Karle-Hauptman Matrices and Eigenvalues: a Practical Approach
Abstract
The possible usefulness of eigenvectors and eigenvalues of Karle-Hauptman matrices is examined. The eigenvalue spectra of structures with calculated and measured '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.