Interatomic Coulombic decay of a Li dimer in a coupled electron and nuclear dynamics approach

Interatomic Coulombic decay (ICD) is a fundamental process between atoms or molecules via a neighbor interaction that produces a relaxation of an electronically excited atom or molecule when embedded in an environment. Due to the physical nature of the process, the electronic and nuclear degrees of freedom are coupled. In this paper, we study the ICD process for a lithium dimer by means of the electron and nuclear dynamics (END) approach. The END approach incorporates a full time-dependent description of the electronic and nuclear degrees of freedom, although its current version does not properly account for continuum states and has limitations in the electronic description by using a single determinantal wave function. Despite this, we confirm that the ICD process takes place via a dipole interaction that induces the nuclear motion of the dimer with a consequent electronic population transfer to higher excited states simulating the ionization process. When the dimer approaches a distance of around 11.5 a.u. (6 Å), this ionization process takes place due to the dipole coupling and occurs at the place of the strongest attractive dipole force. Passing that point, we find that the two lithium atoms repel each other via a Coulomb explosion process followed with a consequent kinetic-energy release (KER). We determine the KER and the timing of the ICD process. We point out the strengths and weaknesses of the END approach and the required enhancements to account for a better description of the ICD process in a coupled electron and nuclear dynamics.

Figure 1

Sketch of the Li dimer ICD process. Initially the dimer is separated a distance $R_0$ with the atom $B$ being the ion (a $1s$ electron has been removed) and atom $A$ being the neutral atom (neighbor). As time passes, the dipole interaction causes them to attract and the ICD process occurs at a critical distance $R_{\text{ICD}}$ where they decelerate and then the Coulomb repulsion occurs with a kinetic-energy release (KER).

Figure 2

(a) Li dimer relative distance, $R\left(t\right)$, as a function of time for several initial distances $R_0$. The open triangle symbols and the dashed line that horizontally joins them denote the positions at which the ICD $2s$ electron from atom $A$ is promoted to higher excited states (see Fig. 3). (b) Li dimer relative momentum, $P\left(t\right)$, as a function of time. The open triangle symbols denote when the ICD excitation and ionization occur. Notice that initially the ion and atom attract each other and then after the ICD has taken place they repel each other. The time of closest approach occurs when $P\left(t_{\text{min}}\right)=0$.

Figure 3

(a) Probability to find the valence electron of the system $A$ lithium in its $2s$ state as a function of time for several relative initial distances $R_0$. The dashed line represents the Woods-Saxon function that fits the excitation process. Notice that in the ICD process the $2s$ orbital of the initially neutral atom is emptied at a time $t_0$ with a width $\delta$. (b) Probability to find an electron in the $1s$ core orbital of the system $B$ lithium as a function of time.

Figure 4

(a) Potential-energy curves (PECs) for the ${\mathrm{Li}}^{+}+$ Li dimer as a function of the relative distance, $R_0$, as obtained at the Hartree-Fock level. The initial potential-energy curve is shown as a (green) broken line and carries the label ${\mathrm{Li}}^{+}\left(1s2s\right)+\mathrm{Li}\left(1s^{2}2s\right)$. (b) Transition dipole moment (coupling term) between the initial $2s$ electron in system $A$ and its $2p$ state, as obtained at the Hartree-Fock level as a function of the distance $R_0$. The vertical line is the distance at which the ICD takes place, $R_{\text{ICD}}$. It is seen to correspond to the maximum of the dipole transition moment.