The investigation of nonadiabatic effects for the N + ND → N2 + D reaction

Nonadiabatic quantum dynamical calculations have been carried out on the two coupled potential energy surfaces (1²A′ and 2²A′) (Mota et al., J Theor Comput Chem 2009, 8, 849) for the title reaction. Initial state‐resolved reaction probabilities and cross sections for ground and excited states for collision energies of 0.005–1.0 eV are determined, respectively. Nonadiabatic transition is enhanced about four times by isotopic substitution of N + NH by N + ND reaction. It turns out that the nonadiabatic effects exert no significant contribution in the N + ND → N₂ + D reaction. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Molecular beam scattering studies of the reaction D + H2 (v = 0) and D + H2 (v = 1) → HD + H

The reaction D + H₂ → HD + H has been investigated in two molecular beam scattering experiments. Angular and time-of-flight distributions have been measured for the initial vibrational ground state (v = 0) at a most probable collision energy of E_cm = 1.5 eV and for the first vibrational excited state (v = 1) at E_cm = 0.28 eV with the same apparatus. Results for the ground-state experiment are compared with quasiclassical trajectory calculations(QCT) on the LSTH-hypersurface transformed into the laboratory system and averaged over the apparatus distributions. The agreement isquite satisfactory. At this high collision energy the HD products are no longer scattered in a backward direction but in a wide angular region concentrated about θ = 90° in the center-of-mass system. The absolute reactive cross section has been determined and the agreement with the theoretical value from QCT calculations is within the experimental error. The high sensitivity of the experiment to different properties of the doubly differential cross section has also been demonstrated. A preliminary evaluation of the experiment with initial vibrational excitation (v = 1) shows that the HD-product molecules are preferably backward scattered and the change of internal energy is small supporting the concept of a reaction which is adiabatic with respect to the internal degrees of freedom.     

Quantum wave packet calculation of reaction probabilities,cross sections,and rate constants for the C(1D) + HD reaction

The time‐dependent real wave packet method has been used to study the C(¹D) + HD reaction. The state‐to‐state and state‐to‐all reactive scattering probabilities for a broad range of energies are calculated at zero total angular momentum. The probabilities for J > 0 are estimated from accurately computed J = 0 probabilities by using the J‐shifting approximation. The integral cross sections for a large energy range, and thermal rate constants are calculated. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Collision-energy dependence of HD(nu'=1,j') product rotational distributions for the H + D2 reaction

Product rotational distributions for the reaction H + D2 --> HD(nu'=1,j') + D have been measured for 16 collision energies in the range of 1.43 < or = E(coll) < or = 2.55 eV. Time-dependent quantum-mechanical calculations agree well in general with the experimental results, but they consistently yield slightly colder distributions. In terms of the average energy channeled into rotation, the differences between experiment and theory amount to approximately 10% for all collision energies sampled. No peculiarity is found for E(coll)=2.55 eV at which the system has sufficient energy to access the first HD2 electronically excited state.     

Effctive nonadiabatic calculations on the ground state of the HD+ molecule

The nonadiabatic methodology, which is based on an effective elimination of the center-of-mass motion rather than explicit separation achieved by a coordinate transformation, is applied to the ground state of the HD⁺ molecule. The many-body nonadiabatic wave function is generated in terms of explicitly correlated Gaussian functions. The analytical first and second derivatives of the variational functional with respect to the Gaussian exponents are applied in conjunction with the Newton–Raphson optimization method to find the nonadiabatic energy and the ground–wave function. The numerical results are compared with conventional nonadiabatic calculations. © 1995 John Wiley & Sons, Inc.     

Experimental and theoretical investigations of the reactions NH(X 3Sigma-) + D(2S)-->ND(X 3Sigma-) + H(2S) and NH(X 3Sigma-) + D(2S)-->N(4S) + HD(X 1Sigmag+)

The rate coefficient of the reaction NH(X (3)Sigma(-))+D((2)S)-->(k(1) )products (1) is determined in a quasistatic laser-flash photolysis, laser-induced fluorescence system at low pressures. The NH(X) radicals are produced by quenching of NH(a (1)Delta) (obtained in the photolysis of HN(3)) with Xe and the D atoms are generated in a D(2)/He microwave discharge. The NH(X) concentration profile is measured in the presence of a large excess of D atoms. The room-temperature rate coefficient is determined to be k(1)=(3.9+/-1.5) x 10(13) cm(3) mol(-1) s(-1). The rate coefficient k(1) is the sum of the two rate coefficients, k(1a) and k(1b), which correspond to the reactions NH(X (3)Sigma(-))+D((2)S)-->(k(1a) )ND(X (3)Sigma(-))+H((2)S) (1a) and NH(X (3)Sigma(-))+D((2)S)-->(k(1b) )N((4)S)+HD(X (1)Sigma(g) (+)) (1b), respectively. The first reaction proceeds via the (2)A(") ground state of NH(2) whereas the second one proceeds in the (4)A(") state. A global potential energy surface is constructed for the (2)A(") state using the internally contracted multireference configuration interaction method and the augmented correlation consistent polarized valence quadrupte zeta atomic basis. This potential energy surface is used in classical trajectory calculations to determine k(1a). Similar trajectory calculations are performed for reaction (1b) employing a previously calculated potential for the (4)A(") state. The calculated room-temperature rate coefficient is k(1)=4.1 x 10(13) cm(3) mol(-1) s(-1) with k(1a)=4.0 x 10(13) cm(3) mol(-1) s(-1) and k(1b)=9.1 x 10(11) cm(3) mol(-1) s(-1). The theoretically determined k(1) shows a very weak positive temperature dependence in the range 250< or =TK< or =1000. Despite the deep potential well, the exchange reaction on the (2)A(") ground-state potential energy surface is not statistical.     

Nonadiabatic effects in the H+D2 reaction

The state-to-state dynamics of the H+D2 reaction is studied by the reactant-product decoupling method using the double many-body expansion potential energy surface. Two approaches are compared: one uses only the lowest adiabatic sheet while the other employs both coupled diabatic sheets. Rotational distributions for the reaction H+D2 (upsilon = 0, j = 0)-->HD(upsilon' = 3, j')+D are obtained at eight different collision energies between 1.49 and 1.85 eV; no significant difference are found between the two approaches. Initial state-selected total reaction probabilities and integral cross sections are also given for energies ranging from 0.25 up to 2.0 eV with extremely small differences being observed between the two sets of results, thus showing that the nonadiabatic effects in the title reaction are negligible at least for small energies below 2.0 eV.     

Study of nonadiabatic effects in the Li-Li 2 + system. Location of nonadiabatic regions

Nonadiabatic coupling between the lowest two singlet potential energy surfaces of the Li-Li ₂ ⁺ system is calculated using the diatomics-in-molecules method. Location of nonadiabatic regions in the configuration space of Li-Li ₂ ⁺ and their analysis is used to estimate those inner and translational states of the reactants which can lead to nonadiabatic behavior.     

On the dynamics of the H+ +D2(v=0,j=0)-->HD+D + reaction: a comparison between theory and experiment

The H+ +D2(v=0,j=0)-->HD+D + reaction has been theoretically investigated by means of a time independent exact quantum mechanical approach, a quantum wave packet calculation within an adiabatic centrifugal sudden approximation, a statistical quantum model, and a quasiclassical trajectory calculation. Besides reaction probabilities as a function of collision energy at different values of the total angular momentum, J, special emphasis has been made at two specific collision energies, 0.1 and 0.524 eV. The occurrence of distinctive dynamical behavior at these two energies is analyzed in some detail. An extensive comparison with previous experimental measurements on the Rydberg H atom with D2 molecules has been carried out at the higher collision energy. In particular, the present theoretical results have been employed to perform simulations of the experimental kinetic energy spectra.     

Semiclassical nonadiabatic dynamics based on quantum trajectories for the O(3P,1D) + H2 system

The O(3P,1D) + H2 --> OH + H reaction is studied using trajectory dynamics within the approximate quantum potential approach. Calculations of the wave-packet reaction probabilities are performed for four coupled electronic states for total angular momentum J = 0 using a mixed coordinate/polar representation of the wave function. Semiclassical dynamics is based on a single set of trajectories evolving on an effective potential-energy surface and in the presence of the approximate quantum potential. Population functions associated with each trajectory are computed for each electronic state. The effective surface is a linear combination of the electronic states with the contributions of individual components defined by their time-dependent average populations. The wave-packet reaction probabilities are in good agreement with the quantum-mechanical results. Intersystem crossing is found to have negligible effect on reaction probabilities summed over final electronic states.     

Imaging the nonadiabatic dynamics of the CH3 + HCl reaction

LAB-frame velocity distributions of Cl-atoms produced in the photoinitiated reaction of CH(3) radicals with HCl have been measured for both the ground Cl ((2)P(3/2)) and excited Cl* ((2)P(1/2)) spin-orbit states using a DC slice velocity-map ion imaging technique. The similarity of these distributions, as well as the average internal excitation of methane co-products for both Cl and Cl* pathways, suggest that all the reactive flux proceeds through the same transition state on the ground potential energy surface (PES) and that the couplings which promote nonadiabatic transitions to the excited PES correlating to Cl* occur later in the exit channel, beyond the TS region. The nature of these couplings is discussed in light of initial vibrational excitation of CH(3) radicals as well as previously reported nonadiabatic reactivity in other polyatomic molecule reactions. Furthermore, the scattering of the reaction products, derived using the photoloc method, suggests that at the high collision energy of our experiment (E(coll) = 22.3 kcal mol(-1)), large impact parameter collisions are favoured with a reduced kinematic constraint on the internal excitation of the methane co-product.     

Energy partitioning in the reaction O(1D) + H2O → OH + OH.: The influence of O(1D) translational energy on the reaction rate constant

For the exothermic reaction O (¹D) + H₂O → OH + OH the rate constant and its energy dependence were determined by monitoring the concentration of the OH product. This was done by integrating the distribution of product molecules over all accessible states. The rate constant, determined at different velocity distributions of the reacting metastable over a wide range, is energy independent.     

Exact state-to-state quantum dynamics of the F + HD --> HF(v' = 2) + D reaction on model potential energy surfaces

In this paper, we present the results of a theoretical investigation on the dynamics of the title reaction at collision energies below 1.2 kcal/mol using rigorous quantum reactive scattering calculations. Vibrationally resolved integral and differential cross sections, as well as product rotational distributions, have been calculated using two electronically adiabatic potential energy surfaces, developed by us on the basis of semiempirical modifications of the entrance channel. In particular, we focus our attention on the role of the exothermicity and of the exit channel region of the interaction on the experimental observables. From the comparison between the theoretical results, insight about the main mechanisms governing the reaction is extracted, especially regarding the bimodal structure of the HF(v = 2) nascent rotational state distributions. A good overall agreement with molecular beam scattering experiments has been obtained.     

Quantum dynamics of Br + HD reaction

In this article we report the results of three-dimensional time-dependent quantum wavepacket calculations carried out for the Br + HD( v = 0, j = 0) reaction in the collision energy range 0.0-1.2 eV. An accurate potential energy surface computed by Kurosaki was used for the dynamical calculations. Both reactive channels, BrH + D and BrD + H, show vibrational enhancement of the reaction cross sections. For the three initial vibrational states considered, the production of BrD channel dominates over that of BrH for the considered collision energy range. The two arrangement channels exhibit different initial rotational state dependence. The cross section for the formation of BrD is almost independent of j whereas the same for the formation of BrH increases with increase in j. A comparison with the results on an e-LEPS surface shows that the two surfaces behave very differently with respect to the cross section for the initial rotational states.     

A time-dependent wave packet quantum scattering study of the reaction HD+ (v = 0 - 3;j0 = 1) + He --> HeH+(HeD+) + D(H)

Time-dependent wave packet quantum scattering (TWQS) calculations are presented for HD(+) (v = 0 - 3;j(0)=1) + He collisions in the center-of-mass collision energy (E(T)) range of 0.0-2.0 eV. The present TWQS approach accounts for Coriolis coupling and uses the ab initio potential energy surface of Palmieri et al. [Mol. Phys. 98, 1839 (2000)]. For a fixed total angular momentum J, the energy dependence of reaction probabilities exhibits quantum resonance structure. The resonances are more pronounced for low J values and for the HeH(+) + D channel than for the HeD(+) + H channel and are particularly prominent near threshold. The quantum effects are no longer discernable in the integral cross sections, which compare closely to quasiclassical trajectory calculations conducted on the same potential energy surface. The integral cross sections also compare well to recent state-selected experimental values over the same reactant and translational energy range. Classical impulsive dynamics and steric arguments can account for the significant isotope effect in favor of the deuteron transfer channel observed for HD(+)(v<3) and low translational energies. At higher reactant energies, angular momentum constraints favor the proton-transfer channel, and isotopic differences in the integral cross sections are no longer significant. The integral cross sections as well as the J dependence of partial cross sections exhibit a significant alignment effect in favor of collisions with the HD(+) rotational angular momentum vector perpendicular to the Jacobi R coordinate. This effect is most pronounced for the proton-transfer channel at low vibrational and translational energies.     

IR kinetic spectroscopy investigation of the CH4 + O(1D) reaction

The branching of the title reaction into several product channels has been investigated quantitatively by laser infrared kinetic spectroscopy for CH(4) and CD(4). It is found that OH (OD) is produced in 67 +/- 5% (60 +/- 5%) yield compared to the initial O((1)D) concentration. H (D) product is produced in 30 +/- 10%(35 +/- 10%). H(2)CO is produced in 5% yield in the CH(4) system (it was not possible to measure the CD(2)O yield in the CD(4) case). D(2)O is produced in 8% yield in the CD(4) system (it was not feasible to measure the H(2)O yield). The ratio of the overall rate constant of the CD(4) reaction to the overall rate constant of the O((1)D) + N(2)O reaction was determined to be 1.2(5) +/- 0.1. A measurement of the reaction of O((1)D) with NO(2) gave 1.3 x 10(-10) cm(3) molecule(-1) s(-1) relative to the literature values for the rate constants of O((1)D) with H(2) and CH(4). Hot atom effects in O((1)D) reactions were observed.     

Differential cross section for the H+D(2)-->HD(v(')=1,j(')=2,6,10)+D reaction as a function of collision energy

We have measured differential cross sections (DCSs) for the HD (v(')=1,j(')=2,6,10) products of the H+D(2) exchange reaction at five different collision energies in the range 1.48< or =E(coll)< or =1.94 eV. The contribution from the less energetic H atoms formed upon spin-orbit excitation of Br in the photolysis of the HBr precursor is taken into account for two collision energies, E(coll)=1.84 and 1.94 eV, allowing us to disentangle the two different channels. The measured DCSs agree well with new time-dependent quantum-mechanical calculations. As the product rotational excitation increases, the DCSs shift from backward to sideward scattering, as expected. We also find that the shapes of the DCSs show only a small overall dependence on the collision energy, with a notable exception occurring for HD (v(')=1,j(')=2), which appears bimodal at high collision energies. We suggest that this feature results from both direct recoil and indirect scattering from the conical intersection.     

An investigation of nonadiabatic interactions in Cl(2Pj) + D2 via crossed-molecular-beam scattering

We have determined limits on the cross section for both electronically nonadiabatic excitation and quenching in the Cl((2)P(j)) + D(2) system. Our experiment incorporates crossed-molecular-beam scattering with state-selective Cl((2)P(12,32)) detection and velocity-mapped ion imaging. By colliding atomic chlorine with D(2), we address the propensity for collisions that result in a change of the spin-orbit level of atomic chlorine either through electronically nonadiabatic spin-orbit excitation Cl((2)P(32)) + D(2)-->Cl(*)((2)P(12)) + D(2) or through electronically nonadiabatic spin-orbit quenching Cl(*)((2)P(12)) + D(2)-->Cl((2)P(32)) + D(2). In the first part of this report, we estimate an upper limit for the electronically nonadiabatic spin-orbit excitation cross section at a collision energy of 5.3 kcal/mol, which lies above the energy of the reaction barrier (4.9 kcal/mol). Our analysis and simulation of the experimental data determine an upper limit for the excitation cross section as sigma(NA)< or =0.012 A(2). In the second part of this paper we investigate the propensity for electronically nonadiabatic spin-orbit quenching of Cl(*) following a collision with D(2) or He. We perform these experiments at collision energies above and below the energy of the reaction barrier. By comparing the amount of scattered Cl(*) in our images to the amount of Cl(*) lost from the atomic beam we obtain the maximum cross section for electronically nonadiabatic quenching as sigma(NA)< or =15(-15) (+44) A(2) for a collision energy of 7.6 kcal/mol. Our experiments show the probability for electronically nonadiabatic quenching in Cl(*) + D(2) to be indistinguishable to that for the kinematically identical system of Cl(*) + He.