Charge transfer in ultrafast isomerization of acetylene ions

First-principle calculations are employed to investigate the ultrafast isomerization of the acetylene cation and dication. We use the time-dependent density functional theory together with the Ehrenfest dynamics to track the coupled electron-nuclear dynamics. For both the acetylene cation and the dication, we observe nonadiabatic behaviors during the isomerization. We find that the charge transfer not only alters the electronic structure through nonadiabatic transitions, but also plays a key role in the subsequent hydrogen migration. We show that nonadiabatic transitions affect the structural modification of the excited potential energy surface, and also facilitate the ultrafast isomerization through the creation of a channel of increased negative charge that facilitates the proton movement. For the acetylene cation, we find a timescale for hydrogen isomerization of $66\pm 4$ fs, which is consistent with previous pump-probe experiments and on-the-fly calculations. For the dication, we find nonadiabatic transitions occur before the isomerization and identify a similar channel for the proton. Moreover, we find the formation of vinylidene-like structures is always accompanied by a characteristic charge separation on the carbon skeleton. These heuristics will be useful in identifying tautomers and motivating the ultrafast charge-transfer detection methods for future experiments.

Figure 1

(a) Time evolution of the ensemble-averaged vinylidene fraction for the ${\left[\mathrm{H}\mathrm{C}\mathrm{C}\mathrm{H}\right]}^{+}$. Statistical error is computed as the standard error of the mean. (b) Dynamical properties of a typical ${\left[\mathrm{H}\mathrm{C}\mathrm{C}\mathrm{H}\right]}^{+}$ isomerization trajectory. Time evolution of the kinetic energy of the isomerized hydrogen ($E_{\text{kin}}^{\text{iso}}$) and the potential energy ($E_{\text{pot}}$) along the isomerization route. Oblique patterns label the duration of the V-like conformation. Inset snapshots: the CDD with positive (cyan, isovalues: 0.01, 0.02) and negative (golden, isovalues: $-0.02, -0.01$) isosurfaces in atomic units.

Figure 2

Dynamical properties of the typical ${\left[\mathrm{H}\mathrm{C}\mathrm{C}\mathrm{H}\right]}^{+}$ trajectory in Fig. 1 using the Ehrenfest-TDDFT. (a) Time evolution of PECs and projection probabilities along the isomerization route. Open squares: $A{}^2{\mathrm{\Sigma }}_g^{+}$ state. Solid circles: $X{}^2{\mathrm{\Pi }}_u$ state. Solid stars: projection probability onto the $1{\pi }_u$ eigenstate of $A{}^2{\mathrm{\Sigma }}_g^{+}$. Solid squares: projection probability onto the $3{\sigma }_g$ eigenstate of $X{}^2{\mathrm{\Pi }}_u$. (b) Time evolution of the partial charge. Inset snapshots: the hole density with positive (magenta, isovalues: 0.01, 0.02) and negative (gray, isovalues: $-0.02, -0.01$) isosurfaces in atomic units.

Figure 3

Asymmetry parameter distributions for all cationic isomerization trajectories as a function of the isomerization time delay.

Figure 4

Time evolution of the partial charge for a typical ${\mathrm{[HCCH]}}^{2+}$ isomerization trajectory. Oblique patterns: the duration of the V-like structures. Inset snapshots: the CDD structures with positive (cyan, isovalues: 0.01, 0.02) and negative (golden, isovalues: $-0.02, -0.01$) isosurfaces in atomic units.

Figure 5

Potential energy (left column) and kinetic energy of the isomerized hydrogen (right column) as a function of reaction coordinates along the typical cationic isomerization route using the Ehrenfest-TDDFT. The insert in subfigure (a) is the schematic diagram for reaction coordinates. ${\mathrm{H}}_{\mathrm{b}}$ is the isomerized hydrogen. $\theta$ is the angle of intersection between the vector ${\mathbf{C}}_{\mathbf{a}}{\mathbf{C}}_{\mathbf{b}}$ and ${\mathbf{C}}_{\mathbf{b}}{\mathbf{H}}_{\mathbf{b}}$. ${\mathrm{B}}_{{\mathrm{C}}_{\mathrm{b}}{\mathrm{H}}_{\mathrm{b}}}$ and ${\mathrm{B}}_{{\mathrm{C}}_{\mathrm{a}}{\mathrm{C}}_{\mathrm{b}}}$ are the ${\mathrm{C}}_{\mathrm{b}}$–${\mathrm{H}}_{\mathrm{b}}$ and ${\mathrm{C}}_{\mathrm{a}}$–${\mathrm{C}}_{\mathrm{b}}$ bond lengths, respectively. The energy units are eV.

Figure 6

Time evolution of projection probabilities for the typical ${\mathrm{[HCCH]}}^{+}$ trajectory along the isomerization path.