Geometry optimization procedure

Note that current calculations performed in Gaussinn may result in slightly different values due to changes in the geometry optimization procedures. 

Numerical methods. Computer-intensive numerical methods like quantum mechanics, molecular mechanics, or distance geometry [8] do not normally fall into the scope of automatic model builders. However, some model builders have built-in fast geometry optimization procedures or make use of distance geometry in order to generate fragment conformations. 

Finally, it needs to be stated that calculated geometries are also subject to errors in precision (due to incomplete convergence of the geometry optimization procedure). However, these errors may be reduced as much as desired. 

Limited knowledge exists with respect to detailed molecular structures of simple pyrans and heteropyrans. The semiempirical CNDO/2 calculations, using a full geometry optimization procedure, predict 4 and 5 to exhibit small deviations of the heterocyclic rings from the planar conformations.34 Unfortunately, similar calculated data for thiopyrans 6, 7, and 9 were not presented.45 Accounts of several X-ray diffraction investigations on compounds possessing pyran or thiopyran fragments are available.46 51... 

The main practical difficulty in optimizing the geometry of solvated molecules arises from the fact that Efv(p, p ) is not, in general, a continuous function of the parameters A . Discontinuities are indeed introduced by the mesh generator. Efficient, robust geometry optimization procedures for solvated molecules are still to be designed. 

The first version of the tesserae cutting scheme [23] in GEPOL was based on a simple partition in sub-tesserae. The resulting tessellation was not differentiable. Because a differentiable tessellation is essential to use gradient-based automatic geometry optimization procedures, an analytical calculation of the cut tessera area has been introduced [16]. 

With the above described techniques, a general mono-and multiconfigurational geometry optimization procedure... 

These geometry optimization procedures paid an additional dividend. With a true minimum in hand, it becomes possible to compute the vibrational spectrum of a given system. A straightforward formulation allows one to extract the normal vibrational modes of the system, complete with the corresponding frequencies, hut with the important proviso that... 

A program system that strictly uses the methods described above is MULTIC, developed by Lipton and Still [36]. MULTIC generates starting geometries for a following geometry optimization procedure. 

After performing the defined number of optimization steps, the resulting set of conformations has to be checked for steric interactions and for identical geometries. Finally, they can be submitted to a geometry optimization procedure. 

Spurious results are more likely to occur when the hypersurface being traversed is flat. Because it is difficult to know ahead of time when such a flat surface exists for a complex molecule, the only safe course is to always try out and/or use the tightest available SCF convergence and minimization criteria offered by the programs. Papers reporting MO results from a geometry optimization procedure should be explicit about how the calculations were done. 

Usually, the first derivatives of the energy, which are necessary for the geometry optimization procedures are calculated analytically with expressions derived by Fournier et al. [57] or techniques from Versluis and Ziegler [62]. However, second derivatives of the energy were calculated numerically. Analytical treatments have been implemented into DFT computer codes [61] only quite recently. ... 

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