Contour plot

DNA Minor Groove Binding - Compare AAA and CCC Double Helix 

The first study to investigate selectivity profiles using MIFs in connection with a chemometric analysis was published about 10 years ago [5]. There, the behavior of all 64 possible DNA triplets with respect to 31 GRID probes was studied with GRID/PCA. 

This publication is the first example to demonstrate that MIFs can be used to differentiate between affinity and selectivity, and that, using the appropriate probe, selectivity for one of two targets may be achieved. 

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We can now planimeter the thickness of the different NOS contours, plot thickness versus area and then integrate both with the planimeter. The resulting value is the volume of net oil sand (4) and not the GRV ... 

Figure Al.6.27. Equipotential contour plots of (a) the excited- and (b), (c) ground-state potential energy surfaces. (Here a hamionic excited state is used because that is the way the first calculations were perfomied.) (a) The classical trajectory that originates from rest on the ground-state surface makes a vertical transition to the excited state, and subsequently undergoes Lissajous motion, which is shown superimposed, (b) Assuming a vertical transition down at time (position and momentum conserved) the trajectory continues to evolve on the ground-state surface and exits from chaimel 1. (c) If the transition down is at time 2 the classical trajectory exits from chaimel 2 (reprinted from [52]).

Figure A3.7.1. Two-dimensional contour plot for direct collinear reaction A + BC —> AB + C. Transition state is indicated by J.

As an example, figure A3.7.5 shows a polar contour plot of the HE product velocity distribution at a reactant... 

Figure A3.7.5. Velocity-flux contour plot for FIF product from the reaction F + para- i2 HF + F1 at a reactant collision energy of 1.84 kcal mol ...

Figure A3.7.7. Two-dimensional contour plot of the Stark-Wemer potential energy surface for the F + H2 reaction near the transition state. 0 is the F-H-H bend angle.

Figure B2.3.6. CM angle-velocity contour plot for the F + D2 reaction at an incident relative translational energy of 1.82 kcal mol [26], Contours are given at equally spaced intensity intervals. This CM differential cross section was used to generate the calculated laboratory angular distributions given in figure B2.3.4. (By pennission from AIP.)...

Figure B3.2.10. Contour plot of the electron density obtained by an orbital-free Hohenberg-Kolnr teclmique [98], The figure shows a vacancy in bulk aluminium in a 256-site cell containing 255 A1 atoms and one empty site, the vacancy. Dark areas represent low electron density and light areas represent high electron density. A Kolm-Sham calculation for a cell of this size would be prohibitively expensive. Calculations on smaller cell sizes using both techniques yielded densities that were practically identical.

Figure B3.3.10. Contour plots of the free energy landscape associated with crystal niicleation for spherical particles with short-range attractions. The axes represent the number of atoms identifiable as belonging to a high-density cluster, and as being in a crystalline environment, respectively, (a) State point significantly below the metastable critical temperature. The niicleation pathway involves simple growth of a crystalline nucleus, (b) State point at the metastable critical temperature. The niicleation pathway is significantly curved, and the initial nucleus is liqiiidlike rather than crystalline. Thanks are due to D Frenkel and P R ten Wolde for this figure. For fiirther details see [189].

Figure Cl.3.6. Contour plot of the H6(4,3,2) potential for Ar—HF, which was fitted principally to data from far-...

Fig. 5. The left hand side figure shows a contour plot of the potential energy landscape due to V4 with equipotential lines of the energies E = 1.5, 2, 3 (solid lines) and E = 7,8,12 (dashed lines). There are minima at the four points ( 1, 1) (named A to D), a local maximum at (0, 0), and saddle-points in between the minima. The right hand figure illustrates a solution of the corresponding Hamiltonian system with total energy E = 4.5 (positions qi and qs versus time t).

IlyperCl hem can display molecular orbitals and the electron density ol each molecular orbital as contour plots, showing the nodal structure and electron distribution in the molecular orbitals. 

IlyperChetn displays the electrostatic potential as a contour plot when you select th e appropriate option in th e Con tour Plot dialog box. Choose the values for the starting contour and the contour increment so that you can observe the minimum (typically about 0.5 for polar organ ic molecules) and so that the zero potential line appears. 

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 ... 

The second summation is over all the orbitals of the system. This equation is used in IlyperChem ah imiio calculations to generate contour plots of electrostatic potential, [fwe choose the approximation whereby we n eglect the effects of the diatomic differen tial overlap (NDDO). then the electrostatic potential can be rewritten... 

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. 

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. 

You can use the semi-empirical and ab initio Orbitals dialog box in HyperChem to request a contour plot of any molecular orbital. When requested, the orbital is contoured for a plane that is parallel to the screen and which is specified by a subset selection and a plane offset, as described above. The index of the orbital and its orbital energy (in electron volts, eV) appears in the status line. 

If a molecule is rotated by changing the position of the viewer (left mouse button rotation) then the molecule s position in the molecular coordinate system has not changed and another contour plot can be requested without recomputing the wave function. That is, many orbitals can be plotted after a single point ab initio or semi-empirical calculation. Any contour map is available without recomputation of the wave function. 

The results of electrostatic potential calculations can be used to predict initial attack positions of protons (or other ions) during a reaction. You can use the Contour Plot dialog box to request a plot of the contour map of the electrostatic potential of a molecular system after you done a semi-empirical or ab initio calculation. By definition, the electrostatic potential is calculated using the following expression ... 

Example of a two-factor response surface displayed as (a) a pseudo-three-dimensional graph and (b) a contour plot. Contour lines are shown for intervals of 0.5 response units. 

Figure 26-7 is an example of an individual risk contour plot, which shows the expec ted frequency of an event causing a specified level of harm at a specified location, regardless whether anyone is present at that location to suffer that level of harm. 

Let us now turn to the influence of vibrations on exchange chemical reactions, like transfer of hydrogen between two O atoms in fig. 2. The potential is symmetric and, depending on the coupling symmetry, there are two possible types of contour plot, schematically drawn in fig. 17a, b. The O atoms participate in different intra- and intermolecular vibrations. Those normal skeleton... 

Fig. 17. Contour plots for a

Fig. 28. Contour plot and instanton trajectory for PES (4.28) with the parameters of fig. 25, ojqP = 35.

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