Bond polarization
= Bond polarization
<Bond polarization> is unequal sharing of <electron density> across a <chemical bond>. An <electronegativity> difference is a heuristic for its direction and tendency, not a unique <partial atomic charge>.
A simple two-site model makes the notation explicit. Represent each site by effective positive <electric charge> $+e$, and allocate expected <electron> populations $1-s$ to $A$ and $1+s$ to $B$, with $0\leq s<1$. Here $e$ is the <elementary charge>; these effective sites omit the internal structure of real <chemical atoms>. Subtraction gives
$$
q_A=e-e(1-s)=se,\qquad q_B=e-e(1+s)=-se,\qquad q_A+q_B=0.
$$
For the stipulated illustration $s=0.35$, the populations are $0.65$ and $1.35$, and the effective <partial atomic charges> are $+0.35e$ and $-0.35e$. Fractional expected populations do not split an individual <electron> into pieces. The total population remains two, and the pair remains neutral. No formula connecting $s$ to $\Delta\chi$ has been assumed; many <electron density> distributions and partitioning conventions can share one qualitative <electronegativity> ordering.
\Image[/bond-polarization-populations-and-arrows.png]
{title=Stipulated two-site <bond polarization>: expected <electron> populations, effective <partial atomic charges>, and opposite chemical and physical arrow conventions}
{id=image-bond-polarization-populations-and-arrows}
{description=Original model with $s=0$ and $s=0.35$, effective positive site charges $+e$, and two expected <electrons> in total. The population bars are bookkeeping weights, not a measured <electron density> map. Arrow lengths illustrate direction only; no empirical <electronegativity> values or charge calibration are implied.}