Hybridization basis

There is, however, a complication in the treatment of the a bonds. Because the states are no longer purely gerade and ungerade, the four simultaneous equations cannot be reduced to two sets of two. In a diatomic molecule this would not be much of a complication, but it is very serious in solids. Fortunately, for many solids containing a bonds, hybrid basis states can be made from s and p states, and these can be treated approximately as independent pairs, which reduces the problem to that of finding two unknowns for each bond. In other cases, solutions can be approximated by use of perturbation theory. The approximations that are appropriate in solids will often be very dilTerent from those appropriate for diatomic molecules, Therefore, we will not discuss the special case of ir-bonded hetero-polar molecule. 

We now make the orthogonal transformation O of the original basis to the hybridized basis (Magnasco, 2009b Magnasco, 2009c) ... 

Since the AOs of the hybridized basis are now properly directed along the z axis, we see that in the range 0 < w < 45° (namely, from pure p to equivalent digonal hybrids) /3a, decreases and /3, h increases from the value assumed for co = 0. The transformed Hiickel matrix ... 

We now analyse the charge distribution in ground state HF resulting from the a bond orbitals in the hybridized basis (Figure 2.15) ... 

Afterwards, the relative activation energies of the diastereoisomeric transition structures are split into contributions able to represent the factors the organic chemist is used to invoke in the attempt to "understand" the variety of the reaction outcome, i.e. steric and electrostatic repulsions, deformation energy of reactants, incipient bond energies, trough-space delocalisations and their subsets often called secondary interactions. The an ysis of delocalisation energies rests on the use of hybrid basis sets derived from Del Re s Maximum Localisation Criterion. ... 

Thus, there are four basic representation of the molecular structure which can be used as basis to build up the optimal descriptors (Fig. 12.3) (i) hydrogen suppressed graph (ii) hydrogen hlled graph (iii) GAO and (iv) SMILES. These representations also can be involved into hybrid version of the optimal descriptor where molecular features extracted from e.g. GAO and SMILES play the role of hybrid basis for a QSPR/QSAR predictions [27-32]. 

Each of these hybrids, when squared, is one part s to two parts p and is called an sp hybrid. The coefficients for the p AOs are determined from simple vector considerations One merely calculates how x and y vectors must be combined to produce resultant vectors pointing toward the corners of an equilateral triangle. The resulting hybridized basis set for CH is, plus the 2p STO on carbon and a 1 s STO on... 

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