The importance of hybrid atomic orbitals, both historically and mathematically, is reviewed. Our new analysis of the original derivation of the sp3, sp2, sp model reveals serious errors. Based on a critical survey of the literature, we submit six formal criteria that deprecate the use of hybrid orbitals in a pedagogical context. A sound mathematical basis of sp3 and sp2 formulae does not exist; hybrid atomic orbitals have hence no legitimate role in the teaching of organic chemistry.
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