Dissociation dynamics of diatomic molecules in intense laser fields: A scheme for the selection of relevant adiabatic potential curves

We investigated the nuclear dynamics of diatomic molecular ions in intense laser fields by analyzing their fragment kinetic-energy release (KER) spectra as a function of the pump-probe delay $\tau$. Within the Born-Oppenheimer (BO) approximation, we calculated ab initio adiabatic potential-energy curves and their electric dipole couplings, using the quantum chemistry code gamess. By comparing simulated KER spectra as a function of either $\tau$ or the vibrational quantum-beat frequency for the nuclear dynamics on both individual and dipole-coupled BO potential curves with measured spectra, we developed a scheme for identifying electronic states that are relevant for the dissociation dynamics. We applied this scheme to investigate the nuclear dynamics in O${}_2$${}^{+}$ ions that are produced by ionization of neutral O${}_2$ molecules in an ultrashort infrared (IR) pump pulse and dissociate due to the dipole coupling of molecular potential curves in a delayed IR probe laser field.

Figure 1

Potential energies for the O${}_2$${}^{+}$ molecular ion calculated using the MCSCF–cc-pVTZ method. The zero of the energy axis is taken as the $\nu =0$ level of the $X{}^3{\Sigma }_g^{-}$ ground state of O${}_2$.

Figure 2

(a) Calculated potential energies and (b) dipole-coupling matrix elements from [18] using the MRD-CI–DZD method in comparison with our MCSCF–cc-pVTZ calculation. Blue dots in (a) correspond to the FSOCI–cc-pVTZ method.

Figure 3

The nuclear dynamics in oxygen molecular ions. The pump-laser pulse launches a nuclear vibrational wave packet onto O${}_2$${}^{+}$ potential curves (shown for $a{}^4{\Pi }_u$ and $f{}^4{\Pi }_g$ states) by ionizing O${}_2$. After a variable time delay, an intense short probe pulse can cause the dissociation of the molecular ion through one-photon or net two-photon processes.

Figure 4

Single-curve calculations for the (a), (b) $A{}^2{\Pi }_u$ and (c), (d) $a{}^4{\Pi }_u$ states of O${}_2$${}^{+}$. (a), (c) Probability densities of the evolving vibrational wave packet and (b), (d) corresponding power spectra.

Figure 5

(a) Probability density $\rho$($R,t$) [Eq. (10)] for O${}_2$${}^{+}$ at fixed pump-probe delay $\tau =10$ fs for the $a{}^4{\Pi }_u$-$f{}^4{\Pi }_g$ two-state calculation. The yellow dashed line corresponds to $R_1=4$. The vibrational wave packet is considered purely dissociative and propagated for 800 fs after the probe pulse. (b) Probability density as a function of internuclear distance $R$ at $t=800$ fs (logarithmic scale).

Figure 6

Calculated KER spectra for the dipole-coupled states $a{}^4{\Pi }_u$ and $f{}^4{\Pi }_g$ as a function of pump-probe delay for (a) $R_1=3$, (b) 4, (c) 4.5, and (d) 5 for a 10 fs, $3\times {10}^{14}$ W/cm${}^2$ probe laser pulse.

Figure 7

Partitioning of the numerical grid into propagation, virtual detector (VD), and absorption intervals. The VD covers the interval [$R_{\min }^{\mathrm{VD}}$, $R_{\max }^{\mathrm{VD}}$].

Figure 8

KER for dipole-coupled $a{}^4{\Pi }_u$ and $f{}^4{\Pi }_g$ states as a function of the pump-probe delay for calculations using the VD method [22] and a 10 fs, $3\times {10}^{14}$ W/cm${}^2$ probe laser pulse.

Figure 9

KER as a function of pump-probe delay for the calculations using the FT method described in Sec. 3b with $R_1=4$. The probe pulse includes the Gaussian pedestal. The parameters used for the main pulse were 10 fs, with a peak intensity of $3\times {10}^{14}$ W/cm${}^2$, and for the pedestal 100 fs and $5\times {10}^{11}$ W/cm${}^2$ (propagated for 800 fs after the end of the probe).

Figure 10

Schematic of the temporal profile of pump and probe pulses.

Figure 11

(a), (b) Calculated and (c), (d) measured [7] KER spectra for O${}_2$${}^{+}$ as a function of (a), (c) pump-probe delay and (b), (d) frequency $f$. Calculated KER spectra include dipole coupling of the $a{}^4{\Pi }_u$ and $f{}^4{\Pi }_g$ states by the 10-fs probe laser pulse with $3\times {10}^{14}$ W/cm${}^2$ peak intensity and a 100 fs, $5\times {10}^{11}$ W/cm${}^2$ Gaussian pedestal. The power spectra in (b) and (d) are obtained for a sampling time of 2 ps.

Figure 12

(a) Franck-Condon amplitudes $\left\{\right|a_{\nu }{|}^2\}$ for the vertical ionization from the ground state of O${}_2$ to the $a{}^4{\Pi }_u$ state of O${}_2$${}^{+}$. (b) Delay-integrated focal-volume-averaged KER as a function of the pump-probe delay, with a main pulse length of 10 fs and a Gaussian pedestal length of 100 fs and for $R_1=4$. The focal-volume average is performed for peak intensities of the probe pulse between ${10}^{13}$ and $4\times {10}^{14}$ W/cm${}^2$, with a fixed ratio of the peak intensities of the main pulse and pedestal of 0.01. (c) Delay-dependent focal-volume-averaged KER spectrum.