Quantum Crystallography Applied to Crystalline Maleic Anhydride

摘要

Quantum crystallography (QCr) is a team 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 molecular orbitals and a single-determinant density matrix formalism to develop a quantum mechanical model. Our initial application to a test material, crystalline maleic anhydride, involved the adjustment of the elements in the density (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 mechanical model. The adjustment of the projector matrix preserved the idempotency and normalization properties of the matrix. In this application, it was also found that it was necessary to correct the X-ray diffraction data for systematic errors. An effective statistical method for doing this was developed from quantum mechanical theory. There were a number of special features of this investigation that emerged as it progressed. The mirror plane in maleic anhydride, for example, was quite useful because, in the absence of significant interactions between the molecules in the crystal, charge distributions on both sides of the mirror plane should be essentially the same. Deviations raised questions that resulted in improved procedures. The quality of theoretical results as a function of basis set and mode of calculation is also part of this investigation. One result of the information obtained from various aspects of this study is the potential for greater efficiency in the procedures and calculations. The calculations for maleic anhydride 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.