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If two molecular orbitals are orthogonal, their net overlap is 0. Which means that the mixture of them would result in no observable change in any of the orbitals if they occur. However, this contrasts totally with the Molecular Orbital Theory as well as the Valence Bond Theory, whereby atomic orbitals are often combined. In this manner, is it not plausible that the orthogonality condition of the wave function hinders the combination of orthogonal wave functions -i.e. atomic orbitals?

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    $\begingroup$ Atomic orbitals of one atom are orthogonal, but those of different atoms aren't. $\endgroup$ Apr 24, 2023 at 20:22
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    $\begingroup$ This makes sense to explaining chemical bonds, but not to explaining hybridization in an atom. $\endgroup$ Apr 24, 2023 at 20:25
  • $\begingroup$ In MO theory, you first mix orbitals to fit them to the symmetry of the molecule. That in itself does not explain bonding, but it prepares you for then combining the symmetry-adapted combinations of one set of atoms (e.g. the hydrogen atoms of methane) with the symmetry matched of another set of atoms (e.g. the carbon atom of methane). $\endgroup$
    – Karsten
    Apr 24, 2023 at 21:49
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    $\begingroup$ Within MO theory, there (strictly speaking) is no hybridisation. For a single atom such a description (without an external potential) doesn't make much sense. And in VB theory there are (strictly speaking) no eigenvalues of the hybrid orbitals. A VB description of a single atom also doesn't make much sense; the theory is not designed for this. You also cannot just mix and match both approaches. $\endgroup$ Apr 25, 2023 at 0:17
  • $\begingroup$ @Karsten thus, in MO Theory, I first mix the present orbitais from the atoms to find if the orbitals can make one MO - with aid of Group Theory - for then populating the MO according to the Aufbau Principle, which in turn enable me to analyse the degree of bonding in the molecule? $\endgroup$ Apr 27, 2023 at 19:09

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A bond is formed between two atoms, and a pair of AOs from each doesn't share the same coordinate system. Obviously, because there is a finite distance, the bond lenght, between the (0,0,0) coordinates of each AO.

That means the concept of orthogonality makes no sense for the constituent AOs of a MO. Simply speaking you can freely align the two coordinate systems to give the biggest overlap. Which is what nature does, because that gives the biggest energy gain from the bond.

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  • $\begingroup$ Thanks to you and the other guys' clarifications, it was clear to me that I was mixing Quantum Mechanics theories with VB theory, which is not applicable. $\endgroup$ Apr 27, 2023 at 19:13

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