= Valence shell electron pair repulsion theory
{wiki=VSEPR_theory}
= VSEPR model
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= VSEPR theory
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The <VSEPR model> predicts approximate <molecular geometry> by arranging the <electron domains> around a central <chemical atom> to reduce their mutual repulsion. Start with a <Lewis structure>, count the domains, and then distinguish the resulting <electron pair geometry> from the positions of the <chemical atoms> themselves. A <lone pair> counts as a domain even though it is not another <chemical atom>.https://ocw.mit.edu/courses/3-091-introduction-to-solid-state-chemistry-fall-2018/g9v8zj6VObw_transcript.pdf[MIT 3.091, lecture 11: Lewis structures, domains and molecular shapes]{ref}
Three worked counts have the same total of eight <valence electrons>. In <methane>, <carbon>'s four plus the contributions of four <hydrogen> <chemical atoms> give $4+4=8$: four <bond pairs>, no <lone pairs>, and <tetrahedral molecular geometry>. In <Ammonia>, <nitrogen>'s five plus three from <hydrogen> give $5+3=8$: three <bond pairs> and one <lone pair>, producing <trigonal pyramidal molecular geometry>. In <water>, <oxygen>'s six plus two from <hydrogen> give $6+2=8$: two <bond pairs> and two <lone pairs>, producing <bent molecular geometry>. All three have four <electron domains>; their <molecular geometries> differ.
\Image[/vsepr-four-domain-shapes.png]
{title=Four electron domains give three molecular shapes as lone pairs replace bonded neighbours}
The regular tetrahedral directions can be represented by the <unit vectors>
$$
\frac1{\sqrt3}(1,1,1),\quad
\frac1{\sqrt3}(1,-1,-1),\quad
\frac1{\sqrt3}(-1,1,-1),\quad
\frac1{\sqrt3}(-1,-1,1).
$$
Each pair has <dot product> $-1/3$, so the ideal <bond angle> is $\theta=\arccos(-1/3)\approx109.47^\circ$. This is a geometric calculation, rather than a prediction that every four-domain <molecule> has that exact <bond angle>. <Lone pairs> and different kinds of <chemical bonds> distort the ideal arrangement; <water>'s H–O–H angle is about $104.5^\circ$.<Chemistry 2e by Paul Flowers and others>[Chemistry 2e, 7.6: ideal geometry and water's bond angle]{ref}
The model is attractive because small-number bookkeeping produces a spatial prediction without first solving for every <molecular orbital>. Shape then helps explain <chemical polarity> and which <hydrogen bond donor> or <hydrogen bond acceptor> sites are accessible. It is a qualitative model, not a full calculation of the electronic <energy> or a universal solution for every <chemical compound>. Gillespie and Nyholm's 1957 review https://doi.org/10.1039/QR9571100339[Inorganic stereochemistry, Quarterly Reviews 11, 339–380]{ref} is a historical anchor for its development.
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