Correlation effects in strong-field ionization of heteronuclear diatomic molecules

We develop a time-dependent theory to investigate electron dynamics and photoionization processes of diatomic molecules interacting with strong laser fields including electron-electron correlation effects. We combine the recently formulated time-dependent generalized-active-space configuration interaction theory [D. Hochstuhl and M. Bonitz, Phys. Rev. A 86, 053424 (2012); S. Bauch et al., Phys. Rev. A 90, 062508 (2014)] with a prolate spheroidal basis set including localized orbitals and continuum states to describe the bound electrons and the outgoing photoelectron. As an example, we study the strong-field ionization of the two-center four-electron lithium hydride molecule in different intensity regimes. By using single-cycle pulses, two orientations of the asymmetric heteronuclear molecule are investigated: Li-H, with the electrical field pointing from H to Li, and the opposite case of H-Li. The preferred orientation for ionization is determined and we find a transition from H-Li, for low intensity, to Li-H, for high intensity. The influence of electron correlations is studied at different levels of approximation, and we find a significant change in the preferred orientation. For certain intensity regimes, even an interchange of the preferred configuration is observed, relative to the uncorrelated simulations. Further insight is provided by detailed comparisons of photoelectron angular distributions with and without correlation effects taken into account.

Figure 1

Sketch of the coordinate systems for diatomic molecules [65]. The nuclei are labeled A and B, respectively.

Figure 2

Isosurfaces of the restricted Hartree-Fock HOMO (orbital to the right, green) and the core orbital (blue, to the left) of the LiH molecule. The Li nucleus is located to the left (this corresponds to configuration Li-H in Sec. 4). The iboview program was used for the generation of the orbitals using an isosurface with a density threshold of 90.99% [81].

Figure 3

GAS divisions used in this work. Orbitals (labeled by ${\varphi }_i$) of different spin are assumed to have the same energy. The (red) arrows with dots show the allowed excitations. Arrows with strikeouts mean that no excitations are allowed. The nomenclature is SAE, single-active electron; CIS, configuration interaction singles; CAS, complete-active space with $\nu$ spatial orbitals (the star indicates single excitations out of the CAS).

Figure 4

Convergence of the PAD for different GAS at a field intensity of $2.2\times {10}^{13}\mathrm{W}{\mathrm{cm}}^{-2}$ with $m_{\max }=1$. Data are shown for single-cycle excitation of configuration H-Li; see Sec. 4 for details. The PAD for ${\mathrm{CAS}}^{*}$(2,10) with $m_{\max }=2$ [${\mathrm{CAS}}^{*}$(4,4) ] coincides with that of ${\mathrm{CAS}}^{*}$(2,8) [${\mathrm{CAS}}^{*}$(2,3) ] and is therefore not shown.

Figure 5

Photoelectron energy spectrum for the ionization of LiH with a short ($2.01\mathrm{fs}$) pulse with $40.8\mathrm{eV}$ and an intensity of $0.088\times {10}^{13}\mathrm{W}{\mathrm{cm}}^{-2}$ within SAE and ${\mathrm{CAS}}^{*}$(2,8) (converged) approximation.

Figure 6

Photoelectron momentum distribution of LiH after one-photon excitation for a ${\mathrm{CAS}}^{*}$(2,8). An integration cutoff of $r_c=150a_0$ (radial coordinates) was used. See Fig. 5 and text for parameters.

Figure 7

Sketch of the two ionization scenarios of LiH. Panels (a) and (c) show the potential at the peak of the field at $t_0$ for the configuration Li-H (H-Li). The black horizontal line denotes the energy of the active orbital. Panel (b) shows the time dependence of the single-cycle pulse.

Figure 8

Snapshots of the charge density (logarithmic plot) for the two orientations of the LiH molecule at different times during the excitation with the single-cycle pulse using an intensity of $2.20\times {10}^{13}\mathrm{W}{\mathrm{cm}}^{-2}$ for both scenarios, Li-H (left) and H-Li (right); cf. Fig. 7. The classical force $\mathit{F}=-\mathbf{\nabla }V$ points downwards.

Figure 9

Ratio $\varsigma$ [cf. Eq. (22)] of the photoionization yields for the two configurations (see Fig. 7) as a function of the field intensity for the relevant GAS approximations. $\varsigma <1$ ($\varsigma >1$) corresponds to ionization from the $\mathrm{Li}$ ($\mathrm{H}$) end. See text for all other parameters.

Figure 10

Comparison of the PADs for the two configurations Li-H and H-Li at different field intensities for a correlated simulation with ${\mathrm{CAS}}^{*}$(2,8) using single-cycle pulses. All distributions have been scaled to fit in the range $[0,1]$. Note that the schematic (bottom right) gives the potential at the maximum of the electrical field. The dominant direction of the PAD includes also the propagation of the electrons in the field after ionization; see the text for a discussion.

Figure 11

Molecular PADs at different field strengths showing the converged correlated simulations with a ${\mathrm{CAS}}^{*}$(2,8) and with the SAE approximation for the two orientations of the molecule (left two columns, Li-H; right columns, H-Li). The arrows indicate the predominating direction of electron emission.