Bonding bonds

Bond Bond Bond Bond Bond Bond Bond Bond... 

The ternary (1,1,l)j junctive process resulting from atom-atom-atom associations is given by 48- [49]. Similarly, (l,l,2)j processes arise from atom-atom-bond, atom-atom-face interactions (e.g. 50- [51], 52- [53]), whereas (l,2,2)j processes stem from atom-bond-bond, atom-bond-face and atom-face-face interactions (e.g. 54- [55], 56- [57], 58- [59]. Finally, the ternary bond-bond-bond, bond-bond-face, bond-face-face, and face-face-face associations are designated (2,2,2)j as in 60- [61], 62- [63], 64- [65], and 66- [67], respectively. 

Lone pair —> Bond, Bond —> Bond, Bond —> Lone pair... 

Lone pair > Bond, Bond - Bond, Bond — Lone pair... 

To derive statistical parameters in the postgel stage, we have to determine the probability of having a finite continuation when leaving a fragment from (+) bonds, (—) bonds, (+)bonds, (—)bonds and arrows. We will call these probabilities Z(+), Z(—), Z (+), Z (—) and Z(A), respectively. For example, Z(—) is defined as... 

It is important to point out that recent results on density based overlap integrals [16] confirm the interest of the formulation of Erep as a sum of bond-bond, bond-lone pair and lone pair-lone pair repulsion indeed, core electrons do not contribute to the value of the overlap integrals. 

When the molecule is planar, i.e., when cci + 0 2 + 3 = 27T, the determinant A = 0 and A cannot be inverted. This is because in this particular situation, Ci, 62, and 63 are linearly dependent and there are infinitely many possible values of ( Bond, Bond Bond) casc, wc Can cxprcss fl in terms of Cl and 62 only... 

Localization of the delocalized SCF— MO s leads to a description of molecular structure in terms of localized bonds and lone pairs. The total energy is then a sum of bond and lone-pair energies Ei which are made up of an internal (bond or lone-pair) energy component Ef, and a bond-bond, bond-lone pair, lone pair-lone pair, interaction component 2 yB 168)h> ... 

Symmetrical covalent Polar covalent Ionic bond bond bonds... 

The simplest binary junctive process (l,l)j results from atom-atom combination e.g. 32- [33], 34- [35], 36- [37]. The (l,2)j atom-bond, atom-face junctive processes are exemplified by transformations 38- [39] and 40- [41], respectively. The (2,2)j junctive processes resulting from bond-bond, bond-face, and face-face associations are represented by 42- [43], 44- [45] and 46- [47], respectively. 

Erep in first-order is formulated under the form of a sum of bond-bond, bond-lone pair, and lone pair-lone pair interactions. This was inspired by an earlier proposal by Murrell et al. [91] following which the exchange-repulsion is proportional to the square of the intermolecular overlap between locahzed orbitals. For each pair of interacting orbitals, it could be formulated as S /R , S denoting their overlap and R the distance between their centroids, n taking the values of 1, 2 and possibly beyond. In the context of SIBFA, representations of the orbitals are the chemical bonds and the lone-pairs. 

---