= Bond dipole
{title2=$\mathbf p_b$}
A <bond dipole> represents the separation of positive and negative <electric charge> associated with a <chemical bond>. In a neutral two-<point charge> model put $+q$ at $\mathbf r_A$ and $-q$ at $\mathbf r_B$, with $q>0$. Its physical <electric dipole moment> is
$$
\mathbf p_b=q\mathbf r_A-q\mathbf r_B=-q\mathbf d,\qquad
\mathbf d=\mathbf r_B-\mathbf r_A,\qquad |\mathbf p_b|=q|\mathbf d|.
$$
If $B$ is the negative end, the physical <electric dipole moment> points from $B$ to $A$. The customary crossed-tail chemical arrow points towards the negative, more <electronegative> end, from $A$ to $B$. It therefore has the opposite direction. State the convention before doing <vector addition>; use physical <electric dipole moments> in the interaction <potential energy> $U=-\mathbf p\cdot\mathbf E$, where $\mathbf E$ is the <electric field>.<Chemistry 2e>[§7.6, “Molecular Polarity and Dipole Moment”, Figure 7.26: arrow towards the more electronegative end, with a plus at the tail]{ref}
For a fixed neutral <molecule>, its complete <electric dipole moment> follows from all <atomic nuclei> and the <electron density>, not just <point charges> assigned to sites. If $n(\mathbf r)$ is the expected number of <Electrons> per unit <volume>, the corresponding <charge density> is $\rho_e(\mathbf r)=-en(\mathbf r)$; the nuclear terms contribute separately. Partitioning that distribution into <bond dipoles> is a model. <Lone pairs> and <electric polarization> within a <chemical atom> can contribute as well. A measured molecular <electric dipole moment> cannot uniquely recover every individual <bond dipole> or <partial atomic charge>.
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