Quantum crystallography applied to crystalline maleic anhydride

Quantum crystallography (QCr) is a term that concerns techniques for using crystallographic information to enhance quantum mechanical calculations and the information derived from them. In our approach to QCr, we use molecula r orbitals and a single-determinant density matrix formalism to develop a q uantum mechanical model. Our initial application to a test material, crysta lline maleic anhydride, involved the adjustment of the elements in the dens ity (projector) matrix and some others in the quantum mechanical model. The purpose was to optimize the fit between the experimental structure factor magnitudes and the values of those magnitudes obtained from the quantum mec hanical model. The adjustment of the projector matrix preserved the idempot ency and normalization properties of the matrix. In this application, it wa s also found that it was necessary to correct the X-ray diffraction data fo r systematic errors. An effective statistical method for doing this was dev eloped from quantum mechanical theory. There were a number of special featu res of this investigation that emerged as it progressed. The mirror plane i n maleic anhydride, for example, was quite useful because, in the absence o f significant interactions between the molecules in the crystal, charge dis tributions on both sides of the mirror plane should be essentially the same . Deviations raised questions that resulted in improved procedures. The qua lity of theoretical results as a function of basis set and mode of calculat ion is also part of this investigation. One result of the information obtai ned from various aspects of this study is the potential for greater efficie ncy in the procedures and calculations. The calculations for maleic anhydri de based on its structure concern the number of electrons per atom, various energies, and electron density contours. Related theoretical calculations based on geometry optimization were also made. (C) 1999 John Wiley & Sons, Inc.