Contour representations

Fig. 12.41 Contour representation of key features from a CoMFA analysis of a scries ofcoumarin substrates and inhibitors ofq/tochrome fPosn el al. 1995], T...

Fig. 6.10. Contour representation of calculated pump-probe delta absorption spectra of mutant RCs of Kb. sphaeroides R26. The electronic coupling between the B band and the higher excitonic band of the special pair is included in the simulation.

Electron-density map A contour representation of electron density in a crystal structure. Peaks appear at atomic positions. The map is computed by a Fourier synthesis, that is, the summation of waves of known amplitude, periodicity, and relative phase. The electron density is expressed in electrons per cubic A. 

Figure 5.21. Stacked and contour representations of the A1 MQMAS NMR spectra of lanthanum aluminate gels of (A) low-lanthanum content, in which three resonances assigned to Al, Al and Al can be distinguished, and (B) high-lanthanum content gel, in which only the octahedral and tetrahedral A1 resonances are observed. The solid line indicates the isotropic chemical shift, the dashed line shows the direction of the anisotropic quadrupolar line broadening and the dotted-dashed line indicates the direction of the quadrupolar-induced shift. From luga et al. (1999), by permission of the American Chemical Society.

Figure 6-7 The contour representation of the COSY experiment for two coupled nuclei of 3-chloroacetic acid. (Reproduced from A. E. Derome, Modern NMR Techniques for Chemistry Research, Pergamon Press, Oxford. UK, 1987. p. 191.)...

The 3D fluorescence data set consisting of 20 (Ex 455-575nm) x 640 (Em 468-731 nm) x 24 (x 0.5-23.5 ns) data points was measured for the mixed solution. The acquisition time was just a few seconds. The Ex-Em maps at various X are presented in the contour representation in Figure 32.7. The dotted white line is the scattering of the excitation light. It can be seen that the fluorescence pattern of the mixture varies drastically with x. The small fluorescence pattern located around 470 nm (Ex) and 500 nm (Em) disappears with x, and the broad fluorescence pattern located around the center of the map changes and becomes narrower with x. 

Figure 53 Contour representation of the potential-energy surface.

Fig. 12 41 Contour representation of key features from a CoMFA analysis of a senes of coumann substrates and inhibitors o cytochrome P glAS fPoso el al 1995] The red and blue regions indicate positions where it wnild he fnmi ahlp n id nnfnrnrnlle esperineh, fo place n p p , PfPgj, eo C - j. r k...

One widely used method of representing orbital shape is to draw a boundary surface that encloses. some substantial portion, say 90%, of the electron density for the orbital. This type of drawing is called a contour representation, and the contour representations for the s orbitals are spheres (T FIGURE 6.19). All the orbitals have the same shape, but they differ in size, becoming larger as n increases, reflecting the fact that the electron density becomes more spread out as n increases. Although the details of how... 

SECTION 6.6 Contour representations are useful for visualizing the shapes of the orbitals. Represented this way, 5 orbitals appear as spheres that increase in size as n increases. The radial probability function tells us the probability that the electron will be found at a certain distance from the nucleus. The wave function for each p orbital has two lobes on opposite sides of the nucleus. They are oriented along the x, y, and z axes. Four of the d orbitals appear as shapes with four lohes around the nucleus the fifth one, the d orbital, is represented as two lobes along the z axis and a doughnut in the xy plane. Regions in which the wave function is zero are called nodes. There is zero probability that the electron will be found at a node. 

The contour representation of one of the orbitals for the n = 3 shell of a hydrogen atom is shown below, (a) What is the quantum number I for this orbital (b) How do we label this orbital (c) How would you modify this sketch to show the analogous orbital for the n = 4 shell [Section 6.6]... 

For orbitals that are symmetric but not spherical, the contour representations (as in Figures 6.22 and 6.23) suggest where nodal planes exist (that is, where the electron density is zero). For example, the px orbital has a node wherever x = 0. This equation is satisfied by all points on the yz plane, so this plane is called a nodal plane of the orbital, (a) Determine the nodal plane of the p orbital, (b) What are the two nodal planes of the d y orbital (c) What are the two nodal planes of the orbital ... 

Molecular orbitals have many of the same characteristics as atomic orbitals. For example, an MO can hold a maximum of two electrons (with opposite spins), it has a definite energy, and we can visualize its electron-density distribution by using a contour representation, as we did with atomic orbitals. Unlike atomic orbitals, however, MOs are associated with an entire molecule, not with a single atom. 

FIGURE 9.36 Contour representations of the molecular orbitals formed by 2p orbitals. 

Figure 6.20 Comparison of the Is, 2s, and 3s orbitals, (a) Electron-density distribution of a Is orbital, (b) Contour representations of the Is, 2s, and 3s orbitals. Each sphere is centered on the atom s nucleus and encloses the volume in which there is a 90% probability of finding the electron. 

Although the details of how electron density varies within a given contour representation are lost in these representations, this is not a serious disadvantage. For qualitative discussions, the most important features of orbitals are shape and relative size, which are adequately displayed by contour representations. 

Beginning with the n = 2 shell, each shell has three p orbitals (Table 6.2). Thus, there are three 2p orbitals, three 3p orbitals, and so forth. Each set of p orbitals has the dumbbell shapes shown in Figure 6.23(a) for the 2p orbitals. For each value of n, the three p orbitals have the same size and shape but differ from one another in spatial orientation. We usually represent p orbitals by drawing the shape and orientation of their wave functions, as shown in the contour representations in Figure 6.23(b). It is convenient to label these as p py, and pj orbitals. The letter subscript indicates the Cartesian axis along which the orbital is oriented. Like s orbitals, p orbitals increase in size as we move from 2p to 3p to 4p, and so forth. 

When is 3 or greater, we encounter the d orbitals (for which / = 2). There are five 3d orbitals, five 4d orbitals, and so forth, because in each shell there are five possible values for the m/ quantum number —2, — 1,0,1, and 2. The different d orbitals in a given shell have different shapes and orientations in space, as shown in Figure 6.24. Four of the d-orbital contour representations have a four-leaf clover shape, with four lobes, and each lies primarily in a plane. The d y, d z, and dy orbitals lie in the xy, xz, and yz planes. 

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