Abstract
Objectives
The main objective of this project has been the dynamic and kinetic of atom+diatom reactions (i.e., A + BC → AB + C) where the Renner-Teller (RT) effect is present. To do this the time dependent real wave-packet (RWP) method(1) has been used. The RT rovibronic effect(2) arises when two electronic states are degenerate for collinear geometries of the A + BC system and then, for these arrangements, the system should be able to change the electronic state (non adiabatic effect). This fact makes impossible the separation of nuclear and electronic motions and breaks down the Born-Oppenheimer (BO) approximation. Moreover, the coupled-channel (CC) scheme is used to account for the Coriolis coupling that couples the K and K±1 states (K is the quantum number corresponding to the total angular momentum projection along the z axis). If the Hamiltonian operator includes both the RT and the Coriolis terms, the dynamic method is exact. When we carry out the propagation of a WP for a given value of J (total angular momentum quantum number), and for a selected initial condition specified by the v0, j0, K0 quantum numbers (where v0 and j0 are the vibrational and rotational quantum numbers, respectively), there will be several final K values for the system (e.g., for v0=1, j0=1, K0=1, J=40, the possible values of K are from K=0 to K=40, that is to say, 41 propagations are required). Thus, in this context the best way to proceed is to use a parallel computing framework, where each processor is involved in the propagation of a RWP involving a single K value. The first reaction studied is the NH(a1Δ)+H’(2S) one, where several reaction products can be obtained: NH(a1Δ)+H’(2S) → N(2D)+H2(1Σg+) (1) depletion NH(a1Δ)+H’(2S) → NH’(a1Δ)+H(2S) (2) exchange NH(a1Δ)+H’(2S) → NH(X3Σ−)+H’(2S) (3) quenching NH(a1Δ)+H’(2S) → NH’(X3Σ−)+H(2S) (4) exchange + quenching From these set of reaction channels, reactions (3) and (4) can only occur if the RT effect is taken into account. Thus, the propagation of the RWP starts in the A2A1 excited potential energy surface(3) (PES), and when it reaches the H-N-H’ collinear arrangements it becomes possible to change the electronic state (jump into the X2B1 PES(3)) thanks to the RT effect. Moreover, the NH2 X2B1 state has a deep minimum that traps the RWP for long time, increasing in this way the probability of nonadiabatic electronic transition (change of the electronic state). Finally, the part of the RWP corresponding to reaction channels (1), (2), (3) and (4) is determined and the probability of each one of them is calculated, as a function of the initial conditions. The second and last reaction studied is the isotopic substitution reaction N(2D)+HD(X1Σg+), where two possible channels are possible: N(2D)+HD(X1Σg+) → NH(X3Σ-)+D(2S) (1) N(2D)+HD(X1Σg+) → ND(X3Σ-)+H(2S) (2) This study is based on the previous work of our group(4) on N(2D)+H2, where the main conclusion was that only the ground PES(3) (X2B1) plays an important role in the rate constants calculations, at least in the range of the experimental conditions available. According to this, we have used the BO approximation and the RWP propagation considering only the X2B1 ground PES. Of course, the inclusion of the CC method is very important for a good treatment of these reactions and the parallel code is the most convenient way to perform the propagation of the RWPs.

References

(1) S. K. Gray and G. G. Balint-Kurti, J. Chem. Phys. 108, 950 (1998) (2) C. Petrongolo, J. Chem. Phys. 89, 1297 (1988) (3) Z.-W. Qu, H. Zhu, R. Schinke, L. Adam, and W. Hack, J. Chem. Phys. 122, 204313 (2005) (4) S. Akpinar, P. Defazio, P. Gamallo and C. Petrongolo, J. Chem. Phys. 129, 174307 (2008)

Achievements
The first thing we had to do was the conversion of our parallel code to an open/mpi code, due to the requirements of the CINECA machines. After this, we checked the code running some jobs and comparing the results with others obtained using other computers. The success of this step allowed us to begin the dynamic study of the reactions indicated in the previous section. At the beginning we checked the convergence of the RT-CC-RWP (NH(a1Δ)+H’(2S)) and BO-CC-RWP (N(2D)+HD(X1Σg+)) calculations verifying a large number of numerical parameters (e.g., rotational basis, mesh, number of iterations, etc.). Once the results were well converged, we performed the RWPs propagations for the two reactions selected. For the first reaction, NH(a1Δ)+H’(2S), the different initial conditions investigated have been the following: NH (v0=0, j0=2,3,4) and J=0,1,2,…,40, and K0=0,1,…,min(j,J). Because the CC method has been used, the RWP has been propagated so many times as given by the number of possible K final values (J+1), using a single processor for each propagation. A total of 80000 iteration steps are required to reach convergence and due to this the propagations of the RWPs have been very time demanding. At present, we are carrying the analysis of the data using the flux and the asymptotic methods to obtain the probability of the four reaction channels. These probabilities will be the basis to obtain both the cross section and the rate constants for all processes. For the second reaction, N(2D)+HD(X1Σg+), the method employed is simpler, since the BO approximation has been used. The convergence is reached at 40000 iterations and then the RWP propagation has not been so time demanding as in the first reaction studied. At this point, we are performing the analysis of the RWPs to obtain the reaction probabilities using the flux method for both reaction channels. After this and in the same manner as in the NH(a1Δ)+H’(2S) reaction, we will determine the cross sections and rate constants and compare the theoretical data with the experimental data of the literature.