The fragment molecular orbital-based molecular dynamics (FMO-MD) was improved by the introduction of the three-body extension (FMO3) and the generalized dynamic fragmentation. An analytical energy gradient was derived for FMO3 to realize FMO3-MD. An algorithm of generalized dynamic fragmentation was devised to treat each covalent-bonded and, optionally, hydrogen-bonded atom cluster as a fragment in the course of FMO-MD. The new algorithms were tested by performing conventional MO-MD, FMO2-MD, based on two-body extension, and FMO3-MD simulations of (H2O)(32) and H+(H2O)(32). FMO2-MD resulted in lower precision, especially in H+(H2O)(32), while FMO3-MD gave a precision comparable to that of MO-MD. (C) 2009 Elsevier B.V. All rights reserved.