Static second hyperpolarizability of Λ shaped alkaline earth metal complexes

A number of Lambda shaped complexes of alkaline earth metals Be, Mg and Ca with varying terminal groups have been considered for the theoretical study of their second hyperpolarizability. The chosen complexes are found to be sufficiently stable and for a chosen ligand the stability decreases in the order: Be-complex > Ca-complex > Mg-complex. The calculated results of second hyperpolarizability obtained at different DFT functionals for the 6-311++G(d,p) basis set are found to be fairly consistent. The Lambda shaped ligands upon complex formation with metals lead to strong enhancement of second hyperpolarizability. The highest magnitude of cubic polarizability has been predicted for the metal complex having > C(C2H5)(2) group. For a chosen ligand, the magnitude of second hyperpolarizability increases in the order Be-complex < Mg-complex < Ca-complex which is the order of increasing size and electropositive character of the metal. The variation of second hyperpolarizability among the investigated metal complexes has been explained in terms of the transition energy and transition moment associated with the most intense electronic transition.