Kinetics of the reaction of the heaviest hydrogen atom with H2, the 4Heμ + H2 → 4HeμH + H reaction: experiments, accurate quantal calculations, and variational transition state theory, including kinetic isotope effects for a factor of 36.1 in isotopic mass

The neutral muonic helium atom (4)Heμ, in which one of the electrons of He is replaced by a negative muon, may be effectively regarded as the heaviest isotope of the hydrogen atom, with a mass of 4.115 amu. We report details of the first muon spin rotation (μSR) measurements of the chemical reaction rate constant of (4)Heμ with molecular hydrogen, (4)Heμ + H(2) → (4)HeμH + H, at temperatures of 295.5, 405, and 500 K, as well as a μSR measurement of the hyperfine coupling constant of muonic He at high pressures. The experimental rate constants, k(Heμ), are compared with the predictions of accurate quantum mechanical (QM) dynamics calculations carried out on a well converged Born-Huang (BH) potential energy surface, based on complete configuration interaction calculations and including a Born-Oppenheimer diagonal correction. At the two highest measured temperatures the agreement between the quantum theory and experiment is good to excellent, well within experimental uncertainties that include an estimate of possible systematic error, but at 295.5 K the quantum calculations for k(Heμ) are below the experimental value by 2.1 times the experimental uncertainty estimates. Possible reasons for this discrepancy are discussed. Variational transition state theory calculations with multidimensional tunneling have also been carried out for k(Heμ) on the BH surface, and they agree with the accurate QM rate constants to within 30% over a wider temperature range of 200-1000 K. Comparisons between theory and experiment are also presented for the rate constants for both the D + H(2) and Mu + H(2) reactions in a novel study of kinetic isotope effects for the H + H(2) reactions over a factor of 36.1 in isotopic mass of the atomic reactant.     

Radiative association of He+ with H2 at temperatures below 100 K

The paper presents a theoretical study of the low-energy dynamics of radiative association processes in the He+ + H2 collision system. Formation of the triatomic HeH2(+) ion in its bound rotation-vibration states on the potential-energy surfaces of the ground and of the first excited electronic states is investigated. Close-coupling calculations are performed to determine detailed state-to-state characteristics (bound <-- free transition rates, radiative and dissociative widths of resonances) as well as temperature-average characteristics (rate constants, photon emission spectra) of the two-state (X <-- A) reaction He+(2S) + H2(X1sigma(g)+) --> HeH2(+)(X2A') + h nu and of the single-state (A <-- A) reaction He+(2S) + H2(X1sigma(g)+) --> HeH2(+)(A2A') + h nu. The potential-energy surfaces of the X- and A-electronic states of HeH2(+) and the dipole moment surfaces determined ab initio in an earlier work [Kraemer, Spirko, and Bludsky, Chem. Phys. 276, 225 (2002)] are used in the calculations. The rate constants k(T) as functions of temperature are calculated for the temperature interval 1 < or = T < or = 100 K. The maximum k(T) values are predicted as 3.3 x 10(-15) s(-1) cm3 for the X <-- A reaction and 2.3 x 10(-20) s(-1) cm3 for the A <-- A reaction at temperatures around 2 K. Rotationally predissociating states of the He+-H2 complex, correlating with the upsilon = 0, j = 2 state of free H2, are found to play a crucial role in the dynamics of the association reactions at low temperatures; their contribution to the k(T) function of the X <-- A reaction at T < 30 K is estimated as larger than 80%. The calculated partial rate constants and emission spectra show that in the X <-- A reaction the HeH2(+)(X) ion is formed in its highly excited vibrational states. This is in contrast with the vibrational state population of the ion when formed via the (X <-- X) reaction He(1S) + H2(+)(X2sigma(g)+) --> HeH2(+)(X2A') + h nu.     

Spectroscopic and spin-orbit calculations on the SO+ radical cation

Highly correlated ab initio methods were used in order to generate the potential-energy curves of the SO+ electronic states correlating to S+(4Su)+O(3Pg) and S+(2Du)+O(3Pg). These curves were used for deducing accurate spectroscopic properties for these electronic states. Our calculations predict the existence of a 2Phi state lying close in energy to the well-characterized b 4Sigma- state and several weakly bound quartet and doublet states located in the 6-9 eV internal energy range not identified yet. The spin-orbit integrals between these electronic states were evaluated using these highly correlated wave functions, allowing the discussion of the metastability and the predissociation processes forming S+ +O in their electronic ground states. Multistep spin-orbit-induced predissociation pathways are suggested. More specifically, the experimentally determined dissociative potential-energy curve [H. Bissantz et al., Z. Phys. D 22, 727 (1992)] proposed to explain the rapid SO+(b 4Sigma-, v> or =13)-->S+(4Su)+O(3Pg) reaction is found to coincide with the 2 4Pi potential-energy curve for short internuclear distances and with the repulsive 1 6Pi state for longer internuclear separations.     

Combined valence bond-molecular mechanics potential-energy surface and direct dynamics study of rate constants and kinetic isotope effects for the H + C2H6 reaction

This article presents a multifaceted study of the reaction H+C(2)H(6)-->H(2)+C(2)H(5) and three of its deuterium-substituted isotopologs. First we present high-level electronic structure calculations by the W1, G3SX, MCG3-MPWB, CBS-APNO, and MC-QCISD/3 methods that lead to a best estimate of the barrier height of 11.8+/-0.5 kcal/mol. Then we obtain a specific reaction parameter for the MPW density functional in order that it reproduces the best estimate of the barrier height; this yields the MPW54 functional. The MPW54 functional, as well as the MPW60 functional that was previously parametrized for the H+CH(4) reaction, is used with canonical variational theory with small-curvature tunneling to calculate the rate constants for all four ethane reactions from 200 to 2000 K. The final MPW54 calculations are based on curvilinear-coordinate generalized-normal-mode analysis along the reaction path, and they include scaled frequencies and an anharmonic C-C bond torsion. They agree with experiment within 31% for 467-826 K except for a 38% deviation at 748 K; the results for the isotopologs are predictions since these rate constants have never been measured. The kinetic isotope effects (KIEs) are analyzed to reveal the contributions from subsets of vibrational partition functions and from tunneling, which conspire to yield a nonmonotonic temperature dependence for one of the KIEs. The stationary points and reaction-path potential of the MPW54 potential-energy surface are then used to parametrize a new kind of analytical potential-energy surface that combines a semiempirical valence bond formalism for the reactive part of the molecule with a standard molecular mechanics force field for the rest; this may be considered to be either an extension of molecular mechanics to treat a reactive potential-energy surface or a new kind of combined quantum-mechanical/molecular mechanical (QM/MM) method in which the QM part is semiempirical valence bond theory; that is, the new potential-energy surface is a combined valence bond molecular mechanics (CVBMM) surface. Rate constants calculated with the CVBMM surface agree with the MPW54 rate constants within 12% for 534-2000 K and within 23% for 200-491 K. The full CVBMM potential-energy surface is now available for use in variety of dynamics calculations, and it provides a prototype for developing CVBMM potential-energy surfaces for other reactions.     

Isotopic replacement in ionic systems: the 4He2+ + 3He-->3He 4He+ + 4He reaction

Full quantum dynamics calculations have been carried out for the ionic reaction (4)He(2) (+)+(3)He and state-to-state reactive probabilities have been obtained using both time-dependent and time-independent approaches. An accurate ab initio potential-energy surface has been employed for the present quantum dynamics and the two sets of results are shown to be in agreement with each other. The results for zero total angular momentum suggest a marked presence of atom exchange (isotopic replacement) reaction with probabilities as high as 60%. The reaction probabilities are only weakly dependent on the initial vibrational state of the reactants, while they are slightly more sensitive to the degree of rotational excitation. A brief discussion of the results for selected higher total angular momentum values is also presented, while the l-shifting approximation [S. K. Gray et al., Phys. Chem. Chem. Phys. 1, 1141 (1999)] has been used to provide estimates of the total reaction rates for the title process. Such rates are found to be large enough to possibly become experimentally accessible.     

Theoretical rate coefficients for the exchange reaction OH + D--> OD + H

In this work quasiclassical trajectory calculations were carried out to determine directly the rate coefficients for the isotopic exchange reaction, OH + D-->OD + H, using a potential-energy surface that carefully accounts for the long-range interactions. The calculated thermal rate coefficients are in good agreement with the experimental results.     

On the existence and lifetimes of Cu2+ complexes with water, ammonia, and hydrogen cyanide

High-level ab initio calculations have been carried out to evaluate the lifetimes of complexes formed by the association of Cu2+ to water, ammonia, and hydrogen cyanide. The corresponding binding energies were evaluated at the CCSD(T)6-311+G(3df,2pd) level of theory. The potential-energy curves corresponding to their dissociation into Cu+ + L+ (L=H2O, NH3, and HCN) were obtained at the CCSD(T)6-311+G(3df,2p) level on BHLYP6-311+G(d,p) optimized geometries. Lifetimes were calculated using the exterior complex scaling and the semiclassical WKB methods. Although all the complexes investigated are thermodynamically unstable with respect to their dissociation into Cu+ + L+ in a typical Coulomb explosion, the activation barrier is high enough to accommodate several vibrational resonances, with very large lifetimes. As a matter of fact, if the three complexes are produced in the lowest vibrational levels, they behave as totally bound (with almost infinite lifetime) species.     

Sensitivity of the H + CH3 → CH4 recombination rate constant to the shape of the CH stretching potential

Using a potential-energy surface obtained in part from ab initio calculations, the H + CH₃ → CH₄ bimolecular rate constant at T = 300 K is determined from a Monte Carlo classical trajectory study. Representing the CH stretching potential with a standard Morse function instead ofthe ab initio curve increases the calculated rate constant by an order of magnitude. The experimental recombination rate constant is intermediate of the rate constants calculated with the Morse and ab initio stretching potentials.Two properties of the H + CH₃ α CH₄ potential-energy surface which significantly affect the recombination rate constant are the shape of the CH stretching potential and the attenuation of the H₃CH bending frequencies. Ab initio calculations with a hierarchy of basis sets and treatment of electron correlation indicate the latter is properly described [13]. The exact shape of the CH stretching potential is not delineated by the ab initio calculations, since the ab initio calculations are not converged for bond lengths of 2.0–3.0 Å [12]. However, the form of this stretching potential deduced from the highest-level ab initio calculations, and fit analytically by eq. (2), is significantly different from a Morse function. The experimental recombination rate constant is intermediate of the rate constants calculated with the Morse and ab initio CH stretching potentials. This indicates that the actual CH potential energy curve lies between the Morse and ab initio curves. This is consistent with the finding that potential energy curves for diatomics are not well described by a Morse function [12].     

Real wave packet and quasiclassical trajectory studies of the H+ + LiH reaction

Time-dependent real wave packet (RWP) and quasiclassical trajectory (QCT) calculations have been carried out to study the H(+) + LiH reaction on the ab initio potential-energy surface of Martinazzo et al. [J. Chem. Phys., 2003, 119, 11241]. Total initial state-selected and final state-resolved reaction probabilities for the two possible reaction channels, H(2)(+) + Li and LiH + H(+), have been calculated for total angular momentum J=0 at a broad range of collision energies. Integral cross sections and thermal rate coefficients have been calculated using the QCT method and from the corresponding J=0 RWP reaction probabilities by means of a capture model. The calculated thermal rate coefficients are found to be nearly independent of temperature in the 100-500 K interval with a value of approximately 10(-9) cm(3) s(-1), which is in good agreement with estimates used in evolutionary models of early-Universe lithium chemistry. The RWP results are found to be in good agreement overall with the corresponding QCT calculations.     

Experimental and modeling study of the ion-molecule association reaction H3O+ + H2O (+M) --> H5O2(+) (+M)

Experimental results for the rate of the association reaction H3O+ + H2O (+M) --> H5O2(+) (+M) obtained with the Cinetique de Reactions en Ecoulement Supersonique Uniforme flow technique are reported. The reaction was studied in the bath gases M=He and N2, over the temperature range of 23-170 K, and at pressures between 0.16 and 3.1 mbar. At the highest temperatures, the reaction was found to be close to the limiting low-pressure termolecular range, whereas the limiting high-pressure bimolecular range was approached at the lowest temperatures. Whereas the low-pressure rate coefficients can satisfactorily be reproduced by standard unimolecular rate theory, the derived high-pressure rate coefficients in the bath gas He at the lowest temperatures are found to be markedly smaller than given by simple ion-dipole capture theory. This result differs from previous observations on the related reaction NH4(+) + NH3 (+M) --> N2H7(+) (+M). This observation is tentatively attributed to more pronounced contributions of the valence part of the potential-energy surface to the reaction in H5O2(+) than in N2H7(+). Falloff curves of the reaction H3O+ + H2O (+M) --> H5O2(+) (+M) are constructed over wide ranges of conditions and represented in compact analytical form.     

Ab initio global potential-energy surface for H5(+) --> H3(+) + H2

An accurate global potential-energy surface (PES) is reported for H5(+) based on more than 100,000 CCSD(T)/aug-cc-pVTZ ab initio energies. This PES has full permutational symmetry with respect to interchange of H atoms and dissociates to H3(+) and H2. Ten known stationary points of H5(+) are characterized and compared to previous ab initio calculations. Quantum diffusion Monte Carlo calculations are performed on the PES to obtain the zero-point energy of H5(+) and the anharmonic dissociation energy (D0) of H5(+) --> H3(+) + H2. The rigorous zero-point state of H4D+ is also calculated and discussed within the context of a strictly classical approach to obtain the branching ratio of the reaction H4D+ --> H3(+) + HD and H2D+ + H2. Such an approach is taken using the PES and critiqued based on the properties of the quantum zero-point state. Finally, a simple procedure for adding the long range-interaction energy is described.     

Theoretical study of the dynamics of the H+CH4 and H+C2H6 reactions using a specific-reaction-parameter semiempirical Hamiltonian

We present a theoretical study of the reactions of hydrogen atoms with methane and ethane molecules and isotopomers. High-accuracy electronic-structure calculations have been carried out to characterize representative regions of the potential-energy surface (PES) of various reaction pathways, including H abstraction and H exchange. These ab initio calculations have been subsequently employed to derive an improved set of parameters for the modified symmetrically-orthogonalized intermediate neglect of differential overlap (MSINDO) semiempirical Hamiltonian, which are specific to the H+alkane family of reactions. The specific-reaction-parameter (SRP) Hamiltonian has then been used to perform a quasiclassical-trajectory study of both the H+CH4 and H+C2H6 reactions. The calculated values of dynamics properties of the H+CH4-->H2+CH3 reaction and isotopologues, including alkyl product speed distributions, diatomic product internal-state distributions, and cross sections, are generally in good agreement with experiment and with the results provided by the ZBB3 PES [Z. Xie et al., J. Chem. Phys. 125, 133120 (2006)]. The results of trajectories propagated with the SRP Hamiltonian for the H+C2H6-->H2+C2H5 reaction also agree with experiment. The level of agreement between the results calculated with the SRP Hamiltonian and experiment in both the H+methane and H+ethane reactions indicates that semiempirical Hamiltonians can be improved for not only a specific reaction but also a family of reactions.     

Theoretical study of isomerization and decomposition of propenal

We investigated the dynamics of isomerization and multi-channel dissociation of propenal (CH(2)CHCHO), methyl ketene (CH(3)CHCO), hydroxyl propadiene (CH(2)CH(2)CHOH), and hydroxyl cyclopropene (cyclic-C(3)H(3)-OH) in the ground potential-energy surface using quantum-chemical calculations. Optimized structures and vibrational frequencies of molecular species were computed with method B3LYP∕6-311G(d,p). Total energies of molecules at optimized structures were computed at the CCSD(T)∕6-311+G(3df,2p) level of theory. We established the potential-energy surface for decomposition to CH(2)CHCO + H, CH(2)CH + HCO, CH(2)CH(2)∕CH(3)CH + CO, CHCH∕CH(2)C + H(2)CO, CHCCHO∕CH(2)CCO + H(2), CHCH + CO + H(2), CH(3) + HCCO, CH(2)CCH + OH, and CH(2)CC∕cyclic-C(3)H(2) + H(2)O. Microcanonical rate coefficients of various reactions of trans-propenal with internal energies 148 and 182 kcal mol(-1) were calculated using Rice-Ramsperger-Kassel-Marcus and Variational transition state theories. Product branching ratios were derivable using numerical integration of kinetic master equations and the steady-state approximation. The concerted three-body dissociation of trans-propenal to fragments C(2)H(2) + CO + H(2) is the prevailing channel in present calculations. In contrast, C(3)H(3)O + H, C(2)H(3) + HCO and C(2)H(4) + CO were identified as major channels in the photolysis of trans-propenal. The discrepancy between calculations and experiments in product branching ratios indicates that the three major photodissociation channels occur mainly on an excited potential-energy surface whereas the other channels occur mainly on the ground potential-energy surface. This work provides profound insight in the mechanisms of isomerization and multichannel dissociation of the system C(3)H(4)O.     

Quasiclassical trajectory study of the Cl + Hl → HCl + I reaction

Monte Carlo quasiclassical trajectory calculations have been carried out for the reaction Cl + Hl → HCl + I for 300, 1000, and 2000 K. A semi-empirical potential-energy surface (London equation) was obtained by “transfering” parameters from surfaces computed for other reaction systems. The computed results are in general accord with experimental measurements. Thermal rate coefficients, differential scattering cross sections, and product vibrational and rotational distributions were computed for the three temperatures. Angular scattering distributions are in agreement with experiment only at elevated temperatures.     

Reaction OH + OH studied over the 298-834 K temperature and 1-100 bar pressure ranges

Self-reaction of hydroxyl radicals, OH + OH → H(2)O + O (1a) and OH + OH → H(2)O(2) (1b), was studied using pulsed laser photolysis coupled to transient UV-vis absorption spectroscopy over the 298-834 K temperature and 1-100 bar pressure ranges (bath gas He). A heatable high-pressure flow reactor was employed. Hydroxyl radicals were prepared using reaction of electronically excited oxygen atoms, O((1)D), produced in photolysis of N(2)O at 193 nm, with H(2)O. The temporal behavior of OH radicals was monitored via transient absorption of light from a dc discharge in H(2)O/Ar low-pressure resonance lamp at ca. 308 nm. The absolute intensity of the photolysis light was determined by accurate in situ actinometry based on the ozone formation in the presence of molecular oxygen. The results of this study combined with the literature data indicate that the rate constant of reaction 1a, associated with the pressure independent component, decreases with temperature within the temperature range 298-414 K and increases above 555 K. The pressure dependent rate constant for (1b) was parametrized using the Troe expression as k(1b,inf) = (2.4 ± 0.6) × 10(-11)(T/300)(-0.5) cm(3) molecule(-1) s(-1), k(1b,0) = [He] (9.0 ± 2.2) × 10(-31)(T/300)(-3.5±0.5) cm(3) molecule(-1) s(-1), F(c) = 0.37.     

Theoretical determination of highly excited states of K2 correlated adiabatically above K4p + K4p

The electronic structure of the K(2) molecule is revisited to describe the 36 highly excited states dissociating into the three limits K(4s) + K(4f), K(4s) + K(6p), and K(4s) + K(5d), which have not yet been investigated theoretically. Potential energy curves and spectroscopic constants are (re)displayed for the 98(1,3)Lambda(g,u) ((+,-)) molecular states correlated adiabatically to the limits up to K(4s) + K(5d). For the 10 states dissociating adiabatically into K(4p) + K(4p) and limits above for which experimental data are available, averaged errors of present results are found to be Delta R(e) = 0.07a(0), Delta T(e) = 50 cm(-1), Delta omega(e) = 0.8 cm(-1) and Delta D(e) = 60 cm(-1). Full energy data are available at the following address http://lasim.univ-lyon1.fr/allouche/k2.html     

Ab initio and direct quasiclassical-trajectory study of the F+CH4-->HF+CH3 reaction

We present an electronic structure and dynamics study of the F+CH4-->HF+CH3 reaction. CCSD(T)/aug-cc-pVDZ geometry optimizations, harmonic-frequency, and energy calculations indicate that the potential-energy surface is remarkably isotropic near the transition state. In addition, while the saddle-point F-H-C angle is 180 degrees using MP2 methods, CCSD(T) geometry optimizations predict a bent transition state, with a 153 degrees F-H-C angle. We use these high-quality ab initio data to reparametrize the parameter-model 3 (PM3) semiempirical Hamiltonian so that calculations with the improved Hamiltonian and employing restricted open-shell wave functions agree with the higher accuracy data. Using this specific-reaction-parameter PM3 semiempirical Hamiltonian (SRP-PM3), we investigate the reaction dynamics by propagating quasiclassical trajectories. The results of our calculations using the SRP-PM3 Hamiltonian are compared with experiments and with the estimates of two recently reported potential-energy surfaces. The trajectory calculations using the SRP-PM3 Hamiltonian reproduce quantitatively the measured HF vibrational distributions. The calculations also agree with the experimental HF rotational distributions and capture the essential features of the excitation function. The results of the SRP semiempirical Hamiltonian developed here clearly improve over those using the two prior potential-energy surfaces and suggest that reparametrization of semiempirical Hamiltonians is a promising strategy to develop accurate potential-energy surfaces for reaction dynamics studies of polyatomic systems.     

丁烯和丁烷自由基阳离子的分子结构和超精细结构的 理论研究

用密度函数理论B3LYP方法和6-31G(d,p),6-311G(d,p)及6-311+G(d,p)基组，分别对1-C4H^+~8,2-C4H^+~8和C4H^+~10进行了构型优化和频率分析计算，预言1-C4H^+~8具有非平面构型，与以往报道的从头算和密度函数理论计算结果不同。在各自由基阳离子的B3LYP构型上，进行了B3LYP、MP2及MRSDCI方法的超精细偶合常数计算，得到了比以往更好的结果，特别是MP2/B3LYP计算值是至今与实验值符合得最好的理论计算结果。     

Termolecular kinetics for the Mu + CO + M recombination reaction: A unique test of quantum rate theory

The room-temperature termolecular rate constants, k0, for the Mu + CO + M<==>MuCO + M (M = He, N2, Ar) recombination reaction have been measured by the muSR technique, and are reported for moderator gas pressures of up to approximately 200 bar (densities less, similar 0.4 x 10(22) molec cm(-3)). The experimental relaxation rates reveal an unusual signature, in being dominated by the electron spin-rotation interaction in the MuCO radical that is formed in the addition step. In N2 moderator, k0 = 1.2+/-0.1 x 10(-34) cm(6) s(-1), only about 30% higher than found in Ar or He. The experimental results are compared with theoretical calculations carried out on the Werner-Keller-Schinke (WKS) surface [Keller et al., J. Chem. Phys. 105, 4983 (1996)], within the framework of the isolated resonance model (IRM). The positions and lifetimes of resonance states are obtained by solving the complex Hamiltonian for the nonrotating MuCO system, using an L2 method, with an absorbing potential in the asymptotic region. Accurate values of the vibrational bound and resonance states of MuCO reveal unprecedented isotope effects in comparisons with HCO, due to the remarkable effect of replacing H by the very light Mu atom (m(Mu) approximately (1/9)m(H)). Due to its pronounced zero-point energy shift, there are only two (J = 0) bound states in MuCO. Contributions from nonzero J states to the termolecular rate constants are evaluated through the J-shifting approximation, with rotational constants evaluated at the potential minimum. The value of the important A constant (181 cm(-1)) used in this approximation was supported by accurate J = K = 1 calculations, from which A = 180 cm(-1) was obtained by numerical evaluation. The calculations presented here, with a "weak collision factor" beta c = 0.001, indicative of the very sparse density of MuCO states, give a very good account of both the magnitude and pressure dependence of the experimental rates, but only when the fact that the two initially bound (J = 0) states become resonances for J > 0 is taken into account. This is the first time in IRM calculations of atom-molecule recombination reactions where J not equal to 0 states have proven to be so important, thus providing a truly unique test of quantum rate theory.