The second hyperpolarizabilities (gamma) of the one-dimensional Cr(II) and Mo(II) tetrametallic systems are investigated by focusing on their dependences on the open-shell singlet characters and by comparing with those of their dimetallic analogs. Significant enhancements of gamma are observed in tetrametallic systems, which are attributed to the d sigma electrons with an intermediate open-shell character. The present results enable us to extend the concept of 'sigma-dominant third-order NLO' obtained in dimetallic transition-metal systems to general one-dimensional polymetallic systems. (C) 2012 Elsevier B. V. All rights reserved.