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.