Fifth-order bonds

Elements in the second row of the period table do not form higher-order bonds than triple bonds, but elements in the higher rows can form higher-order bonds, which can be represented with linear combinations using d orbitals as well as s and p orbitals. A fifth-order bond has been reported between two chromium(I) ions. ... 

In bicyclobutane, the CH bonds to Ci and C4 all lie in the xz plane and are not interconvertible. Accordingly, two of the four CH-bonding combinations are totally symmetric (ai) and the remaining two are labelled 61. In contrast, the CC bonds that form the four-membered ring are inter con verted by the sym-ops of C2VJ and their combinations span its four irreps. For completeness, we add the fifth CC-bonding orbital. In zeroth order, it is localized in the central bond between C2 and C3, but it interacts - favorably and unfavorably - with the totally symmetric acc combination to produce two ai orbitals, Ci and (T5. Since the analysis of the reaction is being formulated as an 18-electron problem, butadiene too has to be represented by nine doubly-occupied orbitals To the six in Fig. 5.5 we add three (Tcc orbitals to house the three electron pairs in the... 

Saito, S., Ohmine, I. (1998). Off-resonant fifth-order nonlinear response of water and CS2 Analysis based on normal modes. J. Chem. Phys. 108 240-251 Saito, S., Ohmine, I. (1999) Water dynamics Fluctuation, relaxation, and chemical reactions in hydrogen bond network rearrangement. Acc. Chem. Res. 32 741-749. 

Another factor comes into play here. In the first coordination sphere, deviations in metal-ligand bond distances are normally small enough to be neglected. The nearest 14 K+ ions lie at seven separate distances, from 4.3 to 6.0 A. The variation in the magnitude of the perturbation with distance must be considered, and it is not straightforward. Classical crystal field theory shows an inverse fifth power dependence of Dq on distance from the metal, but this result is specific to octahedral symmetry, in which lower order dependencies drop out. For individual perturbers we have proposed a dependence of the form aR-3 + bR-5 for both e and e [7]. For counterions we also suggest that the n contribution and the R-5 part of the a contribution can be neglected. 

This sequence covers fnlly the macroscopic descriptions of chemical phenomena and then begins to interpret them in terms of molecular structure. Instructors could choose either of the two bonding approaches suggested earlier for the specific order of Chapters 3-6 late in this course. This sequence represents a rather pnre form of the macro-to-micro approach that was followed in the first three editions. Alternatively, they conld cover Chapter 3 between Chapter 2 and Chapter 9, as was done in the fonrth and fifth editions. This approach has the advantage of building a snbstantial fonndation in structure—and a complete discussion of chemical nomenclatnre—as the basis for the macroscopic descriptions, while leaving the quantum theory of bonding to come later in the course. 

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