Very recently, we have shown the suitability to combine the G-particle-hole Hypervirial (GHV) equation method (Alcoba et al. in Int J Quantum Chem 109:3178, 2009) with the Hermitian Operator (HO) method (Bouten et al. in Nucl Phys A 202:127, 1973) for computing various energy differences of an electronic system spectrum (Valdemoro et al. in J Math Chem 50:492, 2012). The purpose of this paper is to extend our preliminary studies by applying the combined GHV-HO method to obtain the set of ground and low-lying excited states potential energy curves of several selected electronic systems. The calculations confirm the reliability of the method.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas