Hybrid molecular modeling problems with

The steepest descent method is very effective far from the minimum of , but is always much less efficient than the Gauss-Newton method near the minimum of . Marquardt (1963) has proposed a hybrid method that combines the advantages of both Gauss-Newton and steepest descent methods. Mar-quardt s method, combined with the Hellmann-Feynman pseudolinearization of the Hamiltonian energy level model, is the method of choice for most nonlinear molecular spectroscopic problems. 

Open problems in writing the basic organic chonistry textbook include the selection of concepts for the representation of the material, but also the level of the explanation of the complex phenomena such as reaction mechanisms or the electron structure. Here I propose the compromises. First compromise is related to the mode of the systematization of the contents, which can traditionally be based either on the classes of compounds, or on the classes of reactions. Here, the main chapter titles contain the reaction types, but the subtitles involve the compound classes. The electronic effects as well as the nature of the chemical bond is described by using the quasi-classical approach starting with the wave nature of the electron, and building the molecular orbitals from the linear combination of the atomic orbitals on the principle of the qualitative MO model. Hybridization is avoided because all the phenomena on this level can be simply explained by non-hybridized molecular orbitals. 

WORKED PROBLEM 2.3 Use the hybridization model to build a picture of the bonding in the linear molecule H—C—H. (Recall that a molecular orbital picture of this linear molecule was constructed in Problem 1.67, p. 49). If you didn t do that problem, you might go back, try it now, and contrast your molecular orbital answer with your hybridization answer. 

In addition to the VSEPR theory8 mentioned above, other theoretical or semiempirical approaches have addressed the problem of the positions occupied by various ligands as a function of their nature, for comparison with the numerous experimental results now available molecular orbital calculations, (four-electron, three-centre model with neglect of the P d orbitals)18,19 semiempirical calculations20,21 non-empirical calculations22,23 and hybrid orbitals24,25. 

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