  We introduce a method for global optimization of the structure of atomic
systems that uses additional atoms with fractional existence. The method allows
for movement of atoms over long distances bypassing energy barriers encountered
in the conventional position space. The method is based on Gaussian processes,
where the extrapolation to fractional existence is performed with a vectorial
fingerprint. The method is applied to clusters and two-dimensional systems,
where the fractional existence variables are optimized while keeping the atomic
positions fixed on a lattice. Simultaneous optimization of atomic coordinates
and existence variables is demonstrated on copper clusters of varying size. The
existence variables are shown to speed up the global optimization of large and
particularly difficult-to-optimize clusters.
