Laser-induced alignment of weakly bound molecular aggregates

The rotational and torsional dynamics of the prototypical floppy $\mathrm{indole}\left({\mathrm{H}}_2\mathrm{O}\right)$ molecular cluster was theoretically and computationally analyzed. The time-dependent Schrödinger equation was solved for a reduced-dimensionality description of the cluster, taking into account overall rotations and the internal rotation of the water moiety. Based on our results, it became clear that the coupling between the internal and the overall rotations is small, and that for typical field strengths in alignment and mixed-field-orientation experiments the rigid-rotor approximation can be employed to describe the investigated dynamics. Furthermore, the parameter space over which this is valid and its boundaries where the coupling of the internal and overall rotation can no longer be neglected were explored.

Figure 1

Sketch of the $\mathrm{indole}\left({\mathrm{H}}_2\mathrm{O}\right)$ dimer cluster. The most polarizable axis defines the $z$ axis of the molecular frame. The torsional angle is defined as the dihedral angle between the indole and water planes. For the experimentally determined structure, see Ref. [29].

Figure 2

(a) The ab initio 1D potential-energy surface (blue circles) and corresponding fit (blue line) and the lowest two field-free torsional energy levels of $\mathrm{indole}\left({\mathrm{H}}_2\mathrm{O}\right)$, obtained from the pure torsional part of the Hamiltonian (1). Each torsional level, denoted by the vibrational quantum number $v$, is split into two sublevels $\sigma =0,1$ of opposite parity. (b) Field-free rotation-torsional energy levels for $J=0,...,3$ corresponding to the torsional ground state, obtained from the Hamiltonian (1). Due to the small coupling between the internal and overall rotation, the energy levels are approximately given by the sum of the pure torsional and pure rotational energies. Thus, for each $J$, there are $2J+1$ rotational energy levels in a given torsional sublevel; see text for more details.

Figure 3

For the ground state of $\mathrm{indole}\left({\mathrm{H}}_2\mathrm{O}\right)$ ($T=0\text{K}$), the time evolution of the expectation values (a) $\langle {cos}^2\theta \rangle$, (b) $\langle cos\theta \rangle$, and (c) $〈{cos}^2\tau 〉$ using $\underline{\underline{\alpha }}\left(\tau \right)$ from ab initio calculations [thick blue (dark gray) lines] and the modified $\widetilde{\underline{\underline{\alpha }}}\left(\tau \right)$ (thick black lines). For comparison, results using the rigid-rotor approximation for the two polarizabilities are shown [thin red (light gray) lines and thin green (gray) lines, respectively]. The results for the ab initio polarizability $\underline{\underline{\alpha }}\left(\tau \right)$ and the rigid-rotor approximation in (a) and (b) are practically indistinguishable. The smallest values of $\langle {cos}^2\theta \rangle$ and $\langle cos\theta \rangle$ and the largest value of $〈{cos}^2\tau 〉$ at the peak intensity are obtained for the modified polarizability $\widetilde{\underline{\underline{\alpha }}}\left(\tau \right)$. The result for the modified polarizability differs from the corresponding rigid-rotor result at the peak intensity. The insets in (a) and (b) show a zoom of $\langle {cos}^2\theta \rangle$ and $\langle cos\theta \rangle$ close to the peak intensity. The gray area illustrates the envelope of the laser field with $E_0=2.74\times {10}^7\mathrm{V}/\mathrm{cm}$. The static field strength is ${\mathbf{E}}_{\mathrm{stat}}=600$ $\mathrm{V}/\mathrm{cm}$.

Figure 4

The ab initio results for the components of (a) the EDM $\mathbf{\mu }\left(\tau \right)$ and (b) the polarizability $\underline{\underline{\alpha }}\left(\tau \right)$ (symbols). The solid lines are the analytical functions fitted to the ab initio results; see Appendix pp3.