Femtosecond-laser induced dynamics of CO on Ru(0001): Deep insights from a hot-electron friction model including surface motion

A Langevin model accounting for all six molecular degrees of freedom is applied to femtosecond-laser induced, hot-electron driven dynamics of Ru(0001)($2\times 2$):CO. In our molecular dynamics with electronic friction approach, a recently developed potential energy surface based on gradient-corrected density functional theory accounting for van der Waals interactions is adopted. Electronic friction due to the coupling of molecular degrees of freedom to electron-hole pairs in the metal are included via a local density friction approximation, and surface phonons by a generalized Langevin oscillator model. The action of ultrashort laser pulses enters through a substrate-mediated, hot-electron mechanism via a time-dependent electronic temperature (derived from a two-temperature model), causing random forces acting on the molecule. The model is applied to laser induced lateral diffusion of CO on the surface, “hot adsorbate” formation, and laser induced desorption. Reaction probabilities are strongly enhanced compared to purely thermal processes, both for diffusion and desorption. Reaction yields depend in a characteristic (nonlinear) fashion on the applied laser fluence, as well as branching ratios for various reaction channels. Computed two-pulse correlation traces for desorption and other indicators suggest that aside from electron-hole pairs, phonons play a non-negligible role for laser induced dynamics in this system, acting on a surprisingly short time scale. Our simulations on precomputed potentials allow for good statistics and the treatment of long-time dynamics (300 ps), giving insight into this system which hitherto has not been reached. We find generally good agreement with experimental data where available and make predictions in addition. A recently proposed laser induced population of physisorbed precursor states could not be observed with the present low-coverage model.

Figure 1

(a) Irreducible wedge of the Ru(0001) surface according to the ${\mathrm{C}}_{3v}$ point group. Shown are the six adsorption sites used in the interpolation of the 6D CRP-RPBE-D2 PES. Ru atoms are gray balls. (b) Contour plot of the CRP-RPBE-D2 PES for the interaction of CO with Ru(0001) (one molecule per $2\times 2$ cell), in the lateral ($X, Y$) space, with all other (four) coordinates optimized. Blue valleys are minima corresponding to upright on-top adsorption, while dark-red spots are local maxima corresponding to hcp and fcc sites, respectively. Values of thick contours are written on the color bar, contours are always separated by 0.025 eV.

Figure 2

Total energy $E$ (relative to the potential minimum) of CO on Ru(0001) as a function of time, obtained from a MDEF calculation, after selective excitation of adsorbate vibrations along $Z$ and $r$, respectively. $E$ is normalized to the excitation energy $E_0=\hslash {\omega }_i$ for each mode. The molecule resides initially in the most stable on-top position, and is excited along the $r$ or $Z$ mode, with a momentum $p_i=m_i{v}_i=\sqrt{2m_i\hslash {\omega }_i}$ directed towards the surface [where $m_r=m_{\mathrm{C}}{m}_{\mathrm{O}}/(m_{\mathrm{C}}+m_{\mathrm{O}})$ and $m_Z=m_{\mathrm{C}}+m_{\mathrm{O}}]$.

Figure 3

(a) $T_{\mathrm{el}}\left(t\right)$ (solid lines) and $T_{\mathrm{ph}}\left(t\right)$ (dashed lines) for a Ru surface driven with 50-fs laser pulses of 400 nm, for two different fluences $F=140 \mathrm{J}/{\mathrm{m}}^2$ and 200 $\mathrm{J}/{\mathrm{m}}^2$, respectively, according to the 2TM. The initial temperature is 300 K, the pulse is maximal at $t=0$. The inset shows the short-time behavior. (b) Adsorbate temperature $T_{\mathrm{ads}}$ over time after excitation with the laser pulse with $F=140$ $\mathrm{J}/{\mathrm{m}}^2$, computed from MDEF and MDEF-GLO kinetic energies and Eq. (9) (see text). The laser pulse in the 2TM has its maximum again at $t=0$ fs. The equilibration phase of $T_{\mathrm{ads}}\left(t\right)$ starts at $-10$ ps and lasts for 10 ps. (c) $T_{\mathrm{el}}\left(t\right)$ (solid lines) and $T_{\mathrm{ph}}\left(t\right)$ (dashed lines) for a Ru surface driven with two laser pulses of 800 nm, with a fluence of 125 $\mathrm{J}/{\mathrm{m}}^2$ and a pulse width of 130 fs each. The first pulse peaks at $t=0$, the second one after a delay time of $t=20$ ps. The base temperature was 200 K in this case.

Figure 4

Time evolution of a typical trajectory of a single CO molecule within the MDEF model, starting from its global minimum, i.e., on top a Ru atom ($X=Y=0, \theta =\varphi =0$), when driven by hot electrons generated from a 140 $\mathrm{J}/{\mathrm{m}}^2$ laser pulse (at $t=0$), $\lambda =400$ nm, FWHM $=50$ fs, base temperature 300 K. The top and middle left panels show the COM coordinates $Z$ and $Y$ over time, the top right and middle panels the entire trajectory in the $(X,Z)$ and $(X,Y)$ planes, respectively. The lower left panel gives the tilt angle $\theta$ as a function of time. The top Ru is visualized by gray circles and the $2\times 2$ unit cell (for which the PES was calculated) in red in the middle right panel. Note, only a single moving CO is shown and the PES is translationally invariant according to $1\times 1$ periodic boundaries.

Figure 5

Diffusion coefficients $D$ as a function of time for three different laser fluences, $\lambda =400$ nm, FWHM $=50$ fs, base temperature of 300 K, within the MDEF (a) and MDEF-GLO models (b), respectively. The diffusion coefficients were obtained using Eq. (11) from $20000$ trajectories over 300 ($+10$) ps, removing those trajectories which lead to desorption (see text). The data were slightly smoothed by averaging over 750-fs time intervals.

Figure 6

“Arrhenius plots” for surface diffusion of CO on Ru(0001), for laser pulses with three different fluences: $\lambda =400$ nm, FWHM $=50$ fs, base temperature of 300 K. The straight lines represent linear fits to our data and determine the Arrhenius parameters. Shown are results from the MDEF model, those from the MDEF-GLO model look similar.

Figure 7

Distribution of ($X,Y$) values for all ($20000$) trajectories at various times, given for two fluences, 100 and 140 $\mathrm{J}/{\mathrm{m}}^2$, 50-fs pulses, base temperature 300 K, MDEF-GLO model. Shown is the $1\times 1$ cell with top, hcp, and fcc sites indicated. For analysis, snapshots of all trajectories were made at several times, and $(X,Y)$ values counted and assigned to certain small ($X+\mathrm{\Delta }X, Y+\mathrm{\Delta }Y$) boxes. Shown are the numbers $N_i$ in a given box.

Figure 8

Distribution of $Z$ and $\theta$ values for all ($20000$) trajectories at various times, given for a fluence of 200 $\mathrm{J}/{\mathrm{m}}^2$, 50-fs pulse, base temperature 300 K. Results for MDEF-GLO (left) and MDEF (right) are shown (for the first $120+10$ ps). For analysis, snapshots of all trajectories were taken every $\mathrm{\Delta }t\sim 0.1$ ps and $Z$ ($\theta$) values determined and assigned to a certain ($Z+\mathrm{\Delta }Z, t+\mathrm{\Delta }t$) or ($\theta +\mathrm{\Delta }\theta , t+\mathrm{\Delta }t$) box. The logarithmic representation $\log (N_i$) (where $N_i$ is the number assigned to a given box) is used to emphasize small structures.

Figure 9

Double-logarithmic plot of desorption yield vs fluence (symbols), including power-law fits (straight lines). Results from MDEF-GLO and MDEF models are shown, and experimental data from Ref. [6]. The laser wavelength was 800 nm, FWHM $=130$ fs, and the base temperature was 200 K. The experimental data were represented such that the desorption yield for $F=305 \mathrm{J}/{\mathrm{m}}^2$ corresponds to 0.2, the value stated in Ref. [6] for this particular fluence.

Figure 10

Two-pulse correlation simulations for desorption yields. (a) Comparison of MDEF-GLO (black curve referring to right scale, see black arrow) and MDEF models (red curve referring to left scale, red arrow). (b) Comparison of MDEF-GLO model and experimental data taken from Ref. [6]. Experimental values have been scaled by a factor of 4.5. For theory, two identical 800-nm pulses each with 130-fs FWHM and a fluence of 125 $\mathrm{J}/{\mathrm{m}}^2$ were used. The coverage was (formally) 0.25 and the base temperature 200 K. In experiment, two slightly different laser pulses of 800 nm, 130-fs FWHM, and total fluence of 250 $\mathrm{J}/{\mathrm{m}}^2$ (for both pulses, individual ratio 52:48) were adopted; coverage was 0.68 and base temperature 200 K. [In Ref. [6], no absolute experimental values are given for 2PC yields. We estimate them by deriving from the reported, experimental single-pulse yield for $F=305 \mathrm{J}/{\mathrm{m}}^2$ of 0.2 (see above), the absolute single-pulse yield at $F=250 \mathrm{J}/{\mathrm{m}}^2$ (0.071), and equaling this value to the yield for two strongly overlapping pulses ($\mathrm{\Delta }t\sim 0$) having the same total fluence.] Each theory data point was obtained with 5000 trajectories. Only the positive delay times were calculated, data with negative $\mathrm{\Delta }t$ were simply obtained by mirroring the data for positive delays. Lines between data points are drawn to guide the eye. Dashed vertical lines in (a) indicate correlation times (of about 18 and 29 ps, respectively), after which desorption yields dropped to $\frac{1}{2}$ of their maximum value (HWHM values).

Figure 11

Potential of mean force $W\left(Z\right)$ (relative to the values for large $Z$) along the molecule-surface distance $Z$, obtained with the RPBE-D2 PES (a) or the RPBE PES (b), both of Ref. [32], for various temperatures. The insets show zoomed-in versions of the main figures.

Figure 12

PMF with $a_2$ inserted by hand and (a) with the correct Eq. (B4) $g\left(Z\right)=g_{\mathrm{trans}}^2\left(Z\right)g_{\mathrm{rot}1}\left(Z\right)g_{\mathrm{rot}2}\left(Z\right)$ or (b) with the presumably incorrect Eq. (B5) $g\left(Z\right)=2g_{\mathrm{trans}}\left(Z\right)g_{\mathrm{rot}1}\left(Z\right)g_{\mathrm{rot}2}\left(Z\right)$, as employed in Refs. [8, 13].

Figure 13

PMF with (a) $a_2=0$ and (b) $a_2=100$ times the $a_2$ value of Fig. 12. For both cases $g\left(Z\right)=g_{\mathrm{trans}}^2\left(Z\right)g_{\mathrm{rot}1}\left(Z\right)g_{\mathrm{rot}2}\left(Z\right)$ was used.