Molecular replacement: the revival of the molecular Fourier transform method

The molecular Fourier transform method, perhaps the first application of the molecular-replacement approach, used in the 1950s for the two-dimensional structure determination of small molecules, has been modernised for the efficient solution of complex structures. In the modern application of the molecular Fourier transform (MFT), the three-dimensional transform of the molecular model is calculated and fitting is achieved by rotating the weighted reciprocal lattice with respect to the calculated transform. The fit between the transform and the weighted reciprocal lattice is gauged by three different criteria corresponding to R factor, correlation coefficient and product 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 enabled the renovation of the rotation-translation search method ULTIMA, which utilizes low-order data and packing considerations for the efficient solution of large structures.