Isosurfacing 46

D-CTViewer allows to create up to three different Isosurfaces inside the data volume with each having different color and transparency value. The number of polygons inside the Isosurface hull can be decimated using a special polygon reduction tool (Fig. 5). 

Another interesting tool is to export the samples Isosurface hull to CAD for best matehing and afterwards comparison in 3D. Therefor a polygon export in DXF and the polygon reduction is implemented. 

Number of polygons in the outer Isosurface hull (wireframe representation) before and after two stages of polygon reduction... 

Knowledge of the spatial dimensions of a molecule is insufficient to imderstand the details of complex molecular interactions. In fact, molecular properties such as electrostatic potential, hydrophilic/lipophilic properties, and hydrogen bonding ability should be taken into account. These properties can be classified as scalar isosurfaces), vector field, and volumetric properties. 

Molecular orbitals were one of the first molecular features that could be visualized with simple graphical hardware. The reason for this early representation is found in the complex theory of quantum chemistry. Basically, a structure is more attractive and easier to understand when orbitals are displayed, rather than numerical orbital coefficients. The molecular orbitals, calculated by semi-empirical or ab initio quantum mechanical methods, are represented by isosurfaces, corresponding to the electron density surfeces Figure 2-125a). 

Figure 2-125. Different isovalue-based surfaces of phenylalanine a) isoelectronic density b) molecular orbitals (HOMO-LUMO) c) isopotential surface and d) isosurface of the electron cryo-microscopic volume of the ribosome of Escherichia coii.

Molecular volumes are usually computed by a nonquantum mechanical method, which integrates the area inside a van der Waals or Connolly surface of some sort. Alternatively, molecular volume can be determined by choosing an isosurface of the electron density and determining the volume inside of that surface. Thus, one could find the isosurface that contains a certain percentage of the electron density. These properties are important due to their relationship to certain applications, such as determining whether a molecule will fit in the active site of an enzyme, predicting liquid densities, and determining the cavity size for solvation calculations. 

Many functions, such as electron density, spin density, or the electrostatic potential of a molecule, have three coordinate dimensions and one data dimension. These functions are often plotted as the surface associated with a particular data value, called an isosurface plot (Figure 13.5). This is the three-dimensional analog of a contour plot. 

There are ways to plot data with several pieces of data at each point in space. One example would be an isosurface of electron density that has been colorized to show the electrostatic potential value at each point on the surface (Figure 13.6). The shape of the surface shows one piece of information (i.e., the electron density), whereas the color indicates a different piece of data (i.e., the electrostatic potential). This example is often used to show the nucleophilic and electrophilic regions of a molecule. 

FIGURE 13.5 Isosurface plots, (a) Region of negative electrostatic potential around the water molecule. (A) Region where the Laplacian of the electron density is negative. Both of these plots have been proposed as descriptors of the lone-pair electrons. This example is typical in that the shapes of these regions are similar, but the Laplacian region tends to be closer to the nucleus. 

FIGURE 13.6 A plot showing two data values. The shape is an isosurface of the total electron density. The color applied to the surface is based on the magnitude of the electrostatic potential at that point in space. 

The self-consistent reaction held (SCRF) method is an adaptation of the Poisson method for ah initio calculations. There are quite a number of variations on this method. One point of difference is the shape of the solvent cavity. Various models use spherical cavities, spheres for each atom, or an isosurface... 

The original PCM method uses a cavity made of spherical regions around each atom. The isodensity PCM model (IPCM) uses a cavity that is defined by an isosurface of the electron density. This is defined iteratively by running SCF calculations with the cavity until a convergence is reached. The self-consistent isodensity PCM model (SCI-PCM) is similar to IPCM in theory, but different in implementation. SCI-PCM calculations embed the cavity calculation in the SCF procedure to account for coupling between the two parts of the calculation. 

The molecular structures were rendered with good-quality shading on a blue background. Isosurfaces produced from cube files or checkpoint files also looked nice. Molecular vibrations can be animated on screen and vibrational displacement vectors displayed. The vibrational line spectrum may be displayed too, but the user has no control over the axes. There is no way to set the background color. The display can be saved using several image file formats. 

Wave functions can be visualized as the total electron density, orbital densities, electrostatic potential, atomic densities, or the Laplacian of the electron density. The program computes the data from the basis functions and molecular orbital coefficients. Thus, it does not need a large amount of disk space to store data, but the computation can be time-consuming. Molden can also compute electrostatic charges from the wave function. Several visualization modes are available, including contour plots, three-dimensional isosurfaces, and data slices. 

SCF (self-consistent field) procedure for solving the Hartree-Fock equations SCI-PCM (self-consistent isosurface-polarized continuum method) an ah initio solvation method... 

We also plotted the electron spin polarization, by itself (top row) and projected onto the electron density isosurface for the molecules containing the CH2, O and Be substituents (the orientation of the atoms in the plots is indicated at the left) ... 

The second set of illustrations show the spin density plotted on the electron density isosurface the spin density provides the shading for the isodensity surface dark areas indicate positive (excess a) spin density and light areas indicate negative (excess P) spin density. For example, in the allyl radical, the spin density is concentrated around the two terminal carbons (and away from the central carbon). In the Be form, it is concentrated around the substituent, and in acetyl radical, it is centered around the C2 carbon atom. 

As this example illustrates, plots such as these can be useful for providing a qualitative understanding of the electron density and its relationship to reactivity, but you would be wise to use and interpret them with care. It is all too easy to unintentionally manipulate such illustrations to create the effect that one expects to observe. For example, any one slice or isosurface of the electron density can be used to argue for a given viewpoint. It is important to examine and visualize the entire volumetric data set before reaching conclusions based on it. ... 

An isosurface plot of the electron density is shown in Figure 7.8. 

Some of the major packages are better at visualization than others. In any case, there are a host of third-party providers with software on offer. Here then is what you might like to do with the results of the calculations above (and I used HyperChem to produce the following screen grabs). First of all an isosurface plot of the electron density (Figure 10.16). Next are isosurface densities for the highest... 

Chemists also need to know the distribution of electric charge in a molecule, because that distribution affects its physical and chemical properties. To do so, they sometimes use an electrostatic potential surface (an elpot surface), in which the net electric potential is calculated at each point of the density isosurface and depicted by different colors, as in Fig. C.2f. A blue tint at a point indicates that the positive potential at that point due to the positively charged nuclei outweighs the negative potential due to the negatively charged electrons a red tint indicates the opposite. 

Numerical simulation of a spirming detonation in Hj/air mixture in a circular tube at various times. Gray and green space isosurfaces in pressure are the detonation front and the pressure of 6 MPa. White arrow propagating direction of the detonation front, pink arrow rotating direction of the transverse detonation. TD—transverse detonation, and LT—long pressure trail. (Reprinted from Tsuboi, N., Eto, K., and Hayashi, A.K., Combust. Flame, 149,144,2007. With permission.)... 

Figure 4-3. Illustration of the X-pol potential represented by the electron density isosurface of BTPI. The color scheme is used purely for distinction of different residues...

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