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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 isIf $B$ 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.^[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.

Electronegativity describes a chemical atom's tendency to attract electron density towards itself in a chemical bond. It helps answer a useful question: when two different chemical atoms share Electrons, which end of the chemical bond tends to be richer in electron density? For hydrogen chloride, the answer is chlorine: the covalent bond is a polar covalent bond, conventionally written ${\mathrm{H}}^{\delta +}-{\mathrm{Cl}}^{\delta -}$. The symbols indicate partial atomic charges, not isolated ions carrying whole elementary electric charges.^[ref]

Electronegativity is a comparison scheme, not the number of Electrons on a chemical atom. A partial atomic charge depends on how the electron density is partitioned; formal charge instead follows an integer allocation in a Lewis structure. Neither is numerically equal to electronegativity. Nor is electronegativity identical to electron affinity, which concerns adding an Electron to an isolated species. Different electronegativity scales use different measured inputs and conventions; compare numbers only after specifying the scale.^[ref]

For a concrete comparison, the Royal Society of Chemistry lists Pauling electronegativities ${\chi }_{\mathrm{P}}(\mathrm{H})=2.20$ and ${\chi }_{\mathrm{P}}(\mathrm{Cl})=3.16$. Their difference is $0.96$, so the electronegativity rule predicts bond polarization towards chlorine in hydrogen chloride. An isolated molecular hydrogen molecule has identical ends and zero electronegativity difference. These examples explain a direction of unequal sharing, not a quantitative partial atomic charge.^[ref][ref]

A larger electronegativity difference often suggests stronger bond polarization, but there is no universal numerical boundary where a covalent bond suddenly becomes ionic bonding. Tables of cutoffs are classification aids with exceptions. Hydrogen fluoride, for example, is described by a polar covalent bond even when its electronegativity difference exceeds a textbook's nominal ionic threshold. The actual electron density, physical setting, and chemical substance's structure matter.^[ref]

The distinction from ionization energy is equally useful: an ionization energy measures the cost of removing an Electron from a specified isolated species, whereas electronegativity compares attraction for electron density in a bonded environment. Neither the removal cost alone nor the attachment release alone supplies a unique bonded-atom electronegativity. A scale combines selected measured inputs with a model and a convention.^[ref]

For an original relative comparison, stipulate fictitious bonded sites $A,B,C$ on one chosen dimensionless electronegativity scale:The electronegativity heuristic predicts bond polarization towards $B$ in $A-B$, towards $C$ in $B-C$, and towards $C$ in $A-C$. Shifting ${\chi }_0$ leaves every comparison unchanged. Although the $A-C$ difference is twice the $A-B$ difference, this does not make its partial atomic charge or bond dipole twice as large: those require additional information about electron density and bond length. These symbols describe a stipulated ordering, not a table of measured chemical elements.

Keep the chemical context attached to that ordering. A chemical atom in a molecule has neighbours and an electron configuration; an isolated-atom energy scale and a bonded-atom comparison are different constructions. The chemical environment dependence of electronegativity explains why a table is a useful approximation rather than an immutable property of every site. Furthermore, an applied electric field can induce bond polarization even between identical chemical atoms, through electric polarizability; equal tabulated electronegativity does not forbid that response.

Molecular dipole cancellation occurs when nonzero contributions to a molecule's electric dipole moment cancel under vector addition. In a bond dipole model, use ${\mathbf{p}}_{\mathrm{mol}}={\sum }_b{\mathbf{p}}_b$; adding magnitudes instead discards the molecular geometry. A symmetric linear molecule with two equivalent opposed bond dipoles has ${\mathbf{p}}_1=p_0\hat{\mathbf{x}}$ and ${\mathbf{p}}_2=-p_0\hat{\mathbf{x}}$, hence zero total electric dipole moment even though each chemical bond is polarized. Carbon dioxide provides the familiar molecular example; water's bent molecular geometry permits a nonzero total.^[ref]

For an original geometry calculation, give a fictitious three-site model $A{B}_2$ a central effective electric charge $+2q$ at the origin and two terminal electric charges $-q$ atHere $r$ is the stipulated bond length, $\theta$ the angle between the two connections, and $q>0$ is independent of any electronegativity scale. Equivalently, split the central $+2q$ into two colocated $+q$ contributions, one for each neutral bond dipole. With $p_0=qr$, the physical electric dipole moments point from the terminal sites towards the central site:The sideways components cancel; the components along the angle bisector add. Thus $|{\mathbf{p}}_{\mathrm{mol}}|=2p_0\cos (\theta /2)$. At $\theta =180^{\circ }$ the result is zero; at the stipulated $\theta =120^{\circ }$ it is exactly $p_0$. This is an angle example for a model, not the measured angle or electric dipole moment of water.

Opposition alone is insufficient: a linear molecule with unequal opposed bond dipoles of magnitudes $p_1$ and $p_2$ retains magnitude $|p_1-p_2|$. Conversely, symmetry can enforce exact cancellation beyond a particular bond dipole partition. If the complete charge density invariant under point reflection about the origin satisfies $\rho (\mathbf{r})=\rho (-\mathbf{r})$, contributions to $\int \mathbf{r}\rho (\mathbf{r})d^{3}r$ cancel in pairs. That proof uses the whole electric charge distribution, including lone pairs and atomic nuclei. It explains why molecular symmetry is stronger evidence for zero permanent electric dipole moment than a rule based only on tabulated electronegativity differences.

A permanent molecular electric dipole moment is specified relative to the molecule's orientation. An ensemble with random orientations can have zero mean laboratory vector while each molecule is polar. That orientational average differs from internal molecular dipole cancellation. The Stark effect and molecular beam electric resonance probe molecular electric dipole moments through state-dependent responses to an electric field.

A polar covalent bond shares Electrons unequally, as in hydrogen chloride.

The word “polar” qualifies the sharing within a covalent bond; it does not require complete transfer of an Electron or an isolated cation–anion pair. In $A^{\delta +}-B^{\delta -}$, the signs identify the relatively electron-poor and electron-rich ends, while $\delta$ leaves the amount unspecified. A neutral Lewis structure can give both chemical atoms zero formal charge and still correspond to a polar covalent bond: equal division of the bond pair is a formal allocation, whereas bond polarization concerns the actual electron density.

Local and molecular descriptions answer different questions. Calling one chemical bond a polar covalent bond does not establish that the whole molecule is a polar molecule. Combine the bond dipoles with the molecular geometry, then check for molecular dipole cancellation. This lets a short electronegativity comparison explain a local tendency without confusing it with the observable electric dipole moment of the whole molecule.