Teoría de Hückel y la actividad óptica

El método de orbitales moleculares de Hückel constituye la aproximación más simple de la teoría de orbitales moleculares. Su aplicación está restringida al tratamiento de sistemas planos con enlaces π conjugados, de modo que solo resulta operativo en el estudio de aquellas propiedades que estén dominadas por los orbitales moleculares π. 

Murphy & Kahr (2015), nos dicen 

Our long-standing ignorance has its origins in both experimental and theoretical impediments. We take aim only at the latter here, but a few remarks about experiment are requisite. Solution rotations are averages of bisignate tensorial quantities. The average value of a set of positive and negative numbers can be many things. By contrast, average values of chemical shielding tensors are readily interpretable. This is because shielding tensors are monosignate; if one component is large, the average is large. 

Lo que nos quieren decir, es que dependiendo el tipo de tensión que se forme durante la rotación, dará un resultado y se podrá comparar en su actividad óptica, lo cual se observaba en los impedimentos teóricos y experimentales.

Ellos aplican la teoría y lo llevan a la práctica. Concluyendo que la actividad óptica de diferentes moléculas puede ser estimulada usando la teoría de Hückel y las características que se presentan de ello en HOMO y LUMO. En sus propias palabras

The optical activity of oriented, achiral, C2v-symmetric conjugated dienes, trienes, tetraenes, and pentaenes can be estimated using nothing more than the characteristics of the HOMO and LUMO derived from simple Hückel theory. In this way, we have subverted for this class of compounds the vexing SOS problem that has plagued the interpretation of longwavelength OR and connected the circular birefringence to the real electronic structure of an important class of organic compounds. This leads to some recommendations for teachers of a first course in organic chemistry. Continue to introduce optical activity as a method for detecting chiral molecules in solution and establishing enantiopurity, but return to the subject when discussing the electronic structure of conjugated hydrocarbons to explain how OR works for a real molecule such as cyclopentadiene. All that is necessary is to knowledge the qualitative form of the HOMO and the LUMO. For instance, the overlap density arises from the HOMO and LUMO, the relationship of the moments that are generated, and how the projections of these moments onto a light vector can predict the sense of the rotation of linearly polarized light. (...)

(...) Once we break the infelicitous linkage of chirality and optical activity, we can begin to more fully articulate chiroptical mechanisms. (2015)

Es interesante cómo se aplica la teoría para dar nuevos resultados, o resultados que existen y se ignoraban. 

Autores: Verónica L. Murphy y Bart Kahr.

Fuente: http://pubs.acs.org/doi/abs/10.1021/jacs.5b01763

Por: Luis Mauricio Ortiz Gálvez.