Geometric Phase Appears in the Ultracold Hydrogen Exchange Reaction

Quantum reactive scattering calculations for the hydrogen exchange reaction $\mathrm{H}+{\mathrm{H}}_2(v=4,j=0)\to \mathrm{H}+{\mathrm{H}}_2(v^{\prime },j^{\prime })$ and its isotopic analogues are reported for ultracold collision energies. Because of the unique properties associated with ultracold collisions, it is shown that the geometric phase effectively controls the reactivity. The rotationally resolved rate coefficients computed with and without the geometric phase are shown to differ by up to 4 orders of magnitude. The effect is also significant in the vibrationally resolved and total rate coefficients. The dynamical origin of the effect is discussed and the large geometric phase effect reported here might be exploited to control the reactivity through the application of external fields or by the selection of a particular nuclear spin state.

Figure 1

A 2D slice of the 3D Born-Oppenheimer PES for the ${\mathrm{HD}}_2$ system is plotted at a fixed hyperradius $\rho =3.75a_0$. The different scattering pathways around the CI are indicated, panel (a) for $\mathrm{D}+\mathrm{HD}\to \mathrm{D}+\mathrm{HD}$, and panel (b) for $\mathrm{D}+\mathrm{HD}\to \mathrm{H}+{\mathrm{D}}_2$. For clarity, pathways for only one of the symmetric HD channels are depicted.

Figure 2

The total reaction rate coefficient for the $\mathrm{H}+{\mathrm{H}}_2(v=4,j=0)\to \mathrm{H}+{\mathrm{H}}_2$ (para-para) reaction is plotted as a function of collision energy. The solid curves include all values of total angular momentum $J=0–2$. The dashed and long-short dashed curves include only $J=0$ and were done using the BKMP2 and Mielke PESs, respectively. The red curves include the geometric phase (GP) while the black curves do not (NGP).

Figure 3

Reaction rate coefficients for the $\mathrm{D}+\mathrm{HD}(v=4,j=0)\to \mathrm{D}+\mathrm{HD}(v^{\prime },j^{\prime })$ reaction are plotted as a function of collision energy: (a) $v^{\prime }=0$, $j^{\prime }=11$, (b) $v^{\prime }=3$, $j^{\prime }=5$, (c) $v^{\prime }=1$, and (d) total. The results are for even exchange symmetry, include all values of total angular momentum $J=0–2$, and are based on the BKMP2 PES. The red curves include the geometric phase (GP) while the black curves do not (NGP).