Fused spheres van der Waals surface

Figure 4.1 An illustration of a fused sphere Van der Waals surface (VDWS) of a molecule.

In particular, if the atomic radii are taken as some of the recommended values of the atomic Van der Waals radii, then one obtains a fused sphere Van der Waals surface (VDWS) of the molecule. Several different sets of atomic radii have been proposed [85-87,255], and the fused sphere molecular surface obtained depends on this choice. 

In Figure 4.1 an example of a fused spheres Van der Waals surface is shown. This figure illustrates an important difference between a MIDCO and a VDWS at the seam of interpenetration of the spheres the latter surfaces are not differentiable. 

Shape Analysis of Fused Sphere Van der Waals Surfaces and Other Locally Nondifferentiable Molecular Surfaces... 

Fused sphere surfaces, such as fused sphere Van der Waals surfaces (VDWS ) are simple approximations to molecular contour surfaces. By specifying the locations of the centers and the radii of formal atomic spheres in a molecule, the fused sphere surface is fully defined as the envelope surface of the fused spheres and can be easily generated by a computer. Although fused sphere VDW surfaces are not capable of representing the fine details of molecular shape, such surfaces are very useful for an approximate shape representation. 

The input data for the shape analysis methods are provided by well-established quantum chemical or empirical computational methods for the calculation of electronic charge distributions, electrostatic potentials, fused spheres Van der Waals surfaces, or protein backbones. The subsequent topological shape analysis is equally applicable to any existing molecule or to molecules which have not yet been synthesized. This is precisely where the predictive power of such shape analysis lies based on a detailed shape analysis, a prediction can be made on the expected activity of all molecules in the sequence and these methods can select the most promising candidates from a sequence of thousands of possible molecules. The actual expensive and time-consuming synthetic work and various chemical and biochemical tests of... 

Classical shape representations of molecules are based on assumed analogies between quantum mechanical molecules and macroscopic, classical objects. Since most of the mass of molecules is concentrated in the nuclei, it has appeared natural to place emphasis on nuclear arrangements, and the chemically more relevant shapes of electron densities have become the focus of molecular shapes analysis only recently. It is important to distinguish stereochemistry and molecular shape analysis. The term stereochemistry is commonly used for the 3D pattern of formal bonds, whereas molecular shape often refers to the shape of the fuzzy electron density cloud, or to simpler representations of large-scale molecular features, such as an a-helix or a -sheet of a protein. Several alternative shape representations are also used, such as fused sphere van der Waals (VDW) surfaces, Connolly surfaces, solvent accessibility surfaces, or molecular electrostatic potential (MEP) surfaces. 

Figure 2-118, Cross-section of the 3D model of formic add (HCOOH), The van der Waals radius of each atom of the molecule is taken and by fusing the spheres the van der Waals surface is...

The 3D space requirements of most molecules can be represented to a good approximation by such Van der Waals surfaces. Fused sphere VDWS s are used extensively in molecular modeling, especially in the interpretation of biochemical processes and computer aided drug design. These approximate molecular surfaces are conceptually simple, their computation and graphical display on a computer screen take relatively short time, even for large biomolecules. 

Fortuitously, for most molecules, the MIDCO s G(a) of the chemically most important small density threshold values a are those where the deviations are small from the simple fused sphere model surfaces. The usual Van der Waals surfaces fall within this range. For a molecule containing N nuclei, these VDWS s are obtained as the envelope surfaces of N interpenetrating spheres... 

The simplest molecular surface is the van der Waals surface, a fused-sphere envelope resulting from the superposition of atomic spheres with van der Waals radii. This surface models qualitatively the space occupied by a molecule. The interaction with other molecules in the environment can be taken into account by considering the part of the surface accessible to the solvent.The smoothed surface derived from solute—solvent contacts is an improved model.i °... 

All of the above tests were for hard chains at surfaces. The only comparison between theory and simulation for various values of fluid-fluid and bulk fluid attractions is that done by Patra and Yethiraj (PY) [137], who presented a simple van der Waals DFT for polymers and compared to simulations of fused-sphere chains. In their theory, PY used the Yethiraj functional [39] for the hard-chain contribution to the free energy and a simple mean-field term for the attractive contribution. Their excess free energy functional is given by... 

An effective approach is to compute V(r) on an appropriately-defined molecular surface, because this is what is seen or felt by the other reactant. Such a surface is of course arbitrary, because there is no rigorous basis for it. A common procedure has been to use a set of fused spheres centered on the individual nuclei, with van der Waals or other suitable radii [34—37]. We prefer, however, to follow the suggestion of Bader et al. [38] and take the molecular surface to correspond to an outer contour of the electronic density. This has the advantage of reflecting features such... 

This is the surface that envelops fused hard spheres centred at the atom coordinates (atomic nuclei) and having radii equal to some of the recommended values of the van der Waals radii. The spheres interpenetrate one another in such a way that the distance between the centres of two spheres equals the formal bond length. 

We will look in particular at the detailed features of V(r) computed on the surfaces of energetic molecules, which is designated Vs(r). This raises the question of how to define a molecular surface. In the past, this has often been done by means of fused spheres centered at the nuclear positions and having, for example, the corresponding van der Waals atomic radii [112,113]. More recently, however, there has been an increasing tendency to follow Bader et al [WA] and take the surface to be some outer contour of the electronic density. This has the advantage that the surface then reflects the specific features of that molecule, such as lone pairs and strained bonds. We use this approach, with p(r) = 0.001 electrons/bohr other outer contours, e.g. p(r) = 0.002 electrons/bohr, would serve just as well [115]. 

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