Contour Visualization

The contour drawing capabilities of most graphics software finds the regions of constant peak amplitude through interpolation. Typically, 10-20 contour amplitudes are picked from maximum to minimum. This interpolation can be sophisticated and may include a noise minimizing basis function. However, the use of this filtering may sometimes distort the data presentation. Because 2DLC data are typically performed 

FIGURE 5.15 A typical gray-scale contour plot of the 2DLC separation of tryptic digest peptides from BSA. From Stoll and Carr (2005). Reprinted with permission of the American Chemical Society. 

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Fig. 10. Conformational flooding accelerates conformational transitions and makes them accessible for MD simulations. Top left snapshots of the protein backbone of BPTI during a 500 ps-MD simulation. Bottom left a projection of the conformational coordinates contributing most to the atomic motions shows that, on that MD time scale, the system remains in its initial configuration (CS 1). Top right Conformational flooding forces the system into new conformations after crossing high energy barriers (CS 2, CS 3,. . . ). Bottom right The projection visualizes the new conformations they remain stable, even when the applied flooding potentials (dashed contour lines) is switched off.

The potential indicates what a reactant sees as it approaches a molecule. Yon can use a contour slot of electrostatic potential to visually dctcmiine possible trajectories for the approach of a reactant. 

HyperChem allows the visualization of two-dimensional contour plots for a certain number of variables, fh esc contour plots show the values of a spatial variable (a property f(x,y,z) in normal th rce-dimensional Cartesian space ) on a plane that is parallel to the screen. To obtain these contour plots the user needs to specify ... 

Once the job is completed, the UniChem GUI can be used to visualize results. It can be used to visualize common three-dimensional properties, such as electron density, orbital densities, electrostatic potentials, and spin density. It supports both the visualization of three-dimensional surfaces and colorized or contoured two-dimensional planes. There is a lot of control over colors, rendering quality, and the like. The final image can be printed or saved in several 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. 

Graphitic corrosion of the cast iron produced a soft, mechanically weak corrosion product that is highly susceptible to cavitation damage, even at relatively low cavitation intensities. The black coating on the impeller surface is visual evidence of graphitic corrosion. The spongelike surface contours are typical of cavitation damage (see Chap. 12). 

The spirit of this kind of calculation is to give a rough and ready visualization to the potential reactivity of a molecule. For example, Figure 16.3 is a contour map for aspirin. These maps look much better in colour, and it is often possible to spot the route that an approaching charged reagent would take. 

For molecular systems with up to thirty valence electrons, an amplitude of =t0.1 a.u. was chosen for the contour level. For systems with more than thirty valence electrons it was necessary to reduce this value to 0.08 a.u. to maintain the orbital size at a comfortable visual level. The molecular orbitals were normalized to an occupancy... 

We need ways to visualize electrons as particle-waves delocalized in three-dimensional space. Orbital pictures provide maps of how an electron wave Is distributed In space. There are several ways to represent these three-dimensional maps. Each one shows some important orbital features, but none shows all of them. We use three different representations plots of electron density, pictures of electron density, and pictures of electron contour surfaces. 

Two-dimensional NMR spectra are normally presented as contour plots (Fig. 3.11a), in which the peaks appear as contours. Although the peaks can be readily visualized by such an overhead view, the relative intensities of the signals and the structures of the multiplets are less readily perceived. Such information can be easily obtained by plotting slices (cross-sections) across rows or columns at different points along the Fi or axes. Stacked plots (Fig. 3.11b) are pleasing esthetically, since they provide a pseudo-3D representation of the spectrum. But except for providing information about noise and artifacts, they offer no advantage over contour plots. Finally, the projection spectra mentioned in the previous section may also be recorded. 

It Is usual to visualize the spatial distribution of p(x) within an area A by contouring measured or estimated values p (29c) nodes 29c grid. The resulting estimated map necessarily differs... 

This expression is the same as that for the first-order quadrupole effect in high-field NMR spectra [4, 66]. The angular variation of (4.51) is visualized in Fig. 4.11. The graph on the left shows the contour of the function (3cos 0 1 ... 

ELF can be visualized with different kinds of images. Colored sections through a molecule are popular, using white for high values of ELF, followed by yellow-red-violet-blue-dark blue for decreasing values simultaneously, the electron density can be depicted by the density of colored points. Contour lines can be used instead of the colors for black and white printing. Another possibility is to draw perspective images with iso surfaces, i.e. surfaces with a constant value of ELF. Fig. 10.2 shows iso surfaces with ELF = 0.8 for some molecules from experience a value of ELF = 0.8 is well suited to reveal the distribution of electron pairs in space. 

Elimination from the vitreous occurs by one of two pathways. This can be visualized by injecting fluorescent compounds and examining the concentration distribution in frozen sections obtained after a steady state has been established [230]. If the major route of elimination is by means of the re-tina/choroid, at steady state the lowest concentration would be in the vicinity of the retina. The contours observed in frozen sections of the rabbit eye obtained after intravitreal injection of fluorescein exhibit this pattern, with the highest concentration immediately behind the lens (Fig. 16A). Compounds not chiefly eliminated through the retina exit the vitreous by passive diffusion and enter the posterior aqueous, where they are eliminated by the natural production and outflow of aqueous humor. In such a situation, the contours would be perpendicular to the retina, with the highest concentration towards the rear of the vitreous cavity. This appears to be the case for fluorescently labeled dextran polymer, whose contours decrease in concentration toward the hyaloid membrane (Fig. 16B). 

The experimental set-up usually utilizes a piezoelectric tripod as a support of the tip (Fig. 5.36). This is movable vertically and laterally over the examined surface the vertical distance is fixed by a feedback loop to a constant tunnelling current at each point of the scan. The contours of the surface are thus visualized by voltage changes needed to move the piezoelectric tripod to a desired position. 

Computationally, the use of pseudocomponents improves the conditioning of the numerical procedures in fitting the mixture model. Graphically, the expansion of the feasible region and the rescaling of the plot axes allow a better visualization of the response contours. 

Fig. 5 Example of steric CoMFA contour map results using APO (2-amino-3H-phenoxazin-3-one) for visualization near green area greater toxicity is correlated with more bulky groups and near yellow area with the less bulky group. 

The three quantum numbers may be said to control the size (n), shape (/), and orientation (m) of the orbital tfw Most important for orbital visualization are the angular shapes labeled by the azimuthal quantum number / s-type (spherical, / = 0), p-type ( dumbbell, / = 1), d-type ( cloverleaf, / = 2), and so forth. The shapes and orientations of basic s-type, p-type, and d-type hydrogenic orbitals are conventionally visualized as shown in Figs. 1.1 and 1.2. Figure 1.1 depicts a surface of each orbital, corresponding to a chosen electron density near the outer fringes of the orbital. However, a wave-like object intrinsically lacks any definite boundary, and surface plots obviously cannot depict the interesting variations of orbital amplitude under the surface. Such variations are better represented by radial or contour... 

The strength of the Fajb interaction and its variations with distance and orientation can be conveniently visualized in terms of the overlap of 7ra and 7tb NBOs, on the basis of a Mulliken-type approximation (cf. Eq. (1.34)). As an example, the top two panels of Fig. 3.38 compare the overlapping 7ta-7tb orbital contours for trails 1 and cis 2 isomers of butadiene. As shown in Fig. 3.38, the overlap in the cis isomer 2 (S = 0.2054) is slightly weaker than that in the trans isomer 1 (S = 0.2209), due to the unfavorable orientation of the 7ta across the nodal plane of the 7tb in the latter case. Consistently with the weaker 7ta-7tb overlap, the JtA F nh ) interaction is less, namely 0.0608 in 1 versus 0.0564 in 2. The delocalization tail of the 7fa NEMO is correspondingly less than its value in the trans isomer... 

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