The tetrahedral nature of carbon bonding was worked out by pre-quantum chemists who had little more knowledge of atoms than Plato did. They reasoned like this: CH 2 Cl 2 has only one isomer, not two. Therefore it cannot be square planar, but it can be tetrahedral. Think about it. It is not proof, but it makes the tetrahedral structure look plausible. Look it up in your old organic book.
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McClain, W.M. (2009). Hybrid orbitals. In: Symmetry Theory in Molecular Physics with Mathematica. Springer, New York, NY. https://doi.org/10.1007/b13137_41
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DOI: https://doi.org/10.1007/b13137_41
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