Inactivation of [Fe?Fe]‐hydrogenase by O2. Thermodynamics and frontier molecular orbitals analyses

The oxidation of H‐cluster in gas phase, and in aqueous enzyme phase, has been investigated by means of quantum mechanics (QM) and combined quantum mechanics–molecular mechanics (QM/MM). Several potential reaction pathways (in the above‐mentioned chemical environments) have been studied, wherein only the aqueous enzyme phase has been found to lead to an inhibited hydroxylated cluster. Specifically, the inhibitory process occurs at the distal iron (Fe_d) of the catalytic H‐cluster (which isalso the atom involved in H₂ synthesis). The processes involved in the H‐cluster oxidative pathways are O₂ binding, e^? transfer, protonation, and H₂O removal. We found that oxygen binding is nonspontaneous in gas phase, and spontaneous for aqueous enzyme phase where both Fe atoms have oxidation state II; however, it is spontaneous for the partially oxidized and reduced clusters in both phases. Hence, in the protein environment the hydroxylated H‐cluster is obtained by means of completely exergonic reaction pathway starting with proton transfer. A unifying endeavor has been carried out for the purpose of understanding the thermodynamic results vis‐à‐vis several other performed electronic structural methods, such as frontier molecular orbitals (FMO), natural bond orbital partial charges (NBO), and H‐cluster geometrical analysis. An interesting result of the FMO examination (for gas phase) is that an e^? is transferred to LUMO_α rather than to SOMO_β, which is unexpected because SOMO_β usually resides in a lower energy rather than LUMO_α for open‐shell clusters. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Dual Metal Active Sites in an Ir1/FeOx Single‐Atom Catalyst: A Redox Mechanism for the Water‐Gas Shift Reaction

Herein, we report a theoretical and experimental study of the water‐gas shift (WGS) reaction on Ir₁/FeO_x single‐atom catalysts. Water dissociates to OH* on the Ir₁ single atom and H* on the first‐neighbour O atom bonded with a Fe site. The adsorbed CO on Ir₁ reacts with another adjacent O atom to produce CO₂, yielding an oxygen vacancy (O_vac). Then, the formation of H₂ becomes feasible due to migration of H from adsorbed OH* toward Ir₁ and its subsequent reaction with another H*. The interaction of Ir₁ and the second‐neighbouring Fe species demonstrates a new WGS pathway featured by electron transfer at the active site from Fe³⁺?O???Ir²⁺?O_vac to Fe²⁺?O_vac???Ir³⁺?O with the involvement of O_vac. The redox mechanism for WGS reaction through a dual metal active site (DMAS) is different from the conventional associative mechanism with the formation of formate or carboxyl intermediates. The proposed new reaction mechanism is corroborated by the experimental results with Ir₁/FeO_x for sequential production of CO₂ and H₂.     

Hemoglobin as a nitrite anhydrase: modeling methemoglobin-mediated N2O3 formation

Nitrite has recently been recognized as a storage form of NO in blood and as playing a key role in hypoxic vasodilation. The nitrite ion is readily reduced to NO by hemoglobin in red blood cells, which, as it happens, also presents a conundrum. Given NO’s enormous affinity for ferrous heme, a key question concerns how it escapes capture by hemoglobin as it diffuses out of the red cells and to the endothelium, where vasodilation takes place. Dinitrogen trioxide (N₂O₃) has been proposed as a vehicle that transports NO to the endothelium, where it dissociates to NO and NO₂. Although N₂O₃ formation might be readily explained by the reaction Hb‐Fe³⁺+NO₂^?+NO?Hb‐Fe²⁺+N₂O₃, the exact manner in which methemoglobin (Hb‐Fe³⁺), nitrite and NO interact with one another is unclear. Both an “Hb‐Fe³⁺‐NO₂^?+NO” pathway and an “Hb‐Fe³⁺‐NO+NO₂^?” pathway have been proposed. Neither pathway has been established experimentally. Nor has there been any attempt until now to theoretically model N₂O₃ formation, the so‐called nitrite anhydrase reaction. Both pathways have been examined here in a detailed density functional theory (DFT, B3LYP/TZP) study and both have been found to be feasible based on energetics criteria. Modeling the “Hb‐Fe³⁺‐NO₂^?+NO” pathway proved complex. Not only are multiple linkage‐isomeric (N‐ and O‐coordinated) structures conceivable for methemoglobin–nitrite, multiple isomeric forms are also possible for N₂O₃ (the lowest‐energy state has an N? N‐bonded nitronitrosyl structure, O₂N? NO). We considered multiple spin states of methemoglobin–nitrite as well as ferromagnetic and antiferromagnetic coupling of the Fe³⁺ and NO spins. Together, the isomerism and spin variables result in a diabolically complex combinatorial space of reaction pathways. Fortunately, transition states could be successfully calculated for the vast majority of these reaction channels, both M_S=0 and M_S=1. For a six‐coordinate Fe³⁺‐O‐nitrito starting geometry, which is plausible for methemoglobin–nitrite, we found that N₂O₃ formation entails barriers of about 17–20 kcal mol^?1, which is reasonable for a physiologically relevant reaction. For the “Hb‐Fe³⁺‐NO+NO₂^?” pathway, which was also found to be energetically reasonable, our calculations indicate a two‐step mechanism. The first step involves transfer of an electron from NO₂^? to the Fe³⁺–heme–NO center ({FeNO}⁶) , resulting in formation of nitrogen dioxide and an Fe²⁺–heme–NO center ({FeNO}⁷). Subsequent formation of N₂O₃ entails a barrier of only 8.1 kcal mol^?1. From an energetics point of view, the nitrite anhydrase reaction thus is a reasonable proposition. Although it is tempting to interpret our results as favoring the “{FeNO}⁶+NO₂^?” pathway over the “Fe³⁺‐nitrite+NO” pathway, both pathways should be considered energetically reasonable for a biological reaction and it seems inadvisable to favor a unique reaction channel based solely on quantum chemical modeling.     

Complexation kinetics of Fe2+ with 1,10‐phenanthroline forming ferroin in acidic solutions

The formation kinetics of ferroin is studied under varied acid conditions at 25°C and fixed ionic strength (0.48 mol dm^?3) under pseudo‐first‐order conditions with respect to Fe²⁺ by using the stopped‐flow technique. The reaction followed is first and third order with respect to Fe²⁺ and 1,10‐phenanthroline (phen)_T, respectively. Increasing the acid concentration retarded the reaction, and the reaction rate showed a positive salt effect. The rate‐limiting step involved the complexation of the phen or protonated phen with [Fe(phen)₂]²⁺ complex ion, leading to formation of [Fe(phen)₃]²⁺ ion. The observed retardation of the reaction rate with increasing [H⁺]₀ is due to the increased [phenH⁺]_eq and low reactivity of phenH⁺ with [Fe(phen)₂]²⁺ complex ion. Simulated curves for the acid variation experiments agreed well with the corresponding experimental curves and the estimated rate coefficients supporting the proposed mechanism. Relatively low energy of activation (26 kJ mol^?1) and high negative entropy of activation (?159.8 J K^?1 mol^?1) agree with the proposed mechanism and the formation of compact octahedral complex ion. © 2008 Wiley Periodicals, Inc. 40: 515–523, 2008     

Density functional theory studies on the external OH−‐induced barrierless proton dissociation mechanism for the forced hydrolysis reaction of Al3+(aq)

The forced hydrolysis reaction of aqueous aluminum ion (Al³⁺) is of critical importance in Al chemistry, but its microscopic mechanism has long been neglected. Herein, density functional calculations reveal an external OH⁻‐induced barrierless proton dissociation mechanism for the forced hydrolysis of Al³⁺(aq). Dynamic reaction pathway modeling results show that the barrierless deprotonations induced by the second‐ or third‐shell external OH⁻ proceed via the concerted proton transfer through H‐bond wires connected to the coordinated waters, and the inducing ability of the external OH⁻ decreases with increasing hydration layers between Al(H₂O)₆³⁺ and the external OH⁻. The OH⁻‐induced forced hydrolysis mechanism of Al³⁺(aq) is quite different from its self‐hydrolysis mechanism without OH⁻. The inducing ability is a unique characteristic of OH⁻, rather than other anions such as F⁻ or Cl⁻.     

Unraveling the Mechanism of Water Oxidation Catalyzed by Nonheme Iron Complexes

Density functional theory (DFT) is employed to: 1) propose a viable catalytic cycle consistent with our experimental results for the mechanism of chemically driven (Ce^IV) O₂ generation from water, mediated by nonheme iron complexes; and 2) to unravel the role of the ligand on the nonheme iron catalyst in the water oxidation reaction activity. To this end, the key features of the water oxidation catalytic cycle for the highly active complexes [Fe(OTf)₂(Pytacn)] (Pytacn: 1‐(2′‐pyridylmethyl)‐4,7‐dimethyl‐1,4,7‐triazacyclononane; OTf: CF₃SO₃^?) ( 1 ) and [Fe(OTf)₂(mep)] (mep: N,N′‐bis(2‐pyridylmethyl)‐N,N′‐dimethyl ethane‐1,2‐diamine) ( 2 ) as well as for the catalytically inactive [Fe(OTf)₂(tmc)] (tmc: N,N′,N′′,N′′′‐tetramethylcyclam) ( 3 ) and [Fe(NCCH₃)(^MePy₂CH‐tacn)](OTf)₂ (^MePy₂CH‐tacn: N‐(dipyridin‐2‐yl)methyl)‐N′,N′′‐dimethyl‐1,4,7‐triazacyclononane) ( 4 ) were analyzed. The DFT computed catalytic cycle establishes that the resting state under catalytic conditions is a [Fe^IV(O)(OH₂)(LN₄)]²⁺ species (in which LN₄=Pytacn or mep) and the rate‐determining step is the O?O bond‐formation event. This is nicely supported by the remarkable agreement between the experimental (ΔG^≠=17.6±1.6 kcal mol^?1) and theoretical (ΔG^≠=18.9 kcal mol^?1) activation parameters obtained for complex 1 . The O?O bond formation is performed by an iron(V) intermediate [Fe^V(O)(OH)(LN₄)]²⁺ containing a cis‐Fe^V(O)(OH) unit. Under catalytic conditions (Ce^IV, pH 0.8) the high oxidation state Fe^V is only thermodynamically accessible through a proton‐coupled electron‐transfer (PCET) process from the cis‐[Fe^IV(O)(OH₂)(LN₄)]²⁺ resting state. Formation of the [Fe^V(O)(LN₄)]³⁺ species is thermodynamically inaccessible for complexes 3 and 4 . Our results also show that the cis‐labile coordinative sites in iron complexes have a beneficial key role in the O?O bond‐formation process. This is due to the cis‐OH ligand in the cis‐Fe^V(O)(OH) intermediate that can act as internal base, accepting a proton concomitant to the O?O bond‐formation reaction. Interplay between redox potentials to achieve the high oxidation state (Fe^V?O) and the activation energy barrier for the following O?O bond formation appears to be feasible through manipulation of the coordination environment of the iron site. This control may have a crucial role in the future development of water oxidation catalysts based on iron.     

A computational mechanistic study of the deamination reaction of melamine

A detailed computational study of the deamination reaction of melamine by OH^–, n H₂O/OH^–, n H₂O (where n = 1, 2, 3), and protonated melamine with H₂O, has been carried out using density functional theory and ab initio calculations. All structures were optimized at M06/6‐31G(d) level of theory, as well as with the B3LYP functional with each of the basis sets: 6‐31G(d), 6‐31 + G(d), 6‐31G(2df,p), and 6‐311++G(3df,3pd). B3LYP, M06, and ω B97XD calculations with 6‐31 + G(d,p) have also been performed. All structures were optimized at B3LYP/6‐31 + G(d,p) level of theory for deamination simulations in an aqueous medium, using both the polarizable continuum solvation model and the solvation model based on solute electron density. Composite method calculations have been conducted at G4MP2 and CBS‐QB3. Fifteen different mechanistic pathways were explored. Most pathways consisted of two key steps: formation of a tetrahedral intermediate and in the final step, an intermediate that dissociates to products via a 1,3‐proton shift. The lowest overall activation energy, 111 kJ mol^?1 at G4MP2, was obtained for the deamination of melamine with 3H₂O/OH^?.     

Formation of the iron-oxo hydroxylating species in the catalytic cycle of aromatic amino acid hydroxylases

The first part of the catalytic cycle of the pterin‐dependent, dioxygen‐using nonheme‐iron aromatic amino acid hydroxylases, leading to the Fe^IV?O hydroxylating intermediate, has been investigated by means of density functional theory. The starting structure in the present investigation is the water‐free Fe? O₂ complex cluster model that represents the catalytically competent form of the enzymes. A model for this structure was obtained in a previous study of water‐ligand dissociation from the hexacoordinate model complex of the X‐ray crystal structure of the catalytic domain of phenylalanine hydroxylase in complex with the cofactor (6R)‐L ‐erythro‐5,6,7,8‐tetrahydrobiopterin (BH₄) (PAH‐Fe^II‐BH₄). The O? O bond rupture and two‐electron oxidation of the cofactor are found to take place via a Fe‐O‐O‐BH₄ bridge structure that is formed in consecutive radical reactions involving a superoxide ion, O₂^?. The overall effective free‐energy barrier to formation of the Fe^IV?O species is calculated to be 13.9 kcal mol^?1, less than 2 kcal mol^?1 lower than that derived from experiment. The rate‐limiting step is associated with a one‐electron transfer from the cofactor to dioxygen, whereas the spin inversion needed to arrive at the quintet state in which the O? O bond cleavage is finalized, essentially proceeds without activation.     

Off‐atomic site charges in some anions,metal cations,and complexes: Significance for electrostatic properties and binding

Electronic structures and properties of several anions, metal cations, and their complexes with neutral molecules were investigated at the HF/6‐31G** and B3LYP/6‐31G** levels of theory. Charges shifted from atomic sites due to atomic orbital hybridization called hybridization displacement charges (HDC) were investigated in detail. It has been found that many components of HDC are associated with each atom of ion that are shifted from the atomic sites, those associated with metal cations being shifted by large distances as found previously in electrically neutral systems. It is shown that atomic orbitals are appreciably rehybridized in going from neutral molecules to anions and cations. Molecular dipole moments and surface molecular electrostatic potentials (MEP) are obtained satisfactorily using HDC for the various types of species mentioned above. In the OH^?? H₂O complex, reversal of direction of shift of an HDC component associated with the hydrogen atom of H₂O involved in hydrogen bonding, indicates that the hydrogen bond between OH^? and H₂O would have some covalent character. Other atomic site‐based point charge models cannot provide such information about the nature of bonding. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem 2007     

Kinetics and mechanism of complexation of iron(III) bycis-(salicylato)(methyl/ethylamine)bis(ethylenediamine)cobalt(III) ions

The formation and dissociation of the binuclear complexes of Fe^III withcis-[Co(en)₂(RNH₂)SalH]²⁺ [R=Me, Et and SalH=C₆H₄(OH)CO ₂ ⁻ ] were studied by a stopped-flow technique at 20–35°C, and I=1.0 mol dm⁻³ (ClO ₄ ⁻ ). The formation of the binuclear species, N₅CoSalFe⁴⁺, involves reactions of the phenol form of the Co^III substrates with Fe(OH₂) ₆ ³⁺ and Fe(OH₂)₅OH²⁺. The mechanism of reaction of Fe(OH₂)₅OH²⁺ is essentially Id, while that of Fe(OH₂) ₆ ³⁺ appears to be Ia. The formation rate constant, k₁, for Fe(OH₂) ₆ ³⁺ /N₅CoSalH²⁺ reaction decreases as the amine chain length increases, whereas the same (k₂) for the Fe(OH₂)₅OH²⁺/N₅CoSalH²⁺ reaction does not show any such trend. The binuclear species, N₅CoSalFe⁴⁺, dissociates to yield a Co^III substrate and Fe^III speciesvia a predominantly spontaneous dissociation path and a minor acid catalysed path which are relatively insensitive to the variation in size of the non-labile amine chain length.     

A Redox‐Induced Spin‐State Cascade in a Mixed‐Valent Fe3(μ3‐O) Triangle

One‐electron reduction of a pyrazolate‐bridged triangular Fe₃(μ₃‐O) core induces a cascade wherein all three metal centers switch from high‐spin Fe³⁺ to low‐spin Fe^2.66+. This hypothesis is supported by spectroscopic data (¹H‐NMR, UV‐vis‐NIR, infra‐red, ⁵⁷Fe‐Mössbauer, EPR), X‐ray crystallographic characterization of the cluster in both oxidation states and also density functional theory. The reduction induces substantial contraction in all bond lengths around the metal centers, along with diagnostic shifts in the spectroscopic parameters. This is, to the best of our knowledge, the first example of a one‐electron redox event causing concerted change in multiple iron centers.     

Theoretical studies on a possible synthesis reaction pathway on N8 (CS) clusters

The potential energy surfaces of N₈ clusters were investigated by density functional theory (DFT) and a possible synthesis reaction pathway for N₈ (C_S) was suggested. The species involved were fully optimized up to the B3LYP/6‐311+G* level of theory. Relative energies were further calculated at the QCISD/6‐311+G*//B3LYP/6‐311+G* level. The reaction rate constants of these steps from the 1 (N₅⁺?N₃^?, complex, C_S) to 2 (N₈, C_S), 2 (N₈, C_S) to 3 (N₈, C_S), 3 (N₈, C_S) to 4 (N₈, D_2d), and 4 (N₈, D_2d) to 5 (N₈, C_S) reactions were predicted by the VTST theory. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1334–1339, 2001     

The Nitrogenase FeMo‐Cofactor Precursor Formed by NifB Protein: A Diamagnetic Cluster Containing Eight Iron Atoms

The biological activation of N₂ occurs at the FeMo‐cofactor, a 7Fe–9S–Mo–C–homocitrate cluster. FeMo‐cofactor formation involves assembly of a Fe_6–8–S_X–C core precursor, NifB‐co, which occurs on the NifB protein. Characterization of NifB‐co in NifB is complicated by the dynamic nature of the assembly process and the presence of a permanent [4Fe–4S] cluster associated with the radical SAM chemistry for generating the central carbide. We have used the physiological carrier protein, NifX, which has been proposed to bind NifB‐co and deliver it to the NifEN protein, upon which FeMo‐cofactor assembly is ultimately completed. Preparation of NifX in a fully NifB‐co‐loaded form provided an opportunity for Mössbauer analysis of NifB‐co. The results indicate that NifB‐co is a diamagnetic (S=0) 8‐Fe cluster, containing two spectroscopically distinct Fe sites that appear in a 3:1 ratio. DFT analysis of the ⁵⁷Fe electric hyperfine interactions deduced from the Mössbauer analysis suggests that NifB‐co is either a 4Fe²⁺–4Fe³⁺ or 6Fe²⁺–2Fe³⁺ cluster having valence‐delocalized states.     

C?H bond dissociation enthalpies of fluorinated formates and estimation of their rate constants for the reactions with OH radicals: A DFT study

Density functional theory was used to estimate the lifetime of fluorinated formates, which are primary products from the oxidation of hydrofluoroethers. First, the C? H bond dissociation enthalpies (BDEs) of 10 fluorinated formates, C_nF_{2n + 1}OC(O)H (n = 1–4) and C_nHF_2nOC(O)H (n = 1–3) have been calculated by using the density functional theory with (RO)B3LYP/6‐311G(d,p). Secondly, from these computed BDEs, the rate constants k_OH of the hydrogen abstraction reaction between the fluorinated formates and OH radicals have been estimated using the formulation proposed by Heicklen (Int. J. Chem. Kinet. 13 , 651, 1981). We modified the formulation proposed by Heicklen in order to relate BDEs to k_OH for formates based on the results of the ab initio studies using standard transition state theory with the G2(MP2) level. Consequently, the k_OH of all the formates considered here are estimated to be around 1.5–4.7 × 10^?14 cm³ molecule^?1 s^?1 at 298 K. Their lifetimes concerning with the decomposition by OH radicals (τ_OH) in atmosphere have been evaluated as 0.4–4.5 years from the estimated k_OH. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 34: 524–530, 2002     

[DBU‐H]+ and H2o as effective catalyst form for 2,3‐dihydropyrido[2,3‐d]pyrimidin‐4(1H)‐ones: A DFT Study

DFT investigations are carried out to explore the effective catalyst forms of DBU and H₂O and the mechanism for the formation of 2,3‐dihydropyrido[2,3‐d]‐pyrimidin‐4(1H)‐ones. Three main pathways are disclosed under unassisted, water‐catalyzed, DBU and water cocatalyzed conditions, which involves concerted nucleophilic addition and H‐transfer, concerted intramolecular cyclization and H‐transfer, and Dimroth rearrangement to form the product. The results indicated that the DBU and water cocatalyzed pathway is the most favored one as compared to the rest two pathways. The water donates one H to DBU and accepts H from 2‐amino‐nicotinonitrile ( 1 ), forming [DBU‐H]⁺‐H₂O as effective catalyst form in the proton migration transition state rather than [DBU‐H]⁺‐OH^?. The hydrogen bond between [DBU‐H]⁺···H₂O··· 1 ^? decreases the activation barrier of the rate‐determining step. Our calculated results open a new insight for the green catalyst model of DBU‐H₂O. © 2015 Wiley Periodicals, Inc.     

Electrocatalytically Active Fe‐(O‐C2)4 Single‐Atom Sites for Efficient Reduction of Nitrogen to Ammonia

Single‐atom catalysts have demonstrated their superiority over other types of catalysts for various reactions. However, the reported nitrogen reduction reaction single‐atom electrocatalysts for the nitrogen reduction reaction exclusively utilize metal–nitrogen or metal–carbon coordination configurations as catalytic active sites. Here, we report a Fe single‐atom electrocatalyst supported on low‐cost, nitrogen‐free lignocellulose‐derived carbon. The extended X‐ray absorption fine structure spectra confirm that Fe atoms are anchored to the support via the Fe‐(O‐C₂)₄ coordination configuration. Density functional theory calculations identify Fe‐(O‐C₂)₄ as the active site for the nitrogen reduction reaction. An electrode consisting of the electrocatalyst loaded on carbon cloth can afford a NH₃ yield rate and faradaic efficiency of 32.1 μg h^?1 mg_cat.^?1 (5350 μg h^?1 mg_Fe^?1) and 29.3 %, respectively. An exceptional NH₃ yield rate of 307.7 μg h^?1 mg_cat.^?1 (51 283 μg h^?1 mg_Fe^?1) with a near record faradaic efficiency of 51.0 % can be achieved with the electrocatalyst immobilized on a glassy carbon electrode.     

The Role of Bi3+ in Promoting and Stabilizing Iron Oxo Clusters in Strong Acid

Metal oxo clusters and metal oxides assemble and precipitate from water in processes that depend on pH, temperature, and concentration. Other parameters that influence the structure, composition, and nuclearity of “molecular” and bulk metal oxides are poorly understood, and have thus not been exploited. Herein, we show that Bi³⁺ drives the formation of aqueous Fe³⁺ clusters, usurping the role of pH. We isolated and structurally characterized a Bi/Fe cluster, Fe₃BiO₂(CCl₃COO)₈(THF)(H₂O)₂, and demonstrated its conversion into an iron Keggin ion capped by six Bi³⁺ irons ( Bi₆Fe₁₃ ). The reaction pathway was documented by X‐ray scattering and mass spectrometry. Opposing the expected trend, increased cluster nuclearity required a pH decrease instead of a pH increase. We attribute this anomalous behavior of Bi/Fe(aq) solutions to Bi³⁺, which drives hydrolysis and condensation. Likewise, Bi³⁺ stabilizes metal oxo clusters and metal oxides in strongly acidic conditions, which is important in applications such as water oxidation for energy storage.     

Generation and characterization of ionic and neutral methylene isothiocyanate by a combined tandem mass spectrometry and computational study

The heterocumulene, methyleneisothiocyanate ion, CH₂?N?C?S⁺ (1a⁺), is generated by the dissociative electron ionization of 2‐mercaptoimidazole. This conclusion follows from tandem mass spectrometry experiments and theoretical calculations at the B3LYP/6‐311G** and G2/G2(MP2) levels. The calculations predict that 1a⁺ is separated by high energy barriers from its isomers CHNCHS (1b⁺), CHNCSH (1d⁺), CNCHSH (1e⁺) and CHNHCS (1f⁺). The low energy metastable ions 1a⁺ dissociate by loss of HCN via the pathway 1a⁺ → 1b⁺ → HCS⁺ + HCN. Neutralization‐reionization experiments confirm the theoretical prediction that the hitherto unknown heterocumulene CH₂?N?C?S ^. is a stable species in the rarefied gas phase. Copyright © 2004 John Wiley & Sons, Ltd.