Ultrafast Dynamics of Photoionized Acetylene

Acetylene cations $[\mathrm{HCCH}{]}^{+}$ produced in the $A^2{\Sigma }_g^{+}$ state by extreme ultraviolet (XUV) photoionization are investigated theoretically, based on a mixed quantum-classical approach. We show that the decay of the $A^2{\Sigma }_g^{+}$ state occurs via both ultrafast isomerization and nonradiative electronic relaxation. We find a time scale for hydrogen migration and electronic decay of about 60 fs, in good agreement with recent XUV-pump/XUV-probe time-resolved experiments on the same system [Phys. Rev. Lett. 105, 263002 (2010)]. Moreover, we predict an efficient vibrational energy redistribution mechanism that quickly transfers excess energy from the isomerization coordinates to slower modes in a few hundred femtoseconds, leading to a partial regeneration of acetylenelike conformations.

Figure 1

Upper part: Potential energy surfaces for the $X^2{\Pi }_u$ and $A^2{\Sigma }_g^{+}$ states of the monocation. Lower part: Two one-dimensional cuts along the ${\mathrm{C}}_2\mathrm{\text{−}}{\mathrm{C}}_1\mathrm{\text{−}}{\mathrm{H}}_a$ angle (${\alpha }_a$) and the ${\mathrm{C}}_1\mathrm{\text{−}}{\mathrm{H}}_a$ distance ($r_{1a}$) for the PESs of the $X^2{\Pi }_u$ and $A^2{\Sigma }_g^{+}$ states. In all curves the rest of coordinates are kept at their ground-state values.

Figure 2

(a) Potential energy cuts along the isomerization (dashed lines) and trans-bend (solid lines) paths for the $X^2{\Pi }_u$ and $A^2{\Sigma }_g^{+}$ states as a function of the ${\alpha }_a$ angle. The ${\mathrm{C}}_1\mathrm{\text{−}}{\mathrm{H}}_a$ distance is linearly varied from 1 to 2.25 Å along the isomerization path. Along the trans-bend path, both ${\alpha }_a$ and ${\mathrm{H}}_b\mathrm{\text{−}}{\mathrm{C}}_2\mathrm{\text{−}}{\mathrm{C}}_1$ (${\alpha }_b$) angles are varied by the same amount, and the ${\mathrm{H}}_b\mathrm{\text{−}}{\mathrm{C}}_2\mathrm{\text{−}}{\mathrm{C}}_1\mathrm{\text{−}}{\mathrm{H}}_a$ dihedral angle is set to 180 deg. All other coordinates are kept frozen. Only the higher energy $X^2{\Pi }_u$ state is shown. (b) Potential energy curves along the cis-bend path. Both ${\alpha }_a$ and ${\alpha }_b$ angles are varied by the same amount, and the ${\mathrm{H}}_b\mathrm{\text{−}}{\mathrm{C}}_2\mathrm{\text{−}}{\mathrm{C}}_1\mathrm{\text{−}}{\mathrm{H}}_a$ dihedral angle is set to 0 deg.

Figure 3

(a) Time evolution of the vinylidene fraction when starting from the $A^2{\Sigma }_g^{+}$ state of the acetylene monocation. (b) Time evolution of the electronic population of the $A^2{\Sigma }_g^{+}$ and $X^2{\Pi }_u$ states for initial preparation of the acetylene cation in the $A^2{\Sigma }_g^{+}$ state.

Figure 4

Time evolution of the ensemble average of the total vibrational energy for $A^2{\Sigma }_g^{+}$ and $X^2{\Pi }_u$ initial states. The inset presents the evolution of the vibrational energy of the C-C mode.