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Qualitative & Quantitative Models.

Fkkize
Posts: 2,149
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6/28/2016 4:03:25 PM
Posted: 5 months ago
Here is an example from chemistry:

Pericyclic reactions take place in a single kinetic step via a stable transition state in a closed circle of bonds.
The easiest instance of such an reaction would be the Diels-Alder addition of 1,3-butadiene and ethene.

http://puu.sh...

(The electrons are "moved" in a circle)

Both quantitative & qualitative quantum chemical models of such reactions have been developed using MO-theory (Molecular Orbital). Fukui's frontier MO approach uses perturbation theory to calculate the activation energies of two molecules. The resulting perturbation is to difficult to solve for all intents and purposes and as such, only the term with the smallest denominator is taken into account:
the HOMO (highest occupied molecular orbital) of one and the LUMO (lowest unoccupied molecular orbital) of the other reactant. It reduces a difficult perturbation to a single term. But that's to complicated for ordinary use.As a result, a qualitative version of this model was developed.

http://personalpages.manchester.ac.uk...

What you see here are the individual molecular orbitals. As you notice, each orbital has a white and a colored part. These represent the coefficients of that orbital (only orbital lobes of the same coefficient can overlap, i.e., form a bond).
Butadiene has 4 Pi-electrons (2 double bonds containing 2 electrons each) and all we do is to fill up the molecular orbitals, from lowest energy, to highest. The lowest MO is filled (not shown in the pic), as well as the second one. The second one is thus the HOMO of this molecule. We do the same for ethene and identify the upper MO as its LUMO. The last step is to simply look at the resulting orbital symmetries and see whether they fit:

http://puu.sh...

As we can see, the orbital lobes align perfectly, no mathematics involved.

I was rather surprised to see such a model working so well.
: At 7/2/2016 3:05:07 PM, Rational_Thinker9119 wrote:
:
: space contradicts logic
Fkkize
Posts: 2,149
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6/28/2016 4:07:11 PM
Posted: 5 months ago
So what do you think?
Are you the kind of person that takes the pragmatic approach or do you prefer the more exact, complicated approach?
: At 7/2/2016 3:05:07 PM, Rational_Thinker9119 wrote:
:
: space contradicts logic
Fkkize
Posts: 2,149
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6/28/2016 4:10:10 PM
Posted: 5 months ago
http://puu.sh...
(This is the product from a similar perspective, in case the orbitals covering up the one bond in the previous illustration was too confusing.)
: At 7/2/2016 3:05:07 PM, Rational_Thinker9119 wrote:
:
: space contradicts logic
RuvDraba
Posts: 6,033
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6/29/2016 5:25:15 PM
Posted: 5 months ago
At 6/28/2016 4:07:11 PM, Fkkize wrote:
So what do you think?
Are you the kind of person that takes the pragmatic approach or do you prefer the more exact, complicated approach?
My last foray into theoretical chemistry is now some decades behind me, Fkkize, so I only skimmed the modeling to get the gist of the simplification, but thank you for an interesting example. What follows is an informatician's perspective.

The accuracy of modeling depends in on the model's precision, the accuracy of observational data feeding it, and isomorphisms with observed behaviour. But the principle job of modeling is to predict; the principle job of prediction is to inform effective decisions, and so in the end our modeling is a decision support service: it's information engineering. Like all engineering it can trade off priorities, and information engineering can trade off accuracy vs availability vs usability vs robustness. Since different decisions have different needs it's legitimate to construct different kinds of models to meet them.

If one model meets all needs, good. But if the needs of industrial chemistry (say) are met by simpler modeling, then benefits can include ease of training, lower staff costs, simpler computation, simpler validation and verification of processing, more effective communication, and lower risk of computational imprecision in a method no less accurate for intended purposes. Physicists and engineers use Newtonian mechanics at times too, for similar rationale.

Empirical prediction is verified only proximately, so I take a pragmatic view, Fkkize, and don't see the need to use just one model. Obviously, there's need for a standard model, and need to do diligence on alternatives used though.