Momentum density bond additivity

To understand the formation of a triple bond between two CH fragments it is noted that no more than two p-electrons can be directed along the C-C (z) axis, allowing the formation of a linear H(s)1C(sp)1C(sp)1H(s)1 molecule. The remaining pair of p-electrons circulate in the xy-plane with opposite angular momenta. There is no barrier to rotation. The conventional description of a triple bond in terms of one a and two 7r interactions is inconsistent, not only for the reasons already discussed, but also because it violates the conservation of total angular momentum when assigning 2 pairs of p-electrons to px and py orbitals, in addition to the p-density in the sp hybrid orbitals. There is a total of only four p-electrons (l = 1) in the system. 

Momentum-space similarity and dissimilarity indices tend to be especially useful in situations for which the bonding topology is less important than the long-range valence electron density. In addition to model systems, the approach has now been applied successfully to a number of real problems, such as... 

The electron transfer from a partially filled band is obtained by multiplying Nj.j by the fractional occupation of the T band. The purely ionic model is transformed by the latter two equations into a model containing a bonding charge that reproduces the essential features of the electronic structure of NaCl-type compounds when the hybridization is reasonably weak. Whereas the atom and angular-momentum projected densities of states in the unhybridized model arose simply from the T unhybridized bands, they now contain additional parts due to hybridization with the T bands. Dashed lines have been added to complete the hybridized density of states in fig. 58. The number of electrons transferred between the atoms by this interaction is estimated from eq. (68) to be, with UN as example,... 

---