  Low-lying electronically excited states in metallic and semiconductor
nanoparticles continue to be actively investigated because of their relevance
in a wide variety of technological applications. However, first-principles
electronic structure calculations on metallic and semiconductor nanoparticles
are computationally challenging due to factors such as large system sizes,
evaluation and transformation of matrix elements, and high density of
particle-hole states. In this work, we present the development of the
frequency-dependent explicitly-correlated electron-hole interaction kernel
(FD-GSIK) to address the computation bottleneck associated with these
calculations. The FD-GSIK method obtains a zeroth-order description of the
dense manifold of particle-hole states by constructing a transformed set of
dressed particle-holes states. Electron-hole correlation is introduced by using
an explicitly correlated, frequency-dependent two-body operator which is local
in real-space representation. The resulting electron-hole interaction kernel
expressed in an energy-restricted subspace of particle-hole excitations is
derived using the Lowdin's partitioning theory. Finally, the excitation
energies are calculated using an iterative solution of the energy-dependent,
generalized pseudoeigenvalue equation. The FD-GSIK method was used to
investigate low-lying excited states of a series of silver linear clusters and
nanowires. The results from this investigation demonstrate that FD-GSIK is an
effective method for investigating electronic excitations and capturing
electron-hole correlation in nanomaterials.
