Orbital Hybridization - Real or Approximation

[dalcde]

I've been reading the book "why chemical reactions happen", and according to my understanding, it seems as though orbital hybridization is just an "approximation" and not real, as in there is no such orbital, while MO are (real). Is my understanding correct? Or are MOs also just approximations too and we should solve the Schordinger equation every time to know precisely how the electrons behave?

 

[DrDu]

Both MO and valence bond method are mathematical methods to find approximate solutions of the Schroedinger equation as it is not possible to find exact solutions to the latter. So both are certainly not real but simplified pictures of a very compicated problem.
Mathematically, quantitative VB calculations are much more demanding than MO calculations, so that with the advent of computers with still very restricted power, the MO methods gained considerably in popularity.
However, there are methods to refine both the VB and the MO methods further and both will yield the same answer at the very end.
Usually, VB methods describe bonding better in compounds of non-metals, while MO theory is a better first approximation in compounds containing metallic elements.
Usually it is important to know about the strengths and weaknesses of either method to arrive at a consistent picture of bonding in a given substance.

 

[DrStupid]

I've been reading the book "why chemical reactions happen", and according to my understanding, it seems as though orbital hybridization is just an "approximation" and not real, as in there is no such orbital, while MO are (real).

As DrDu already wrote MOs are approximations of solutions of the Schrödinger Equation. Hybridization is something different. Hybrid orbitals are formed by mixing of orbitals. If the original orbitals are approximations than the resulting hybrid orbital is an approximation too. But if the original orbitals would be exact solutions than the hybrid orbital would be an exact solution too because linear combinations of solutions of a differential equation are also solutions of this differential equation. Therefore hybrid orbitals are as "real" as any other orbital.

 

[dalcde]

As DrDu already wrote MOs are approximations of solutions of the Schrödinger Equation. Hybridization is something different. Hybrid orbitals are formed by mixing of orbitals. If the original orbitals are approximations than the resulting hybrid orbital is an approximation too. But if the original orbitals would be exact solutions than the hybrid orbital would be an exact solution too because linear combinations of solutions of a differential equation are also solutions of this differential equation. Therefore hybrid orbitals are as "real" as any other orbital.

I mean is there such a wavefunction of electrons in an atom, or are the only existing ones are the original ones, or are they both different description of the same thing?

 

[DrDu]

Hybridization is a concept of valence bond (VB) theory. The real difference is between MO and VB theory.
Basically, in MO theory one assumes that the individual electrons move in an average potential created by all nuclei and other electrons of the whole molecule. The resulting single electron wavefunctions are the MO's and they can be combined into a "Slater determinant" which is an approximation to the wavefunction for the entire molecule.
On the other hand in VB, one considers formation of the molecule to be but a small perturbation of the atomic wavefunctions. Hence one starts out from the atomic orbitals of the isolated atoms and selects a combination where spins are paired as much as possible with the effect to minimize Pauli repulsion.
In both methods there is considerable freedom in the choice of the orbitals. E. g. in MO theory one can often transform to localized orbitals which differ from 0 only in a neighbourhood of two atoms bound together. On the other hand, in VB theory, one may chose different linear combinations of the atomic orbitals (sometimes also including atomic orbitals from neighbouring atoms) so as to increase overlapp of orbitals which form a bond. This are then the hybrid orbitals.

You could read SS Shaik et al. "A chemists guide to valence bond theory" 2007.
When you look it up in Google Scholar, there may be some pages where you could download that book. It discusses the relation between VB and MO in detail and is quite an easy read.

 

[DrStupid]

I mean is there such a wavefunction of electrons in an atom, or are the only existing ones are the original ones, or are they both different description of the same thing?

The original orbitals and the resulting hybrid orbitals are solutions of the same Schrödinger equation. I do not know if we can determine which solutions are realized in an atom.

 

[asym]

Whole orbital idea is an approximation. Orbital is a one-electron wave function, while exact solution involves N-electron wavefunction (Frankly speaking, even this is still approximative [Born-Oppenheimer or adiabatic approximation]. We should work with nuclear coordinates as well:-)