Quantized nonadiabatic coupling terms of ${\mathrm{H}}_3{}^{+}$

Nonadiabatic coupling terms between the four lowest singlet states of ${\mathrm{H}}_3{}^{+}$ were calculated ab initio. The analysis according to the criteria suggested by Baer and Alijah [Baer and Alijah, Chem. Phys. Lett. 319, 489 (2000)] shows that as many as four electronic states may be required for an accurate description of the reactions $\mathrm{H}+{\mathrm{H}}_2{}^{+}(v,j)\rightleftarrows {\mathrm{H}}^{+}+{\mathrm{H}}_2(v^{\prime },j^{\prime })$, depending on the collision energy.

Figure 1

Potential energy surfaces of the four lowest singlet states of ${\mathrm{H}}_3{}^{+}$ in a hyperspherical representation with the hyper-radius fixed at $\rho =3.0a_0$. The equilateral configuration is at the center of the figure. This configuration corresponds to the minimum of the ground-state surface, while a conical intersection occurs between the first and second excited states.

Figure 2

NACTs in the coordinate $\varphi$ between the four lowest singlet states. The value of the hyper-radius, $\rho$, was fixed at $\rho =3.0a_0$. The hyperangle ${\theta }_{\text{hyp}}$ was varied between ${\theta }_{\text{hyp}}=5^{\circ }$ and ${\theta }_{\text{hyp}}={70}^{\circ }$. In hyperspherical coordinates ${\theta }_{\text{hyp}}=0^{\circ }$ corresponds to the equilateral triangular configuration, while ${\theta }_{\text{hyp}}={90}^{\circ }$ describes linear configurations.

Figure 3

Cuts of the four lowest singlet potential energy surfaces in the coordinate $\varphi$ at $\rho =3.0a_0$ and two values of the hyperangle ${\theta }_{\text{hyp}},{\theta }_{\text{hyp}}={20}^{\circ }$ (left) and ${\theta }_{\text{hyp}}={80}^{\circ }$ (right).

Figure 4

NACTs and transformation angles ${\theta }_{ij}$ for the sequence $\left(12\right)\times \left(23\right)\times \left(13\right)$ and two values of the hyperangle, ${\theta }_{\text{hyp}}={20}^{\circ }$ (left) and ${\theta }_{\text{hyp}}={60}^{\circ }$ (right).

Figure 5

NACTs and transformation angles ${\theta }_{ij}$ for the sequence $\left(34\right)\times \left(23\right)\times \left(24\right)$ and two values of the hyperangle, ${\theta }_{\text{hyp}}={20}^{\circ }$ (left) and ${\theta }_{\text{hyp}}={60}^{\circ }$ (right).

Figure 6

Cuts of the four lowest singlet potential energy surfaces in the coordinate $\varphi$ at $\rho =8.0a_0$ and two values of the hyperangle ${\theta }_{\text{hyp}},{\theta }_{\text{hyp}}={20}^{\circ }$ (left) and ${\theta }_{\text{hyp}}={80}^{\circ }$ (right).

Figure 7

Cuts of the four lowest singlet potential energy surfaces in the atomic-diatomic Jacobi coordinate $R$ for two values of the diatomic distance, $r,r=2.0a_0$ (left) and $r=2.5a_0$ (right), and for two orientations, $C_{2v}$ (solid lines) and linear (dashed lines).

Figure 8

NACTs ${\tau }_{12;\rho },{\tau }_{12;{\theta }_{\text{hyp}}},$ and ${\tau }_{12;\varphi }$ as a function of the Jacobi coordinate $R$, for two values of the diatomic distance, $r,r=2.0a_0$ and $r=2.5a_0$, and for two orientations, $C_{2v}$ and linear.