The geometries, stabilities, and optical properties of lead sulfide (PbS) n clusters (n = 1-16) have been studied by using density functional theory method in order to exposit the structural evolutions and size-dependent stabilities and optical properties. The clusters favor the galena structures and follow a simple cubic growth pattern. The even number clusters show higher stabilities than the odd ones do and the magic numbers appear at n = 4, 8, 10, and 14. The mean static polarizabilities of the lowest-energy structures exhibit a linearly increased tendency while the largest mean second hyperpolarizabilities of each size present the exponentially increased character. (C) 2008 Elsevier B.V. All rights reserved.