We propose and implement an alternative approach to the original Car-Parrin
ello method where the density matrix elements (instead of the molecular orb
itals) are propagated together with the nuclear degrees of freedom. Our new
approach has the advantage of leading to an O(N) computational scheme in t
he large system limit. Our implementation is based on atom-centered Gaussia
n orbitals, which are especially suited to deal effectively with general mo
lecular systems. The methodology is illustrated by applications to the thre
e-body dissociation of triazine and to the dynamics of a cluster of a chlor
ide ion with 25 water molecules. (C) 2001 American Institute of Physics.