In the present work, a number of cyclic planar molecules M(2)A(2) (M = Be, Mg, Ca; A = Li, Na, K) are considered to calculate second-hyperpolarizability using HF, MP2, CCSD, CCSD(T) and DFT methods and 6-311 + + G(d,p), Sadlej-pVTZ, aug-pc-2 and aug-cc-pVTZ basis sets. The molecules are thermodynamically stable. The diffuse electrons on alkali metals are more efficient on enhancing the magnitude of second-hyperpolarizability. The two-state model can explain the origin of second-hyperpolarizability. The rather highest magnitude of second-hyperpolarizability (10(7) au) of the Ca2K2 complex arises from the intense lower energy transition. The vibrational contribution to second-hyperpolarizability has been found to be significant.