# sp, sp2 and sp3 hybrid orbitals are actual solutions of Schrodinger's equation or only a heuristic?

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?

• 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. – Jon Custer May 1 '15 at 14:35
• @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. – Sparkler May 2 '15 at 15:32
• 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. – Gowtham May 2 '15 at 15:40
• 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. – Siddharth Yadav May 2 '15 at 19:58
• 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? – Ben Norris May 3 '15 at 10:52