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

G.E. MASSACCESI; J.J. TORRES-VEGA; E. RIOS; A. CAMJAYI; A. TORRE; L. LAIN; O.B. OÑA; W. TIZNADO; D.R. ALCOBA

Buenos Aires

Congreso; Mathematical Congress of the Americas 2021 (MCA 2021); 2021

Universidad de Buenos Aires

The natural space to analyze the electron distribution in a linear crystal is generated by the functions corresponding to the lowest energy orbitals associated with the atoms of the system. The periodic repetition of the atoms makes this a Shift Invariant Space. A similar structure is associated with one-dimensional cyclic crystals in which the translational symmetry is analogous to rotations. 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 CN 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.