Jerome Karle

Crystallography and Computational Quantum Mechanics


The structural results from an X-ray diffraction experiment, for example, can facilitate calculations in quantum mechanics. This is because many types of calculations can proceed when atomic positions or the various intensities of scattering are known [1,2]. Our experience so far has indicated that knowledge of atomic positions is the most useful form for the structural information [2]. The combination of the two techniques, crystallography and quantum mechanics, can readily extend the information obtained from a diffraction experiment, in terms of electron densities, charge distributions, the nature of the bonding and various energies including the energy that holds the molecules together in a crystal [3].

Much research has been performed in the applications of quantum mechanical theory to free molecules. The calculations involved would start generally with a geometric optimization, which is a minimum energy calculation by quantum mechanical means from which the structure of the molecule is determined. If the interest is in a free molecule and a sufficiently sophisticated bases set and mode of calculation are used, this type of calculation could be quite satisfactory. However, the structure of molecules and charge distributions may change in crystals and if a molecule in the crystalline state is of interest, the free molecule approximation may not be good enough. In addition, calculations of the structures of large molecules and of crystals by geometric optimization become impractical because of the complexity.

In general, knowledge of the space group and packing in a crystal, as well as the structure of the molecules, must come from an experimental structure determination.

In order to illustrate the interaction between crystallographic data and quantum mechanics, the following topics will be discussed.

1.Some illustrations will be given of the extent to which changes may occur in molecules in the crystalline state as compared to the free state.

2.Some methods, empirical and quantum mechanical, for determining the packing energies (the glue that holds crystals together) will be discussed [3,4].

3.A fragment method for performing quantum mechanical calculations on peptides and proteins will be described [1,5].


1.L. Massa, L. Huang and J. Karle, Quantum Crystallography and The Use of Kernel Projector Matrices, International. J. of Quantum Chemistry: Quantum Chemistry Symp. 29, 371--384 (1995).

2.L. Huang, L. Massa and J. Karle, Quantum Crystallography Applied to Crystalline Maleic Anhydride, International J. of Quantum Chemistry 73, 439-450 (1999).

3.SAPT96: An Ab Initio Program of Intermolecular Interaction Energies, by R. Bukowski, P. Jankowski, B. Jeziorski, M. Jeziorski, S. A. Kucharski, R. Moszynski, S. Rybak, K. Szalewicz, H. L. Williams and P. E. S. Wormer, University of Delaware and University of Warsaw.

See also

B. Jeziorski, R. Moszynski, A. Ratkiewicz, S. Rybak, K. Szalewicz and H. L. Williams, “SAPT: A Program for Many-Body Symmetry-Adapted Perturbation Theory Calculations of Intermolecular Interaction Energies”, in Methods and Techniques in Computational Chemistry: METECC-94, edited by E. Clementi, STEF, 1993, Vol. B, p. 79

4.G. Filippini and A. Gavezzotti, Empirical Intermolecular Potentials for Organic Crystals: the ‘6-exp’ Approximation Revisited, Acta Cryst. B49, 868-880 (1993).

5.L. Huang, L. Massa and J. Karle, Kemel Projector Matrices for Leu1-zervamicin, International, J. of Quantum Chemistry: Quantum Chemistry Symp. 30, 479-488 (1996).


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