Ehrenfest dynamics with a time-dependent density-functional-theory calculation of lifetimes and resonant widths of charge-transfer states of ${\text{Li}}^{+}$ near an aluminum cluster surface

We present a time-dependent density-functional-theory (TDDFT) Ehrenfest dynamics approach to study the lifetime and the charge neutralization rate of a lithium ion near an aluminum cluster surface. The lifetime of the excited state as a function of the surface-atom distance can be determined, including the effects of level crossings, without prior quantitative information about the coupling between atomic levels and surface states. This method can be used to compute lifetimes of excited atomic states near a surface in both the weak- and the strong-coupling regions and in the avoided crossing region. Because TDDFT Ehrenfest dynamics is a mean-field theory, the wave function consists of contributions from several different excited states during the time propagation. The shortest lifetime is predicted near the region of the avoided crossing between the ${\text{Li}}^{+}\text{-Al}$ and the ${\text{Li-Al}}^{+}$ states.

Figure 1

Linear-response TDDFT potential-energy surfaces of the charge-transfer states of a Li adsorbate on an Al(100) surface. The isolated species energy gap between ${\text{Li}}^{+}\text{-Al}$ and ${\text{Li-Al}}^{+}$ starts at $\sim 1\text{eV}$ and decreases until the avoided crossing region, which occurs at $\sim 4.5\text{Å}$ at the TDDFT level of theory. The figure inset shows the Al cluster with the ${\text{Li}}^{+}$ atom at a distance of $7\text{Å}$.

Figure 2

TDDFT Ehrenfest time evolution of the electron occupation in the $\text{Li}2s$ level. The dynamics start with ${\text{Li}}^{+}$ at $8\text{Å}$, and the charge is transferred into the $\text{Li}2s$ level from interaction with the Al surface. Highlighted segments are fit to exponential functions to obtain the lifetime and the resonant broadening at a variety of distances. Either side of the oscillation can be used for the fitting, and the light and the dark highlighting is for distinguishing different exponential fits.

Figure 3

Resonant width of the $\text{Li}2s$ level as a function of surface-adsorbate distance. Black square points and standard deviation error bars are obtained from exponential fits to the highlighted sections of the TDDFT Ehrenfest $\text{Li}2s$ electron occupation (see Fig. 2). Gray triangles are from exponential fits to real-time TDDFT $\text{Li}2s$ electron occupation, and gray circles are from exponential fits to real-time TDDFT $\text{Li}2s$ electron occupation using a larger Al cluster (see text). The solid line is a least-square fit of a third-order polynomial.