Molecular replacement (MR)[1] is a method of solving the phase problem in X-ray crystallography.
Then, in the absence of phases (Φ), we are unable to complete the shown Fourier transform relating the experimental data from X-ray crystallography (in reciprocal space) to real-space electron density, into which the atomic model is built.
This principle lies at the heart of MR, and can allow us to infer information about the orientation and location of an unknown molecule with its unit cell.
Due to historic limitations in computing power, an MR search is typically divided into two steps: rotation and translation.
Historically r-factors and/or correlation coefficients were used to score the rotation function, however, modern programs use maximum likelihood-based algorithms.