Orbital mapping

Electron densities, bond densities, and spin densities, as well as particular molecular orbitals may be displayed as graphical surfaces. In addition, the value of the electrostatic potential or the absolute value of a particular molecular orbital may be mapped onto an electron density surface. These maps provide information about the environment around the accessible surface of a molecule. Electrostatic potential maps show overall charge distribution, while orbital maps reveal likely sites for electrophilic and/or nucleophilic attack. Surface displays may be combined with any type of model display. 

Orbital mapping analysis of thermal isomerization of aza- and diaza-bicyclo[2.2.0]hexa-dienes has been carried out (80MI51205). Molecular orbital calculations (MNDO) of a series of bisdehydropyridines showed that the 2-azabicyclo[2.2.0]hexa-l,3,5-triene (125) is the least stable form having a calculated heat of formation of 728.4 kJ mol-1 (77CC539). 

So far we have described only the lowest-energy wave function in the hydrogen atom, the I5 orbital. Flydrogen has many other orbitals, which we will describe in the next section. Flowever, before we proceed, we should summarize what we have said about the meaning of an atomic orbital. An orbital is difficult to define precisely at an introductory level. Technically, an orbital is a wave function. Flowever, it is usually most helpful to picture an orbital as a three-dimensional electron density map. That is, an electron "in" a particular atomic orbital is assumed to exhibit the electron probability indicated by the orbital map. 

All orbitals up to and including t2g(P) are occupied. Spin-allowed excitations must therefore be from the t2g(P) to the e iP) orbitals. Mapping the ground and spin-allowed d—>d excited states onto Hcf yields... 

For each such orbit, map one of the edges to ei (there is some arbitrary choice involved here), and map the other one to C2. 

Frontier orbital mapping Thus far we have presented systematic relationships which are purely empirical. However, it is instructive to merge these electrochemical and spectroscopic observations into one conceptual framework. We ascribe notional redox potentials (E i/2) to the nitrile acceptor and halide donor, as before, and so express the charge-transfer transition energies as follows. 

The figure shows a frontier orbital map of metal and ligands constructed for the [RuCl6-n(PhCN)n] family, by use of equations 1 and 2. Note that the vertical axis is related to electrode potential i.e. these data are electron-transfer couples, not orbital energies, and as such they are particularly appropriate for describing both redox and optical charge-transfer phenomena. For example, the metal-centered electron/electron... 

More importantly, in the context of orbital mapping or "electrochemical spectroscopy" the same redox-active orbital (dxy) figures in the primary CT process and in interconfigurational d-d excitations and in the d5/d6 reduction.. Do we find a faithful and illuminating correlation We have tested this on an archetypal system OSX4L2. This system starkly illustrates how the incremental electronic response to progressive substitution can be linear or non-linear depending on the nature of L (and X). 

In a sense, the shape and relative phase of molecular orbitals are a physical observable because these influence reaction mechanisms as described by the Woodward-Hoffmann orbital symmetry rules. One can see what individual MOs look like either by computing electron density or orbital maps, which is fairly easy with modern programs, or by manually examining the LCAO-MO coefficient matrix. To interpret this matrix, one needs to know how the molecule is oriented in the coordinate system (Table 4). Knowing this, the orbital lobes can be sketched in a way consistent with the signs of the coefficients (Figure 5). Such sketches show qualitatively what the MOs look like. In ac-... 

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