Wave function contour maps

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%.

We will not construct wave functions for the d orbitals but simply show them. The wave function, contour maps, and isosurfaces for the and 3dz2 orbitals are shown in Figure 8-29 these graphs are realistic representations of the shapes of these orbitals. Simplified representations of the all five d orbitals are shown in Figure 8-30. Two of the d orbitals ( d -yi and d ) are directed... 

These tendencies are illustrated in the contour maps of the relevant MOs in Fig. 5.2, which clearly show the contraction of the wave function contours to the impurity core in the series C N O, and the lowering of the electronic density along the Ti-X bond. 

View the contour map m several planes to see the general Torm of the distiibiiiioii. As long as you don t alter the molecular coordinates, you don t need to repeat th e wave function calculation. Use the left mouse button and the IlyperChem Rotation or Translation tools (or Tool icons ) to change the view of amolecnle without changing its atomic coordinates. 

If a iTioleciile is rotated by chan gin g th c position of the viewer (left mouse btiLlon rotation) ih en the moleetile s position in ihetnolee-ular eoorditi ale system h as not ch an ged and anolb er con lour plot can be requested without recotn pu tin g the wave ftinetion. fb at is, m any orbitals can he plotted after a sin gle poin t ah initio or setn i-einpirical calculation,. iti y contour map is available without recotn putation of the wave function. 

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. 

A more practical representation of the electron distribution in a molecule can be obtained from the probability density contour maps. Isodensity contours in the molecular plane and in a plane parallel to the molecular plane at an altitude of 0.8 atomic unit have been calculated230 for three nucleic acid bases (adenine, thymine, and cytosine) from non-empirical wave functions. The first type of contour gives an overall picture of cr-bonding in the molecule, and the second characterizes the 77-electron density. 

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. 

Fig. 18 Contour maps of MO wave functions for Fejg cluster...

The shape of individual valence states around the vacancy can be seen from the contour maps of the relevant MOs (Fig. 4.3). The spatial deformation of the wave functions near the C vacancy results in an increase in the electron density between the metal atoms closest to the vacancy. This can be interpreted as the formation of additonal Ti-Ti bonds. These peculiarities which were found in cluster calculations have been reproduced in band APW calculations of ordered TiC by Redinger et al (1985). 

Fig. 4.3 Contour maps of wave functions and total charge densities in complete...

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. 

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