Localization of Molecular Orbitals

[brydustin]

Just curious why chemical physicists bother with localization procedures for molecules. Because atomic orbitals become de-localized when they form molecular bonds, but then it seems people wish to come up with procedures to re-localize. I've read quite a bit on how the de-localization algorithms work (through unitary transformations)... but my question is, "Why bother?" With benzene, for example, de-localization explains so many of its interesting properties... all of which we group under the term "aromatic".

 

[SpectraCat]

Just curious why chemical physicists bother with localization procedures for molecules. Because atomic orbitals become de-localized when they form molecular bonds, but then it seems people wish to come up with procedures to re-localize. I've read quite a bit on how the de-localization algorithms work (through unitary transformations)... but my question is, "Why bother?" With benzene, for example, de-localization explains so many of its interesting properties... all of which we group under the term "aromatic".

It's a good question, and one I don't have time to give a complete answer to right now. Let me just give one reason why local orbitals can be useful. In general, when two molecules react, from chemical intuition we expect the electronic representation of the process to involve largely the "frontier orbitals" .. the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) ... although other orbitals that are not too far away from these in energy can also be involved. We also expect from chemical intuition that certain molecules (i.e. Lewis acids and Lewis bases) should have reaction sites that are fairly well localized. Using local MO's provides a way of representing these features in electronic structure calculations ... you might look up the papers on natural bond orbitals if you are interested in more details on these sorts of arguments.

 

[cgk]

Just curious why chemical physicists bother with localization procedures for molecules. Because atomic orbitals become de-localized when they form molecular bonds, but then it seems people wish to come up with procedures to re-localize. I've read quite a bit on how the de-localization algorithms work (through unitary transformations)... but my question is, "Why bother?"

There are three very different reasons for that:
(i) Because you can. There is no inherent reason to prefer the canonical orbitals to any other of their unitary transformations.

(ii) In general, interpreting anything delocalized over the entire molecule will be rather hard. Basically, the only solid chemical information canonical orbitals give you are (poor) approximations to ionization energies via Koopman's theorem (and even that only in closed-shell or unrestricted HF methods). In contrast, natural bond orbital (NBO) interpretations can sometimes give chemists actual chemical or even quantitative insight into what is happening.

(iii) Using local orbitals allows you to do some approximations in post-HF methods which can break the scaling walls otherwise obtained. For example, with Molpro you can run local CCSD(T)-F12 calculations on molecules with 50 to 100 atoms, on a desktop machine. With standard CCSD(T) (typically using canonical orbitals), that would not even be possible if using the largest supercomputers there currently are.

 

[DrDu]

You also have to take in mind that localized and delocalized orbitals lead only to an equivalent description on Hartree Fock level. Once electron correlation is taken into account, for the calculation of energies, localized orbitals form usually a better starting point.

 

[cgk]

You also have to take in mind that localized and delocalized orbitals lead only to an equivalent description on Hartree Fock level. Once electron correlation is taken into account, for the calculation of energies, localized orbitals form usually a better starting point.

I think one has to differentiate here: For many methods in solid state physics which are applied to model systems this is true (or some some hybrids like LDA+U). But at least in quantum chemistry, most methods used in practice nowadays are unitarily invariant[1]. That is, they also give the same results for unitarily equivalent sets of input orbitals. That is widely considered to be a desirable feature of a correlation method.

[1] However, for perturbation methods like MP2 variants or the (T) of CCSD(T), using canonical orbitals allows one to obtain very significant simplifications of the equations; so these methods are typically applied in a canonical basis, and an actual implementation might assume to get one such basis as input and produce wrong results if fed with non-canonical orbitals.

 

[DrDu]

Yes, unitary invariance is certainly a desirable feature. I had in mind the choice of the active space in CAS SCF and the like.