Pseudo-Newton-Raphson methods

Pseudo-Newton-Raphson methods have traditionally been the preferred algorithms with ab initio wave function. The interpolation methods tend to have a somewhat poor convergence characteristic, requiring many function and gradient evaluations, and have consequently primarily been used in connection with semi-empirical and force field methods. 

Hessian or " Eigenvector Following (EF), depending on how A is chosen. We wili p pseudo-Newton-Raphson or variable metric methods. It is clear that they do not... 

The use of approximate Hessians within the NR method is known as pseudo-Newton-Raphson or variable metric methods. It is clear that they do not converge as fast as true NR methods, where the exact Hessian is calculated in each step, but if for example five steps can be taken for the same computational cost as one true NR step, the overall computational effort may be less. True NR methods converge quadratically near a stationary point, while pseudo-NR methods display a linear convergence. Far from a stationary point, however, the true NR method will typically also only display linear convergence. 

Consider an inclusion complex with known ATas, which is the reflection of the energy difference (AAG ) between complexed and isolated species. How can this AAG° be computed Most of the MM force fields compute accurate A//f based on bond and group increments previously parametrized (see Heats of Formation). More recently, the inclusion of optimization methods based on the full matrix Newton-Raphson method allows the computation of AG° and A5°. Inclusion complexes can be considered as translational isomers (or pseudo-conformers) of the supra-assembly formed by host and guest owing to the absence of new bonds between them. The A//° or AG° of binding can thus be considered as the difference between that for the complex and that for the sum of isolated host and guest. Again, care has to be taken with these results since solvent effects are usually not considered. 

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