Generator-coordinate approach

We thank Dr. S.P.A. Sauer of University of Copenhagen for fruitful collaboration in a project since 1994 of which this article is an overview, and Professor P. van Leuven for helpful comments about the generator coordinate approach. Much preparation of this article occurred whilst JFO was a visiting professor in Kemisk Institut at Syddansk Universitet, for which hospitality he is grateful. 

It has also been pointed out that there is an interpretation to our theory based upon the generator coordinate approach [44 6]. A close scrutiny of Lathouwers et al. paper shows that the present approach can be embedded into the methodology of the generator coordinate method (GCM), as it was pointed out by one referee. The postulate PI ensures the existence of a set of fixed nuclei so that the GCM, initially thought for... 

DR. WILLIAM TR0GLER (Northwestern University) I wish to make a brief presentation of some results which relate to Dr. Geoffroy s talk. We have been employing a different approach to generate coordinatively unsaturated centers, utilizing a reduc-... 

In the cuboctahedron case, we were able to introduce the large number of the sites to represent each edge between the vertices of the polyhedron using the simple arithmetic mean to generate coordinates of new sites. In contrast, here such an approach is not possible since we want the new points to be everywhere inside the molecule, not only along the bonds. To arrive at approximately uniformly distributed points in the interior of the van der Waals contour of the molecule we select the coordinates of the points at random and then check that indeed the point is inside the molecular interior. In Figure 22 we illustrate distributions of 1000 and 5000 random points that represent a planar model of the H2O molecule (i.e., the projection of H2O on a plane). 

Atoms not explicitly included in the trajectory must be generated. The position at which an atom may be placed is in some sense arbitrary, the approach being analogous to the insertion of a test particle. Chemically meaningful end states may be generated by placing atoms based on internal coordinates. It is required, however, that an atom be sampled in the same relative location in every configuration. An isolated molecule can, for example, be inserted into... 

CWG van Gelder, EJJ Leusen, JAM Leunissen, JH Noordik. A molecular dynamics approach for the generation of complete protein structures from limited coordinate data. Proteins 18 174-185, 1994. 

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