f ,3p2d). At the PUMP2͑FC͒ level and for all basis sets ͓with the only exception of ts2 for the 6-311G(d,p) basis set͔ and at the highest level of the calculation, the PUMP4͑FU͒//UMP2͑FC͒/6-311G͑3d2 f ,3p2d) method, however, ts8 and ts2 become energetically below reactants and products, respectively. Because of this we have only considered in the fitting ͑Sec. II B͒ three stationary points between reactants and products for the insertion mechanism of reaction ͑1͒: min1, ts9, and H 2 O 2 , all of them placed energetically below reactants ͑Fig. 2͒. Reaction ͑1͒ can also occur according to a second reaction pathway ͑abstraction microscopic mechanism͒. Thus, a saddle point ͑ts10͒ responsible for the abstraction of an H atom of the H 2 O molecule by the attacking O( 1 D) atom to give two OH radicals has been found. This saddle point leads to an energy barrier of 10.92 kcal mol Ϫ1 . The absence of any energy barrier above reactants along the minimum energy path of reaction ͑1͒ predicted by the ab initio calculations is consistent with the nonexistence of an experimental activation energy. 4 Thus, within the temperature range for which experimental data are available (T ϭ200-350 K), the rate constant is independent of the temperature. 4 The ab initio equilibrium geometry of the H 2 O 2 hydrogen peroxide is very close to the experimental one ͓R͑OO͒ϭ1.4556 Å, R͑OH͒ϭ0.967 Å, Ͻ͑OOH͒ ϭ102.32°, and Ͻ͑HOOH͒ϭ113.70°͔. 27 The agreement with experiments is good and very good in the case of the harmonic frequencies ͑Table II͒ and energy ͑Table I͒, respectively. The isomerization of H 2 O 2 through ts9 to give min1 was previously described in the context of a CCSD͑T͒ ab initio study ͓coupled-cluster approach including single and double excitations ͑CCSD͒ with connected triple excitations͔. 19 In that work the TZ2Pϩf and DZP basis sets were used for geometry optimizations and harmonic frequency calculations. But, for the harmonic frequency calculations of ts9 and H 2 O 2 the CCSD method was used instead of the CCSD͑T͒ one. The geometries and harmonic frequencies of min1, ts9, and H 2 O 2 reported here are quite similar to those given in Ref. 19. The barrier for isomerization from min1 to H 2 O 2 obtained here ͑2.83 kcal mol Ϫ1 ͒ is also quite close to that reported in Ref. 19 ͑3.2 kcal mol Ϫ1 ͒. A saddle point similar to ts2 has been reported previously at the MRCI-SD level ͓multireference, single, and doubles, configuration interaction ͑CI͒ calculation͔, 21 where the main differences are the Ͻ͑HOOH͒ dihedral angle ͑143°2 1 vs 180.0°i n our case͒ and the Ͻ͑OOH͒ angle ͑59°2 1 vs 78.5°in our case͒.
For reaction ͑2͒ only a stationary point ͑ts11͒ with two imaginary frequencies that connects min1 with the H 2 ϩO 2 (a 1 ⌬ g ) products has been found. The difficulties to determine the true saddle point that allows one to connect with products of reaction ͑2͒ are probably due to the fact that in this case to evolve from reactants to products two bonds should be formed and two bonds should be removed. This should also involve a significant energy barrier with respect to reactants. The energy barrier associated to the secondorder saddle point ts11 ͑28.3 kcal mol Ϫ1 ͒ is consistent with this fact, although, of course, the energy barrier corresponding to the true saddle point must be lower than this value. A saddle point ͑ts3͒ which connects these products with the ones of reaction ͑3͒ (HϩHO 2 ͒, with an energy of 12.52 kcal mol Ϫ1 ͑2.25 kcal mol Ϫ1 above HϩHO 2 ) has also been obtained. The production of H 2 ϩO 2 (a 1 ⌬ g ) has not been considered in the fitting ͑Sec. II B͒, because it is not possible according to the proposed triatomic model ͑an OH group of the H 2 O molecule has been taken as a pseudoatom͒. In fact, while a triatomic model can be used in a QCT study to describe the dynamics of formation of the new OH bond arising from reaction ͑1͒, a tetratomic analytical fitting is required to account for the dynamics of reaction ͑2͒. Moreover, while it would be possible to compare the dynamics of reaction ͑1͒ resulting from triatomic and tetratomic descriptions of the system ͑that, of course, may be based on the same set of ab initio calculations͒, this would not be the case for reaction ͑2͒.
The production of atomic hydrogen and hydroperoxy radical ͓reaction ͑3͔͒, as in the case of reaction ͑1͒, can also take place along two possible reaction pathways. The first one ͓insertion microscopic mechanism ͑via H atom migra-tion͔͒, analogous to that for reaction ͑1͒, involves the formation of products when the reactants evolve through the H 2 O 2 hydrogen peroxide minimum ͓O( 1 D)ϩH 2 O→ts8→min1 →ts9→H 2 O 2 →ts1→HϩHO 2 ͔. Thus, this reaction path coincides with the corresponding one for reaction ͑1͒ until the formation of H 2 O 2 . The saddle point ts1 has only been found at the lowest level calculation ͓UMP2͑FC͒/6-311G͑d,p͔͒. Thus, the connection between the hydrogen peroxide and products probably take place without the presence of any barrier. Reaction ͑3͒ can also occur according to a second pathway ͑substitution microscopic mechanism͒. Hence, in this case reaction ͑3͒ differs from reaction ͑1͒. Thus, a saddle point ͑ts7͒ responsible for the evolution from min1 to the hydroperoxy radical has been found with an energy of 15.67 kcal mol Ϫ1 .
In Fig. 2 are also included other saddle points ͑ts4 and ts5͒ which are associated with the internal rotation of the hydrogen peroxide molecule; ts4 has a dihedral angle of 0°͑ cis arrangement͒ and ts5 has a dihedral angle of 180°͑trans arrangement͒. The saddle point ts4 has a larger energy than ts5 because two different repulsive interactions are possible in the cis geometry: one between the oxygen lone pair electrons and the other one between the OH bond dipole moments. In the trans geometry ͑ts5͒ only the first repulsive interaction is possible. The calculated barriers for the internal rotation of H 2 O 2 are 7.38 kcal mol Ϫ1 ͑cis͒ and 1.23 kcal mol Ϫ1 ͑trans͒, both without including the ZPE. These values compare very well with the experimental data: 7.11 kcal mol Ϫ1 ͑cis͒ and 1.10 kcal mol Ϫ1 ͑trans͒; 33 7.33 kcal mol Ϫ1 ͑cis͒ and 1.11 kcal mol Ϫ1 ͑trans͒. 34 The saddle point ͑ts6͒ of the exchange process of the two hydrogen atoms between the two hydroxyl radicals ͑ts6͒ has also been located; it is a quite symmetric (C 2v ) and energetic saddle point ͑Fig. 2͒.
Similar stationary points to those described above for the O( 1 D)ϩH 2 O ground PES have been found at the UMP2͑FU͒/6-31G(d) level for the related O( 1 D)ϩH 2 S system. 35 However, at this point it is worth noting that, as indicated at the beginning of this section, the UMP2 geometries of open-shell singlet stationary points, due to spin contamination, are probably located between the singlet and triplet ones. In the O( 1 D)ϩH 2 O system, with the exception of min1, ts9, H 2 O 2 , ts4, and ts5, which have closed-shell character (͗S 2 ͘/ប 2 ϭ0.00), the stationary points placed between reactants and products have open-shell character (͗S 2 ͘/ប 2 ϭ0.8-1.0), this fact being a bit more evident for ts10. From preliminary complete active space self-consistent field ͑CASSCF͒ calculations that are in progress in our group, it turns out that the structures reported in the present work are quite similar to the CASSCF ones, with the only exception being what happens for ts10. Thus, at the CASSCF level this stationary point is closer ͑in geometry and energy͒ to reactants than in the case of the UMP2 level.

B. Analytical potential energy surface
A triatomic model, where an OH fragment of the H 2 O molecule has been treated as a single atom ͑OH͒ of 17 amu placed in its center of mass, has been considered to obtain an analytical representation of the ground PES. This model has been suggested from the experimental data, which clearly show that most of the internal energy excitation is channeled towards the OH molecule arising from the new OH bond. This kind of modeling has been previously used in our group in the case of the O( 1 D)ϩCH 4 36 and O( 3 P)ϩCH 4 37 reactions with quite good results.
The same type of analytical expression ͑many-body expansion 38 ͒ and programs 39,40 used in previous works of our group ͓e.g., N( 4 S)ϩNO, 41 O( 3 P)ϩCS, 42 H( 2 S)ϩCl 2 , and Cl( 2 P)ϩHCl, 43 N( 4 S)ϩO 2 , 44 HϩClF, and FϩHCl, 45 O( 1 D)ϩCH 4 ͑triatomic model͒, 36 and O( 3 P)ϩCH 4 ͑triatomic model͒ 37 ͔ have also been employed here. According to this approach, for the present system the analytical PES can be represented as follows: where V (2) and V (3) are the two-body and three-body terms, respectively, and R 1 ,R 2 ,R 3 are the O-H, H-͑OH͒, and O-͑OH͒ distances, respectively. The three asymptotic channels of the ground PES which can be described by the triatomic model ͓O( 1 D)ϩH 2 O, OHϩOH, and HϩHO 2 , involved in reactions ͑1͒ and ͑3͔͒ do not correlate with the same electronic state of the oxygen atom. Thus, reactants correlate with the first excited state of the O atom ͓O( 1 D)͔, while the products of reactions ͑1͒ and ͑3͒ correlate with the ground state of the O atom ͓O( 3 P)͔. Because of this, a modified form of the usual many-body equation ͑4͒, including a monoatomic term V (1) with a switching function should be used. 38 Although this is a quite well known fact, it was not indicated accurately enough in the text. Of course, this improvement does not affect the contents of the paper at all. Nevertheless, this modification can be avoided if in the fitting of the two-body terms ͑diatomic potential energy curves͒ the dissociation limits of those molecules that correlate with O( 3 P) are modified so as to reproduce ''artificial'' dissociation limits leading to O( 1 D). This approximation only changes the high energy part of the diatomic curve, and the low and moderate energy regions explored in most usual dynamical calculations remain almost unaltered. Hence, analogously as it was done previously by our group in the case of the O( 1 D)ϩCH 4 reaction, 36  The diatomic potential energy curves have been fitted using the extended-Rydberg potential up to third order where D e and R e are the dissociation energy ͓altered for OH and O͑OH͒ as it was stated above͔ and equilibrium bond length of the corresponding diatomic or pseudodiatomic molecule, respectively, and is defined as being equal to R ϪR e . The optimal ͕a i ͖ diatomic parameters have been obtained for each molecule using a nonlinear least-squares procedure, 39 by fitting a set of diatomic or pseudodiatomic ab initio points calculated around the equilibrium distance ͓PUMP4͑FU͒//UMP2͑FC͒ level͔. For the X-͑OH͒ molecules (XϭH, O) the OH ab initio geometry was optimized in all points of the X-͑OH͒ pseudodiatomic curve. The extended-Rydberg function provides a very good fitting of the curves in all cases. The optimal diatomic parameters of the OH, H͑OH͒, and O͑OH͒ molecules are shown in Table III, and the spectroscopic constants derived from them are given in Table IV. The three-body term consists of a third-order polynomial, P( 1 , 2 , 3 ), multiplied by a range function, T( 1 , 2 , 3 ). The polynomial is expressed in terms of three internal coordinates ( 1 , 2 , 3 ), defined as i ϭR i ϪR i o , where the selected reference structure (R 1 o ,R 2 o ,R 3 o ) corresponds to the average pseudotriatomic structure resulting from the two minima of the PES placed between reactants and products ͑min1 and H 2 O 2 ). The range function cancels the three-body term as one of the three atoms is separated from the other two. Thus, we have where with i, j, and k being positive integer numbers, and

͑8͒
The 20 linear parameters (͕c i jk ͖ polynomial coefficients͒ and three nonlinear ones (͕␥ i ͖ range function parameters͒ of the three-body term have been determined by a weighted nonlinear least-squares procedure, 40 taking into account the three ab initio saddle points ͑ts7, ts9, and ts10͒, the two minima ͑min1 and H 2 O 2 ), and 113 additional points corresponding to the connections between the different stationary points of the ground 1  The dissociation energies and equilibrium distances used in the fitting are given in Table IV.   b Units are: stitution͒ ͑42 points͒; O( 1 D)ϩH͑OH͒→HO͑OH͒ ͑hydrogen peroxide minimum͒→OHϩ͑OH͒, HϩO͑OH͒ ͑insertion mechanism͒ ͑47 points͒. In the fitting procedure different weights were used for each one of these regions and for the first partial potential energy derivatives ͑equal to zero͒ at the saddle points and minima geometries with respect to the R OH and R H͑OH͒ distances and Ͻ͑OH͑OH͒͒ angle. The optimal three-body parameters and the properties of the saddle points and minima of the two analytical expressions selected ͑PES1 and PES2͒ are given in Tables III and V, respectively. The root-mean-square deviation ͑RMSD͒ for the 118 ab initio points fitted is equal to 0.1054 eV ͑2.43 kcal mol Ϫ1 ͒ for PES1 and 0.0944 eV ͑2.18 kcal mol Ϫ1 ͒ for PES2. Overall there is a reasonably good agreement between the ab initio properties of the stationary points and those resulting from the fitting, except for the saddle point ts10 ͑Table V͒. Both analytical PES give a ts10 with an Ͻ͑OH͑OH͒͒ angle of 180°and a barrier much smaller than the ab initio one. We have tried to improve this result including the bending of ts10, but although we have obtained an improvement in the description of ts10, with an Ͻ͑OH͑OH͒͒ angle of 169°and a higher energy ͑9.65 kcal mol Ϫ1 without including the ZPE͒, the description of min1 and H 2 O 2 was quite unsatisfactory. Nevertheless, in this context ͑triatomic modeling͒, which can be considered as a starting point for the dynamics study of this reaction, the optimal analytical expressions obtained ͑PES1 and PES2͒ can be considered as an acceptable representation of the quite complicated ground PES. As it will be   : 100.63, 101.62, and 92.73 for ab initio, PES1, and PES2, respectively. seen in Sec. III, in spite of the low energy barrier that ts10 presents in both analytical PES considered, at the moderate collision energies considered in this work nearly all reactive trajectories evolve through geometrical arrangements close to that of the HO͑OH͒ hydrogen peroxide minimum. This means that the dominant microscopic mechanism clearly corresponds to the insertion process, the abstraction process through the saddle point ts10 playing a minor role.

III. QCT DYNAMICS CALCULATIONS
To study the dynamics of reaction ͑1͒ the QCT method [50][51][52] has been applied as implemented in the TRIQCT program, 53 considering the PES1 and PES2 triatomic analytical representations of the ground 1 A PES. The accuracy of the numerical integration of Hamilton's differential equations has been verified by checking the conservation of total energy and angular momentum along every trajectory, and performing back integrations on some batches of trajectories. An integration step of 2.5ϫ10 Ϫ17 s and an initial distance of 10 Å between the O( 1 D) atom and the H-͑OH͒ center of mass have been selected. At this separation the reactants interaction energy can be neglected with respect to the reactants available energy.
The QCT dynamics study has been mainly focused on the calculation of the rovibrational distributions of the OH product from reaction ͑1͒ and the corresponding microscopic reaction mechanism, although other properties have also been considered ͑rate constant and rotational alignment͒. The reported experimental OH rovibrational distributions arising from reaction ͑1͒ correspond to several reaction conditions, concerning mostly the identity of the O( 1 D) precursor and the wavelength used in its photodissociation. The different conditions yield, in turn, different relative translational energy ͑collision energy͒ distributions for O( 1 D)ϩH 2 O. In the QCT calculations three different relative translational energies (E T ) for the O( 1 D)ϩH 2  at 266 nm͒. In these calculations the rovibrational distribution of the H-͑OH͒ pseudodiatomic molecule has been sampled from a Maxwell-Boltzmann distribution at 300 K. Both the collision energy and the H-͑OH͒ rovibrational levels have been sampled from Maxwell-Boltzmann distributions at 300 K in the rate constant calculation of reaction ͑1͒. For each initial condition around 10 000 trajectories have been run.

A. Rate constant and rovibrational distributions
The QCT reaction cross section ͑͒ of O( 1 D) ϩH-͑OH͒͑300 K͒→OHϩ͑OH͒ has been calculated at the three E T values explored for the two triatomic analytical PES derived. decreases with E T , as it corresponds for a barrierless reaction ͑e.g., for PES1 ϭ26.4, 21.2, and 16.0 Å 2 for E T ϭ0.234, 0.303, and 0.443 eV, respectively͒. This behavior is due to the decrease of the maximum impact parameter (b max ) with E T , the reaction probability being almost constant ͑around 50%͒. A large amount of energy is released as OH internal energy, appearing in very similar energy amounts as vibration and rotation. For PES1 at 0.303 eV, the average fraction of energy appearing in products as relative translation (͗f T Ј͘), vibration (͗f V Ј ͘), and rotation (͗f R Ј͘) is equal to 0.29, 0.34, and 0.38, respectively.
The QCT rate constant of reaction ͑1͒ at 300 K has been estimated from the rate constant obtained for the ground PES ( 1 AЈ in C s ) by dividing its value by five, as there are five degenerated PES in the reactants region ͑four of them correlating with products͒. Hence, in the absence of additional information on the excited PES of the O( 1 D)ϩH 2 6,7,10,11,15 which is substantially more excited than that associated with the old one. For vЈϭ3 and 4, however, there is no experimental information available. The QCT OH average rotational energies obtained are in general much larger than the experimental ones for the new OH bond. 6,7,10,11,15

B. Two-vector properties and microscopic reaction mechanism
An l→lЈ angular momentum transformation has been found, with l(lЈ) being the reactants ͑products͒ orbital angular momentum. This is what can be expected for a reaction with H-L-H ͑heavy-light-heavy͒ kinematics. In what respects the two-vector properties, the angular distribution ͑reactive trajectories vs scattering angle͒ is very broad and presents a somewhat larger tendency towards forward scattering, the forward/backward ͑f/b͒ ratio being higher than unity in all cases. The f/b ratio increases with E T ͑e.g., for PES1 f/bϭ1.09, 1.16, and 1.30 at E T ϭ0.234, 0.303, and 0.443 eV, respectively͒, and the initial (k) and final (kЈ) relative velocity vectors exhibit an average angle of about 90°in all cases. The OH rotational angular momentum (jЈ) has some tendency to be perpendicular to k and kЈ, and the kjЈ and kЈjЈ angular distributions are very similar ͑broad, peaking at 90°, and symmetrical around 90°͒. The lЈjЈ angular distribution is broad and both vectors show a slight tendency to be antiparallel, with an average angle between 102°a nd 106°.
At E T ϭ0.234 eV, the QCT value of ͗P 2 (cos )͘ for kjЈ, defined as ͗3 cos 2 Ϫ1͘/2, with being the angle defined by k and jЈ, is equal to Ϫ0.0106 and Ϫ0.0155 for PES1 and PES2, respectively, and these values compare well with the experiment (0.14Ϯ0.22). 11 P 2 (cos ) presents the following range of values: Ϫ0.5рP 2 (cos )р1.0, where Ϫ0.5 ͑1.0͒ corresponds to jЈ perpendicular ͑parallel͒ to k. Hence, for reaction ͑1͒ there is no clear tendency to a particular rotational alignment of the OH product with respect to the initial relative velocity vector. The situation for kЈjЈ is very similar to that for kjЈ. Thus, the associated ͗P 2 (cos )͘ value is equal to Ϫ0.0099 and Ϫ0.0080 for PES1 and PES2, respectively.
For PES1, the consideration of the reactive trajectories obtained ͑4475͒ at E T ϭ0.303 eV has allowed the study of the microscopic mechanism of reaction ͑1͒. The lowest potential energy reached on PES1 by each reactive trajectory has been analyzed. For PES1, the energy of reactants, OHϩ͑OH͒ products and HO͑OH͒ hydrogen peroxide minimum are: Ϫ5.44, Ϫ6.72, and Ϫ8.95 eV, respectively. Only 1.8% of reactive trajectories have evolved from reactants to products with a lowest potential energy higher than Ϫ7.0 eV. The lowest potential energy values reached by the remaining reactive trajectories are the following: 0.4% between Ϫ7.0 and Ϫ8.0 eV, 1.7% between Ϫ8.0 and Ϫ8.4 eV, 46.8% between Ϫ8.4 and Ϫ8.9 eV, and 49.3% below Ϫ8.9 eV. Similar results have been obtained for PES2. Hence, the HO͑OH͒ deep minimum plays a very important role in the dynamics, since nearly all reactive trajectories leading to OHϩ͑OH͒ evolve through geometries close to this minimum. Therefore, reaction ͑1͒ takes place nearly exclusively through an insertion mechanism instead of by abstraction of the H atom by the attacking O( 1 D) atom.
To complete the microscopic mechanism analysis, the collision complex lifetimes, C , has been determined for the reactive trajectories ͑4379͒ leading to OHϩ͑OH͒ products on PES1 at E T ϭ0.443 eV, the highest collision energy considered, and these values have been compared with the average rotational period (͗ R ͘ϭ0.18 ps) estimated according to this where ͗I͘ is the moment of inertia of the collision complex, which has been taken to be equal to an average over the principal moments of inertia of the HO͑OH͒ hydrogen peroxide minimum at its equilibrium geometry, is the reduced mass of reactants, and ͗b͘ is the average impact parameter. Although, as indicated above, nearly all reactive trajectories evolve through an insertion mechanism involving the HO͑OH͒ minimum, the analysis of the C values for the above-mentioned condition reveals that reactive trajectories leading to OHϩ͑OH͒ can be classified into three groups: ͑a͒ direct reactive trajectories ͑30%͒; ͑b͒ nondirect reactive trajectories involving short-lived collision complexes, i.e., those collision complexes with lifetimes shorter than a rotational period ͑15%͒,   tion of the border line between direct and nondirect reactive trajectories at 0.025 ps. The QCT average lifetime values obtained must be considered as a lower limit of the theoretical value which would result after including explicitly all degrees of freedom of the H 2 O molecule. The QCT results show that, even at the highest E T value explored, nearly all reactive trajectories leading to reaction ͑1͒ take place through an insertion mechanism which is mainly ͑70%͒ a nondirect one. The HO͑OH͒ collision complex formation with an average lifetime of about three rotational periods is consistent with the experimental information available. 10,11,16 Moreover, the highly asymmetrical energy partitioning between the two OH fragments arising from reaction ͑1͒ experimentally found, 6,7,10,11,15 indicates that the energy equidistribution between both OH fragments in the collision complex cannot take place within the time scale of only a few rotational periods.

IV. SUMMARY AND CONCLUDING REMARKS
An ab initio study of the ground potential energy surface ( 1 A) of the O( 1 D)ϩH 2 O system has been performed, employing the second-and fourth-order Mo "ller-Plesset methods and mainly using the 6-311G(3d2 f ,3p2d) basis set. Reactants, products, ten saddle points, and two minima, one of them corresponding to the hydrogen peroxide molecule, have been characterized. The ground PES has been modeled as a triatomic system, with an OH group of the H 2 O molecule treated as a single atom of 17.0 amu. This model has been suggested from the experimental data. From the PES stationary points and more than one hundred additional points calculated, two triatomic analytical PES models ͑PES1 and PES2͒ have been derived using as analytical expression a many-body expansion. Both analytical PES have been employed quite satisfactorily to study the dynamics of reaction ͑1͒ by means of the quasiclassical trajectory ͑QCT͒ method. In general, PES1 provides a slightly better description of the ab initio data and dynamics than PES2.
The QCT dynamics study has been mainly focused on the determination of properties for which experimental data are available. The rate constant of reaction ͑1͒ estimated from the QCT calculations is reasonably close to the recommended experimental value in the case of PES1. For E T ϭ0.234, 0.303, and 0.443 eV with H 2 O at 300 K, overall the QCT OH vibrational populations are in good agreement with the experimental values reported for the OH which corresponds to the new OH bond formed. However, the QCT OH average rotational energies are in general quite larger than the experimental ones for the new OH bond. The QCT values of ͗P 2 (cos )͘ for kjЈ at E T ϭ0.234 eV compare well with the experiment. Thus, there is not a clear tendency to a particular rotational alignment of the OH product ͑new OH bond͒ with respect to the initial relative velocity vector. The QCT results also show that nearly all reactive trajectories leading to reaction ͑1͒ take place through insertion microscopic mechanism, which, even at the highest collision energy considered (E T ϭ0.443 eV), is mainly ͑70%͒ a nondirect one and involves the formation of a collision complex. The collision complex has an average lifetime of about three rotational periods and geometry around that of the HO͑OH͒ hydrogen peroxide molecule. From this theoretical data, and taking into consideration the highly asymmetrical energy partitioning between the two OH fragments from reaction ͑1͒ experimentally found, it turns out that the energy redistribution between the two OH fragments in the collision complex cannot take place in the time scale of only a few rotational periods. The QCT results concerning the microscopic mechanism of reaction ͑1͒ are in agreement with the suggestions made by the experimentalists to interpret their results.
The ab initio-based QCT triatomic study presented here should be considered as a starting point in the study of the O( 1 D)ϩH 2 O→2OH reaction, from which different aspects about the dynamics may be learned. At present, further developments, which take into account explicitly all atoms involved in this tetratomic system, are in progress.