It is worth noting that the bond path, which is correlated with the
λ3 eigenvalues of the e3eigenvector, does not take into consideration contrasts within
λ2 and λ1 eigenvalues of thee2 ande1 eigenvectors. The bond-path
framework set indicated by B = {p , q , r } will be
used, which demonstrates the new QTAIM interpretation of the chemical
bond. This viably implies that in the most well-known cases, a bond is
comprised of three ‘linkages’; p , q, andr associated with the e1 ,e2 , and e3 eigenvectors, individually. Subsequently, Scheme 1 clearly
illustrates that the p parameter interprets eigenvector-following
paths with lengths\(\mathbb{H=}\sum_{i=1}^{n-1}\left|\mathbf{q}_{i+1}-\mathbf{q}_{i}\right|\)whilst the q parameter interpret eigenvector-following paths with
lengths\(\ \mathbb{H}^{\mathbf{*}}=\sum_{i=1}^{n-1}\left|\mathbf{p}_{i+1}-\mathbf{p}_{i}\right|\).
The scaled e1 ore2 eigenvectors will sweep out alongside
the extent of the bond-path, specified by thee3 eigenvector, between the two bonded
nuclei that the bond-path interfaces, resulting ineigenvector-following paths with lengths H* or
H. For shared-shell BCP s From the forms of p and q,we observed that within the constrain of the ellipticity ε ≈ 0
comparing to single bonds, as a result, we obtain thep i = q i =ri , the value of the lengths H and
H* reaches its lowest point; the bond-path length
(r ) BPL. In contrast, for double bonds which have higher values
of the
ellipticity
ε, results show in values of H* and H
>BPL. Moreover, H = H* if identical
scaling factor εi is used in their equations
since H* and H are defined by the distances swept out
by the e1 ande2 tip path points respectively.