Excitation, relaxation, and quantum diffusion of CO on copper

We investigate the effect of intermode coupling and anharmonicity on the excitation and relaxation dynamics of CO on Cu(100). The nonadiabatic coupling of the adsorbate to the surface is treated perturbatively using a position-dependent state-resolved transition rate model. Using the potential energy surface of Marquardt et al. [J. Chem. Phys. 132, 074108 (2010)], which provides an accurate description of intermode interactions, we propose a four-dimensional model that represents simultaneously the diffusion and the desorption of the adsorbate. The system is driven by both rational and optimized infrared laser pulses to favor either selective mode and state excitations or lateral displacement along the diffusion coordinate. The dissipative dynamics is simulated using the reduced density matrix in its Lindblad form. We show that coupling between the degrees of freedom, mediated by the creation and annihilation of electron-hole pairs in the metal substrate, significantly affects the system excitation and relaxation dynamics. In particular, the angular degrees of freedom appear to play an important role in the energy redistribution among the molecule-surface vibrations. We also show that coherent excitation using simple IR pulses can achieve population transfer to a specific target to some extent but does not allow enforcement of the directionality to the diffusion motion.

Figure 1

Definition of the coordinates for the CO on Cu(100) system. Only the copper atoms of the first layer are represented. A cartoon of the 1D PES along the $X$ axis bisecting the central copper atoms of three adjacent unit cells is depicted in the lower panel.

Figure 2

Probability density of the $9^{\mathrm{th}}$ excited state of the T mode before localization (left panels) and after localization (right panels). The 2D profiles are obtained by integrating all remaining coordinates. The dotted lines mark the separation between unit cells.

Figure 3

Relaxation dynamics of selected eigenstates of CO on Cu(100) located in a single unit cell. The initial states belong to the T mode ($|2,0,0,0;c\rangle$, top left panel), the S mode ($|0,1,0,0;c\rangle$, bottom left panel), and the R mode ($|0,0,0,1;c\rangle$ and $|0,0,1,0;c\rangle$ in the top and bottom right panels, respectively).

Figure 4

Contribution of the different dissipative channels for the energy relaxation of highly excited states of the T mode. The quantum number $m$ refers to the initial state, $|m,0,0,0;c\rangle$. The inverse transition rates ($1/{\Gamma }_{m\to n}$) for the relaxation from state $|m,0,0,0;c\rangle$ to state $|n,0,0,0;c\rangle$ are depicted in red ($m-n=1$ quantum), green ($m-n=2$ quanta), blue ($m-n=3$ quanta), and black ($m-n=4$ quanta), respectively.

Figure 5

Relaxation of a highly excited central state. The 2D density in the $XZ$ plane of the initial state is shown in the inset. The sum of population of states localized in the left, central, and right wells are shown in green, black, and blue, respectively.

Figure 6

Structure of Cu${}_{18}$ clusters used to compute the dipole moment of CO adsorbed on top (left) and at the bridge site (right) of a Cu(100) surface. The yellow, orange, and red balls represent copper, carbon, and oxygen atoms, respectively.

Figure 7

Excitation of the S mode using short $z$-polarized laser fields. The ground state, the first, second, and third excited states, as well as the mixed $Z-\phi$ state are shown in solid red, dashed green, dotted magenta, dotted black, and dotted blue, respectively. The sum of the population of the states depicted is shown as dashed gray lines ($\sum p_i$). Top panel: $\pi$ pulse excitation. Central panel: Locally optimal pulse for the direct excitation of state $|0,1,0,0;c\rangle$ (${\alpha }_0=5$, fluence: $f=780$ mJ/cm${}^2$). Bottom panel: Locally optimal pulse for the sequential excitation of state $|0,3,0,0;c\rangle$; ${\alpha }_0=5$. (${\alpha }_0=5$, fluence: $f=2.0$ J/cm${}^2$) The Fourier transforms of the optimized fields are shown in their respective insets.

Figure 8

Excitation of the T mode and of the R mode using short polarized laser fields. The sum of the population of the states depicted is shown as dashed gray lines ($\sum p_i$). Top left panel: $z$-polarized $\pi$ pulse excitation of the T mode. The ground state (solid red), as well as the second (dashed green), fourth (dotted blue), sixth (dashed magenta), and eighth (dashed dotted cyan) excited states, are shown. Bottom left panel: Locally optimal $z$-polarized pulse for the sequential excitation of state $|0,4,0,0;c\rangle$ (${\alpha }_0=0.1$, fluence: $f=56$ mJ/cm${}^2$) and its Fourier transform (see inset). The key is the same as in the top right panel. Top right panel: $x$-polarized $\pi$ pulse excitation of the R mode. States $|0,0,0,0;c\rangle$ (solid red), $|1,0,0,0;c\rangle$ (dashed magenta), $|2,0,0,0;c\rangle$ (dotted black), $|0,0,0,1;c\rangle$ (dashed green), $|0,0,1,0;c\rangle$ (dotted blue), $|2,0,1,0;c\rangle$ (dashed dotted orange), $|0,1,0,2;c\rangle$ (dotted gray), and $|0,1,1,0;c\rangle$ (dashed dotted cyan) are depicted. Bottom right panel: Locally optimal $x$-polarized pulse for the sequential excitation of state $|0,0,1,0;c\rangle$ (${\alpha }_0=10$, fluence: $f=$ 3.0 J/cm${}^2$). The key is the same as in the top right panel. The Fourier transforms of the optimized fields are shown in their respective insets.

Figure 9

Diffusion along the $x$ direction using $xz$-polarized laser fields. The sums of populations in the left, central, and right wells are depicted in cyan, blue, and magenta, respectively. Top panel: Simultaneous resonant pulses for the S-mode ($z$-polarized, with $\hslash \omega =308$ $hc$/cm and a duration of 1 ps) and R-mode ($x$-polarized, with $\hslash \omega =288$ $hc$/cm and a duration of 4 ps) excitations. Central panel: Sequential resonant pulses using the same parameters as above. Bottom panel: Circularly polarized pulse with energy $\hslash \omega =308$ $hc$/cm and dephasing $\varphi =\pi /2$. The fields' time profiles (in MV/cm), along with their projection on the $x$ ($F_x$, red) and $z$ ($F_z$, green) axes, are shown in black in their respective insets.

Figure 10

Population of the states localized on top of the central copper atom excited simultaneously by a 1-ps $z$-polarized pulse and a 4-ps $x$-polarized pulse. The $z$-polarized pulse is tuned to the S-mode frequency ($\hslash \omega =308$ $hc$/cm). The frequency of the $x$-polarized pulse is chosen as $\hslash {\omega }_u=269$ $hc$/cm (“undertuned,” red), $\hslash {\omega }_{\mathrm{res}}=288$ $hc$/cm (“resonant,” green), and $\hslash {\omega }_o=310$ $hc$/cm (“overtuned,” blue).