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We introduce a new augmented adaptation of the recently developed fullcoupled-cluster reduction (FCCR) with a second-order perturbative correction,abbreviated as FCCR(2). FCCR is a selected coupled-cluster expansion aimed atoptimally reducing the excitation manifold and commutator expansions forhigh-rank excitations to obtain accurate solutions of the electronicSchrodinger equation in a size-extensive manner. The present FCCR(2) enablesthe estimation of the residual correlation of FCCR by the second-orderperturbative correction $E^{(2)}$ from the complementary space of the FCCRprojection manifold. The linear relationship between $E^{(2)}$ and the energyof FCCR(2) allows accurate estimates of near-exact energies for a wide varietyof molecules with strong electron correlations. The potential of the method isdemonstrated using challenging cases, such as the ground state electronicenergy of the benzene molecule in equilibrium and stretched geometries, and theisomerization energy of the transition metal complex,[Cu(NH$_3$)]$_2$O$_2$$^{2+}$.

Towards near-exact solutions of molecular electronic structure: Full coupled-cluster reduction with a second-order perturbative correction