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According to Wikipedia's article about orbital hybridisation:

[...] today it is considered an effective heuristic for rationalising the structures of organic compounds. [...] Hybrid orbitals are assumed to be mixtures of atomic orbitals, superimposed on each other in various proportions.

So are sp, sp2, sp3 hybrid orbitals 'real'? Are they solutions of Schrodinger equation? Are they a superposition of atomic orbitals?

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    $\begingroup$ The classic solutions to the orbitals for hydrogen atoms (s,p,d,... Legendre polynomials) form a complete basis set. Any wave function can be written using linear combinations of them. As for 'are they real', various STM and other surface imaging techniques show them to be amazingly accurate in some circumstances. $\endgroup$ – Jon Custer May 1 '15 at 14:35
  • $\begingroup$ @JonCuster, I was actually asking about the hybrid orbitals sp, sp2 and sp3. In Modern valence band theory it says that the molecular orbitals are LCAO and not superposition of only s and p. $\endgroup$ – Sparkler May 2 '15 at 15:32
  • $\begingroup$ From the wikipedia link it says , LCAO is a quantum superposition, which again will lead you to a dead end . Reality and Quantum mechanics just dont go well together, yet. $\endgroup$ – Gowtham May 2 '15 at 15:40
  • $\begingroup$ As far as I remember, hybrid orbitals are not real. I don't exatly remember were I read it. Maybe in Atkins or in Class Notes. $\endgroup$ – Siddharth Yadav May 2 '15 at 19:58
  • $\begingroup$ Obligatory reminder that in general "orbitals" are not real - they are the solutions to mathematical models of the behavior of electrons. The electrons are real. Thus, the hybridized orbitals are no less real than molecular orbitals or atomic orbitals. They are just the solutions to a different set of equations modelling electron behavior. The better question would be Are hybridized orbitals a useful model? $\endgroup$ – Ben Norris May 3 '15 at 10:52
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As soon as you move to systems with more than one electron them all orbitals are approximations (i.e. not real). Hybridized orbitals are no more "heuristic" than atomic orbitals.

The transformation between hybrid and atomic orbitals can be mathematically, though not uniquely, defined (e.g. as the minimization of inter-orbital electrostatic repulsion) and the transformation does not affect the total electron density.

See for example http://molecularmodelingbasics.blogspot.dk/2010/03/canonical-and-localized-molecular.html and http://molecularmodelingbasics.blogspot.dk/2010/04/double-bonds-banana-and-otherwise.html

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  • $\begingroup$ so minimization of LCAO energy is not an asymptotic approximation of actual ("real") orbitals? $\endgroup$ – Sparkler May 4 '15 at 3:39
  • $\begingroup$ No, because there are no actual ("real") orbitals $\endgroup$ – Jan Jensen May 4 '15 at 6:44
  • $\begingroup$ I'm not sure what you mean. It sounds like you're rejecting a core assumption: hydrogen AOs obtained from solving Schrodinger equation represent actual orbitals of the electron of hydrogen. $\endgroup$ – Sparkler May 5 '15 at 15:11
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    $\begingroup$ No, for hydrogen what you are calling AOs are actually wavefunctions, from which you can compute the densities which is are physical observables. It's when you start using these 1-electron functions to describe multi-electron wavefunctions that they cease to be "real". $\endgroup$ – Jan Jensen May 6 '15 at 7:39

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