The relationship of orbital hybridization between quantum mechanics

[soulhunter]

is the hybrid orbital the solution of Schrödinger equation ?
Or why we have to make orbital hybridization?

 

[Simon Bridge]

is the hybrid orbital the solution of Schrödinger equation ?

Sort of.
http://www.dpcdsb.org/NR/rdonlyres/...46QuantumMechanicsandBondingHybridization.pdf
http://en.wikipedia.org/wiki/Orbital_hybridisation

Any linear combination of solutions to the Schrödinger equation is also a solution.

 

[DrDu]

You must be very careful here to what Schrödinger equation you are referring. Hybrid orbitals aren't solutions of the time independent effective one particle Schrödinger equation for electrons in an isolated atom. But note that we use them to construct approximate many particle wavefunctions not for isolated atoms but for atoms in a molecule. It turns out that, considering as an example carbon, an atomic wavefunction constructed from one s and three p orbitals -each occupied with one electron- is completely identical to a wavefunction constructed from four singly occupied sp3 orbitals. However, the latter representation is more apt to describe directed bonds in the valence bond formalism.

 

[soulhunter]

Is this means that the hybrid orbitals is an solution of many atoms Schrödinger equation,like we can not get the exact solution so we, depending on the symmetric of molecular, hybridize the s orbital and p orbitals of isolated atom to form the wave function of many atom solution? Or we just solution the equation by computer and found that solution shows like hybridized orbital?

 

[DrDu]

Yes, it is an "ansatz" or trial wavefunction.

 

[soulhunter]

Yes, it is an "ansatz" or trial wavefunction.

Thank you Drdu!