Waals surface

The following models describe those definitions of molecular surfaces that are most widely used. The van dcr Waals surface, the solvent-accessible surface, and the Connolly surface (sec below) based on Richards definitions play a major role [182],... 

The van der Waals surface (or the hard sphere model, also known as the scale model or the corresponding space-filling model) is the simplest representation of a molecular surface. It can be determined from the van dcr Waals radii of all... 

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...

In contrast to the van der Waals surface, the Connolly surface [183, 184] has a smoother surface structure. The spiky and hard transition between the spheres of neighboring atoms is avoided. The Connolly surface can be obtained by rolling... 

Figure 2-119. The Connolly surface is determined by inoving a probe sphere (usually a water molecule) over the van der Waals surface. The surface thus obtained is also called the molecular or solvent-encluded surface (see Section 2,10,4 and Figure 2-120).

Tn general, the. solvent-accessible surface (SAS) represents a specific class of surfaces, including the Connolly surface. Specifically, the SAS stands for a quite discrete model of a surface, which is based on the work of Lee and Richards [182. They were interested in the interactions between protein and solvent molecules that determine the hydrophobicity and the folding of the proteins. In order to obtain the surface of the molecule, which the solvent can access, a probe sphere rolls over the van der Waals surface (equivalent to the Connolly surface). The trace of the center of the probe sphere determines the solvent-accessible surjace, often called the accessible swface or the Lee and Richards surface (Figure 2-120). Simultaneously, the trajectory generated between the probe and the van der Waals surface is defined as the molecular or Connolly surface. 

Figure 2-120. The center ofthe rolling probe sphere defines the solvent-accessible surface during movement of the probe over the van der Waals surface. Thus, the molecular surface is expanded by the radius of the solvent molecule,...

Besides the expressions for a surface derived from the van der Waals surface (see also the CPK model in Section 2.11.2.4), another model has been established to generate molecular surfaces. It is based on the molecular distribution of electronic density. The definition of a Limiting value of the electronic density, the so-called isovalue, results in a boundary layer (isoplane) [187]. Each point on this surface has an identical electronic density value. A typical standard value is about 0.002 au (atomic unit) to represent electronic density surfaces. 

The acce.ssible surface is also widely used. As originally defined by Lee and Richards [Lee and Richai ds 1971] this is the surface that is traced by the centre of the probe molecule as it rolls on the van der Waals surface of the molecule (Figure 1.6). The centre of the probe molecule can thus be placed at any point on the accessible surface and not penetrate the van der Waals spheres of any of the atoms in the molecule. 

Fig. 11.22 Small surface elements can be created on the van der Waals surface of an atom using constant increments of the polar angles, 6 and 0.

Electrostatic potential-derived charges assign point charges to fit the computed electrostatic potential at a number of points on or near the van der Waals surface. This sort of analysis is commonly used to create input charges for molecular mechanics calculation. 

Electrostatic Potential Map. A graph that shows the value of the Electrostatic Potential on an Electron Density Surface corresponding to a van der Waals Surface. 

The simplest shape for the cavity is a sphere or possibly an ellipsoid. This has the advantage that the electrostatic interaction between M and the dielectric medium may be calculated analytically. More realistic models employ moleculai shaped cavities, generated for example by interlocking spheres located on each nuclei. Taking the atomic radius as a suitable factor (typical value is 1.2) times a van der Waals radius defines a van der Waals surface. Such a surface may have small pockets where no solvent molecules can enter, and a more appropriate descriptor may be defined as the surface traced out by a spherical particle of a given radius rolling on the van der Waals surface. This is denoted the Solvent Accessible Surface (SAS) and illustrated in Figm e 16.7. 

Since an SAS is computationally more expensive to generate than a van der Waals surface, and since the difference is often small, a van der Waals surface is often used in practice. Alternatively, the cavity may be calculated directly from the wave function, for example by taking a surface coiTesponding to an electron density of 0.001. It is... 

The Polarizable Continuum Model (PCM) employs a van der Waals surface type cavity, a detailed description of the electrostatic potential, and parameterizes the cavity/ dispersion contributions based on the surface area. The COnductor-like Screening... 

Fig. la. Structure of the complex bis( -butoxysilane-diyl)tetracarbonyliron(O) x HMPA 4. b. Molecular structure of the chromium complex bis( -butoxy-silanediyl)pentacarbonylchromium(O) x HMPA 9. c. Van der Waals surface of 9... 

An example of a reaction cavity is illustrated by the van der Waals surface plots derived from the X-ray structures of di-2,6-dihydroxy-2,6-diphenylcyclohexanone 51 and its photodecarbonylation products, the cis- and tra i-2,6-diphenylcyclopen-tane-l,2-diols 52 and 53 (Scheme While the two products are formed in... 

Use a combination of computational methods to determine bond lengths and bond angles, and electronic distributions at van der Waals surfaces, in the transition state. 

Fig. 36. Spatial fit between host and guest in 47 benzene (1 1) (see Ref. 64) (a) Electron density in the mean plane of a benzene revealing the encasing hexagonal environment aroung the guest and (b) and (c) van der Waals surfaces of the dimeric benzene units as seen in Fig. 27 (indicated dimensions were calculated by the aid of the CHEM X program system, see Ref. 139). The lack of extensive-enough overlapping to yield in pi-pi interactions is visible from this drawing...

Fig. 7. Cross-sectional representation of the cavities in 8 when crystallised with benzene. The cavities, which are linked along two-fold axes parallel to c, are shown as the van der Waals surfaces due to the hydrogen atoms of the host molecules. Benzene guest molecules are shown in their major orientation 13>...

Fig. 2.3 The solvent accessible surface (SAS) area corresponds to that mapped out by the center of a sphere representing the solvent molecule (gray) as it is rolled over the van der Waals surface of the solute (light gray). In the COSMO model, the SAS is then divided into a series of segments of area S and charge density cr, centered at a position R(j. ...

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