Trajectory-Surface-Hopping Study of the Renner−Teller Effect in the N(2D) + H2 Reaction

Quantum Dynamics of Nonadiabatic Renner-Teller Effects in Atom + Diatom Collisions

We review the quantum nonadiabatic dynamics of atom + diatom collisions due to the Renner-Teller (RT) effect, i.e., to the Hamiltonian operators that contain the total spinless electronic angular momentum L̂. As is well-known, this rovibronic effect is large near collinear geometries when at least one of the interacting states is doubly degenerate. In general, this occurs in insertion reactions and at short-range, where the potential wells exhibit deep minima and support metastable complexes. Initial-state-resolved reaction probabilities, integral cross sections, and thermal rate constants are calculated via the real wavepacket method, solving the equation of motion with an approximated or with an exact spinless RT Hamiltonian. We present the dynamics of 10 single-channel or multichannel reactions showing how RT effects depend on the product channels and comparing with the Born-Oppenheimer (BO) approximation or coexisting conical-intersection (CI) interactions. RT effects not only can significantly modify the adiabatic dynamics or correct purely CI results, but also they can be very important in opening collision channels which are closed at the BO or CI level, as in electronic-quenching reactions. In the OH(A²Σ⁺) + Kr electronic quenching, where both nonadiabatic effects (CI and RT) coexist, they are in competition because CI dominates the reactivity but RT couplings reduce the large CI cross section and open a CI-forbidden evolution toward products, so that CI + RT quantum results are in good agreement with experimental or semiclassical findings. The different roles of these couplings are due to the unlike nuclear geometries where they are large: rather far from or near to linearity for CI or RT, respectively. The OH(A²Σ⁺) + Kr electronic quenching was investigated with the exact RT Hamiltonian, validating the approximated one, which was employed for all other collisions.

The effect of intersystem crossings in N((2)D) + H2 collisions

The transitions between quartet and doublet states of the NH2 molecule are studied for the first time, allowing the evaluation of the N((4)S) + H2 reactive channel. High level ab initio calculations of the spin-orbit coupling are performed over the whole configurational space of the NH2 molecule and fitted to a proposed analytic form. Quasiclassical trajectories coupled with the surface hopping method are employed to calculate reaction cross section and rate constants. The reaction is largely affected by the initial rovibrational states of H2, while the formation of long-lived complexes enhances the reaction probability.

DYNAMICS OF THE N(2D)+H2 REACTION ON THE $\tilde{X}^2 A^{\prime\prime}$ SURFACE, PROPAGATING REAL WAVE PACKETS WITH AN ARCCOS MAPPING OF THE HAMILTONIAN

We have investigated the dynamics of the title reaction with the Gray and Balint-Kurti approach, which propagates real wave packets (WP) under an arccos mapping of a scaled and shifted Hamiltonian. We have considered H 2 rotational quanta j=0 and 1 and obtained reaction probabilities using reactant coordinates and the flux analysis. We have calculated accurate reaction probabilities for total angular momentum quantum number J=0, centrifugal-sudden probabilities for J>0, cross sections, and the room temperature rate constant. The present cross sections are in good agreement with previous quasiclassical trajectory (QCT) results and the theoretical rate constant compares rather well with that observed. WP snapshots show that the reaction occurs via a C2v insertion mechanism, confirming previous QCT calculations.

Differential and Integral Cross Sections of the N(2D) + H2 → NH + H Reaction from Exact Quantum and Quasi-Classical Trajectory Calculations

Exact quantum mechanical state-to-state differential and integral cross sections and their energy dependence have been calculated on an accurate NH2 potential energy surface (PES), using a newly proposed Chebyshev wave packet method. The NH product is found to have a monotonically decaying vibrational distribution and an inverted rotational distribution. The product angular distributions peak in both forward and backward directions, but with a backward bias. This backward bias is more pronounced than that observed previously on a less accurate PES. Both the differential and integral cross sections oscillate mildly with collision energy, indicating the dominance of short-lived resonances. The quantum mechanical results are compared with those obtained from quasi-classical trajectories. The agreement is generally reasonable and the discrepancies can be attributed to the neglect of quantum effects such as tunneling. Detailed analysis of the trajectories revealed that the backward bias in the differential cross section stems overwhelmingly from the fast insertion component of the reaction, augmented with some flux from the abstraction channel, particularly at high collision energies.

Dynamics of insertion reactions of H2 molecules with excited atoms

Recent progress in the study of insertion reactions of hydrogen molecules with excited atoms is reviewed in this article. In particular, the dynamics of the reaction of O(1D), N(2D), C(1D), and S(1D) with H2 and its isotopomers, which have received a great deal of attention over the past decade, are examined in detail. All of these systems have in common the existence of several potential energy surfaces (PES) correlating with the reagents' states, and consequently, they can give rise to reaction following different adiabatic and nonadiabatic pathways. The main contribution, however, arises from their ground singlet PESs which feature the existence of deep wells with small or null barriers for insertion. Accordingly, these reactions proceed mainly via formation of relatively long-lived collision complexes and display an overall nearly statistical behavior. In spite of their similarities, the various reactions have peculiar characteristics caused by important differences of their respective PESs. The contribution of excited PES to the global reactivity, which has also become an important issue and a challenge both for theory and experiment, is also examined. The different theoretical approaches are discussed in the text, along with the experimental results obtained by a variety of techniques. The recent exact quantum treatments of these reactive systems together with the development of a rigorous statistical model have contributed to a very accurate description which in many cases matches very well the detailed measurements. The quasi-classical trajectory (QCT) method has also provided a fairly accurate description of the reaction dynamics for these systems. In particular, the analysis in terms of collision times has yielded interesting clues about the reaction mechanisms.

Exploring Renner-Teller induced quenching in the reaction H(S2)+NH(aΔ1): A combined experimental and theoretical study

Experimental rate coefficients for the removal of NH(a (1)Delta) and ND(a (1)Delta) in collisions with H and D atoms are presented; all four isotope combinations are considered: NH+H, NH+D, ND+H, and ND+D. The experiments were performed in a quasistatic laser-flash photolysis/laser-induced fluorescence system at low pressures. NH(a (1)Delta) and ND(a (1)Delta) were generated by photolysis of HN(3) and DN(3), respectively. The total removal rate coefficients at room temperature are in the range of (3-5)x10(13) cm(3) mol(-1) s(-1). For two isotope combinations, NH+H and NH+D, quenching rate coefficients for the production of NH(X (3)Sigma(-)) or ND(X (3)Sigma(-)) were also determined; they are in the range of 1 x 10(13) cm(3) mol(-1) s(-1). The quenching rate coefficients directly reflect the strength of the Renner-Teller coupling between the (2)A(") and (2)A(') electronic states near linearity and so can be used to test theoretical models for describing this nonadiabatic process. The title reaction was modeled with a simple surface-hopping approach including a single parameter, which was adjusted to reproduce the quenching rate for NH+H; the same parameter value was used for all isotope combinations. The agreement with the measured total removal rate is good for all but one isotope combination. However, the quenching rates for the NH+D combination are only in fair (factor of 2) agreement with the corresponding measured data.

Renner-Teller quantum dynamics of the N(D2)+H2→NH+H reaction

We present the Born-Oppenheimer (BO) and Renner-Teller (RT) quantum dynamics of the reaction (14)N((2)D)+(1)H(2)(X (1)Sigma(g) (+))-->NH(X (3)Sigma(-))+H((2)S), considering the NH(2) electronic states X (2)B(1) and A (2)A(1). These states correlate to the same (2)Pi(u) linear species, are coupled by RT nonadiabatic effects, and give NH(X (3)Sigma(-))+H and NH(a (1)Delta)+H, respectively. We develop the Hamiltonian matrix elements in the R embedding of the Jacobi coordinates and in the adiabatic electronic representation, using the permutation-inversion symmetry, and taking into account the nuclear-spin statistics. Collision observables are calculated via the real wave-packet (WP) and flux methods, using the potential-energy surfaces of Santoro et al. [J. Phys. Chem. A 106, 8276 (2002)]. WP snapshots show that the reaction proceeds via an insertion mechanism, and that the RT-WP avoids the A (2)A(1) potential barrier, jumping from the excited to the ground surface and giving mainly the NH(X (3)Sigma(-)) products. X (2)B(1) BO probabilities and cross sections show large tunnel effects and are approximately four to ten times larger than the A (2)A(1) ones. This implies a BO rate-constant ratio k(X (2)B(1))k(A (2)A(1)) approximately 10(5) at 300 K, i.e., a negligible BO formation of NH(a (1)Delta). When H(2) is rotationally excited, RT couplings reduce slightly the X (2)B(1) reaction observables, but enhance strongly the A (2)A(1) reactivity. These couplings are important at all collision energies, reduce the collision threshold, and increase remarkably reaction probabilities and cross sections. The RT k(A (2)A(1)) is thus approximately 3.3 order of magnitude larger than the BO value, and degeneracy-averaged, initial-state-resolved rate constants increase by approximately 13% and by approximately 47% at 300 and 500 K, respectively. Owing to an overestimation of the X (2)B(1) potential barrier, the calculated thermal rate is too low with respect to that observed, but we obtain a good agreement by shifting down the calculated cross section.

Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method

The most widely used algorithm for Monte Carlo sampling of electronic transitions in trajectory surface hopping (TSH) calculations is the so-called anteater algorithm, which is inefficient for sampling low-probability nonadiabatic events. We present a new sampling scheme (called the army ants algorithm) for carrying out TSH calculations that is applicable to systems with any strength of coupling. The army ants algorithm is a form of rare event sampling whose efficiency is controlled by an input parameter. By choosing a suitable value of the input parameter the army ants algorithm can be reduced to the anteater algorithm (which is efficient for strongly coupled cases), and by optimizing the parameter the army ants algorithm may be efficiently applied to systems with low-probability events. To demonstrate the efficiency of the army ants algorithm, we performed atom-diatom scattering calculations on a model system involving weakly coupled electronic states. Fully converged quantum mechanical calculations were performed, and the probabilities for nonadiabatic reaction and nonreactive deexcitation (quenching) were found to be on the order of 10(-8). For such low-probability events the anteater sampling scheme requires a large number of trajectories ( approximately 10(10)) to obtain good statistics and converged semiclassical results. In contrast by using the new army ants algorithm converged results were obtained by running 10(5) trajectories. Furthermore, the results were found to be in excellent agreement with the quantum mechanical results. Sampling errors were estimated using the bootstrap method, which is validated for use with the army ants algorithm.

A Quantum Wave Packet Dynamics Study of the N(2D) + H2 Reaction

We report a dynamics study of the reaction N((2)D) + H(2) (v=0, j=0-5) --> NH + H using the time-dependent quantum wave packet method and a recently reported single-sheeted double many-body expansion potential energy surface for NH(2)(1(2)A' ') which has been modeled from accurate ab initio multireference configuration-interaction calculations. The calculated probabilities for (v=0, j=0-5) are shown to display resonance structures, a feature also visible to some extent in the calculated total cross sections for (v=0, j=0). A comparison between the calculated centrifugal-sudden and coupled-channel reaction probabilities validate the former approximation for the title system. Rate constants calculated using a uniform J-shifting scheme and averaged over a Boltzmann distribution of rotational states are shown to be in good agreement with the available experimental values. Comparisons with other theoretical results are also made.

Experimental and Theoretical Differential Cross Sections for the N(2D) + H2 Reaction

In this paper, we report a combined experimental and theoretical study on the dynamics of the N(2D) + H2 insertion reaction at a collision energy of 15.9 kJ mol(-1). Product angular and velocity distributions have been obtained in crossed beam experiments and simulated by using the results of quantum mechanical (QM) scattering calculations on the accurate ab initio potential energy surface (PES) of Pederson et al. (J. Chem. Phys. 1999, 110, 9091). Since the QM calculations indicate that there is a significant coupling between the product angular and translational energy distributions, such a coupling has been explicitly included in the simulation of the experimental results. The very good agreement between experiment and QM calculations sustains the accuracy of the NH2 ab initio ground state PES. We also take the opportunity to compare the accurate QM differential cross sections with those obtained by two approximate methods, namely, the widely used quasiclassical trajectory calculations and a rigorous statistical method based on the coupled-channel theory.

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.