Femtosecond dynamics of excited states of $\mathrm{C}\mathrm{O}$ adsorbed on $\mathrm{Mg}\mathrm{O}\left(001\right)\text{‐}(1\times 1)$

We have investigated the time development of excited electronic states of $\mathrm{C}\mathrm{O}$ molecules adsorbed on the $\mathrm{Mg}\mathrm{O}\left(001\right)\text{–}(1\times 1)$ surface using a state-of-the-art first principles approach. Density-functional theory is used to calculate the ground state geometry of the clean surface and of the molecules adsorbed on the surface. Thereafter, the quasiparticle band structures of bulk MgO, of the $\mathrm{Mg}\mathrm{O}\left(001\right)\text{–}(1\times 1)$ surface, and of $\mathrm{C}\mathrm{O}$ adsorbed on the surface are calculated within the GW approximation. Taking the electron-hole interaction into consideration the electron-hole excitations and their optical spectrum are obtained from the solution of the Bethe-Salpeter equation for the electron-hole two-particle Green function. The optical spectra of bulk MgO, the $\mathrm{Mg}\mathrm{O}\left(001\right)\text{–}(1\times 1)$ surface, and $\mathrm{C}\mathrm{O}$ adsorbed on the surface are calculated, yielding good agreement with available experimental data. Finally, based on the solution of the BSE for the adsorbate system $\mathrm{C}\mathrm{O}:\mathrm{Mg}\mathrm{O}\left(001\right)\text{–}(1\times 1)$, the time propagation of molecular excitations is studied employing the time-dependent Schrödinger equation. An initial $\mathrm{C}\mathrm{O}$ excitation exhibits a very fast decay due to its coupling to charge-transfer exciton states between the substrate and the adsorbate. The decay is characterized by a lifetime of about 1.6 fs, which is a factor of 5 faster than the decay of single-particle states.

Figure 1

Bulk band structure of MgO, as obtained within GWA (solid curves) and within LDA (dotted curves).

Figure 2

Optical absorption spectrum ${ϵ}_2^B\left(\omega \right)$ of bulk MgO, calculated from three valence and four conduction bands (solid curve), as well as from three valence and one conduction bands (dashed curve), respectively. The dash–dotted curve shows the independent-particle spectrum, i.e., without including the electron–hole interaction. A Lorentzian broadening of 0.3 eV has been used. The open circles denote the experimental result taken from Ref. 38.

Figure 3

Surface band structure of $\mathrm{Mg}\mathrm{O}\left(001\right)\text{–}\left(1\times 1\right)$, obtained within GWA. Only the bands that are included in the Bethe-Salpeter equation are shown. The vertical lines indicate the projected bulk band structure.

Figure 4

Optical absorption spectrum of the $\mathrm{Mg}\mathrm{O}\left(001\right)\text{–}\left(1\times 1\right)$ surface (calculated for normal incidence of light) is shown as solid curve. For comparison the independent-particle spectrum, calculated without electron–hole interaction, is shown as a dashed curve. Lorentzian broadening of 0.14 eV is included.

Figure 5

Optimal adsorption geometry of $\mathrm{C}\mathrm{O}$ on $\mathrm{Mg}\mathrm{O}\left(001\right)\text{–}\left(1\times 1\right)$ (side view). Note that the figure shows a plane ([100] plane of the underlying MgO bulk crystal) in which second-nearest-neighbor $\mathrm{C}\mathrm{O}$ molecules are displayed (at a distance of 4.21 Å).

Figure 6

Left panel: GW band structure of an isolated $\mathrm{C}\mathrm{O}$ monolayer, center panel: GW band structure of $\mathrm{C}\mathrm{O}:\mathrm{Mg}\mathrm{O}\left(100\right)\text{–}\left(1\times 1\right)$, solid and dashed curves denote $\mathrm{C}\mathrm{O}$ and MgO bands, respectively. The energies refer to the vacuum level [at $\mathrm{VBM}\left(\mathrm{Mg}\mathrm{O}\right)+7.4\mathrm{eV}$]. The vertical lines indicate the projected bulk band structure. Right panel: onsite energies of the $\mathrm{C}\mathrm{O}$ bands of the center panel, as obtained by tight-binding analysis, indicating the energetic positions of a single $\mathrm{C}\mathrm{O}$ molecule adsorbed on MgO. The numbers given in brackets denote the onsite energies, allowing the direct comparison with the energy levels of gas-phase $\mathrm{C}\mathrm{O}$.

Figure 7

Left panel: Optical absorption spectrum of the isolated $\mathrm{C}\mathrm{O}$ monolayer, right panel: optical absorption spectrum of $\mathrm{C}\mathrm{O}:\mathrm{Mg}\mathrm{O}\left(100\right)\text{–}\left(1\times 1\right)$. A broadening of 0.14 eV is included in the figure.

Figure 8

Panels (a) and (b) show the distribution (side view) of the electron relative to the hole and the hole relative to the electron, respectively, for the first exciton state $\mid {}^1\mathrm{\Pi }⟩$ (at 7.9 eV) of the isolated $\mathrm{C}\mathrm{O}$ monolayer. The hole in panel (a) and the electron in panel (b) are both located at the $\mathrm{C}$ atom. Panels (c) and (d) show the distribution (side view) of the electron relative to the hole and the hole relative to the electron, respectively, for the first exciton state (at 4.9 eV) of $\mathrm{C}\mathrm{O}:\mathrm{Mg}\mathrm{O}\left(001\right)\text{–}\left(1\times 1\right)$. The hole in panel (c) is located at the surface $\mathrm{O}$ atom and the electron in panel (d) is located at the $\mathrm{C}$ atom.

Figure 9

Projected density of excitonic states $\mathrm{\Gamma }\left(E\right)$ (solid curve) of the molecular $\mid {}^1\mathrm{\Pi }⟩$ state in the coupled $\mathrm{C}\mathrm{O}:\mathrm{Mg}\mathrm{O}\left(100\right)\text{–}\left(1\times 1\right)$ system. For comparison, the excitation energy of $\mid {}^1\mathrm{\Pi }⟩$ of the isolated $\mathrm{C}\mathrm{O}$ monolayer (7.9 eV) is indicated by the dashed line.

Figure 10

Density distribution of the excited hole (starting from $\mid {}^1\mathrm{\Pi }⟩$) with increasing time for ${\mathbf{r}}_e$ at the central molecule. For better visibility, the charge density values in the substrate have been amplified by a factor of 5.

Figure 11

Vertical electron-hole correlation function of the singlet excitation state (starting from $\mid {}^1\mathrm{\Pi }⟩$) with increasing time. $z_h\left(z_e\right)$ denote the vertical position of the excited hole (electron). The vertical and horizontal grid lines indicate the $z$ position of the atoms of the $\mathrm{C}\mathrm{O}$ molecule (on the right and at the top, respectively, of each panel), as well as the atomic layers of the six-layer substrate slab (on the left and at the bottom, respectively).

Figure 12

Survival amplitude of the molecular excitation as a function of time (on a logarithmic scale). The three curves in panel a were calculated for the four-, six-, and seven-layer substrate slab, respectively, using 36 $\mathbf{k}$ points. The three curves in panel (b) were calculated for the four-layer substrate slab, using 36, 64, and 100 $\mathbf{k}$ points, respectively. The straight dashed line denotes a fit to the exponential decay as a guide to eye.

Figure 13

Vertical density distribution $\rho \left(z_h,t\right)$ of the hole of the $\mathrm{C}\mathrm{O}$ exciton for increasing time. As counting from the left to the right, the first six circles denote six atomic layers of the substrate and the last two solid circles denote the $\mathrm{C}$ atom sublayer and the $\mathrm{O}$ atom sublayer of the $\mathrm{C}\mathrm{O}$ adlayer, respectively. For comparison, $\rho \left(z_h,t=0\right)$ is included in every panel.

Figure 14

Survival amplitude (on a logarithmic scale) of the $\mathrm{C}\mathrm{O}$ $5\sigma$ single hole state at $\mathbf{k}=\left(0.4167,0.4167\right)2\mathrm{\pi }∕a$ (dashed-dotted curve), $\mathbf{k}=\left(0.5,0.4\right)2\mathrm{\pi }∕a$ (long dashed curve), and $\mathbf{k}=\left(0.5,0.45\right)2\mathrm{\pi }∕a$ (short dashed curve) in the coupled system containing six substrate atomic layers. As a guide to the eye, the thin and thick solid lines denote exponential decay with time constants of 8 and 27 fs, respectively.