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We report full quantum reaction probabilities, computed within the framework of time-independent quantum mechanics using hyperspherical coordinates, for the 15N + 14N14N inelastic and reactive collision processes, restricted to total angular momentum J = 0, for kinetic energies up to 4.5 eV. We take advantage of the nonzero (i = 1) nuclear spin of 14N, leading to the existence of two nuclear spin isomers of 14N14N, namely, ortho- and para-14N14N, to restrict the study to the ortho molecular nitrogen species, with even rotational quantum number j = 0, 2, ... states. Specifically, we start with diatomic reagents ortho-14N14N in the initial rotational state j = 0. A comparison with similar works previously published by other groups using time-dependent wave packet and quasi-classical trajectory methods for the 14N + 14N14N fully symmetric collision is given. We find that reactive processes 15N + 14N14N involving atom exchange do not happen for collision energies less than 2.2 eV. Collisions at energies of around 2.0 eV are most effective for populating reactants' rovibrational states, that is, for inelastic scattering, whereas those at energies close to 5.0 eV yield a newly formed 14N15N isotopologue in a wide variety of excited vibrational levels.
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We report full quantum dynamical calculations for lifetimes of scattering resonances, among which are true metastable states, of the intermediate heavy ozone complex 50O3 * of the 18O + 16O16O reaction, for any value of the total angular momentum quantum number J. We show that computations for nonzero values of J are mandatory in order to properly analyze resonances and time delays, with a view to establish a somewhat comprehensive eigenlife spectrum of the complex O3 *. Calculations have been performed in a given low to moderate energy range, including the interval between zero-point energies (ZPEs) of reagents and product species. Quasi-bound states tend to be more numerous, and eigenlifetimes themselves are seen to increase with J, reaching unusually large values for J = 30. A very dense forest of O3 * species is pictured already for J greater than 20, especially at the highest energies considered, leading to a quasi-continuum of metastable states. On the contrary, they appear as rather sparse and isolated at J = 0 and lower energies, including the domain between 18O16O and 16O16O ZPEs, embedded among many overlapping resonances that turn out to be not long-lived enough to be associated with genuine metastable states.
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Scattering computations, particularly within the realm of molecular physics, have seen an increase in study since the development of powerful quantum methods. These dynamical processes can be analyzed via (among other quantities) the duration of the collision process and the lifetime of the intermediate complex. We use the Smith matrix Q = -iâSdS/dE calculated from the scattering matrix S and its derivative with respect to the total energy. Its real part contains the state-to-state time delays, and its eigenvalues give the lifetimes of the metastable states [ Smith Phys. Rev. 1960 , 118 , 349 - 356 ]. We propose an extension of the Launay HYP3D code [ Launay and Le Dourneuf Chem. Phys. Lett. 1989 , 163 , 178 - 188 ] for molecular reactive scattering and give the full details of the mathematical elements needed to compute the Q matrix from the wave function without numerical differentiation of S. The log-derivative of the wave function and its energy derivative are propagated asymptotically with an extended Johnson-Manolopoulos integration [ Manolopoulos J. Chem. Phys. 1986 , 85 , 6425 - 6429 ], from which the Q matrix is calculated. As a first test of our new code, lifetimes of the metastable intermediate ozone complex O3* have been calculated for the oxygen exchange reaction 18O + 16O16O â 50O3* â 16O18O + 16O, related to the mass-independent fractionation problem of stratospheric ozone. These preliminary results reproduce previously published works limited to zero total angular momentum as benchmark.
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We show, by performing exact time-independent quantum molecular scattering calculations, that the quality of the ground electronic state global potential energy surface appears to be of utmost importance in accurately obtaining even as strongly averaged quantities as kinetic rate constants. The oxygen isotope exchange reaction, 18O + 32O2, motivated by the understanding of a complex long-standing problem of isotopic ozone anomalies in the stratosphere and laboratory experiments, is explored in this context. The thermal rate constant for this key reaction is now in quantitative agreement with all experimental data available to date. A significant recent progress at the frontier of three research domains, advanced electronic structure calculations, ultrasensitive spectroscopy, and quantum scattering calculations, has therefore permitted a breakthrough in the theoretical modeling of this crucial collision process from first principles.
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We report full quantum integral and differential cross sections and rate constants for the 17O + 32O2 reactive process. This constitutes the first quantum scattering study of the 17O16O16O system. We emphasize the comparison with the 18O + 32O2 collision in close connection to the mass-independent fractionation (hereafter referred to as MIF) puzzle for ozone in atmospheric chemistry. We find similar general trends in the cross sections and rate constants for both rare isotopes, but we note some singular behaviors peculiar to the use of 17O isotope, particularly at the lowest collision energies.
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We report full quantum cross sections and rate constants for the (18)O + (36)O2 â (36)O2 + (18)O collision process. This constitutes to the best of our knowledge the first dynamical study of the (18)O(18)O(18)O system, with three identical (18)O oxygen atoms. We emphasize the comparison with the (16)O + (32)O2 collision as this latter presents the exact same features as the one treated here, except the consistent change of mass for all three atoms. We find very similar behaviors in the cross sections, and we confirm that the rates are faster when three identical nuclei are involved. In particular, we cannot dynamically study this system with classical trajectory methods, and we have to include properly the indistinguishability of the three (18)O nuclei; however, we note some slight differences with the (16)O(16)O(16)O benchmark system, and we focus our analysis on their origin.
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The observed abundances of the methylidyne cation, CH(+), in diffuse molecular clouds can be two orders of magnitude higher than the prediction of the standard gas-phase models which, in turn, predict rather well the abundances of neutral CH. It is therefore necessary to investigate all the possible formation and destruction processes of CH(+) in the interstellar medium with the most abundant species H, H2, and e(-). In this work, we address the destruction process of CH(+) by hydrogen abstraction. We report a new calculation of the low temperature rate coefficients for the abstraction reaction, using accurate time-independent quantum scattering and a new high-level ab initio global potential energy surface including a realistic model of the long-range interaction between the reactants H and CH(+). The calculated thermal rate coefficient is in good agreement with the experimental data in the range 50 K-800 K. However, at lower temperatures, the experimental rate coefficient takes exceedingly small values which are not reproduced by the calculated rate coefficient. Instead, the latter rate coefficient is close to the one given by the Langevin capture model, as expected for a reaction involving an ion and a neutral species. Several recent theoretical works have reported a seemingly good agreement with the experiment below 50 K, but an analysis of these works show that they are based on potential energy surfaces with incorrect long-range behavior. The experimental results were explained by a loss of reactivity of the lowest rotational states of the reactant; however, the quantum scattering calculations show the opposite, namely, a reactivity enhancement with rotational excitation.
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We report extensive, full quantum-mechanical calculations for the (16)O + (16)O(16)O â (16)O(16)O + (16)O collisions, for both inelastic and atom exchange processes, using a time-independent method based on hyperspherical coordinates. The rates obtained in the present study are much larger than the previously reported ones for this system. The discrepancy is attributed to a huge symmetry effect that was missing in the studies so far. This effect differs from the well-known isotope effect. Importance of this quantum effect is further confirmed by comparison with results for the (16)O + (18)O(18)O â (16)O(18)O + (18)O, exchange reaction.
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The D(+) + H2 reaction is investigated by means of a time independent quantum mechanical (TIQM) and statistical quantum mechanical (SQM) methods. Differential cross sections and product rotational distributions obtained with these two theoretical approaches for collision energies between 1 meV and 0.1 eV are compared to analyze the dynamics of the process. The agreement observed between the TIQM differential cross sections and the SQM predictions as the energy increases revealed the role played by the complex-forming mechanism. The importance of a good description of the asymptotic regions is also investigated by calculating rate constants for the title reaction at low temperature.
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The D(+) +H2(v = 0, j = 0, 1) â HD+H(+) reaction has been investigated at the low energy regime by means of a statistical quantum mechanical (SQM) method. Reaction probabilities and integral cross sections (ICSs) between a collisional energy of 10(-4) eV and 0.1 eV have been calculated and compared with previously reported results of a time independent quantum mechanical (TIQM) approach. The TIQM results exhibit a dense profile with numerous narrow resonances down to Ec ~ 10(-2) eV and for the case of H2(v = 0, j = 0) a prominent peak is found at ~2.5 × 10(-4) eV. The analysis at the state-to-state level reveals that this feature is originated in those processes which yield the formation of rotationally excited HD(v' = 0, j' > 0). The statistical predictions reproduce reasonably well the overall behaviour of the TIQM ICSs at the larger energy range (Ec ≥ 10(-3) eV). Thermal rate constants are in qualitative agreement for the whole range of temperatures investigated in this work, 10-100 K, although the SQM values remain above the TIQM results for both initial H2 rotational states, j = 0 and 1. The enlargement of the asymptotic region for the statistical approach is crucial for a proper description at low energies. In particular, we find that the SQM method leads to rate coefficients in terms of the energy in perfect agreement with previously reported measurements if the maximum distance at which the calculation is performed increases noticeably with respect to the value employed to reproduce the TIQM results.
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We report fully-quantum time-independent calculations of cross sections and rate coefficients for the collisional (de)excitation of H(2) by H. Our calculations are based on the H(3) global potential energy surface of Mielke et al. [J. Chem. Phys. 116, 4142 (2002)]. The reactive hydrogen exchange channels are taken into account. We show that the ortho-para and para-ortho conversion of H(2) are significant processes at temperatures above ~300 K and for the last process we provide the first comparison with available experimental rate coefficients between 300 and 444 K. The good agreement between theory and experiment is a new illustration of our detailed understanding of the simplest chemical reaction. The importance of the ortho-para-H(2) conversion by hydrogen exchange in astrophysics is discussed.
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More than 100 reactions between stable molecules and free radicals have been shown to remain rapid at low temperatures. In contrast, reactions between two unstable radicals have received much less attention due to the added complexity of producing and measuring excess radical concentrations. We performed kinetic experiments on the barrierless N((4)S) + OH((2)Π) â H((2)S) + NO((2)Π) reaction in a supersonic flow (Laval nozzle) reactor. We used a microwave-discharge method to generate atomic nitrogen and a relative-rate method to follow the reaction kinetics. The measured rates agreed well with the results of exact and approximate quantum mechanical calculations. These results also provide insight into the gas-phase formation mechanisms of molecular nitrogen in interstellar clouds.
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We present accurate quantum calculations of state-to-state cross sections for the N + OH â NO + H reaction performed on the ground (3)A'' global adiabatic potential energy surface of Guadagnini et al. [J. Chem. Phys. 102, 774 (1995)]. The OH reagent is initially considered in the rovibrational state ν = 0, j = 0 and wave packet calculations have been performed for selected total angular momentum, J = 0, 10, 20, 30, 40,...,120. Converged integral state-to-state cross sections are obtained up to a collision energy of 0.5 eV, considering a maximum number of eight helicity components, Ω = 0,...,7. Reaction probabilities for J = 0 obtained as a function of collision energy, using the wave packet method, are compared with the recently published time-independent quantum mechanical one. Total reaction cross sections, state-specific rate constants, opacity functions, and product state-resolved integral cross-sections have been obtained by means of the wave packet method for several collision energies and compared with recent quasi-classical trajectory results obtained with the same potential energy surface. The rate constant for OH(ν = 0, j = 0) is in good agreement with the previous theoretical values, but in disagreement with the experimental data, except at 300 K.
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The Renner-Teller (RT) coupled-channel dynamics for the C((1)D)+H(2)(X(1)Σ(g) (+))âCH(X(2)Π)+H((2)S) reaction has been investigated for the first time, considering the first two singlet states ãÌ(1)A' and b(1)A'' of CH(2) dissociating into the products and RT couplings, evaluated through the ab initio matrix elements of the electronic angular momentum. We have obtained initial-state-resolved probabilities, cross sections and thermal rate constants via the real wavepacket method for both coupled electronic states. In contrast to the N((2)D)+H(2)(X(1)Σ(g)(+)) system, RT effects tend to reduce probabilities, cross sections, and rate constants in the low energy range compared to Born-Oppenheimer (BO) ones, due to the presence of a repulsive RT barrier in the effective potentials and to long-lived resonances. Furthermore, contrary to BO results, the rate constants have a positive temperature dependence in the 100-400 K range. The two-state RT rate constant at 300 K, lower than the BO one, remains inside the error bars of the experimental value.
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First quasi-classical trajectory calculations have been carried out for the S((3)P) + OH(X (2)Π) â SO(X (3)Σ(-)) + H((2)S) reaction on an ab initio global potential energy surface for the ground electronic state, X (2)A'', of HSO. Cross sections, computed for collision energies up to 1 eV, show no energy threshold and decrease with the increasing collision energy. Rate constants have been calculated in the 5-500 K temperature range. The thermal rate constant is in good agreement with approximate quantum results, while a disagreement is found at 298 K with the experimental data. Product energy distributions have also been reported at four collision energies from 0.001 to 0.5 eV. The shapes of the rovibrational and angular distributions suggest the formation of an intermediate complex that is more and more long-lived as the collision energy increases.
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First accurate quantum mechanical scattering calculations have been carried out for the S((3)P)+OH(X (2)Π)âSO(X (3)Σ(-))+H((2)S) reaction using a recent ab initio potential energy surface for the ground electronic state, X (2)A("), of HSO. Total and state-to-state reaction probabilities for a total angular momentum J=0 have been determined for collision energies up to 0.5 eV. A rate constant has been calculated by means of the J-shifting approach in the 10-400 K temperature range. Vibrational and rotational product distributions show no specific behavior and are consistent with a mixture of direct and indirect reaction mechanisms.
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Faced with the lack of experimental data on the C(3P) + OH(X2Pi) --> CO(X1Sigma+) + H(2S) reaction, we propose here to compare rate constant values and their behavior with temperature following various dynamical models and, in particular, to check the sensivity of these quantities with the long-range part of the potential energy surface. For that, we have evaluated the C + OH rate constant using the quasiclassical trajectory (QCT) method, the adiabatic capture centrifugal sudden approximation (ACCSA), and the mean potential capture theory (MPCT) based on a full ab initio potential energy surface fitted with q12,5 kernels or on a perturbative multipolar expansion (MPE) potential including the monomer spin orbit splittings (MPE-SO) or not. Despite the various approximations involved in the different methods and PESs, an excellent agreement is obtained in a subset of three models: the ACCSA method with PME-SO or ab initio PESs and the QCT method with the latter PES. This suggests that the reaction takes place once the system enters the deep valley of products. In that case, the errors due to these approximate methods and PESs are small and, consequently, the rate constants are accurately calculated. Furthermore, these findings provide evidence of preponderance of the entrance channel in the reactivity of this system.
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We present the Born-Oppenheimer, quantum dynamics of the reactions C((1)D)+HD and C((1)D)+n-D(2) on the uncoupled potential energy surfaces ã (1)A' and b (1)A", considering the Coriolis interactions and the nuclear-spin statistics. Using the real wavepacket method, we obtain initial-state-resolved probabilities, cross sections, isotopic branching ratios, and rate constants. Similarly to the C+n-H(2) reaction, the probabilities present many ã (1)A' or few b (1)A" sharp resonances, and the cross sections are very large at small collision energies and decrease at higher energies. At any initial condition, the C+HD reaction gives preferentially the CD+H products. Thermal cross sections, isotopic branching ratios, and rate constant k vary slightly with temperature and agree very well with the experimental values. At 300 K, we obtain for the various products k(CH+H)=(2.45+/-0.08) x 10(-10), k(CD+H)=(1.19+/-0.04) x 10(-10), k(CH+D)=(0.71+/-0.02) x 10(-10), k(CD+D)=(1.59+/-0.05) x 10(-10) cm(3) s(-1), and k(CD+H)/k(CH+D)=1.68+/-0.01. The b (1)A" contribution to cross sections and rate constants is always large, up to a maximum value of 62% for a rotationally resolved C+D(2) rate constant. The upper b (1)A" state is thus quite important in the C((1)D) collision with H(2) and its deuterated isotopes, as the agreement between theory and experiment shows.
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A detailed quasiclassical trajectory on the N + OH(v=0, j=0,1,5,10) --> NO + H reaction is reported at four collision energies from 0.01 to 0.5 eV. The vibrational distributions which are statistical and the angular distributions, which present a forward/backward symmetry, are consistent with the formation of a long-lived intermediate complex. Our results show globally a weak dependence of the angular and rovibrational distributions on the rotational excitation of OH, but a more pronounced effect of the collision energy.
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We present the Born-Oppenheimer coupled-channel dynamics of the reaction (12)C((1)D)+(1)H(2)(X (1)Sigma(g) (+))-->CH(X (2)Pi)+H((2)S), considering the uncoupled CH(2) states ã (1)A(1) and b (1)B(1), the permutation-inversion symmetry, and Coriolis interactions. Using accurate MRCI potential energy surfaces (PESs), we obtain initial-state-resolved reaction probabilities, cross sections, and rate constants through the time-dependent, real wavepacket (WP) and flux methods, taking into account the proton-spin statistics for both electronic species. Comparing results on both PESs, we point out the role of the b (1)B(1) upper state on the initial-state-resolved dynamics and on the thermal kinetic rate. WP probabilities at J=0 and cross sections at E(col)=0.080 eV agree quite well with quantum-mechanical time-independent findings. Probabilities and WP snapshots show the different reaction mechanisms on the PESs, i.e., an ã (1)A(1) indirect perpendicular insertion and a b (1)B(1) direct sideways collision, associated with many and few sharp resonances, respectively. All cross sections are very large at low E(col), decrease at high energies, and that of the lowest reactant state presents some weak resonances. As the temperature increases from 100 to 400 K, the ã (1)A(1) rate constant increases slightly from 1.37x10(-10) to 1.43x10(-10) cm(3) s(-1), whereas the b (1)B(1) one decreases from 1.30x10(-10) to 0.98x10(-10) cm(3) s(-1). In this temperature range, the b (1)B(1) contribution to the total rate constant thus decreases from 49% to 41%. At 300 K, the WP and experimental rates are equal to (2.45+/-0.08)x10(-10) and (2.0+/-0.6)x10(-10) cm(3) s(-1), respectively.