Theoretical treatment of charge transfer in collisions of ${\mathrm{C}}^{2+}$ ions with HF: Anisotropic and vibrational effect

The charge transfer in collisions of ${\mathrm{C}}^{2+}$ ions with the HF molecule has been studied by means of ab initio quantum chemistry molecular methods followed by a semiclassical dynamical treatment in the keV collision energy range. The mechanism of the process, in particular its anisotropy, has been investigated in detail in connection with nonadiabatic interactions around avoided crossings between states involved in the reaction. The vibration of the molecular target has been analyzed and cross sections on different vibrational levels of ${\mathrm{HF}}^{+}$ have been estimated in the Franck-Condon approximation.

Figure 1

Internal coordinates for the ${\mathrm{C}}^{2+}$-HF collision system.

Figure 2

(a) Potential energy curves for the ${}^1{\Sigma }^{+}$ (solid line) and ${}^1\Pi$ (dashed line) states of the ${\mathrm{C}}^{2+}$-HF molecular system at equilibrium, $\alpha =0^{°}$: curve 1, ${\mathrm{C}}^{+}(1s^{2}2s^{2}2p){}^{2}P+{\mathrm{HF}}^{+}({}^2\Pi )$; curve 2, ${\mathrm{C}}^{+}(1s^{2}2s^{2}2p){}^{2}P+{\mathrm{HF}}^{+}({}^2{\Sigma }^{+})$; curve 3, ${\mathrm{C}}^{2+}(1s^{2}2s^2){}^{1}S+\mathrm{HF}({}^1{\Sigma }^{+})$ entry channel. (b) Radial coupling matrix elements between ${}^1{\Sigma }^{+}$ states of the ${\mathrm{C}}^{2+}$-HF molecular system at equilibrium, $\alpha =0^{°}$ [same labels as in part (a)]. (c) Rotational coupling matrix elements between ${}^1{\Sigma }^{+}$ and ${}^1\Pi$ states for the ${\mathrm{C}}^{2+}$-HF molecular system at equilibrium, $\alpha =0^{°}$ [same labels as in part (a)]: $\mathrm{rot}11=\langle 1^1\Pi \left|\mathit{iLy}\right|1^1{\Sigma }^{+}\rangle$, $\mathrm{rot}12=\langle 1^1\Pi \left|\mathit{iLy}\right|2^1{\Sigma }^{+}\rangle$, $\mathrm{rot}13=\langle 1^1\Pi \left|\mathit{iLy}\right|3^1{\Sigma }^{+}\rangle$, $\mathrm{rot}21=\langle 2^1\Pi \left|\mathit{iLy}\right|1^1{\Sigma }^{+}\rangle$, $\mathrm{rot}22=\langle 2^1\Pi \left|\mathit{iLy}\right|2^1{\Sigma }^{+}\rangle$, $\mathrm{rot}23=\langle 2^1\Pi \left|\mathit{iLy}\right|3^1{\Sigma }^{+}\rangle$.

Figure 3

(a) Potential energy curves for the ${}^1{\Sigma }^{+}$ (solid line) and ${}^1\Pi$ (dashed line) states of the ${\mathrm{C}}^{2+}$-HF molecular system at equilibrium, $\alpha ={90}^{°}$: curve 1, ${\mathrm{C}}^{+}(1s^{2}2s^{2}2p){}^{2}P+{\mathrm{HF}}^{+}({}^2\Pi )$; curve 2, ${\mathrm{C}}^{+}(1s^{2}2s^{2}2p){}^{2}P+{\mathrm{HF}}^{+}({}^2{\Sigma }^{+})$; curve 3, ${\mathrm{C}}^{2+}(1s^{2}2s^2){}^{1}S+\mathrm{HF}({}^1{\Sigma }^{+})$ entry channel. (b) Rotational coupling matrix elements between ${}^1{\Sigma }^{+}$ and ${}^1\Pi$ states for the ${\mathrm{C}}^{2+}$-HF molecular system at equilibrium, $\alpha ={90}^{°}$ [same labels as in part (a)]: $\mathrm{rot}11=\langle 1^1\Pi \left|\mathit{iLy}\right|1^1{\Sigma }^{+}\rangle$, $\mathrm{rot}12=\langle 1^1\Pi \left|\mathit{iLy}\right|2^1{\Sigma }^{+}\rangle$, $\mathrm{rot}13=\langle 1^1\Pi \left|\mathit{iLy}\right|3^1{\Sigma }^{+}\rangle$, $\mathrm{rot}21=\langle 2^1\Pi \left|\mathit{iLy}\right|1^1{\Sigma }^{+}\rangle$, $\mathrm{rot}22=\langle 2^1\Pi \left|\mathit{iLy}\right|2^1{\Sigma }^{+}\rangle$, $\mathrm{rot}23=\langle 2^1\Pi \left|\mathit{iLy}\right|3^1{\Sigma }^{+}\rangle$.

Figure 4

(a) Total and partial charge-transfer cross sections for the ${\mathrm{C}}^{2+}$-HF system at equilibrium, $\alpha =0^{°}$: sectot, total cross section; sec32, partial cross section on ${}^1{\Sigma }^{+}\{{\mathrm{C}}^{+}(1s^{2}2s^{2}2p){}^{2}P+{\mathrm{HF}}^{+}({}^2{\Sigma }^{+})\}$; secpi32, partial cross section on ${}^1\Pi \{{\mathrm{C}}^{+}(1s^{2}2s^{2}2p){}^{2}P+{\mathrm{HF}}^{+}({}^2{\Sigma }^{+})\}$; sec31, partial cross section on ${}^1{\Sigma }^{+}\{{\mathrm{C}}^{+}(1s^{2}2s^{2}2p){}^{2}P+{\mathrm{HF}}^{+}({}^2\Pi )\}$; secpi31, partial cross section on ${}^1\Pi \{{\mathrm{C}}^{+}(1s^{2}2s^{2}2p){}^{2}P+{\mathrm{HF}}^{+}({}^2\Pi )\}$. (b) Total and partial charge-transfer cross sections for the ${\mathrm{C}}^{2+}$-HF system for the vibration coordinate $r_{\mathrm{HF}}=1.5$ a.u., $\alpha =0^{°}$ [same labels as in part (a)]. (c) Total and partial charge-transfer cross sections for the ${\mathrm{C}}^{2+}$-HF system at equilibrium, $\alpha ={45}^{°}$ [same labels as in part (a)].

Figure 5

(a) Total charge-transfer cross sections for the ${\mathrm{C}}^{2+}$-HF system in the linear approach, $\alpha =0^{°}$, for different values of the vibration coordinate $r_{\mathrm{HF}}$: dotted line, $r_{\mathrm{HF}}=2.0$ a.u.; solid line, $r_{\mathrm{HF}}=1.73836832$ a.u. (equilibrium); dashed line, $r_{\mathrm{HF}}=1.5$ a.u. (b) Radial coupling matrix elements between ${}^1{\Sigma }^{+}$ states of the ${\mathrm{C}}^{2+}$-HF system in the linear approach, $\alpha =0^{°}$, for different values of the vibration coordinate $r_{\mathrm{HF}}$. Upper curves, rad23; lower curves, rad12. Dotted line, $r_{\mathrm{HF}}=2.0$ a.u.; solid line, $r_{\mathrm{HF}}=1.73836832$ a.u. (equilibrium); dashed line, $r_{\mathrm{HF}}=1.5$ a.u.

Figure 6

(a) Total charge-transfer cross sections for the ${\mathrm{C}}^{2+}$-HF system at equilibrium, for different orientations $\alpha$ from $0^{°}$ to ${180}^{°}$. Dotted line, $\alpha ={90}^{°}$; dot-dashed line, $\alpha ={45}^{°}$; dashed line, $\alpha$ $=$ ${135}^{°}$; thin solid line, $\alpha =0^{°}$; thick solid line, $\alpha ={180}^{°}$. (b) Radial coupling matrix elements between ${}^1{\Sigma }^{+}$ states of the ${\mathrm{C}}^{2+}$-HF system at equilibrium for different orientations. Upper curves, rad23; lower curves, rad12. Dotted line, $\alpha ={90}^{°}$; dot-dashed line, $\alpha ={45}^{°}$; dashed line, $\alpha$ $=$ ${135}^{°}$; thin solid line, $\alpha =0^{°}$; thick solid line, $\alpha ={180}^{°}$.