Karle–Hauptman Matrices and Eigenvalues: a Practical Approach

The possible usefulness of eigenvectors and eigenvalues of Karle–Hauptman matrices is examined. The eigenvalue spectra of structures with calculated and measured |U|'s are discussed and the result of several attempts at phase refinement are reported. The use of the sum of the square of the negative eigenvalues (SSNE) as a goodness-of-fit criterion is examined. The possible use of a priori information is investigated using the approximation of orthogonal electron densities corresponding to eigenvectors with eigenvalues greater than zero.