[Corribus]

The first question is relatively easy. Valence Bond slightly predates MO theory. When Linus Pauling proposed orbital hybridization as an outshoot of VB theory, MO theory was still in its infancy and wouldn't be applied to real molecules for several more years. Even beyond that, determining the tetrahedral shape of methane with hybridization/VB is a lot easier than determining it with MO theory, especially without the more recent mathematical tools like group theory and symmetry treatments.

The second question I think is predicated on a false impression that MO theory is somehow superior to VB theory. This isn't really the case. It's true that MO theory is more complex and is far more developed than VB, but this doesn't mean it's always better. VB approaches are still used today in many theoretical calculations of organic molecules. Ironically enough, while I complain about organic chemistry courses doing a disservice to students by glossing over MO theory, I could just as easily complain about physical chemistry courses doing the same thing by glossing over VB theory as a mere historical footnote.

That said, I do think MO theory has a far wider range of applications than VB theory. VB theory uses only atomic orbitals with valence (bonding) electrons to form localized chemical bonds, with most electron density located between neighboring atoms. This may be appropriate in most cases, and indeed theoretical treatments using VB and MO theories very frequently give, within a margin of error, similar results for chemical structure, reactivity, and electron density. VB theory is, I believe, computationally simpler (because only valence orbitals are involved), and so it is often relied upon for large or complex molecules, or where a qualitative result is sufficient. Just as with VB theory, an MO calculation will also tend to show that most electron density is localized between adjacently bonded atoms - although because of its better stage of development, results from modern MO calculations are usually more detailed and offer a better quantitative match to experimental data in many cases. This is especially true in molecules in which delocalized electrons are clearly important, because MO theory allows for the possibility that (indeed, is based on the assumption that) electrons are located in orbitals that span the entire molecule. Understanding spectroscopic behavior is an additional exclusive strength of MO theory, because of its intimate relationship with molecular symmetry and its ability to actually predict electronic transitions.

So, were I to sum it up generally in a sentence: VB theory is a good qualitative approach that does a very good job of describing molecular structure and reactivity in most cases, whereas MO theory does a better job when quantitative predictions of molecular characteristics are important. MO theory also succeeds in some specific situations that VB is simply not well suited, such as open shell or parametric molecules, geometries when lone pairs are involved, and so on.

[Irlanur]

MO theory also succeeds in some specific situations that VB is simply not well suited, such as open shell or parametric molecules, geometries when lone pairs are involved, and so on.

Hartree-Fock based calculations often fail miserably with open-shell transition metal complexes... The Quantum chemistry workhorse at the moment is DFT anyway...

Are there actual calculations done with VB at the moment? I mean I can treat Valence electrons only in MO-theory (what ever you mean by that) as well.

[Corribus]

Are there actual calculations done with VB at the moment? I mean I can treat Valence electrons only in MO-theory (what ever you mean by that) as well.

Absolutely: go to Google scholar, type in "valence bond approach", and you will see dozens of papers that use a valence bond model. Honestly, I think most serious computational chemists view the two models as opposite ends of a spectrum, one (MO) treating electrons as too delocalized and one (VB) treating electrons as too localized. Many modern quantum chemical methods draw on both approximations to get to a better result that's somewhere in the middle. But it's been quite some time since I've been involved in serious research based on quantum chemical calculations, so you'll have to pardon me if my memory of these issues is a little fuzzy. Honestly, I have never done modern VB calculations so I do not know what developments are incorporated into them. I can only speak of VB theory in a general way. Rigorous comparisons between modern VB and modern MO quantum chemical methods are beyond my level of expertise.

DFT is certainly great and is commonly used by professionals, but it's not very useful toward conceptualizing bonding, especially for students. There simply isn't enough time to teach such advanced quantum chemical techniques in a basic undergraduate curriculum.

(What I meant by treating valence electrons only in VB theory is that bonds are assumed to be formed only by adjacent atomic orbitals that are occupied by valence electrons. This is very different from molecular orbital theory, where molecular orbitals are created by combining atomic orbitals spanning the entire molecule, and usually not just those that have valence electrons - although you are right that simple molecular orbital treatments, such as those in homework problems in intro physical chemistry courses - often make the approximation that valence atomic orbitals are the only ones that need to be considered for a qualitative picture of what's going on. In principle, any atomic orbital of the appropriate symmetry, no matter how far away from the valence orbitals, will impact the energy of the molecular orbital, but the degree of interaction of two orbitals scales inversely with the difference in energy between them, so in practice low energy filled shells can be ignored. An example is an MO treatment of a diatomic, in which the 1s orbitals are neglected. A student drawing an MO diagram can do this and still have a nice qualitative understanding of the magnetic and bonding properties of the molecule. A quantum chemist will not neglect these low-lying orbitals, though, because they do impact the actual energy of the molecular orbitals to a small degree.)