Correlated variational treatment of ionization coupled to nuclear motion: Ultrafast pump and ionizing probe of electronic and nuclear dynamics in LiH

We demonstrate a theoretical treatment of dissociative single ionization of the LiH molecule using two-color UV-UV pulse sequences that makes use of a highly correlated description of both the ionization continuum and target molecular ion and neutral states to which it is coupled. The present results emphasize how the details of the ionization process at various internuclear distances combine to form a lens through which such experiments image the dynamics of intermediate electronic states populated by the pump pulse. While ionization yields (dissociative and nondissociative) provide information about the amplitudes and phases that build up the molecular wave packet in the neutral states, molecular frame photoelectron angular distributions exhibit the changing character of those states, i.e., from ionic to covalent. In addition, the time-dependent mean kinetic energy of the wave packet on neutral states is clearly mapped onto the kinetic energy release of the atomic fragments produced by the probe ionization pulse.

Figure 1

Relevant potential energy curves of LiH including the four lowest ${}^1{\mathrm{\Sigma }}^{+}$ and ${}^1\mathrm{\Pi }$ states as well as the ${\mathrm{LiH}}^{+}$ ground state. Schematic representation of two-photon single ionization process. A first photon (400 nm) is used to populate the excited neutral states, and after a time delay a second photon (either 400 nm or 200 nm in the present calculations) ionizes the molecule.

Figure 2

Ionization probability as a function of the time delay between the 5-fs pump (400 nm) and the probe (200 nm). (a) Probability with respect to electron kinetic energy, integrated over kinetic energy release. (b) Probability with respect to kinetic energy release, integrated over electron kinetic energy. (c) Frank Condon overlaps between the wave packet propagating on the $A$ state and the dissociative continuum of the ${}^2\mathrm{X}$ state of ${\mathrm{LiH}}^{+}$ as a function of time. Solid curve in (b) is the expectation value of the wave-packet kinetic energy.

Figure 3

Wave-packet propagation (plotted as $\left|\mathrm{\Psi }\right(R,t\left)\right|$) on the $A$ ${}^1{\mathrm{\Sigma }}^{+}$ state of LiH after being created by a ${sin}^2$ pulse of 5-fs duration at 400 nm with intensity ${10}^{12}$ W/${\mathrm{cm}}^2$ incident on the $v=0$ vibrational state of the $X^1{\mathrm{\Sigma }}^{+}$ ground state.

Figure 4

Ionization cross section from the $A{}^1{\mathrm{\Sigma }}^{+}$ neutral state for different photon energies as a function of the internuclear distance.

Figure 5

Joint distribution of nuclear kinetic energy release and photoelectron kinetic energy for dissociative ionization by a 5-fs 200-nm pulse at delays of (a) 5.1 fs, (b) 15 fs, (c) 44 fs (near outer turning point), and (d) 85 fs (upon return near inner turning point).

Figure 6

MFPADs at different time delays between the pump (400 nm) and the probe (200 nm) for electrons of energy of 2 eV and integrated over kinetic energy release (arbitrary units but same scale for all delays).

Figure 7

As in Fig. 2 but following the dynamics beginning from the $v=1$ vibrational state LiH. (a) Ionization probability integrated over electron kinetic energy as a function of time delay and (solid curve) expectation value of the kinetic energy of the vibrational wave packet. (b) Frank Condon overlaps between the dissociative continuum of the ${}^2\mathrm{X}$ state of ${\mathrm{LiH}}^{+}$ as a function of time.

Figure 8

As in Fig. 3 but for pump and probe beginning from the first excited vibrational state of LiH.

Figure 9

(a) Ionization probability integrated over kinetic energy release, and (b) electron kinetic energy as a function of the time delay between identical 4-fs pump and probe pulses centered at 400 nm both with intensity ${10}^{12}$ W/${\mathrm{cm}}^2$.