Jerome Karle

Kernel Energy Method for Quantum Cristallography


Abstract

In collaboration with Lulu Huang and Lou Massa

The term quantum crystallography (QCr) refers to the combination of structural crystallographic information with quantum-mechanical theory. The objective is to facilitate computational chemistry calculations and thereby enhance the information that may be derived from a crystallographic experiment. This concept has a long history and in recent years has been finding increased attention because of the advances in both theory and computers. In this talk we focus upon calculation of the energy of peptides.

Our method for obtaining quantum mechanical molecular energy involves the use of parts of a whole molecule, which in our formalism are called kernels. The individual calculations based on kernels and double kernels are relatively small, compared to that which would be required to treat the entire molecule all at once. Subsequently, we sum those contributions to obtain the energy for the whole molecule. In so doing we simplify the formidable task of obtaining a true quantum energy calculation for very large molecules. The saving of computational time is significant.

This talk is devoted to a general description of the concepts involved, and moreover to the particular application of calculating the energy for molecules of biological importance, e.g. peptides. The applications are a proof of principle demonstration, and point the way to future computational developments with potentially worthwhile types of investigations. Each macromolecular structure, with known atomic coordinates, is composed of pieces called kernels . The combined total of the kernels forms the complete structure.

The purpose of our calculations is to obtain kernel contributions to the energy when it is not feasible to treat the entire molecule as a whole. Since a structure of interest is assumed to have known coordinates from, an X-ray diffraction experiment, there is no problem in defining a choice of kernels which compose the entire molecule. To saturate dangling bonds at the periphery of a kernel, or double kernel, we attach hydrogen atoms. One rule which must be obeyed, is that all of the atoms in a molecule must be a member of some kernel once and only once. This rule plays a valuable role in defining how the kernel calculations are to be combined in forming the energy of the full molecule. The calculations to be discussed are based on structural data, i.e., atomic positions of the molecule to be studied, obtained from a crystal structure determination.


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