Hückel method

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The Hückel method is used to evaluate energy levels disposition in a molecule. We'd have to solve <math> Hu=\epsilon u </math>. We do recall <math> \alpha \equiv \left\langle u^{p_{z}}_{j}\left| H \right| u^{p_{z}}_{j}\right\rangle </math> the diagonal elements of <math> H </math> and <math> \beta \equiv \left\langle u^{p_{z}}_{j^{\prime }}\left| H \right| u^{p_{z}}_{j}\right\rangle </math> its off-diagonal elements. Hence:  
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The Hückel method is used to evaluate energy levels disposition in a molecule, following the linear combination of atomic orbitals theory (MO-LCAO). We'd have to solve <math> Hu=\epsilon u </math>. We do recall <math> \alpha \equiv \left\langle u^{p_{z}}_{j}\left| H \right| u^{p_{z}}_{j}\right\rangle </math> the diagonal elements of <math> H </math> and <math> \beta \equiv \left\langle u^{p_{z}}_{j^{\prime }}\left| H \right| u^{p_{z}}_{j}\right\rangle </math> its off-diagonal elements. Hence:  
  
 
<math display="block">  H = \begin{bmatrix}  \alpha  
 
<math display="block">  H = \begin{bmatrix}  \alpha  

Revision as of 09:49, 9 April 2020

The Hückel method is used to evaluate energy levels disposition in a molecule, following the linear combination of atomic orbitals theory (MO-LCAO). We'd have to solve . We do recall the diagonal elements of and its off-diagonal elements. Hence:

Hence: , and all the other elements are zeros, except for the case of circular molecules, where also the matrix element that correspond to the first/last atom bound is equal to . Energy levels now can be found solving , that is:

Recall and solve in order to find energy levels. Remember that generally , and it is called hopping parameter.

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