Molecular clouds definition

Depending on the application, models of molecular surfaces arc used to express molecular orbitals, clcaronic densities, van dor Waals radii, or other forms of display. An important definition of a molecular surface was laid down by Richards [182] with the solvent-accessible envelope. Normally the representation is a cloud of points, reticules (meshes or chicken-wire), or solid envelopes. The transparency of solid surfaces may also be indicated (Figure 2-116). 

Each of these columns of this symmetrical matrix may be seen as representing a molecule in the subspace formed by the density functions of the N molecules that constitute the set. Such a vector may also be seen as a molecular descriptor, where the infinite dimensionality of the electron density has been reduced to just N scalars that are real and positive definite. Furthermore, once chosen a certain operator in the MQSM, the descriptor is unbiased. A different way of looking at Z is to consider it as an iV-dimensional representation of the operator within a set of density functions. Every molecule then corresponds to a point in this /V-dimensional space. For the collection of all points, one can construct the so-called point clouds, which allow one to graphically represent the similarity between molecules and to investigate possible relations between molecules and their properties [23-28]. 

Within the quantum chemical description of molecular electron density clouds, a natural criterion, the Density Domain criterion, provides a quantum chemical definition for functional groups [14-18]. Furthermore, techniques that generate fuzzy electron density contributions for local molecular moieties that are analogous to the fuzzy electron density clouds of complete molecules, determined by the analytic Additive Fuzzy Density Fragmentation (AFDF) method [19-21], or the earlier numerical-grid MEDLA method [22,23], are also... 

The ideas which we have arrived at in the preceding chapters with regard to the structure of matter all rest on the possibility of demonstrating the existence of fast-moving particles by direct experiment, and indeed of making their tracks immediately visible, as in the Wilson cloud chamber. These experiments put it beyond doubt that matter is composed of corpuscles. We are now to learn of experiments which just as definitely seem to be only reconcilable with the idea that a molecular or electronic beam is a wave train. Before we enter upon this, however, we shall briefly recall the main facts of wave motion in general, using the phenomena of optical dift raction as a concrete example. 

In speaking of sizes of atoms, we should keep in mind that the electron cloud does not end at any definite distance from the nucleus. As an experimental quantity the radius of the atom is found to depend a good deal on the environment of the atom during the measurement. The following values for the molecular diameter of argon are obtained by the method indicated ... 

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