† Corresponding author. E-mail:
The N(2D) + HD (v = 0, j = 0) reaction has been studied by a quantum time-dependent wave packet approach with a second-order split operator on the potential energy surface of Li et al. (Li Y, Yuan J, Chen M, Ma F and Sun M J. Comput. Chem.
As an important prototype to study the reaction involved nitrogen atom, N(2D) + H2 reaction received considerable attention both experimentally[1–10] and theoretically,[11–56] because it plays an important role in atmospheric chemistry, combustion of nitrogen-containing fuels, and explosion processes.
From the experimental side, the nascent vibrational population ratios, the vibrational and rotational state distribution of the N(2D) + H2 reaction and its isotopic variants as well as the rate constant of the N(2D) + HD isotopic variant were reported by Umemoto et al.[3–6,8] with improved experimental resolution. In order to produce the N(2D) atom, an intense laser pulse at 275.2 nm was employed to irradiate a mixture of NO and H2(D2) and the laser-induced fluorescence was used to detect the products of the N(2D) + H2 reaction and its isotopic variants. Employing a crossed molecular-beam experiment, Alagia et al.[7,9] detected the N(2D) + D2 reaction by mass spectrometric and a forward-backward symmetry differential cross section (DCS) was observed at collision energy 165 meV and 220 meV.
Numerous theoretical calculations have been carried out on the N(2D) + H2 system. With respect to the potential energy surface aspect, using multi-reference configuration interaction (MRCI) plus Davidson correction and aug-cc-pVTZ basis set, Pederson et al.[14] constructed a PES for N(2D) + H2 reaction. Ho et al.[23] improved the PES which was reported by Pederson et al.[14] However, these PESs are not accurate enough, the rate constant based on these PESs are always overestimated. On the other hand, the vibrational levels of NH2 are strongly affected by the Renner–Teller(RT) coupling, which is not included in previous theoretical calculation. So, many groups[25,38,39,41,46,47] have done lots of work for further improving the PES over the next few decades.
For the dynamic aspect, reaction probabilities, integral cross section (ICS), DCS, rate constant, and isotope effect, etc. have been investigated by quasi-classical trajectory (QCT),[7,9,11–14,20,21,24,26,33,34,45,48,50,51,55] quantum dynamics calculation,[12,15,20,22,27–37,39,42–45,49,52,56] and statistical quantum mechanical method.[18,24,26,40] However, there are few works investigating the isotope effects of the N(2D) + HD reaction at the state-to-state level of theory. In order to obtain more accurate information and an accurate physical understanding of the title reaction, the time-dependent quantum wave packet (TDWP) method is employed in the state-to-state dynamic calculation based on the PES of Li et al.[46] in the collision energy range from 0 eV to 1.0 eV. This article is organized as follows. In Section 2, the theoretical method is briefly introduced. In Section 3, the results and discussion are presented, and the conclusions are presented in Section 4.
The Hamiltonian of the N(2D) + HD reaction in body-fixed (BF) reactant Jacobi coordinates for a given total angular momentum J can be written as
In a wave packet calculation, the initial condition of the wave packet has to be set up before its propagation. The initial wave packet in space-fixed (SF) representation (v0, j0, l0) can be constructed by using the Gaussian wave packet in the R direction and it can be written as
To propagate the initial wave packet in the BF frame, one should transform |JMj0l0ɛ〉 to its BF representation counterpart as
![](cpb_25_12_123104/cpb161418ieqn1.gif)
During the propagation, the fast Fourier transform method is adopted to act as the radical kinetic energy operator onto the wave packet combination with an L-shaped grid.[58] The generalized discrete variable representation (DVR) is used to evaluate the action of the potential energy operator, in which the wave packet is converted from the angular finite basis representation (FBR) to a grid representation. To avoid the wave packet reflecting back from the boundaries, a damping function is employed with the same form as that of Ref. [59].
The obtained BF scattering time-independent wave function from an initial state (v0, j0, l0) is obtained by an orthogonal transformation matrix as
![](cpb_25_12_123104/cpb161418ieqn2.gif)
Finally, the scattering matrix
![](cpb_25_12_123104/cpb161418ieqn4.gif)
Li et al.[46] constructed a novel global PES of N + H2 reaction by using the multi-reference configuration interaction (MRCI) approach. The major features of PES are the bond stretching N–H–H and H–N–H configuration, and these features are displayed in Fig.
![]() | Fig. 1. Contour plot of the PES for bond stretching N–H–H (a) and H–N–H (b) linear configuration in internal coordinates (energies are given in unit eV). |
To obtain the optimal numerical parameters, many convergence tests have been carried out for J = 0 as summarized in Table
![]() | Table 1. Numerical parameters used in the dynamic calculations (all parameters are in atomic unit unless otherwise stated). . |
The total and vibrational resolved reaction probabilities of the two channels of N(2D) + HD reaction for angular momentum J = 0 are shown in Fig.
![]() | Fig. 2. Total and vibrational state resolved reaction probabilities of NH + D and ND + H channels are collected in the left and right panel, respectively. |
The rotationally resolved reaction probabilities for the two channels are listed in Fig.
The total and vibrationally resolved ICSs of the two channels of the N(2D) + HD reaction are collected in Fig.
![]() | Fig. 4. The total and vibrational state resolved integral cross sections of NH + D and ND + H channels are shown in panels (a) and (b), respectively. |
The rovibrationally resolved ICSs of the two channels are collected in Figs.
![]() | Fig. 5. The rotational state distribution of the NH + D channel at collision energies of 0.038, 0.101, 0.200, and 0.470 eV. |
The differential cross sections of the two channels are displayed in panels (a) and (b) of Fig.
The initial state specific thermal rate constants of the N(2D) + HD reaction are plotted in Fig.
![]() | Fig. 8. Initial state specific reaction rate constant for the two channels of N + HD (v = 0, j = 0) as well as the experimental data obtained from Ref. [6]. |
For the two output channels of the N(2D) + HD reaction, the experimental data are very scare. The sum of the theoretical rate constant of the two output channels is 1.88 × 10−12 cm3 · s−1, which is in excellent agreement with the experimental data[6] (1.83±0.12 × 10−12 cm3 · s−1) at the temperature T = 300 K. It may imply that the rate constants of the two output channels of the N(2D) + HD reaction are both accurate and reliable.
The N(2D) + HD reaction with initial state (v = 0, j = 0) was calculated by the time-dependent wave packet method in the collision energies from 0 eV to 1.0 eV. The rovibrationally reaction probabilities are investigated for total angular momentum J = 0. Some mild resonances have been found, which can be attributed to the deep well in the entrance channel and large exothermicity. The DCSs have forward–backward symmetry, which may indicate that the insertion mechanism is dominated in the reaction. There are no experimental data of the rate constant for the two channels of the title reaction. However, the sum of the theoretical rate constant of the two output channels are in good agreement with the experimental data. This indicated that the rate constants of the two output channels of the N(2D) + HD reaction may be both accurate and reliable.
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 | |
9 | |
10 | |
11 | |
12 | |
13 | |
14 | |
15 | |
16 | |
17 | |
18 | |
19 | |
20 | |
21 | |
22 | |
23 | |
24 | |
25 | |
26 | |
27 | |
28 | |
29 | |
30 | |
31 | |
32 | |
33 | |
34 | |
35 | |
36 | |
37 | |
38 | |
39 | |
40 | |
41 | |
42 | |
43 | |
44 | |
45 | |
46 | |
47 | |
48 | |
49 | |
50 | |
51 | |
52 | |
53 | |
54 | |
55 | |
56 | |
57 | |
58 | |
59 |