Interactions and chemical reactions in ionic alkali-metal and alkaline-earth-metal diatomic $A{B}^{+}$ and triatomic $A_2{B}^{+}$ systems

We theoretically characterize interactions, energetics, and chemical reaction paths in ionic two-body and three-body systems of alkali-metal and alkaline-earth-metal atoms in the context of modern experiments with cold hybrid ion-atom mixtures. Using ab initio techniques of quantum chemistry such as the coupled-cluster method, we calculate ground-state electronic properties of all diatomic $A{B}^{+}$ and most of the triatomic $A_2{B}^{+}$ molecular ions consisting of Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba, and Yb atoms. Different geometries and wave-function symmetries of the ground state are found for different classes of molecular ions. We analyze intermolecular interactions in the investigated systems including additive two-body and nonadditive three-body ones. As an example we provide two-dimensional interaction potential-energy surfaces for ${\mathrm{KRb}}^{+}+\mathrm{K}$ and ${\mathrm{Rb}}^{+}+{\mathrm{Sr}}_2$ mixtures. We identify possible channels of chemical reactions based on the energetics of the reactants. The present results may be useful for investigating controlled chemical reactions and other applications of molecular ions formed in cold hybrid ion-atom systems.

Figure 1

Ground-state potential-energy curves for the KRb molecule and ${\mathrm{KRb}}^{+}$ molecular ions together with definitions of the adiabatic and vertical ionization potentials (${\mathrm{IP}}_{\mathrm{ad}}$ and ${\mathrm{IP}}_{\mathrm{ver}}$), and the vertical electron attachment energy (${\mathrm{EA}}_{\mathrm{ver}}$).

Figure 2

Ground-state potential-energy curves for selected diatomic molecular ions: (a) homonuclear alkali-metal dimers, (b) heteronuclear alkali-metal dimers containing Rb atoms, (c) heteronuclear alkali-metal–alkaline-earth-metal dimers containing Rb atoms, (d) homonuclear alkaline-earth-metal dimers, (e) heteronuclear alkali-metal–alkaline-earth-metal dimers containing Sr atoms, and (f) heteronuclear alkaline-earth-metal dimers containing Sr atoms.

Figure 3

Permanent electric dipole moments for selected diatomic molecular ions. The $z$ axis is oriented from the atom with a larger ionization potential to the atom with a smaller ionization potential and the origin is in the center of mass. The points indicate values for equilibrium distances.

Figure 4

Molecular orbital isosurfaces of homonuclear alkali-metal triatomic molecular ions in the singlet ${}^{1}A_1$ electronic state having the ${}^1{A}^{\prime }_1$ symmetry within the $D_{3h}$ point group at the equilibrium triangular geometry—(a) closed-shell $a_1^{\prime }$ HOMO, (b) $e^{\prime }$ LUMO, and (c) $e^{\prime }$ $\mathrm{LUMO}+1$—and in the triplet ${}^{3}B_2$ electronic state having the ${}^3\mathrm{\Sigma }_u^{+}$ symmetry within the $C_{\infty v}$ point group at the equilibrium linear geometry: (d) open-shell ${\sigma }_g$ HOMO-1, (e) open-shell ${\sigma }_u$ HOMO, and (f) ${\sigma }_g$ LUMO.

Figure 5

Molecular orbital isosurfaces of homonuclear alkaline-earth-metal triatomic molecular ions in the doublet ${}^{2}A_1$ electronic state having the $\underset{g}{{}^2\mathrm{\Sigma }^{+}}$ symmetry within the $C_{\infty v}$ point group at the equilibrium linear geometry—(a) closed-shell ${\sigma }_g$ HOMO-2, (b) closed-shell ${\sigma }_u$ HOMO-1, (c) open-shell ${\sigma }_g$ HOMO, and (d) ${\sigma }_u$ LUMO—and in the doublet ${}^{2}B_2$ electronic state within the $C_{2v}$ point group at the equilibrium triangular geometry: (e) closed-shell $a_1$ HOMO-2, (f) closed-shell $a_1$ HOMO-1, (g) open-shell $b_2$ HOMO, and (h) $b_1$ LUMO.

Figure 6

Two-dimensional cuts through the ground-state potential-energy surfaces of homonuclear alkaline-earth-metal triatomic molecular ions: (a) ${\mathrm{Ca}}_3^{+}$ in the ${}^{2}A_1$ electronic state, (b) ${\mathrm{Ca}}_3^{+}$ in the ${}^{2}B_2$ electronic state, (c) ${\mathrm{Ba}}_3^{+}$ in the ${}^{2}A_1$ electronic state, and (d) ${\mathrm{Ba}}_3^{+}$ in the ${}^{2}B_2$ electronic state.

Figure 7

Two-dimensional cuts through the ground-state potential-energy surfaces of (a) ${\mathrm{KRb}}^{+}+\mathrm{K}$ and (b) ${\mathrm{Rb}}^{+}+{\mathrm{Sr}}_2$ ion-neutral systems. Insets show the corresponding Legendre components.

Figure 8

Minimum-energy reaction paths for the isomerization of selected alkali-metal triatomic molecular ions between their asymmetric $AA{B}^{+}$ and symmetric $AB{A}^{+}$ forms.