  In finite systems, such as nanoparticles and gas-phase molecules,
calculations of minimum energy paths (MEPs) connecting initial and final states
of transitions as well as searches for saddle points are complicated by the
presence of external degrees of freedom, such as overall translation and
rotation. A method based on quaternion algebra for removing the external
degrees of freedom is described here and applied in calculations using two
commonly used methods: the nudged elastic band (NEB) method for MEPs and the
DIMER method for finding the minimum mode in minimum mode following searches of
first-order saddle points. With the quaternion approach, fewer images in the
NEB are needed to represent MEPs accurately. In both NEB and DIMER calculations
of finite systems, the number of iterations required to reach convergence is
significantly reduced. The algorithms have been implemented in the Atomic
Simulation Environment (ASE) open source software.
