Ultrafast formation dynamics of ${\mathrm{D}}_3{}^{+}$ from bimolecular reaction of the ${\mathrm{D}}_2\text{−}{\mathrm{D}}_2$ dimer

Bimolecular reactions involving small diatomic molecules constitute a fundamental category of chemical processes. Recent experimental breakthroughs have enabled precise timing of the ultrafast formation dynamics of ${\mathrm{D}}_3{}^{+}$ originating from the ${\mathrm{D}}_2\text{−}{\mathrm{D}}_2$ dimer. In this paper, we systematically survey diverse theoretical approaches for numerically simulating bimolecular reaction dynamics, considering various initial geometric configurations of the dimer. Our findings demonstrate the consistency and reliability of both classical and quantum methods in predicting the reaction timescale for ${\mathrm{D}}_3{}^{+}$ formation. Additionally, we illustrate the intricate microscopic details of bimolecular reactions, laying the foundation for comprehending intermolecular interactions.

Figure 1

Different initial configurations of the ${\mathrm{D}}_2\text{−}{\mathrm{D}}_2$ dimer.

Figure 2

Potential energy surfaces of the T-type ${\mathrm{D}}_2\text{−}{\mathrm{D}}_2$ dimer complex in both its (a) cationic and (b) neutral states, with the ground-state probability distribution highlighted by black contour lines. In panel (a), a representative reaction trajectory leading to the formation of ${\mathrm{D}}_3{}^{+}$ is depicted by the orange curve. The dimer configurations at various points along this trajectory are displayed as insets.

Figure 3

Histogram of the ${\mathrm{D}}_3{}^{+}$ formation time calculated by (a) classical-trajectory Monte Carlo (CTMC), (b) Bohmian trajectory (BM), (c) time-dependent Schrödinger equation (TDSE), and (d) backpropagation (BP) methods.

Figure 4

Ultrafast reaction dynamics of the T-shape configuration. Column (1) displays the classical trajectories leading to the formation of ${\mathrm{D}}_3{}^{+}$. Column (2) indicates the average value of these trajectories on the $R_1$ and $R_2$ coordinates at each moment.

Figure 5

Wigner quasiprobability distribution (a) ${\rho }_0(R_1,P_1)$ and (b) ${\rho }_0(R_2,P_2)$, and (c) the formation time distribution using CTMC with Wigner sampling.

Figure 6

Results starting from different initial configurations, including L-type [row (a)], X-type [row (b)], and Z-type [row (c)]. Column 1: PES of cationic (${\mathrm{D}}_2\text{−}{\mathrm{D}}_2{)}^{+}$ at $\theta =0$. Column 2: Histogram of the formation time calculated by CTMC. Column 3: Histogram of the formation time calculated by TDSE.

Figure 7

The potential energy of the T-type ${\mathrm{D}}_2\text{−}{\mathrm{D}}_2$ dimer at $R_1=7.131$ a.u. and $R_2=1.427$ a.u. using different basis sets.

Figure 8

The PES of the (a) neutral (${\mathrm{D}}_2\text{−}{\mathrm{D}}_2{)}_{\mathrm{T}}$ dimer at $R_2=1.42$ a.u. and (b) cationic ${\left({\mathrm{D}}_2\text{−}{\mathrm{D}}_2\right)}_{\mathrm{T}}{}^{+}$ dimer at $R_1=1.61$ a.u. calculated by CASSCF and CASPT2 methods. The black solid curves in panels (c) and (d) are the corresponding difference between the potential energy curves obtained by the two methods in panels (a) and (b).