Frontier orbitals Fragment analysis

The PPP configuration analysis technique and the mo ecules-in-molecules/localized configuration interaction (MIM/LCI) method can provide an explanation of the fact that some cyclic sulfur diimides are colorless, while others are not. Thus, while 1,2,5-thiadiazoles 231 and 232 are colorless, naphtho[l,8- /][l 4,2,6]thiadiazine 229 is colored (low intensity absorption at 642 nm). The energy level of the color band appears to be largely determined by frontier orbital interactions. By considering the overlap between the two fragments, (i) the NSN group and (ii) the... 

We have seen from Coulson s equations (p. 18) that for conjugated polyenes, the odd-numbered MOs are symmetrical and the even-numbered MOs antisymmetrical. Hence the symmetry properties of the frontier orbitals of the k fragment alternate as the polyene gains or loses a double bond. This allows us to generalize the analysis above into the selection rule thermal disrotatory ring openings are forbidden for 4n electron and allowed for 4n + 2 electron systems. The opposite is true for conrotatory opening. 

To produce an interaction diagram we need the frontier orbitals of Cr and CO. The former are 3d, 4s and 4p whereas the latter are 5a and 2ir and Cr possesses six valence electrons whereas each CO has two in the HOMO. For simplicity we will first consider only the CO donor orbitals and then add the acceptor orbital interactions later. For the first problem then we have nine metal functions and six ligand functions plus 18 electrons total. Thus, we must generate 15 MOs of which 9 will be filled. Is this a simplification The full problem requires nine metal functions and 6 x (4 + 4) ligand functions for a total of 57 MOs Of course, in a real calculation, the fragment analysis is done by the computer on the MO solutions of the complete... 

In the first three chapters, instances were noted where the number, symmetry characteristics and occupation numbers of the frontier orbitals of a transition-metal fragment were similar to those of a main-group fragment. Such fragments are said to be isolobal to emphasize similar bonding capabilities. Since its enunciation by Hoffmann and Mingos, the concept has been used effectively for the analysis of both organometallic and cluster problems. Let s explore the idea in a more systematic... 

The effectiveness of a fragment analysis depends on the extent to which the perturbation of the fragment electronic structures is restricted to the frontier orbital... 

The ionization potential in a simple one-electron approximation measures the energy of the highest occupied molecular orbital (HOMO). This orbital is only one of an entire manifold of levels which contribute to the bonding characteristics and total stability of the cluster. Frontier fragment-orbital analysis in organometallic reactivity studies has provided a clear indication... 

Frontier molecular orbital theory. A. Analysis of a [2+2] cycloaddition, showing unfavorable mixing between the HOMO and LUMO of the two ethylene fragments. B. Analysis of a [4+2] cycloaddition, showing the favorable HOMO-LUMO mixings. 

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