Determination of structure parameters in strong-field tunneling ionization theory of molecules

In the strong field molecular tunneling ionization theory of Tong et al. [Phys. Rev. A 66, 033402 (2002)], the ionization rate depends on the asymptotic wave function of the molecular orbital from which the electron is removed. The orbital wave functions obtained from standard quantum chemistry packages in general are not good enough in the asymptotic region. Here we construct a one-electron model potential for several linear molecules using density functional theory. We show that the asymptotic wave function can be improved with an iteration method and after one iteration accurate asymptotic wave functions and structure parameters are determined. With the new parameters we examine the alignment-dependent tunneling ionization probabilities for several molecules and compare with other calculations and with recent measurements, including ionization from inner molecular orbitals.

Figure 1

(a) Effective charge of Ne with and without the iteration (see text). Empirical model potential is from Ref. [20]. (b) Effective charge of CO${}_2$ along the molecular axis.

Figure 2

Normalized alignment dependence of ionization probability. (a) ${\mathrm{N}}_2$ at laser intensity of ${10}^{14}$ W/cm${}^2$; (b) ${\mathrm{O}}_2$ at ${10}^{14}$ W/cm${}^2$; (c) ${\mathrm{F}}_2$ at $2\times {10}^{14}$ W/cm${}^2$; (d) ${\mathrm{H}}_2^{+}$ at $5\times {10}^{14}$ W/cm${}^2$; (e) ${\mathrm{H}}_2$ at $2.3\times {10}^{14}$ W/cm${}^2$; (f) ${\mathrm{C}}_2$H${}_2$ at $5\times {10}^{13}$ W/cm${}^2$. TDDFT${}^a$ from Telnov et al. [29], TDDFT${}^b$ from Otobe et al. [32], TDSE${}^a$ from Kamta et al. [33], TDSE${}^b$ from Kjeldsen et al. [34], Tong et al. [9], and Lin et al. [31].

Figure 3

Alignment dependence of ionization rates of HOMO, HOMO-1, and HOMO-2 for ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and CO${}_2$ and of HOMO and HOMO-1 for ${\mathrm{C}}_2$H${}_2$. (a) ${\mathrm{N}}_2$ at laser intensity of $1.5\times {10}^{14}$ W/cm${}^2$; (b) ${\mathrm{O}}_2$ at $1.3\times {10}^{14}$ W/cm${}^2$; (c) CO${}_2$ at $1.1\times {10}^{14}$ W/cm${}^2$; (d) ${\mathrm{C}}_2$H${}_2$ at $1.5\times {10}^{14}$ W/cm${}^2$.

Figure 4

Alignment dependence of ionization rates of HOMO and HOMO-1. (a) CO at laser intensity of $4\times {10}^{14}$ W/cm${}^2$; (b) HCl at $2\times {10}^{14}$ W/cm${}^2$; (c) CO at $4\times {10}^{14}$ W/cm${}^2$; (d) HCl at $2\times {10}^{14}$ W/cm${}^2$. MO-ADK-S is the averaged MO-ADK rate for angles $\theta$ and $\pi -\theta$.

Figure 5

Comparison of ionization rates of HOMO, HOMO-1, and HOMO-2 of CO${}_2$ at peak laser intensity of $1.5\times {10}^{14}$ W/cm${}^2$. The solid lines are from MO-ADK and the dashed lines are from Spanner and Patchkovskii [48] (a) and from Smirnova et al. [38] (b).

Figure 6

Normalized alignment dependence of ionization probability. (a) ${\mathrm{N}}_2$ at laser intensity of $1.5\times {10}^{14}$ W/cm${}^2$; (b) ${\mathrm{O}}_2$ at $1.3\times {10}^{14}$ W/cm${}^2$; (c) ${\mathrm{H}}_2$ at $2.3\times {10}^{14}$ W/cm${}^2$; (d) HCl at $1.4\times {10}^{14}$ W/cm${}^2$. Linearly polarized lights for (a) and (b); circularly polarized lights for (c) and (d). Exp.${}^a$ from Pavičić et al. [3]; Exp.${}^b$ from Staudte et al. [4] and Exp.${}^c$ from Akagi et al. [5]. Additional symbols for (d), see text.

Figure 7

Normalized alignment dependence of ionization probability of ${\mathrm{H}}_2^{+}$. (a) 1s${\sigma }_g$ at laser intensity of $5\times {10}^{14}$ W/cm${}^2$; (b) 1s${\sigma }_u$ at ${10}^{14}$ W/cm${}^2$; (c) 2p${\pi }_u$ at ${10}^{13}$ W/cm${}^2$; (d) 2p${\pi }_g$ at ${10}^{12}$ W/cm${}^2$. TDSE${}^a$ from Kamta et al. [33], TDSE${}^b$ from Kjeldsen et al. [34] and TDSE${}^c$ from Telnov et al. [51].

Figure 8

(a) $R$ dependence of the normalized ionization probability of ${\mathrm{H}}_2^{+}$ at laser intensity of ${10}^{14}$ W/cm${}^2$; see text. (b) The normalized alignment dependence of ionization rate at $5\times {10}^{14}$ W/cm${}^2$ for 1s${\sigma }_g$; (c) the normalized alignment dependence of ionization rate at ${10}^{14}$ W/cm${}^2$ for 1s${\sigma }_u$. TDSE from Ref. [52].