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