= Formal charge
{title2=$\mathrm{FC}=v-n-b/2$}
{wiki}
The <formal charge> of a <chemical atom> in a <Lewis structure> assigns it all of its nonbonding <electrons> and half of the <electrons> in its connections:
$$
\mathrm{FC}=v-n-\frac b2.
$$
Here $v$ is the neutral <chemical atom>'s <valence electron> count, $n$ is the number of nonbonding <electrons> assigned to it, and $b$ is the number of bonding <electrons> incident on it. Count <electrons>, not <electron pairs>: two <lone pairs> mean $n=4$, and two double connections mean $b=8$. The number $\mathrm{FC}$ gives <electric charge> in units of the positive <elementary charge>. Equal splitting is a bookkeeping convention, regardless of the actual <electron density>. See the https://goldbook.iupac.org/terms/view/08169[IUPAC Gold Book, formal charge].
\Image[/lewis-carbon-dioxide-formal-charge.png]
{title=Sixteen <valence electrons> in two <carbon dioxide> <Lewis structures>: $\mathrm{O=C=O}$ has zero <formal charges>, while $\mathrm{O^-{-}C\equiv O^+}$ has separated <formal charges>}
{description=The first <Lewis structure> has two <lone pairs> on each <oxygen>. The second has three <lone pairs> on the singly connected <oxygen>, one on the triply connected <oxygen>, and none on <carbon>. Both use four <bond pairs> and four <lone pairs>; both satisfy the <octet rule>. Their contributions to <chemical resonance> are unequal, and the drawn <formal charges> are not <partial atomic charges>.}
For $\mathrm{O=C=O}$, each <oxygen> has $v=6$, $n=4$, $b=4$, giving <formal charge> $6-4-4/2=0$. <Carbon> has $v=4$, $n=0$, $b=8$, giving <formal charge> $4-0-8/2=0$. For $\mathrm{O^-{-}C\equiv O^+}$, the left <oxygen> has <formal charge> $6-6-2/2=-1$, <carbon> still has <formal charge> zero, and the right <oxygen> has <formal charge> $6-2-6/2=+1$. The net <electric charge> is zero in either drawing.
The <Lewis structure> with no separated <formal charges> is the dominant contributor in this elementary comparison; the charge-separated drawing is a less important contributor, rather than an equally dominant alternative. This is a qualitative selection rule, not a calculation of <energy> or numerical <chemical resonance> weights. See https://openstax.org/books/chemistry-2e/pages/7-4-formal-charges-and-resonance[Flowers et al., Chemistry 2e, 7.4: comparing carbon dioxide structures]. A zero <formal charge> does not imply zero <partial atomic charge>: the latter depends on partitioning the actual <electron density>, which a <Lewis structure> does not supply.
As a short consistency derivation, summing $n+b/2$ over all <chemical atoms> counts every drawn <electron> once: a nonbonding <electron> is assigned once, and a bonding <electron> contributes half at each of its two endpoints. Thus
$$
\sum_i\mathrm{FC}_i=\sum_i v_i-N_{\mathrm{valence}},
$$
where $N_{\mathrm{valence}}$ is the total drawn <valence electron> count. The right side is the net <electric charge> in units of <elementary charge>. This catches a wrong budget even when individual <octet rule> checks look plausible.
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