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Low-lying electronically excited states in metallic and semiconductornanoparticles continue to be actively investigated because of their relevancein a wide variety of technological applications. However, first-principleselectronic structure calculations on metallic and semiconductor nanoparticlesare computationally challenging due to factors such as large system sizes,evaluation and transformation of matrix elements, and high density ofparticle-hole states. In this work, we present the development of thefrequency-dependent explicitly-correlated electron-hole interaction kernel(FD-GSIK) to address the computation bottleneck associated with thesecalculations. The FD-GSIK method obtains a zeroth-order description of thedense manifold of particle-hole states by constructing a transformed set ofdressed particle-holes states. Electron-hole correlation is introduced by usingan explicitly correlated, frequency-dependent two-body operator which is localin real-space representation. The resulting electron-hole interaction kernelexpressed in an energy-restricted subspace of particle-hole excitations isderived using the Lowdin's partitioning theory. Finally, the excitationenergies are calculated using an iterative solution of the energy-dependent,generalized pseudoeigenvalue equation. The FD-GSIK method was used toinvestigate low-lying excited states of a series of silver linear clusters andnanowires. The results from this investigation demonstrate that FD-GSIK is aneffective method for investigating electronic excitations and capturingelectron-hole correlation in nanomaterials.

Investigation of dense manifold of particle-hole excitations in metallic  nanowires using r12-correlated frequency-dependent electron-hole interaction  kernel