The ground state structures of first-and second-order inverse sandwich (MIS-I and MIS-II) complexes (M-(C4H4-M)(n) n = 1 and 2) of Mg and Ca have been found to be singlet diradical while the third-order complexes MIS-III (n = 3) are pure triplet. The second hyperpolarizability of the open-shell singlet complexes MIS-I and MIS-II are predicted larger than the analogs triplets. The magnitude of second hyperpolarizability enhances on replacing Mg with Ca metal atom. The larger second hyperpolarizability of MIS-I compared to that of MIS-II of the same metal may be attributed to the intermediate singlet diradical character of the former. (C) 2015 Elsevier B.V. All rights reserved.