Three-dimensional similarity, computational

The emerging techniques for computer recognition of the similarity of three-dimensional properties of molecules will be discussed in this review. In particular, we will concentrate on methods or computer programs that examine a database of three-dimensional structures. However, to place such programs in context we will introduce the concepts of chemical information and the terminology, usually derived from molecular graphics, of three-dimensional similarity. Since much of the impetus for this research has been from research on computer-assisted design of bioactive molecules, this field will be introduced also. 

It can be seen that the definition of three-dimensional similarity is not a solved problem but rather an area of active research. It is possible that the most appropriate definition will depend on the structures of the molecules investigated and on the property to be compared. Thus, computer programs that perform three-dimensional searches might need to include a variety of definitions of similarity. 

The advantage of using electron density is that the integrals for Coulomb repulsion need be done only over the electron density, which is a three-dimensional function, thus scaling as. Furthermore, at least some electron correlation can be included in the calculation. This results in faster calculations than FIF calculations (which scale as and computations that are a bit more accurate as well. The better DFT functionals give results with an accuracy similar to that of an MP2 calculation. 

The gas motion near a disk spinning in an unconfined space in the absence of buoyancy, can be described in terms of a similar solution. Of course, the disk in a real reactor is confined, and since the disk is heated buoyancy can play a large role. However, it is possible to operate the reactor in ways that minimize the effects of buoyancy and confinement. In these regimes the species and temperature gradients normal to the surface are the same everywhere on the disk. From a physical point of view, this property leads to uniform deposition - an important objective in CVD reactors. From a mathematical point of view, this property leads to the similarity transformation that reduces a complex three-dimensional swirling flow to a relatively simple two-point boundary value problem. Once in boundary-value problem form, the computational models can readily incorporate complex chemical kinetics and molecular transport models. 

Thorner, D.A., Willett, P., Weight, P.M., and Taylor, R. Similarity searching in files of three-dimensional chemical structures Representation and searching of molecular electrostatic potentials using field-graphs./. Comput.-Aided Mol. Des. 1997, 3 3, 163-174. 

Pepperrell, C. A. and Willett, P. (1991) Techniques for the calculation of three-dimensional structural similarity using inter-atomic distances. J. Comput.-Aided Mol. Design 5, 455-474. 

---