Highly accurate electron affinities and ionization potentials of chemical systems were described by means of the procedure called GHV-EOM (Valdemoro et al, in Int J Quantum Chem 112:2965, 2012), which combines the G-particle-hole hypervirial (GHV) equation method (Alcoba et al, in Int J Quantum Chem 109:3178, 2009) and that of the equations-of-motion (EOM), by Simons and Smith (Simons and Smith, in J Chem Phys 58:4899, 1973). The present work improves that hybrid method by introducing the point group symmetry within its framework, providing a higher computational efficiency. We report results which show the achievements attained by using the symmetry-adapted methodology. The new formulation turns out to be particularly suitable for characterizing solid models, as cyclic one-dimensional chains.