Charge Migration in Propiolic Acid: A Full Quantum Dynamical Study

Ionization of molecules very often populates several cationic states launching pure electron dynamics that appear as ultrafast migration of the hole charge throughout the system. A crucial question in the emerging field of attochemistry is whether these pure electronic coherences last long enough to allow for their efficient observation and eventual manipulation with ultrashort laser pulses. We report a full-dimensional quantum calculation of concerted electron-nuclear dynamics initiated by outer-valence ionization of propiolic acid molecule, showing that the charge will oscillate between the carbon triple bond and the carbonyl oxygen for more than 10 fs before getting trapped by the nuclear motion. This time is enough for the charge migration to be observed and controlled. We argue that the molecule is very suitable for experimental studies.

Figure 1

Top panel: Potential energy surfaces of the first four cationic eigenstates of propiolic acid along the normal mode at $462.2{\mathrm{cm}}^{-1}$ belonging to $a^{\prime }$ symmetry. Adiabatic PESs obtained by Green’s function ADC(3)/DZP calculations (dots) and diabatized PESs from the vibronic-coupling model (solid curves) are presented. Middle panel: Molecular orbitals involved in the hole mixing appearing in the ground and the second excited ionic states. Bottom panel: Hole-mixing weights in the ground ionic state along the normal mode shown in the top panel. Horizontal axis of top and bottom panel is the same.

Figure 2

Time-dependent overlaps of the nuclear wave packets ${\chi }_{ij}(t)$, Eq. (5), propagating on the first 4 cationic states of propiolic acid after removal of a HOMO electron. Upper panel: The diagonal elements ${\chi }_{ii}(t)$ giving the population evolution of corresponding states. Lower panel: The real and imaginary part of the most important nondiagonal element ${\chi }_{13}(t)$ related to the degree of coherence of the system.

Figure 3

Time evolution of the hole density, Eq. (8), along the molecular axis of propiolic acid following ionization out of the HOMO. The equilibrium atomic positions are also denoted. The charge-migration oscillations are dephased by the coupling to the nuclear motion. All nuclear d.o.f. are taken into account.