Detecting Molecular Plasmons by Means of Electron Density Descriptors

Even though collective electronic excitations in extended systems, also called plasmons, can be easily distinguished from single-electron excitations using classical and quantum electromagnetic theory, they are elusive at the molecular scale. Thus, different schemes have been recently proposed to quantify the plasmonicity at molecular scale using classical models and electronic structure quantum methods. The most successful approaches rely on the role played by the electron-electron kernel in the system's response function. Thus, plasmonic character in finite systems has been associated with excitation modes strongly dependent on the electron-electron kernel, whereas those almost independent are considered single-electron excitations. In this work, we explore an alternative way to distinguish between plasmons and single-electron excitations at the molecular scale, based on the analysis of the eigenvalues of the difference density matrix obtained from time-dependent density functional or Hartree-Fock theories. Summation of these eigenvalues represents the electron population effectively promoted from the occupied to the virtual orbital bands when the molecule is excited by electromagnetic radiation. Its value is exactly 1 for an ideal single-electron excitation and significantly exceeds this reference value in the case of plasmons. Such deviation is associated with the emergence of large electronic deexcitation terms, which are known to be crucial to represent plasmon modes correctly. Advantages and disadvantages of this procedure over those previously proposed are also discussed.