The molecular Fourier transform method, perhaps the first application of th
e molecular-replacement approach, used in the 1950s for the two-dimensional
structure determination of small molecules, has been modernised for the ef
ficient solution of complex structures. In the modern application of the mo
lecular Fourier transform (MFT), the three-dimensional transform of the mol
ecular model is calculated and fitting is achieved by rotating the weighted
reciprocal lattice with respect to the calculated transform. The fit betwe
en the transform and the weighted reciprocal lattice is gauged by three dif
ferent criteria corresponding to R factor, correlation coefficient and prod
uct function. Since the procedure involves the rotation of indices and is,
therefore, independent of the number of atoms, it is much faster than other
methods which employ the rotation of the molecular model. This feature ena
bled the renovation of the rotation-translation search method ULTIMA, which
utilizes low-order data and packing considerations for the efficient solut
ion of large structures.