Zero-point Energy Differences Research Articles

Multi-Component Adsorption Behavior of Hydrogen Isotopes on Zeolite 5A and 13X at 77.4 K

Equilibrium isotherms for the adsorption of H2, HD, HT, D2, DT and T2 on synthetic zeolite type 5A or 13X at 77.4 K are estimated by using a theoretical formula, where the isotopic difference in adsorption depends on the zero-point energy difference between hydrogen isotopes. The formula agrees with the experimental isotherms for H2 and D2 on the zeolites. Adsorption of H2-D2 and H2-HD-D2 mixtures on the same adsorbents is experimentally examined. The experiments are performed using a volumetric apparatus and a quadra-pole-type mass spectrograph. The experimental adsorption behavior of H2, D2 and HD shows agreement of separation factors with results calculated according to the ideal adsorbed solution theory describing multi-component behavior, where the equilibrium isotherms estimated for H2, HD and D2 are used. Based on the theoretical adsorption model, the multi-component behavior of HT, DT and T2 is predicted here.

Assessment of Density Functionals for the High‐Spin/Low‐Spin Energy Difference in the Low‐Spin Iron(II) Tris(2,2′‐bipyridine) Complex

In the iron(II) low-spin complex [Fe(bpy)3]2+, the zero-point energy difference between the 5T2g(t4(2g)e2g) high-spin and the 1A(1g)(t(6)2g) low-spin states, Delta(E)0HL, is estimated to lie in the range of 2500-5000 cm(-1). This estimate is based on the low-temperature dynamics of the high-spin-->low-spin relaxation following the light-induced population of the high-spin state and on the assumption that the bond-length difference between the two states Delta(r)HL is equal to the average value of approximately 0.2 A, as found experimentally for the spin-crossover system. Calculations based on density functional theory (DFT) validate the structural assumption insofar as the low-spin-state optimised geometries are found to be in very good agreement with the experimental X-ray structure of the complex and the predicted high-spin geometries are all very close to one another for a whole series of common GGA (PB86, PW91, PBE, RPBE) and hybrid (B3LYP, B3LYP*, PBE1PBE) functionals. This confirmation of the structural assumption underlying the estimation of Delta(E)0HL from experimental relaxation rate constants permits us to use this value to assess the ability of the density functionals for the calculation of the energy difference between the HS and LS states. Since the different functionals give values from -1000 to 12000 cm(-1), the comparison of the calculated values with the experimental estimate thus provides a stringent criterion for the performance of a given functional. Based on this comparison the RPBE and B3LYP* functionals give the best agreement with experiment.

The effect of zero-point energy differences on the isotope dependence of the formation of ozone: A classical trajectory study

The effect of zero-point energy differences (DeltaZPE) between the possible fragmentation channels of highly excited O(3) complexes on the isotope dependence of the formation of ozone is investigated by means of classical trajectory calculations and a strong-collision model. DeltaZPE is incorporated in the calculations in a phenomenological way by adjusting the potential energy surface in the product channels so that the correct exothermicities and endothermicities are matched. The model contains two parameters, the frequency of stabilizing collisions omega and an energy dependent parameter Delta(damp), which favors the lower energies in the Maxwell-Boltzmann distribution. The stabilization frequency is used to adjust the pressure dependence of the absolute formation rate while Delta(damp) is utilized to control its isotope dependence. The calculations for several isotope combinations of oxygen atoms show a clear dependence of relative formation rates on DeltaZPE. The results are similar to those of Gao and Marcus [J. Chem. Phys. 116, 137 (2002)] obtained within a statistical model. In particular, like in the statistical approach an ad hoc parameter eta approximately 1.14, which effectively reduces the formation rates of the symmetric ABA ozone molecules, has to be introduced in order to obtain good agreement with the measured relative rates of Janssen et al. [Phys. Chem. Chem. Phys. 3, 4718 (2001)]. The temperature dependence of the recombination rate is also addressed.

Photoinduced magnetic memory effect in an iron (II) spin-crossover complex

We report a bidirectional reversible light-induced excited spin state trapping (LIESST) effect featuring an associated memorey effect in an Fe(II) spin-crossover complex [FeL(CN)2]·H2O (where L is a Schiff-base macrocyclic ligand). Depending on the illumination history, bidirectional LIESST processes have been successfully observed that are induced by irradiation with the same two wavelengths. A large zero-point energy difference, strong overlapping spectra of the high-spin and low-spin bands and image internal pressure could account for this photomagnetic phenomenon.

The kinetic method reveals secondary deuterium isotope effects on the proton affinity and gas-phase basicity of glycine and alanine methyl esters

The kinetic method for measuring proton affinities (PA) and gas-phase basicities (GB) was applied to the methyl esters of simple amino acids. The experiments show that the GB and PA values for deuterium labeled glycine methyl ester are indeed greater than that of the corresponding unlabelled glycine methyl ester. The PA of l-Ala-OCD 3 is also slightly greater than that of the unlabeled alanine methyl ester. The secondary isotope effects originate, as shown by density functional theory, in differences in zero-point energies and thermal-energy corrections between H and D-bearing molecules.

The first experimental test of the hypothesis that enzymes have evolved to enhance hydrogen tunneling.

The literature hypothesis that "the optimization of enzyme catalysis may entail the evolutionary implementation of chemical strategies that increase the probability of quantum-mechanical tunneling" is experimentally tested herein for the first time. The system employed is the key to being able to provide this first experimental test of the "enhanced hydrogen tunneling" hypothesis, one that requires a comparison of the three criteria diagnostic of tunneling (vide infra) for the same, or nearly the same, reaction with and without the enzyme. Specifically, studied herein are the adenosylcobalamin (AdoCbl, also known as coenzyme B(12))-dependent diol dehydratase model reactions of (i). H(D)(*) atom abstraction from ethylene glycol-d(0) and ethylene glycol-d(4) solvent by 5'-deoxyadenosyl radical (Ado(*)) and (ii.) the same H(*) abstraction reactions by the 8-methoxy-5'-deoxyadenosyl radical (8-MeOAdo(*)). The Ado(*) and 8-MeOAdo(*) radicals are generated by Co-C thermolysis of their respective precursors, AdoCbl and 8-MeOAdoCbl. Deuterium kinetic isotope effects (KIEs) of the H(*)(D(*)) abstraction reactions from ethylene glycol have been measured over a temperature range of 80-120 degrees C: KIE = 12.4 +/- 1.1 at 80 degrees C for Ado(*) and KIE = 12.5 +/- 0.9 at 80 degrees C for 8-MeOAdo(*) (values ca. 2-fold that of the predicted maximum primary times secondary ground-state zero-point energy (GS-ZPE) KIE of 6.4 at 80 degrees C). From the temperature dependence of the KIEs, zero-point activation energy differences ([E(D) - E(H)]) of 3.0 +/- 0.3 kcal mol(-)(1) for Ado(*) and 2.1 +/- 0.6 kcal mol(-)(1) for 8-MeOAdo(*) have been obtained, both of which are significantly larger than the nontunneling, zero-point energy only maximum of 1.2 kcal mol(-)(1). Pre-exponential factor ratios (A(H)/A(D)) of 0.16 +/- 0.07 for Ado(*) and 0.5 +/- 0.4 for 8-MeOAdo(*) are observed, both of which are significantly less than the 0.7 minimum for nontunneling behavior. The data provide strong evidence for the expected quantum mechanical tunneling in the Ado(*) and 8-MeOAdo(*)-mediated H(*) abstraction reactions from ethylene glycol. More importantly, a comparison of these enzyme-free tunneling data to the same KIE, (E(D) - E(H)) and A(H)/A(D) data for a closely related, Ado(*)-mediated H(*) abstraction reaction from a primary CH(3)- group in AdoCbl-dependent methylmalonyl-CoA mutase shows the enzymic and enzyme-free data sets are identical within experimental error. The Occam's Razor conclusion is that at least this adenosylcobalamin-dependent enzyme has not evolved to enhance quantum mechanical tunneling, at least within the present error bars. Instead, this B(12)-dependent enzyme simply exploits the identical level of quantum mechanical tunneling that is available in the enzyme-free, solution-based H(*) abstraction reaction. The results also require a similar, if not identical, barrier width and height within experimental error for the H(*) abstraction both within, and outside of, the enzyme.

Permutational symmetry, isotope effects, side crossing, and singlet-triplet splitting in anthracene⋅HeN (N=1, 2) clusters

We present quantum-mechanical calculations for the vibrational states of anthracene⋅3HeN and anthracene⋅4HeN (N=1, 2) clusters in the ground (S0) and first excited singlet state (S1) of the anthracene molecule. The anthracene-He potential in the S0 state was described in terms of a sum of Lennard-Jones atom-atom potentials, while the potential in the S1 state also included changes in the dispersive energy and in the repulsive interactions. Variational calculations were carried out for anthracene⋅He1. For anthracene⋅He2, configuration interaction calculations were performed, accounting for the boson and fermion permutation symmetry. For both helium isotopes of the N=1 cluster, tunneling splitting is negligible (<0.01 cm−1), as an appreciable interaction of the densities was only found for highly excited states above the potential-energy barrier of side crossing (for energy eigenvalues ⩾−22 cm−1 below the dissociation limit). The two-boson anthracene⋅4He2 system assumes a singlet A11 ground state due to zero spin of the He4 isotope. Because of the dominance of the two-particle over the one-particle interactions, the two-fermion anthracene⋅3He2 system has a triplet (3B2) vibrational ground state. The singlet-triplet (13B2-11B2) splitting between the two lowest states of the same spatial symmetry of anthracene⋅3He2 was calculated to be 10.5 cm−1. Mass and permutation symmetry effects on the vibrational level structure of anthracene⋅He1 and anthracene⋅He2 were explored for anthracene⋅4He1, anthracene⋅3He1, the two-boson system anthracene⋅4He2, the two-fermion system anthracene⋅3He2 and for the hypothetical fermion system of mass 4. While the isotope effect on the zero-point energies ε0 in the S0 state is Δε0(1)/ε0(1)=[ε0(anthracene⋅3He1)−ε0(anthracene⋅4He1)]/ε0(anthracene⋅4He1)=12%, in accord with the mass effect in the harmonic approximation, the zero-point energy difference between the ground states of the two-fermion anthracene⋅3He2 and the two-boson anthracene⋅4He2 system is Δε0(2)/ε0(2)=[ε0(anthracene⋅3He2)−ε0(anthracene⋅4He2)]/ε0(anthracene⋅4He2)=10%, manifesting a cancellation of mass and permutation symmetry effects. The isotope effect on the red spectral shift δ of the electronic origin for the S0→S1 transition of anthracene⋅He1 is Δδ(1)=δ(anthracene⋅4He1)-δ(anthracene⋅3He1)=0.28 cm−1, while Δδ(2)=δ(anthracene⋅4He2)-δ(anthracene⋅3He2)=−0.50 cm−1, being of the opposite sign than Δδ(1). These features of the spectral shifts as well as the small isotope effects on the energetics and Franck-Condon factors for the S0→S1 vibronic spectra exhibit a delicate balance between differences in mass effects, He-He repulsion, and permutational symmetry of the boson and fermion systems.

Isotope dependence of the lifetime of ozone complexes formed in O + O2collisions

Results of classical trajectory calculations are presented for the lifetime of ozone complexes formed in collisions of O atoms with O2 diatoms. The average trajectory lifetimes for the complexes 16O3, 16O18O2 and 18O16O2 are significantly different. The difference decreases with increasing collision energy and is shown to be due to the difference in the quantum mechanical zero-point energies of reactants and products, which is incorporated in a phenomenological way in the classical calculations.

Inverse Isotope Effects of a Late Transition Metal Olefin Polymerization Catalyst: A DFT Study

An unusual inverse KIE of 0.48 was observed for the catalyst [C5Me5(P(OCH3)3)CoCH2CH2-μ-H]+ in the polymerization of ethylene, which prompted the investigation of one full catalytic cycle by density functional theory calculations at the B3LYP/6-311+G(d,p) level of theory. In agreement with results from previous NMR investigations, the alkyl complex exhibiting a strong β-agostic interaction in the ground state could be identified as the catalyst resting state. This interaction leads to a smaller zero-point energy difference in the ground state and to the quantum mechanically calculated free activation energy difference of 0.6 kcal/mol between the hydrogen and the deuterium isotopomer. The migratory insertion step corresponds to the rate-determining transition state with a total activation barrier of 28.6 kcal/mol. The overall reaction profile is exergonic by −7.0 kcal/mol. The calculated inverse kinetic isotope effect (kH/kD = 0.37) is consistent with the experimental value of 0.48. Additionally the equili...

Pronounced Effects of Zero-Point Energy Difference on Intramolecular Electron Transfer in Asymmetric Mixed-Valence Biferrocenium Cations: Structural, EPR, and57Fe Mössbauer Characteristics

The X-ray structural determinations of a series of asymmetric mixed-valence biferrocenium cations have been determined. The observations of the structural characteristics of the series of mixed-valence biferrocenium cations are also consistent with our Mössbauer studies. The features in the Mössbauer spectra of the asymmetric biferrocenium salts include two doublets, one with a quadrupole splitting of 1.5−2.2 mms-1 (Fe(II) site) and the other with a quadrupole splitting of 0.7−0.5 mms-1 (Fe(III) site). This pattern of two doublets is expected for a mixed-valence biferrocenium cation, which is valence-trapped on the time scale of the Mössbauer technique. Our data indicate that the zero-point energy difference plays a crucial role in determining the nature of the intramolecular electron-transfer rate. The electrochemical measurements and the EPR data are also described.

On the theory of the strange and unconventional isotopic effects in ozone formation

The strange mass-independent isotope effect for the enrichment of ozone and the contrastingly unconventional strong mass-dependent effect of individual reaction rate constants are studied using statistical (RRKM)-based theory with a hindered-rotor transition state. Individual rate constant ratios of recombination reactions and enrichments are calculated. The theory assumes (1) an “η-effect,” which can be interpreted as a small deviation from the statistical density of states for symmetric isotopomers, compared with the asymmetric isotopomers, and (2) weak collisions for deactivation of the vibrationally excited ozone molecules. A partitioning effect controls the recombination rate constant ratios. It arises from small differences in zero-point energies of the two exit channels of dissociation of an asymmetric ozone isotopomer, which are magnified into large differences in numbers of states in the two competing exit channel transition states. In enrichment experiments, in contrast, this partitioning factor disappears exactly [Hathorn and Marcus, J. Chem. Phys. 112, 9497 (2000)], and what remains is the η-effect. Both aspects can be regarded as “symmetry driven” isotopic effects. The two experiments, enrichments and rate constant ratios, thus reveal markedly different theoretical aspects of the phenomena. The calculated low-pressure ozone enrichments, the low-pressure recombination rate constant ratios, the effects of pressure on the enrichment, on the individual recombination rate constant ratios, and on the recombination rate constant are consistent with the experimental data. The temperature dependence of the enrichment and of the recombination rate constant ratios is discussed and a variety of experimental tests are proposed. The negative temperature dependence of the isotopic exchange rate constant for the reaction O+16O18O→18O16O+18O18 at 130 K and 300 K is used for testing or providing information on the nature of a variationally determined hindered-rotor transition state. The theory is not limited to ozone formation but is intended to apply to other reactions where a symmetrical stable or unstable gas phase molecule may be formed.

Origin of the Primary Kinetic Hydrogen Isotope Effects on N-dealkylation from N-alkylamine by Hemoproteins

Abstract The atomic level reaction mechanism for N-dealkylation of N,N-dimethylaniline (PhNMe2) by hemoproteins, in which a kinetic hydrogen isotope effect (KHIE) was observed, was investigated by quantum mechanical theoretical calculations. Using quantum mechanical theory, one can determine the primary KHIE by the difference in zero-point vibrational energies on normal vibrational modes which are related to the reaction coordinate of H (D or T) atom abstraction from a C–H (C–D or C–T) bond. On the basis of this idea, we theoretically determined the intramolecular primary KHIE for two cases of hydrogen atom abstraction in N-dealkylation of PhNMe2; i.e., hydrogen atom abstraction from a neutral state and proton abstraction from a cation radical state. When the intramolecular primary KHIE obtained by theoretical calculation was compared with experimental results of the intramolecular KHIE on N-dealkylation of PhNMe2, which was catalyzed by some hemoproteins, it was found that four experimental values can be interpreted only from the primary KHIE. However, many other experimental values can not be interpreted only from the primary KHIE.

The methylene chloride radical cation and its distonic isomers in the gas phase

Metastable methylene chloride radical cations react spontaneously by loss of a chlorine atom with an apparent kinetic isotope effect of 9 ± 1 and a kinetic energy release of <1 meV. It is difficult to account for an isotope effect of this magnitude, inasmuch as the zero-point vibrational energy differences are very small; the decay of an electronically excited state to the ground state may be involved. The stable molecular ions are very reactive toward collision induced dissociation, and the predominant reactions are collision induced even at very high vacuum. Similar behavior is observed for 1,1-dibromoethane radical cations, whose spontaneous reactions almost exclusively result in loss of 79Br·. The H–Cl–CHCl·+ distonic isomer of the methylene chloride radical cation reacts exclusively by loss of a chlorine atom, presumably after rearrangement to the methylene chloride radical cation. The 35Cl/37Cl ratio observed is 1.27 ± 0.01. The kinetic energy release associated with this reaction is moderate. It did not prove possible to prepare the CH2–Cl–Cl·+ distonic isomer of the methylene chloride radical cation.

Free energy of spin-crossover complexes calculated with density functional methods.

A set of iron(II) complexes that exhibit a temperature-dependent spin-crossover between the low-spin and the high-spin state were studied by density functional methods. The total electronic energy, the zero-point vibrational energy, and the entropy were calculated in order to determine the free energy. While the calculated total energy differences between the two spin states have significant errors, qualitative agreement is achieved for the zero-point vibrational energy differences and the entropy differences.

An intramolecular theory of the mass-independent isotope effect for ozone. II. Numerical implementation at low pressures using a loose transition state

A theory is described for the variation in the rate constants for formation of different ozone isotopomers from oxygen atoms and molecules at low pressures. The theory is implemented using a simplified description which treats the transition state as loose. The two principal features of the theory are a phase space partitioning of the transition states of the two exit channels after formation of the energetic molecule and a small (ca. 15%) decrease in the effective density of states, ρ [a “non-Rice–Ramsperger–Kassel–Marcus (RRKM) effect”], for the symmetric ozone isotopomers [B. C. Hathorn and R. A. Marcus, J. Chem. Phys. 111, 4087 (1999)]. This decrease is in addition to the usual statistical factor of 2 for symmetric molecules. Experimentally, the scrambled systems show a “mass-independent” effect for the enrichments δ (for trace) and E (for heavily) enriched systems, but the ratios of the individual isotopomeric rate constants for unscrambled systems show a strongly mass-dependent behavior. The contrasting behavior of scrambled and unscrambled systems is described theoretically using a “phase space” partitioning factor. In scrambled systems an energetic asymmetric ozone isotopomer is accessed from both entrance channels and, as shown in paper I, the partitioning factor becomes unity throughout. In unscrambled systems, access to an asymmetric ozone is only from one entrance channel, and differences in zero-point energies and other properties, such as the centrifugal potential, determine the relative contributions (the partitioning factors) of the two exit channels to the lifetime of the resulting energetic ozone molecule. They are responsible for the large differences in individual recombination rate constants at low pressures. While the decrease in ρ for symmetric systems is attributed to a small non-RRKM effect η, these calculated results are independent of the exact origin of the decrease. The calculated “mass-independent” enrichments, δ and E, in scrambled systems are relatively insensitive to the transition state (TS), because of the absence of the partitioning factor in their case (for a fixed non-RRKM η). They are compared with the data at room temperature. Calculated results for the ratios of individual isotopomeric rate constants for the strongly mass-independent behavior for unscrambled systems are quite sensitive to the nature of the TS because of the partitioning effect. The current data are available only at room temperature but the loose TS is valid only at low temperatures. Accordingly, the results calculated for the latter at 140 K represent a prediction, for any given η. At present, a comparison of the 140 K results can be made only with room temperature data. They show the same trends as, and are in fortuitous agreement, with the data. Work is in progress on a description appropriate for room temperature.

The effect of electron-phonon interaction in iron-doped III-V cubic semiconductors

A theoretical study of optical absorption and emission measurements of Fe2+ as a substitutional impurity in InP and GaP is presented. A new interpretation of the low-temperature absorption spectrum is proposed based on a weak Jahn-Teller interaction between the electronic excited states and a local gap mode of 5 symmetry. The model also includes the crystal potential, hybridization with the orbitals of the ligands of the host crystal, spin-orbit interaction and a weak dynamic Jahn-Teller coupling of the orbital ground state of Fe2+ with transverse acoustic phonons of 3 symmetry. The theoretical model describes with good accuracy the measured positions and relative intensities of the spectral lines. In addition, the mass dependence of the local gap mode of 5 symmetry reproduces the general features of the fine structures associated with the isotopic shifts of the zero-phonon line and the contribution to the isotopic shifts arising from the difference in zero-point energy between the initial and final states of the transition is evaluated.

Deuterium Fractionation in Protoplanetary Disks

We investigate the chemistry of deuterium-bearing molecules in outer regions of protoplanetary disks, where comets may form. We find that molecules formed in the disk have higher D/H ratios (by which we mean abundance ratios between the singly deuterated species and the normal species) than the elemental D/H ratio in protosolar abundance, which is consistent with observations of recent comets. Despite the higher densities in protoplanetary disks, deuterium fractionation occurs in a similar way as in molecular clouds; because of the differences in zero-point energies and the existence of rapid ion-molecule isotopic exchange reactions, species such as H have high D/H ratios, which propagate to other molecules via gas-phase chemical reactions. Our results depend on a variety of factors such as the ionization rate and the temperature of the disk, which is somewhat uncertain because of possible variations in stellar luminosity and the existence of accretion shocks. In order to reproduce the observed cometary values of DCN/HCN and HDO/H2O, a lower ionization rate (~10-18 s-1) than is standard in molecular clouds is more favorable. The calculated DCN/HCN ratio also depends on whether the products assumed for the grain surface recombination reaction between HCO+ and electrons are dissociative or not.

The vibrational spectra of the boron halides and their molecular complexes: Part 7. Ab initio predictions of the infrared spectra of the complexes of boron trifluoride with some linear nitrogen donors

The infrared spectra of the 1:1 molecular complexes of boron trifluoride with five linear nitrogen-containing electron donors (nitrogen, hydrogen cyanide, cyanogen fluoride, cyanogen and cyanoacetylene) have been computed by means of a series of ab initio molecular orbital calculations, at the second order level of Møller–Plesset perturbation theory, using the 6-31G∗∗ basis set. This work extends the calculations of the structures, energetics and Mulliken atomic charges of the same series of complexes, reported earlier. The vibrational properties, specifically the complex–monomer wavenumber shifts and the B⋯N stretching and BF3 librational wavenumbers and their associated force constants, have been correlated with the computed interaction energies, corrected for basis set superposition error and for zero-point energy difference.

Conformational Composition of Gaseous trans-1,4-Dichlorocyclohexane. Molecular Structures and Energy Differences of the aa and ee Components from Gas-Phase Electron Diffraction and ab Initio Calculations

Electron-diffraction patterns from gaseous trans-1,4-dichlorocyclohexane at a temperature of 105 °C have been analyzed with the help of results from ab initio molecular orbital calculations to yield the structures of the ee and aa forms (equatorially and axially disposed chlorine atoms, respectively) of the molecule and the composition of the mixture. The model of this complicated system was defined in terms of the structure of the ee form, tying many of the parameters of the aa form to those of the ee by parameter differences calculated ab initio. Some of the results (rg/Å, ∠e/deg; 2σ uncertainties) for the ee (aa) forms from the preferred model are 〈r(C−H)〉 = 1.115(4) (1.113); r(C1−C2) = 1.525(6) (1.525); r(C2−C3) = 1.542(13) (1.535); r(C−Cl) = 1.799(3) (1.812); r(Cl···Cl) = 6.309(11) (5.236); ∠(C2C1C6) = 109.9(14) (110.1); ∠(CCCl) = 109.7(4) (109.8); flap (the angle between the planes C2C1C6 and C2C3C5C6) = 51.7(19) (47.2(12)). The mole fraction of the ee form was determined to be 0.46(6). The structural predictions of ab initio calculations were tested by optimizations at several levels, among them HF/6-31G*, MP2/6-311G*, QCISD/6-311+G(2df,p), MPw1PW91/6-311G*, B3P86/6-311G*, and B3P86/6-311+G(2df,p). Parameter values from each of these calculations are in good agreement with experiment, but those from the HF/6-31G* are poorest. The experimental composition is most accurately predicted by the MP2/6-311G* and QCISD/6-311+G(2df,p) calculations from the conformational energy differences ΔEtheor corrected for zero-point energy and entropy differences. The composition of the system is discussed in relation to that of monochlorocyclohexane.

Ab initio MO calculations for the reactions of NH 2 with H 2, H 2O, NH 3 and CH 4: prediction of absolute rate constants and kinetic isotope effects

Ab initio calculations for the NH 2+H 2, NH 2+CH 4, NH 2+NH 3, and NH 2+H 2O reactions are performed using the G2M method. Obtained energy barriers and molecular parameters are used for the TST calculations of absolute rate constants. The G2M method is shown to predict the activation energies within 2–3 kcal/mol. Adjustment of the calculated energy barrier by such an amount usually leads to good agreement between observed and predicted rate constants. Fitted three-parameter expressions for theoretical rate constants of the title reactions are obtained and recommended for practical applications. The calculations show significant isotope effects for the NH 2+RH reactions. The primary isotope effect in the reactions of NH 2 with D 2, CD 4, ND 3, and D 2O is due to the absence of tunnelling and the increase of the quantum mechanical barriers because of differences in zero-point energies and results in the significant (up to 25 times) decrease of the reaction rates, especially, at low temperatures. The secondary isotope effect observed for the ND 2 reactions is opposite; the rate constants become slightly higher (up to two times at 300 K), since the quantum chemical barriers decrease.