Ab initio G2M(MP2)//MP2/6-31G** calculations have been performed to study the molecular and radical chain reaction mechanisms of nitrogen hydrogenation through sequential additions of three H2 molecules to N2 producing NH3 + NH3. All reaction steps of the molecular mechanism are shown to be slow owing to high barriers for the molecular hydrogen additions. The three-center 1,1-H2 additions are significantly more preferable as compared to the four-center 1,2-additions. The most favorable reaction pathway involves the steps N2 + H2 → TS1a → NNH2, NNH2 + H2 → TS3a → H2NNH2, H2NNH2 → TS4 → HNNH3, and HNNH3 + H2 → TS5 → NH3 + NH3, with the barriers calculated as 125.2, 30.7, 60.5, and 24.6 kcal/mol, respectively. The addition of the first molecular hydrogen is thus the rate-determining stage of nitrogen hydrogenation. The formation of hydrazine can be facilitated by a spontaneous reaction of two cis-HNNH molecules by the dihydrogen transfer mechanism. The radical chain mechanism includes the N2 + H → N2H, N2H + H2 → HNNH + H, HNNH + H → N2H3, N2H3 + H2 → H2NNH2 + H, H2NNH2 + H → NH2 + NH3, and NH2 + H2 → NH3 + H sequential reactions with the barriers of 17.1, 41.6, 6.4, 29.1, 10.7, and 10.6 kcal/mol, respectively. Nitrogen hydrogenation can be catalyzed by H atoms with the barrier for the slowest reaction step decreasing from 125 to 42 kcal/mol. The reaction of two NH(3Σ-) radicals is predicted to be fast and to form N2 + H2 with high exothermicity. The reaction of two NH2 radicals can produce NNH2 + H2 with exothermicity of 19.8 kcal/mol and a barrier of 10.9 kcal/mol relative to the reactants, or NH3 + NH(3Σ-), through a barrierless, 14.3 kcal/mol exothermic, but spin-forbidden channel. We also report rate constants and equilibrium constants for all considered reactions calculated using the transition state theory and ab initio energies and molecular parameters, which can be employed for kinetic modeling of chemical processes involving nitrogen- and hydrogen-containing substances.

Ab initio calculations of the potential energy surface for the ClϩO 3 reaction have been performed using the MP2, QCISD͑T͒, CCSD͑T͒, G2, G2M, CASPT2, and MRCI methods with various basis sets. The results show that the reaction pathway can be divided in two parts. The reaction starts on the nonplanar pathway when the Cl atom attacks a terminal oxygen of ozone via TS1, producing a virtual intermediate, a nonplanar chlorine trioxide B. B isomerizes to another virtual intermediate, planar C, which immediately dissociates to ClOϩO 2 in the coplanar manner. The ClOOO intermediates B and C disappear at the QCISD level of theory. The calculations confirm the direct reaction mechanism for ClϩO 3 but the existence of a very flat plateau on the potential energy surface in the region of B, TS2, C, and TS3 can have some effect on the reaction dynamics. TS1 is the critical transition state determining the rate of the ClϩO 3 reaction. High level calculations, such as QCISD͑T͒, CCSD͑T͒, MRCI, and CASPT2 with the basis sets from moderate to very large, at the QCISD and CASSCF optimized geometry of TS1, consistently predict the barrier to be about 4-5 kcal/mol, much higher than the experimental value ͑below 1 kcal/mol͒. New experimental measurements as well as even higher level theoretical calculations are encouraged in order to resolve this discrepancy.

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Density functional B3LYP/6-31G**, B3LYP/6-311G**, B3LYP/6-311+G(3df,2p), and ab initio CCSD(T)/ 6-311G** calculations showed the reaction of free iron atoms with water in the ground quintet electronic state to proceed by the formation of a weakly bound Fe-OH 2 molecular complex. The complex is slightly unbound at the CCSD(T)/6-311G** level but stable according to density functional calculations and can isomerize to the HFeOH molecule, overcoming a barrier of 15-33 kcal/mol (with respect to the reactants), but further decomposition of HFeOH to FeO and H 2 is hindered by a high barrier. In the presence of protons (in acidic environment), iron atoms can easily attach H + with formation of the quintet FeH + molecules. The reaction of these molecules with water, q-FeH + + H 2 O f q-HFeOH 2 + f q-FeOH + + H 2 , is exothermic and occurs without activation barrier. In solution, q-FeOH + may attach another proton (if the Coulomb repulsion barrier between the two ions can be overcome) and dissociate to q-Fe 2+ and H 2 O, so the water molecule assists oxidation of a neutral iron atom to Fe 2+ , and two protons can be converted into molecular hydrogen transferring their charge to Fe. The FeH + molecules are also shown to readily react with molecular oxygen, producing FeOOH + without energy barrier. The FeH + + O 2 reaction is more facile than the reaction of FeH + with water due to higher overall exothermicity (68-88 kcal/mol vs 20-34 kcal/mol for FeH + + H 2 O f FeOH + + H 2 ) and a lower barrier for the intermediate reaction step (14-17 vs 35-46 kcal/mol), which can be rate-determining if the reaction occurs in solution. The reaction mechanism involving sequential Fe( 5 D) + H + f q-FeH + , q-FeH + + O 2 f q-HFeO 2 + f q-FeOOH + reactions, followed by dissociation of q-FeOOH + in solution yielding Fe 2+ , may be relevant to the first step of rusting. The calculations showed that electronically excited triplet iron atoms are more reactive with H 2 O. The triplet Fe + H 2 O f Fe-OH 2 f HFeOH reaction is exothermic and has its transition state lying lower in energy than the reactants. No triplet-quintet intersystem crossing was found along the reaction pathway. The mechanism for the Fe + H 2 S reaction in the ground quintet electronic state is found to be similar to that for the reaction with water, but the critical barrier for the formation of the HFeSH intermediate is lower. Because of the reduced endothermicity of the Fe + H 2 S f FeS + H 2 reaction and lower reaction barriers, the reaction of iron atoms with H 2 S is more likely to yield iron sulfide and molecular hydrogen than the reaction with water to produce FeO + H 2 .

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Potential energy surfaces of various reactions in the BO/H2, B2O2/H2, and BS/H2 systems have been studied at the G2M(MP2)//B3LYP/6-311+G(d,p) level of theory. The BO + H2 reaction is shown to proceed by abstraction of a hydrogen atom by B to produce OBH + H with the barrier and exothermicity of 8.3 and 6.8 kcal/mol, respectively. The reaction can also occur by 1,2-insertion of BO into the H−H bond or by H abstraction by the O atom; however, the barriers for these channels are much higher, 36.4 and 42.7 kcal/mol, respectively. Via a low ∼0.3 kcal/mol barrier, the OBH + H reaction produces the OBH2 radical, which is the most stable compound in the BO/H2 system and lies 15.9, 2.5, and 4.2 kcal/mol below BO + H2, trans-HBOH, and cis-HBOH, respectively. OBH2 can isomerize to trans-HBOH overcoming a barrier of 27.7 kcal/mol and the latter can rearrange to the cis conformer with a barrier of 10.8 kcal/mol. BOH and H can recombine and form cis- or trans-HBOH without barriers. In the B + H2O reaction, the reactants can first form a weakly bound B−H2O complex, which then can eliminate an H atom producing BOH + H or undergo insertion of B into an O−H bond giving trans-HBOH with barriers of 4.7 and 6.2 kcal/mol relative to the initial reactants, respectively, and trans-HBOH can eventually decompose to OBH + H and a minor amount of BO + H2. Singlet OBBO is shown to be much less reactive with respect to H2 than the BO monomer. Alternatively, after two BO recombine to form a triplet OBBO molecule over a moderate 8.3 kcal/mol barrier, t-OBBO can easily react with H2 producing either BO + OBH2 (via a t-OBBH2O intermediate) or OBBOH + H with barriers of 4.4 and 7.4 kcal/mol, respectively. The reactions in the BS/H2 system are shown to be similar to those for BO/H2, except that BS cannot insert into H2, SBH2 resides in a much deeper potential well (37.3 kcal/mol below BS + H2) and can rearrange both to trans- and cis-HBSH, the B−H2S complex is more strongly bound than B−H2O, and the B + H2S reaction is expected to be significantly faster than the reaction of B + H2O.

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