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## Characterization of Simple Solids using the G-Particle-Hole Equation and the Fourier Transform in Finite Atomic Systems

### Gustavo Ernesto Massaccesi

Previous works have described treatments which combine the G-particle-hole Hypervirial equation and the method of Equations of Motion. In this work we formulate a symmetry-adapted version of the combined algorithm for Abelian groups, in particular the $C_N$ one. The introduction of the point group symmetry within this hybrid framework provides a remarkable computational improvement. The results obtained in selected sets of small-to-medium-sized cyclic one-dimensional chains, used as prototype to describe solid models, reveal a significant computational saving in both floating-point operations and memory storage.