Symmetry breaking in TDLDA dynamics of symmetric molecules

In a recent series a papers, we have identified an unstable behavior in the electronic response of small molecules to some ultrafast XUV pulses. Calculations have been done using real-time Time-Dependent Density Functional Theory in the Local Density Approximation version complemented by a self-interaction correction. The aim of the present paper is to clarify the mechanism of dipole instability by associating it with a symmetry breaking. The line of arguments develops along two steps. We first discuss the spectral properties of the instability in dynamical scenarios, focusing on the simplified case of direct hole creation at initial time. We discuss in particular the potential relation of the instability to the plasmon. We show that, in some specific cases, the plasmon frequency characterizes the dipole instability. Still, in most cases, an oscillation between 2 single-particle levels pops up. As a second step, we analyze the energy surfaces associated with such single-particle transitions and see that these surfaces do indeed display a maximum in the case of direct drilling of a hole state. This characterizes a typical symmetry breaking in mean-field models.