Electron contour

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. 

Orbital density pictures are probably the most comprehensive views we can draw, but they require much time and care. An electron contour drawing provides a simplified orbital picture. In this representation, we draw a contour surface that encloses almost all the electron density. Commonly, almost all means 90%. Thus, the electron density is high inside the contour surface but very low outside the surface. Figure 7-19c shows a contour drawing of the 2s orbital. 

The quantum number / — 1 corresponds to a p orbital. A p electron can have any of three values for Jitt/, so for each value of tt there are three different p orbitals. The p orbitals, which are not spherical, can be shown in various ways. The most convenient representation shows the three orbitals with identical shapes but pointing in three different directions. Figure 7-22 shows electron contour drawings of the 2p orbitals. Each p orbital has high electron density in one particular direction, perpendicular to the other two orbitals, with the nucleus at the center of the system. The three different orbitals can be represented so that each has its electron density concentrated on both sides of the nucleus along a preferred axis. We can write subscripts on the orbitals to distinguish the three distinct orientations Px, Py, and Pz Each p orbital also has a nodal plane that passes through the nucleus. The nodal plane for the p orbital is the J z plane, for the Py orbital the nodal plane is the X Z plane, and for the Pz orbital it is the Jt plane. 

C07-0084. The conventional method of showing the three-dimensional shape of an orbital is an electron contour surface. What are the limitations of this representation ... 

The next column shows the few values of the median electron-cloud radii which can be obtained from graphical interpolation of published electron-contours based on X-rays. The agreement is fairly good, and the free-ion value for Li+ is roughly acceptable. 

The most interesting compounds described in this paragraph are meso-ionic naphtho[reactions with olefinic compounds. For instance, the reaction with acetylenedicarboxylates gives rise to adducts 458, which are dehydrogenated spontaneously to the new heteroaromatic systems 459 with the aromatic 147r-electron contour [75JCS(PI)556]. 

Equation (3) indicates that the STM tip does probe the density of electronic contours rather than the surface topography in terms of a hard-sphere model [47]. Electronic contours generally coincide with atoms on metals. With semiconductors the interpretation of images is not trivial because electrons are located in bound states (dangling bonds on clean surfaces in UHV, chemical bonds between surface atoms and ligands in liquids) whose density and occupation can vary from one atom to another. 

By applying appropriate voltage ramps to the x- and y-piezo-drives (Fig. 10.7), the tip is scanning along the surface line by line, controlled by the feedback and thus follows the electronic contour of the studied object. 

Height calibration (z) Monoatomic steps on the Au(lll) surface and a nanogrid with defined z-height have proven to be good standards for the z-calibration of an STM. In many respects the calibration procedure for the vertical axis (z-axis) is comparable to that for the lateral axes, however, the vertical movements are often much faster (in order to follow the object s topography or more accurately its electronic contour), than in the lateral directions. In order to obtain accurate results, the parameters of the feedback control system (e.g. proportional factor P and integration time constant I), that influence the dynamic behavior of the SPM in z-direction, need to be adjusted... 

Pauling s classic text, The Nature of the Chemical Bond," first edition in 1939, third edition in 1960, has a title that is equally magisterial and mysterious. It evokes Lucretius ancient classic De Return Natura (On the Nature of Things). Indeed, his goal was perhaps no less than leading a diving expedition into the depths of chemical bonds to sample their electronic contours, waves, and currents. 

Electron contour diagram of diborane in the piane of the terminal H atoms. [Reproduced from J Amer Chem Soc 1979,707, 1389-1395. Used with permission of the American Chemical Society.]... 

Figure 8. Electron contour maps of MO-1 (SOMO singly occupied MO) and MO-2 (HOMO highest doubly occupied MO) along the fragmentation path of ToT( +). a) TTp-1, b) ts-66, c) TTp-2, d) ts-55, h) T T( +), and e) - g) the intermediates of the linear synchronous transition paths coimecting ts-55 and T T( +).

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