Filling space

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 2-123. The most coinmon molecular graphics representations of phenylalanine a) wire frame b) capped sticks c) balls and sticks d) space-filling.

The space filling model developed by Corey, Pauling, and Koltun is also known as the CPK model, or scale model [197], It shows the relative volume (size) of different elements or of different parts of a molecule (Figure 2-123d). The model is based on spheres that represent the "electron cloud . These atomic spheres can be determined from the van der Waals radii (see Section 2.10.1), which indicate the most stable distance between two atoms (non-bonded nuclei). Since the spheres are all drawn to the same scale, the relative size of the overlapping electron clouds of the atoms becomes evident. The connectivities between atoms, the bonds, are not visualized because they are located beneath the atom spheres and are not visible in a non-transparent display (see Section 2.10). In contrast to other models, the CPK model makes it possible to visualize a first impression of the extent of a molecule. 

In order to represent 3D molecular models it is necessary to supply structure files with 3D information (e.g., pdb, xyz, df, mol, etc.. If structures from a structure editor are used directly, the files do not normally include 3D data. Indusion of such data can be achieved only via 3D structure generators, force-field calculations, etc. 3D structures can then be represented in various display modes, e.g., wire frame, balls and sticks, space-filling (see Section 2.11). Proteins are visualized by various representations of helices, / -strains, or tertiary structures. An additional feature is the ability to color the atoms according to subunits, temperature, or chain types. During all such operations the molecule can be interactively moved, rotated, or zoomed by the user. 

Molecules are most commonly represented on a computer graphics screen using stick or space-filling representations, which are analogous to the Dreiding and Corey-PauUng-Koltun (CPK) mechanical models. Sophisticated variations on these two basic types have... 

The earliest ball and stick models were exactly that wooden balls in which holes were drilled to ac commodate dowels that connected the atoms Plastic versions including relatively inexpensive student sets became available in the 1960s and proved to be a valuable learning aid Precisely scaled stainless steel framework and plastic space filling models although relatively expensive were standard equipment in most research laboratories... 

FIGURE 1 6 Molecular models of methane (CH4) (a) Framework (tube) models show the bonds connecting the atoms but not the atoms themselves (b) Ball and stick (ball and spoke) models show the atoms as balls and the bonds as rods (c) Space filling models portray overall molecular size the radius of each sphere approximates the van der Waals radius of the atom (d) An electrostatic potential map of methane... 

SpartanBuild software that you can use to build molecular models of various types include tube ball and spoke and space filling This text includes a number of mod eling exercises for you to do but don t limit yourself to them You can learn a lot by sim ply experimenting with SpartanBuild to see what you can make... 

FIGURE 2 13 Tube (top) and space filling bottom) models of (a) pentane (b) 2 methylbutane and (c) 2 2 dimethylpropane The most branched isomer 2 2 dimethylpropane has the most compact most spherical three dimensional shape... 

FIGURE 2 18 Acetylene is a linear molecule as indicated in (a) the structural formula and (b) a space filling model... 

FIGURE 3 1 The stag gered and eclipsed confer mations of ethane shown as ball and spoke models left) and as space filling models right)... 

FIGURE 3 8 Ball and spoke and space filling models of methyl-methyl eclipsed conformation of butane... 

FIGURE 3 14 (a) A ball and spoke model and (b) a space filling model of the boat confor mation of cyclohexane Torsional strain from eclipsed bonds and van der Waals strain involving the flagpole hydrogens (red) make the boat less stable than the chair... 

FIGURE 5 5 Ball and spoke and space filling models of as and trans 2 butene The space filling model shows the serious van der Waals strain between two of the hydrogens in as 2 butene The molecule ad justs by expanding those bond angles that increase the separation between the crowded atoms The combi nation of angle strain and van der Waals strain makes as 2 butene less stable than trans 2 butene... 

Despite numerous attempts the alkene 3 4 di tert butyl 2 2 5 5 tetramethyl 3 hexene has never been synthesized Can you explain why Try mak mg a space filling model of this compound... 

Examine the models of 1 3 butadiene in Figure 10 6 on Learn mg By Modeling and com pare space filling models of the s CIS and s trans confor mation... 

The compound shown is quite unreactive in Diels-Alder reactions Make a space filling model of it in the conformation required for the Diels-Alder reaction to see why... 

Mesitylene (13 5 trimethylbenzene) is the most stable of the tnmethylbenzene isomers Why2 Which isomer do you think is the least stable" Make a molecular model of each isomer and compare their calculated strain energies with your predictions Do space filling models support your explanation" ... 

The metal-ion complexmg properties of crown ethers are clearly evident m their effects on the solubility and reactivity of ionic compounds m nonpolar media Potassium fluoride (KF) is ionic and practically insoluble m benzene alone but dissolves m it when 18 crown 6 is present This happens because of the electron distribution of 18 crown 6 as shown m Figure 16 2a The electrostatic potential surface consists of essentially two regions an electron rich interior associated with the oxygens and a hydrocarbon like exterior associated with the CH2 groups When KF is added to a solution of 18 crown 6 m benzene potassium ion (K ) interacts with the oxygens of the crown ether to form a Lewis acid Lewis base complex As can be seen m the space filling model of this... 

FIGURE 19 6 Space filling model of a micelle formed by association of car boxylate ions derived from a long chain carboxylic acid The hydrocarbon chains tend to be on the inside and the carboxylate ions on the surface where they are in contact with water mole cules and metal cations... 

FIGURE 27 20 Heme shown as (a) a structural drawing and as (b) a space filling model The space filling model shows the coplanar arrangement of the groups surrounding iron... 

FIGURE 28 5 (a) Tube and (b) space filling models of a DNA double helix The carbohydrate-phosphate backbone is on the out side and can be roughly traced in (b) by the red oxygen atoms The blue atoms belong to the purine and pyrimidine bases and he on the inside The base pairing is more clearly seen in (a)... 

The ball and wire display is used for model building Although it is convenient for this purpose other model displays show three dimensional molecular structure more clearly and may be preferred The space filling display is unique m that it portrays a molecule as a set of atom centered spheres The individual sphere radii are taken from experi mental data and roughly correspond to the size of atomic electron clouds Thus the space filling display attempts to show how much space a molecule takes up... 

One after the other select Wire Tube Ball and Spoke and Space Filling from the Model menu... 

Size density surface (top left) space filling model (top right) potential map (bottom left) and tube model (bottom right) for methanol... 

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