Atomic orbitals contours maps

Figure 3.10 Representations of the electron density ip2 of the Is orbital and the 2p orbital of the hydrogen atom. (b,e) Contour maps for the xe plane. (c,f) Surfaces of constant electron density. (a,d) Dot density diagrams the density of dots is proportional to the electron density. (Reproduced with permission from the Journal of Chemical Education 40, 256, 1963 and M. J. Winter, Chemical Bonding, 1994, Oxford University Press, Fig. 1.10 and Fig. 1.11.)...

Figure 4. Wave function contour maps for ReH 2 molecular orbitals. Contour values and sign convention as in Figure 1. Interior contours close to the rhenium atom center have been omitted. Hatom centers are marked by%.

The 13C chemical shift contour map for the Cp carbon of the L-alanine residue in peptides and polypeptides was made as a function of the dihedral angles(, W) by using the experimental data. Also, the corresponding calculated map was made by using the ab initio coupled Hartree-Fock method with the gauge included atomic orbitals(GIAO-CHF). From these results, it was found that the calculated map explains the chemical shift behavior of the a-helix and p-sheet forms in poly(L-alanine) and some proteins. This suggests that the calculated map is applicable to the structural analysis of proteins with complicated structure. 

Fig. S. (A) Emergent hybrid d orbitals at a metal surface (schematic). [After Bond 24).] (B) (Left) Electron-density contour map for the occupied a2, antibonding surface orbital of a cubooctahedral Ni,3 cluster, corresponding to the energy level —0.413 Ry, plotted in the plane of the square face containing atoms 1-4 of the cubooctahedron structure. (Right) Equivalent map but corresponding to the energy level -0.413 Ry plotted in the equatorial plane containing atoms 5-8 and 13 of the cubooctahedron structure.

The upper limit of CCI mode resolution is determined by the characteristics of the STM tip, assuming that a surface contour map is indeed produced. Where the tip is a semiconductor material, tip-to-surface interactions are presumed to be mediated by a single p orbital. Where the tip is a d-band metal then interactions are presumed to be mediated by a single frontier dz orbital. In either case, single-orbital-mediated interactions should lead to at least atomic-level resolution of surface features. 

A computer then generates a contour map of the surface and the outline of individual atoms can be detected. The atoms resemble the hard spheres proposed by Dalton (Figure 2.10), but the STM images are in fact showing the electrons. The fuzziness occurs because the electrons move in a cloud and are not in fixed energy levels or orbits. Previous generations of chemists believed in atoms, but the STM provides empirical evidence for the existence of atoms. 

Fig. 2.8 Contour plots of the wavefunction amplitudes for the highest occupied molecular orbital HOMO) and lowest unoccupied molecular orbital (LUMO) of 3-methylindole. Positive amplitudes are indicated by solid lines, negative amplitudes by dotted lines, and zero by dot-dashed lines. The plane of the map is parallel to the plane of the indole ring and is above the ring by o as in Fig. 2.7, panels D and E. The contour intervals for the amplitude are 0.05ao. Small contributions from the carbon and hydrogen atoms of the methyl group are neglected. The straight black lines indicate the carbon and nitrogen skeleton of the molecule. The atomic coefficients for the molecular orbitals were obtained as described by Callis [37-39]. Slater-type atomic orbitals (Eq. 2.40) with with f = 3.071/A (1.625/ao) and 3.685/A (1.949/ o) were used to represent C and N, respectively...

Fig. 1.4. Contours maps for (a) 2/ , (b) ip, and (c) 3d atomic orbitals. The cross-sectional plane is any plane containing the z-axis. Reproduced with permission from E.A. Ogryzlo EA, Porter GB (1963) J. Chem. Ed. 40 256...

Figure 20.20 Density contour maps for orbitals in the conduction band, (a) Density map for 63, the LUMO level. Both 4p(+4s) and Ga 4s(+4p) AOs are included, (b) Density map for orbital 64. Major electron density is on Zn atoms, (c) Density map for orbital 65. Major electron density is on Ga atoms, (d) Density map for orbital 69. Electron is localized on Zn 4p AO and Ga 4p AOs...

An analysis of the spatial distribution of the wave functions of the 4bi and 12 2 MOs suggests a larger extent (perpendicular to the surface direction) of metal orbitals as compared with the C atoms. Moreover, the contour map of the ISaj MO exhibits an evident deformation of the charge density in the C-C direction, which stimulates the formation of the direct C-C bonds not present in the bulk. 

Theoretically, the radius of an ion extends from the nucleus to the outermost orbital occupied by electrons. The very nature of the angular wave function of an electron, which approaches zero asymptotically with increasing distance from the nucleus, indicates that an atom or ion has no definite size. Electron density maps compiled in X-ray determinations of crystal structures rarely show zero contours along a metal-anion bond. 

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