Plasmons in molecules: microscopic characterization based on orbital transitions and momentum conservation

In solid state physics, electronic excitations are often classified as plasmons or single-particle excitations. The former class of states refers to collective oscillations of the electron density. The random-phase approximation allows for a quantum-theoretical treatment and a characterization on a microscopic level as a coherent superposition of a large number of particle-hole transitions with the same momentum transfer. However, small systems such as molecules or small nanoclusters lack the basic properties (momentum conservation and uniform exchange interaction) responsible for the formation of plasmons in the solid-state case. Despite an enhanced interest in plasmon-based technologies and an increasing number of studies regarding plasmons in molecules and small nanoclusters, their definition on a microscopic level of theory remains ambiguous. In this work, we analyze the microscopic properties of molecular plasmons in comparison with the homogeneous electron gas as a model system. Subsequently, the applicability of the derived characteristics is validated by analyzing the electronic excitation vectors with respect to orbital transitions for two linear polyenes within second order versions of the algebraic diagrammatic construction scheme for the polarization propagator.