Vsepr — the ladder
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VSEPR, computed
The tetrahedral angle is not 109.5 degrees because a textbook says so. It is arccos(−1/3), and it falls out of minimising the repulsion of four points on a sphere without ever being written down.
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Five sites are not alike
Every other common arrangement has one or two distinct angles. Five has three, because two of its positions are on an axis and three are round an equator — and a molecule built that way does something about it.
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Why water is bent
The standard answer is lone pair repulsion, it predicts the right direction, and it cannot predict the magnitude. A better rule can, and the heavier hydrides show where both accounts run out.
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The shapes above six coordination
Eight points on a sphere do not arrange themselves in a cube. They twist one face by forty-five degrees, and above six the arrangements stop being the ones anybody would name and start being the ones a minimisation finds.
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Bent's rule, against the substituent series
More electronegative substituents get more p character, so the angle between them shrinks. The rule predicts a trend, the trend is observed, and the quantity it depends on turns out not to be one quantity.