= Resonance
{disambiguate=chemistry}
{wiki}
= Chemical resonance
{synonym}
A single <nitrate> <Lewis structure> singles out one N=O connection, yet the three N–O <chemical bonds> of the isolated symmetric <ion> are equivalent. <Chemical resonance> reconciles that symmetry with the integer <electron pair> allocations of a <Lewis structure>. The equal <chemical bond> lengths in <nitrate> are discussed in https://www.open.edu/openlearn/mod/oucontent/view.php?id=87848§ion=_unit5.2[The Open University, Discovering chemistry: resonance structures].
<Chemical resonance> uses several <Lewis structures> with the same <chemical atom> connections and total <electric charge> to describe electronic structure that one allocation cannot fully express. The <chemical atoms> stay in place; the positions of <bond pairs>, <lone pairs>, and <formal charges> differ between drawings. A two-headed arrow $\leftrightarrow$ connects the drawings and is distinct from a <chemical equilibrium> arrow $\rightleftharpoons$. See the https://goldbook.iupac.org/terms/view/08205[IUPAC Gold Book, resonance form].
In each <nitrate> <resonance structure>, use the existing <formal charge> convention $\mathrm{FC}=v-n-b/2$:
$$
\begin{aligned}
\mathrm{FC}(\mathrm N)&=5-0-8/2=+1,\\
\mathrm{FC}(\text{singly connected O})&=6-6-2/2=-1,\\
\mathrm{FC}(\text{doubly connected O})&=6-4-4/2=0.
\end{aligned}
$$
Here $v$ counts neutral-<chemical atom> <valence electrons>, $n$ counts nonbonding <Electrons>, and $b$ counts incident bonding <Electrons>. The sum is $+1-1-1+0=-1$, agreeing with the <nitrate ion>'s net <electric charge>. The <formal charge> rules and their distinction from actual atomic <electric charge> are given in https://openstax.org/books/chemistry-2e/pages/7-4-formal-charges-and-resonance[Flowers et al., Chemistry 2e, 7.4: formal charges and resonance].
Keep one labelled <oxygen> fixed while reading the three <nitrate> <resonance structures>. Its connection is double in one drawing and single in two. Equal weighting within this three-contributor <Lewis structure> model gives the average <bond order>
$$
\overline b_{\mathrm{N-O}}=\frac{2+1+1}{3}=\frac43.
$$
The same calculation applies to all three N–O connections. Averaging the drawn <formal charges> similarly gives $-2/3$ per <oxygen>, while <nitrogen> retains $+1$; $+1+3(-2/3)=-1$. These fractions summarize the chosen contributors. They are not a measurement of <partial atomic charge>, a literal fraction of an <Electron> sitting on an <oxygen>, or time spent in one drawing.
\Image[/nitrate-delocalized-bonding.png]
{title=Equivalent N–O <chemical bonds> in symmetric <nitrate>: the equal-contributor <bond order> count is $4/3$}
{description=All three connections have the same graphical treatment. A solid line with a dashed companion is a schematic indication of shared multiple-<chemical bond> character, not a plot of <electron density> or a physical fractional line. The labels $4/3$ record an average within three octet <Lewis structures>; no universal, directly measured <bond order> of exactly $1.333\ldots$ is asserted.}
The <resonance hybrid> has one spatially continuous <electron density> extending over the <ion>. None of its N–O <chemical bonds> is permanently selected as the double connection of one contributor. The dashed marks above are symbols; <Electrons> do not travel along them or make the marks float between <chemical atoms>. For isolated symmetric <nitrate>, symmetry makes the three N–O <chemical bonds> equivalent; an environment that distinguishes the <oxygen> sites can remove that equivalence. The fraction $4/3$ alone predicts neither a <chemical bond> length nor a dissociation <energy>. The general relation between multiple <chemical bonds>, lengths, and strengths is discussed in <Chemistry 2e by Paul Flowers and others/7.5 Strengths of Ionic and Covalent Bonds>; its tabulated averages are not a nitrate-specific calibration of $4/3$.
<Ozone> provides a useful two-contributor comparison. Its $3\times6=18$ <valence electrons> give three <bond pairs> and six <lone pairs>. One <resonance structure> has a double O–O connection on the left and a single one on the right; the other reverses these allocations while retaining the same <chemical atom> positions and connections. The central <oxygen> has one <lone pair> and <formal charge> $+1$; the singly connected terminal <oxygen> has three <lone pairs> and <formal charge> $-1$; the doubly connected terminal <oxygen> has two <lone pairs> and <formal charge> zero. Thus $6+12=18$ <Electrons> and zero net <electric charge> are conserved. The equal-contributor <bond order> count is $(2+1)/2=3/2$ for either connection. See https://ocw.mit.edu/courses/5-111sc-principles-of-chemical-science-fall-2014/3549685d450773a066a716832634203f_MIT5_111F14_Lec10.pdf[MIT 5.111, lecture 10, pp. 4–5: ozone resonance structures].
For <carbon dioxide>, $\mathrm{O=C=O}$ and $\mathrm{O^-{-}C\equiv O^+}$ share sixteen <valence electrons> and the same O–C–O connections. The mirror drawing $\mathrm{O^+\equiv C{-}O^-}$ is also possible. The two charge-separated drawings are equivalent to one another for an isolated symmetric <carbon dioxide> <molecule>, but neither is equally dominant with $\mathrm{O=C=O}$ in the elementary <formal charge> comparison.
<Chemical resonance> does not mean that a <molecule> rapidly flips between drawings, nor that separate <molecules> at <chemical equilibrium> carry the individual drawings. The actual <electron density> belongs to one combined electronic description. In a <quantum mechanics> treatment, contributors enter a <linear combination> of many-<Electron> <wavefunctions>; a <molecular orbital> treatment can describe the extended electronic arrangement through <molecular orbitals>. The drawings alone provide neither a measured density nor numerical weights. Their usefulness is to expose the limitations of one localized allocation without pretending that every algebraically allowed <Lewis structure> contributes equally.
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